<%BANNER%>

Contingent Claims Analysis of Optimal Investment Decision Making in the Management of Timber Stands

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20101219_AAAADY INGEST_TIME 2010-12-19T21:36:01Z PACKAGE UFE0015611_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 1547 DFID F20101219_AACDVX ORIGIN DEPOSITOR PATH mehrotra_s_Page_052.txt GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
c20447fbab9e0f34968e52da8fb3286b
SHA-1
6f8b2ed19792d05852be26877f2c64f406d48c64
29929 F20101219_AACECG mehrotra_s_Page_054.QC.jpg
65ebd83f1bdc46763bca4201b19d6550
0ac72319222181d0adb70dbdaf9ad79b6af1e3c8
1711 F20101219_AACDXA mehrotra_s_Page_082.txt
549b7b9636c8e9ee85f64076556d7ffe
149e655576ece795001e44f604b599c7f0cfa9bd
7461 F20101219_AACEBR mehrotra_s_Page_043thm.jpg
2b4afb842812b0564d8f04ef4efd1911
daf763a684a3ea6a06b0cdc80d8c78ca92f11bd7
2058 F20101219_AACDWL mehrotra_s_Page_066.txt
ccb1ac9bbaa4696f83e9173380688915
1cd91d165dc0852f0ce1b7876b700bd54dd9da16
1604 F20101219_AACDVY mehrotra_s_Page_053.txt
96e205c93335dcfbaa6e8923e8884e2b
96027d0042a50875cdb1f21fed50e04165ee92e2
7279 F20101219_AACECH mehrotra_s_Page_054thm.jpg
9a82270bea175d432e65020d7008e0e5
a6174a7a858f80d25fbe39201cd31c2cb8e12bc3
1025 F20101219_AACDXB mehrotra_s_Page_084.txt
6d9fcf9a6f9086a2954879600def8e30
82789e77854f822952103cce15e776f1d437c48e
22914 F20101219_AACEBS mehrotra_s_Page_044.QC.jpg
dd0a642c17a0452a31cd38296222a70a
6b2898e9bed268fbe84a39ac34b08aa6797b8c5f
2287 F20101219_AACDWM mehrotra_s_Page_067.txt
71058cbf8bb9be39f11e92d6d3f32a2a
5c7901781626cd3598d38bdea981cbbe853a9a98
1838 F20101219_AACDVZ mehrotra_s_Page_054.txt
a407f33ae67a78782b4e9db8b1897f57
94a9491fca5bb9c8cbd3959a307c9a07420241a2
29917 F20101219_AACECI mehrotra_s_Page_055.QC.jpg
b1b2f9af2b889f2cbf17cdda27c6c867
4ca12754c1e4f223fc5552bd3829df1d6dd2a334
1843 F20101219_AACDXC mehrotra_s_Page_085.txt
58a4966ab276d95387c46f8050067a7b
900826e208c2432f1e0ed6a93103e32ef8e39e39
6322 F20101219_AACEBT mehrotra_s_Page_044thm.jpg
1dae50cbb1833a53ed05dac30e131278
cca8cc76193e9fe37eb1d80982a5c1fad514473c
1912 F20101219_AACDWN mehrotra_s_Page_068.txt
b6404cb0907c97272f73e154eac2bd42
10ff1566734adeb1495a18dd76f619a59d663d8c
7785 F20101219_AACECJ mehrotra_s_Page_055thm.jpg
143b110ea491e1673951ba782df2b19f
802a90c871b1fd866781ff79384f6fb8abe32db2
24038 F20101219_AACEBU mehrotra_s_Page_045.QC.jpg
9a239fe985df6c3b5fbf3b68e62f7730
af3a54e74145d8dd708f3bd7fb90268d84880e80
1825 F20101219_AACDWO mehrotra_s_Page_069.txt
6b8af50d21b8c857e3c9b44785dc286d
5643c1d6e3dda81872564019e4af3f21492d56f8
24072 F20101219_AACECK mehrotra_s_Page_056.QC.jpg
d1d6902dab7d32aaf9cb3005ce54e242
d504d863be6b6179670afe24a924e3cf79dbab6a
1123 F20101219_AACDXD mehrotra_s_Page_086.txt
0f73c145e9d1b716c389296630f04992
99babf3bd4e10ae708fae2bcac6cee4bddd23feb
7108 F20101219_AACEBV mehrotra_s_Page_045thm.jpg
e00cc8b9e4dda8eadfbaf695b1d50046
9a58a216a61dc8f87dfea55892e858c098330d65
1908 F20101219_AACDWP mehrotra_s_Page_070.txt
d954e6c37a4f4a454625c4c13d984f66
bbe0ea9c9f34290ed7b128f2c40c22798fa51162
33742 F20101219_AACECL mehrotra_s_Page_057.QC.jpg
d9f4572f56d116ad53a2e8f4e11f7093
386f009f6d9870bea6fed1fd36ea4e85807c2b50
1563 F20101219_AACDXE mehrotra_s_Page_087.txt
c7871a548d672eb922148d6bacd7f640
cbdb37aab5eeccf0aa42bfa3b8499e5fe77348cc
25826 F20101219_AACEBW mehrotra_s_Page_046.QC.jpg
ef08370b8031bb50547e3c843328b7cf
48bce1f8d484a9d508facf3befc53e471d8e223c
1916 F20101219_AACDWQ mehrotra_s_Page_071.txt
0b7b2528116c97526e263ed1fb2a163c
63dcf3f1d36868d60dda465f6bc9f71a6189f5b2
32213 F20101219_AACEDA mehrotra_s_Page_065.QC.jpg
986d323e4a072d900d8e20bdb6323e5b
0855481744fb00883a904335b64645422eb1e34c
8503 F20101219_AACECM mehrotra_s_Page_057thm.jpg
f807daa197f389c2163cdfac695781c0
f94c3028c9740d4c0497a36b157ed2484efa574f
2645 F20101219_AACDXF mehrotra_s_Page_088.txt
328563eda73c7c3f3b00e8308d10519c
cd79d43b43b1a24860db4104b562172688bb5be1
6422 F20101219_AACEBX mehrotra_s_Page_046thm.jpg
917248bd4e630af16fc6ed6aac5279be
33033a813cf026e9104204d0ca59b576b513ecc5
1733 F20101219_AACDWR mehrotra_s_Page_072.txt
1d1378e40c14086d674fba94c94e11a2
36cbf52313da4dbd5d9abe813e9d326e67bb4449
8109 F20101219_AACEDB mehrotra_s_Page_065thm.jpg
2244c0d1512e3c2db29065def8e107e2
81b7a3e62aa196bd8d4b183ab43291846e0da246
2598 F20101219_AACDXG mehrotra_s_Page_089.txt
f1b49dd71d2740cb75bf0f2355344d58
de75d2e7bab901f4747a2778470a80e187f7896a
19379 F20101219_AACEBY mehrotra_s_Page_048.QC.jpg
8dec52ad5c5358e5ca61ef6637c87ddc
5db8522ae88b206167fd92fc1ace48a64fea0091
1430 F20101219_AACDWS mehrotra_s_Page_073.txt
fda2af77e5849d05213a2935f2b6ac7b
6e71c38733c6b5cfc282abdb147d2df6eb020c5a
34577 F20101219_AACEDC mehrotra_s_Page_066.QC.jpg
3dbeb0f716d058822540563785e9b55b
3e0a84cefc9471e21516951e9796abead032df25
31748 F20101219_AACECN mehrotra_s_Page_058.QC.jpg
5b48bd737b75ba6c50b86f905b5e4665
ba9e780775c9ecbc5d86efa28fd0dc350f491e3e
1697 F20101219_AACDXH mehrotra_s_Page_091.txt
56d7e2cb1d6a70a848ec6bbdee30550a
2ebc583a255907c4fd238e08a19c14258eec971d
5862 F20101219_AACEBZ mehrotra_s_Page_048thm.jpg
cdaf29a0efdddcf04fe0874ad7592a3b
e3701bb912feb83f11c819ebcfef7c51cdd1ad5c
1199 F20101219_AACDWT mehrotra_s_Page_074.txt
c96e27f97f4d7630abe742fabb4eab99
6ff93fb182d5ce23bff2380cd134960a341b27b3
1958 F20101219_AACDAA mehrotra_s_Page_022.txt
4a69d393eb29b75d00ee1231bc50d7bf
62999408b65cb5c171148e3b06291d0c53ed8399
8307 F20101219_AACEDD mehrotra_s_Page_066thm.jpg
9bbbf2ac644f013004157de7f3626daa
f93d6ca4f7548d30ef026c4ec27288bd62a7b5b3
8147 F20101219_AACECO mehrotra_s_Page_058thm.jpg
5de7607d568a903bdddac91f2b999c50
3e896976c7e64ff10b00dba6f9e5c6c7515970cc
1554 F20101219_AACDXI mehrotra_s_Page_092.txt
3b4bc565bf98c100775897fec12289f2
729e2bcfd39fbd36cc21fd792cfe9b05fd4bf7db
1972 F20101219_AACDWU mehrotra_s_Page_075.txt
addfefcc176f84d8f9bad21adecb1ed4
73e1fb7a6b35807f04cac532e3aaa49f49f05107
1837 F20101219_AACDAB mehrotra_s_Page_113.txt
e3dacc48aa2d1b465d5e8ae3b60c2bed
5c0b49be52a01074f70a259acef1959d6d096414
8047 F20101219_AACEDE mehrotra_s_Page_067thm.jpg
81c388194132e301935f974d7a304a8c
6e0ae737e17c643844f03a1d9fcd1db6928b8b0b
35037 F20101219_AACECP mehrotra_s_Page_059.QC.jpg
243eccea175ffd1c856b652943d97410
565416350a7ed37a13a8ae6523189d89e6520874
1934 F20101219_AACDXJ mehrotra_s_Page_093.txt
3532eacc49839eec4099a201c767c16a
1e1271ac082c25e5cc2627f9bdb0e2563eaab27a
1387 F20101219_AACDWV mehrotra_s_Page_077.txt
1a87604cc6764860f42c642fea10f632
62981274836059e2ff6021a8a42c76dd4e6dff51
87562 F20101219_AACDAC mehrotra_s_Page_047.jpg
5c4ed678042a46cf4359e5a496329645
b28372bc3fd04c8bfd323eab5b9e3d94e415c460
31620 F20101219_AACEDF mehrotra_s_Page_068.QC.jpg
d73bdd160bcd8c93ebe329cf1e1775e5
87b8b5e6993c030e2e1c73dc85cfc4d10ce0f776
8469 F20101219_AACECQ mehrotra_s_Page_059thm.jpg
ec37fbd31db604a317c34a761a1b9dac
43ab0ca32e9268b5d4e5f676dedee1b7dceb6fd1
1324 F20101219_AACDXK mehrotra_s_Page_094.txt
6732c50491284c692d8e8f49b8fbd846
1e800aad30942e9658a5abbaa5d61d536b6673c6
1127 F20101219_AACDWW mehrotra_s_Page_078.txt
24a33211fbe87d964c3704ea17a01aad
2f5fba3e8f6deecde816ee9f378306b59ccb7808
56983 F20101219_AACDAD mehrotra_s_Page_067.pro
8780f2cb252ac53204e79729129e0fa3
6351e458381c1515aca731e3aed5e112ff54d9e1
7696 F20101219_AACEDG mehrotra_s_Page_068thm.jpg
189afc0c4a16519b8cd66ece6eeeb76d
15872a0b0bd77abc5fa8be1e1f5eb80c7ed90972
1927 F20101219_AACDYA mehrotra_s_Page_111.txt
914744d36e7c2714ac7f5f3d0c5c3f3a
20486366db7795627fc010fbe52ae03cf44bdc67
31890 F20101219_AACECR mehrotra_s_Page_060.QC.jpg
fed8c202c65c13354a90863224aa62f8
0d6a0fb54da8a714104080dca9ccd098241378d9
1492 F20101219_AACDXL mehrotra_s_Page_095.txt
294f8fbd07514bc0d4beebe910a3a437
e924ed8a4297f3b2aaa58cc78f8870358a950b0c
1485 F20101219_AACDWX mehrotra_s_Page_079.txt
e05397e06b36f1bed5eea7a25b7f9dd2
e0ca7a289952121084437432e742cec73b335819
79552 F20101219_AACDAE mehrotra_s_Page_049.jp2
fcad43c38a52ac774f9228d907cbff8f
a49fe6a9cbd7c17afabee5c557175bbbe5372292
30011 F20101219_AACEDH mehrotra_s_Page_069.QC.jpg
d7cb8260747991d93a315c8ccc5b48d2
a04b87077502631c2a0faf47bf34fa74dde5de3b
2007 F20101219_AACDYB mehrotra_s_Page_112.txt
9dbea351abbbea3a9dae25255cce1c0f
c5ade4c96cd4fc380f268539f30a0f12870fa2b5
7853 F20101219_AACECS mehrotra_s_Page_060thm.jpg
6a75d8a94bc587452b383a0fc6b4a9c8
0970f388b0c2144042324478f5f69ce482d8f203
1528 F20101219_AACDXM mehrotra_s_Page_096.txt
0404c795217375de72c85f8cfbb7ae91
f680d2cc0b86ed0cf309dc715e1f25c3ccb07286
1221 F20101219_AACDWY mehrotra_s_Page_080.txt
f7fdf739ecbd49aa9e92cc5e00eb59ec
a96b54b377088d02c01ddc43345281838522c52e
124700 F20101219_AACDAF mehrotra_s_Page_119.jpg
8d7f9aaadab272efbf709390bbe96161
0be747d258d9f07c583eb58bca45212f0f1ad02b
1110 F20101219_AACDYC mehrotra_s_Page_114.txt
aa202f6c034ef281ac907d4feadd75a0
d584451d9d5861ad20ef78cf6a1db22c9678af9d
31555 F20101219_AACECT mehrotra_s_Page_061.QC.jpg
c7db6e5109ae05701abcf2c48f3b0e0a
f4cb798aa1320b644ebce6c0ed76c7421a3a3613
1302 F20101219_AACDXN mehrotra_s_Page_097.txt
51b55fe74f78e018fd939dfb09fd1f70
5e4aed743e897978b0ab557b8a794fa7ae3e320f
1788 F20101219_AACDWZ mehrotra_s_Page_081.txt
cf25b881b5ef56725afa3bdd8787e434
0205206de6a428bf4e968924b50b7acb46abe504
35434 F20101219_AACDAG mehrotra_s_Page_120.QC.jpg
546d5959d84507a85d6b540432fdb4a0
cb2c0c0fc6f366f09968666c35bb6df1f66c8da1
7393 F20101219_AACEDI mehrotra_s_Page_069thm.jpg
6810d5a332739616de9807e00747f257
3f8be74c5b3f04bc3bbfd0206b734864630e0431
991 F20101219_AACDYD mehrotra_s_Page_115.txt
be9e298c8cd04da6c13a77793b9f171b
f80971a5846aad748abb4f45cef6023ecd5ef8ce
7971 F20101219_AACECU mehrotra_s_Page_061thm.jpg
3d0fba4a422f5d0091a4509ff2954f76
f9aef31605d12ffe161a038c5253d71316bb3ff3
2023 F20101219_AACDXO mehrotra_s_Page_098.txt
488a8ad7a30b43a8b28a63877a52eb70
51e58a593ae0c3c32cb95de3441e948ce358d41a
1053954 F20101219_AACDAH mehrotra_s_Page_009.tif
92691f06681a75923bf501b58b04555e
4c900ee490dda5b95701f427cd95755e1924efec
29222 F20101219_AACEDJ mehrotra_s_Page_070.QC.jpg
3d8d7131afb32d495469706bc706dc0b
6efd696b6d8728907695e6627b0ad155af49fd77
8138 F20101219_AACECV mehrotra_s_Page_062thm.jpg
dfb39ce2dcf9733925639bb3eb2df220
4705c49e54626afc1245d652f4f18cfd25102ca1
1840 F20101219_AACDXP mehrotra_s_Page_099.txt
e47e7dbc72d210cea992089d408d629c
5f0dfe74428a649b4476f18e5274abe33867ebf0
20668 F20101219_AACDAI mehrotra_s_Page_080.QC.jpg
6967d81c1e9c51b045ebf1f12f9f474a
ae284a8afeeeef870f1bdaefd3f1c10281793b65
7834 F20101219_AACEDK mehrotra_s_Page_070thm.jpg
806fa1da5d63e23fadf43e961ee62036
3deb1419e1124a89987df483cacd44e8fa3936f4
2177 F20101219_AACDYE mehrotra_s_Page_116.txt
9fa2e07237034ae1cac82c3f8e11bbc0
0f2187a5e0de5094874ed2d587e51acdc61d0e56
24095 F20101219_AACECW mehrotra_s_Page_063.QC.jpg
99afd9fa0f078fa952dd48dab4d71038
d6dc8a1007694976953187322756422dbefe755f
1941 F20101219_AACDXQ mehrotra_s_Page_100.txt
50d9dbefa8c1827c657e1570026c39d5
9210ff8b3b0d773717dd27614353c435f6b3f557
F20101219_AACDAJ mehrotra_s_Page_015.tif
87682cf18c1060755f960e5e27e2cccb
89d149d0808dc269f0de1d9a752d00a98d45a36b
30952 F20101219_AACEDL mehrotra_s_Page_071.QC.jpg
4c1d75c9d722d816595888d1776c9b82
003aeb50e3232ba709d1b8beb5d7bc83179de4e4
5528 F20101219_AACEEA mehrotra_s_Page_078thm.jpg
a8085e1428da9d0074efa2ee8a97d483
c433fb9ec490b455c733518c20ed944c838a4f79
2273 F20101219_AACDYF mehrotra_s_Page_117.txt
4dac0aa045a2fe096b30f15150545060
3505930977d2c4b4dc3c925d2d6d3deb7c2b7280
6898 F20101219_AACECX mehrotra_s_Page_063thm.jpg
d8e4f732236e6e34c4f96941f8f19aa9
5f9297543e37c6ea8c50ab03ee456dfc2a687b3e
1197 F20101219_AACDXR mehrotra_s_Page_101.txt
6011c9430c5ab82289abe5d82ba621ed
25c39d5048f51eeee84cc739ed3e41caa1c86d58
108410 F20101219_AACDAK mehrotra_s_Page_027.jp2
5a545f92ce3f971e0b3eaa2879bd2c28
1393463ad03642fb1f0a1bab64c8a20978519550
7924 F20101219_AACEDM mehrotra_s_Page_071thm.jpg
72011e087af2eedcda8141e8e92ba6d9
6fb8be983711ec1351fb4027611efb2499bcbc66
6793 F20101219_AACEEB mehrotra_s_Page_079thm.jpg
28d42c29a0fa43977faeb490736b90cc
563f8b92432cf67c9b63e4b6c2f3f6d9d412fc49
2470 F20101219_AACDYG mehrotra_s_Page_118.txt
a8efb045ac82cce1f70ec4c358595a19
07db44cafa92fd9eca53fa2ca0830a6c6ab220d0
30465 F20101219_AACECY mehrotra_s_Page_064.QC.jpg
0b0c2f6a7bbe7e9ea46baa5cf3766b70
43872fb07952ad1dd7e19244f7dc32061fab26cc
1271 F20101219_AACDXS mehrotra_s_Page_102.txt
598314838be0b50f51f50161b8ec3416
12943c6a25689b48b43c9a7918a22b8382c2c20a
38086 F20101219_AACDAL mehrotra_s_Page_052.pro
ee05863b5255b6ca5d73c1ccb0e9d6cd
627da93bae057cf959167c15a1b2e20efd8aaf8f
28601 F20101219_AACEDN mehrotra_s_Page_072.QC.jpg
b63da0a975ca7dbecf6c90d27e6d1ead
852a456e5008b5cddd5dffc9b44da5aced20b458
6045 F20101219_AACEEC mehrotra_s_Page_080thm.jpg
a00189ed5b2b2bbde0ce28baa43b0293
c9d75a0e22e94961125a1df9309389e52f6e4558
2478 F20101219_AACDYH mehrotra_s_Page_119.txt
78f709354c12845c7d7296a09493945e
b250295b3851ff91a72b118d481bf9c741faa5eb
7616 F20101219_AACECZ mehrotra_s_Page_064thm.jpg
397ce7d3e357e941677dbae76e5be8b1
aaf8961ff0a71a4505658906c64f1f10835d5b61
1775 F20101219_AACDXT mehrotra_s_Page_103.txt
f8c247fe44814a0125e29a5378786e5b
8e6ae166ba3a805021c46f8130298ae2e86a4bac
1904 F20101219_AACDBA mehrotra_s_Page_007.txt
bb7a93ab505b604b89f38e8d6a7140e0
5d44fc534d30f2d8d0c8fa98bd864d376e269d2d
30003 F20101219_AACEED mehrotra_s_Page_081.QC.jpg
ed2a13d532180beeba0db57e0c43f614
4b4402cf8c69d4b70dc286411a1309bc6e1ef4d4
2340 F20101219_AACDYI mehrotra_s_Page_120.txt
ab2fb8be22dc51589bc8bd7467889ccf
a07b4fdf0544384f242e5890c26c3920e0181e0b
1588 F20101219_AACDXU mehrotra_s_Page_104.txt
8215af08890997fa89f10dad45189dc3
ece86337e2952d89147f18130d6962b2d616d86f
8841 F20101219_AACDBB mehrotra_s_Page_120thm.jpg
c6b02779c8213ab0f12a4087b63132bf
1b028f8544c8f562e3a8ee4614aa7d4c2b3673e7
F20101219_AACDAM mehrotra_s_Page_075.tif
88d79c7931e28a9b6a3db2548bccf482
c0c9a2b694948602f43f78581f92285d91297165
7223 F20101219_AACEDO mehrotra_s_Page_072thm.jpg
7231c1c22dcb359bb161992f83817c29
8927cbd8af7750b760cff7bf9f311d1a7ba4a390
8141 F20101219_AACEEE mehrotra_s_Page_081thm.jpg
aac89866a8c6e627db5f4a2e5816c066
bb11e053baad6b9cf4b7ece706f6a70a949a73e8
2466 F20101219_AACDYJ mehrotra_s_Page_121.txt
8c957b5ef3f7e190723397b7e1d7766e
b9473947cc20170d5b7000807ed9a84054df7495
2284 F20101219_AACDXV mehrotra_s_Page_105.txt
6a734b662632b104021d1b02e9f1744a
b2cd284cee38d7bef1c2cdd19a0f25ed250e8476
F20101219_AACDBC mehrotra_s_Page_068.tif
1fa4a811c756979ba7c56554db510aaa
f924d94c86c5c22bd94eb2fcd1c60395c63cd7fe
77000 F20101219_AACDAN mehrotra_s_Page_096.jpg
a6d92c7f9a260ca6d98c4346964e4617
c6ef7459b20cc114167b0ba902997a3eb4e15256
23347 F20101219_AACEDP mehrotra_s_Page_073.QC.jpg
a33be1dc4b2eba62c543bb9b270d443f
fb1d85b29d8308115e60f7f3e771cfea5ce04d7d
7681 F20101219_AACEEF mehrotra_s_Page_082thm.jpg
7bd7883c17c10de13d2a4d5b3b34169f
d6500de76636f09bb1e1eaec3f9780a5c76b9d34
2249 F20101219_AACDYK mehrotra_s_Page_122.txt
2cf649cf062215ca3e144b05ba5318f8
cbd632561ae7bd7c3d5f8c56566360b0b723fd14
1449 F20101219_AACDXW mehrotra_s_Page_106.txt
35c806af21fb305aa17cbe3725d4262b
d73cc5af2b8ddaf5ebf0efc3b405a2fe74004359
52053 F20101219_AACDBD mehrotra_s_Page_023.pro
e2b56c6cd291f5f8a1e62c587ccf2597
e4149b58d0edff7d92bc5ba2df72eea1c00493ae
104296 F20101219_AACDAO mehrotra_s_Page_030.jp2
c382f248c9c5b42d75a8033717a9d204
f79ffaca6229972cff612c21285d2f3f8a52b43d
6407 F20101219_AACEDQ mehrotra_s_Page_073thm.jpg
0a811e13d723c130279a5551cc4baeea
3826d689e540c91a84fc8daee3d762501dee1a74
28205 F20101219_AACEEG mehrotra_s_Page_083.QC.jpg
55278b58069b2c917abe3e552d8193f3
73a937f771201b756d7c4e27ccfd27529ec07c6b
819 F20101219_AACDYL mehrotra_s_Page_123.txt
8294934d4e0acb32562793f971292696
5a1b3c367f092b7feea307b031342ad4ec2f09e6
2070 F20101219_AACDXX mehrotra_s_Page_107.txt
863ad3de8bb333a604caeaef01363e35
baa27ae07976df4ea1fea6d551ce996ab23e54e8
F20101219_AACDBE mehrotra_s_Page_061.tif
e99a2886c224cfb54cdae53085729a76
70f7d8bcfa3d6625a34ead6016e8a70c441e75e5
98169 F20101219_AACDAP mehrotra_s_Page_081.jp2
c927a4d270873ceeb0b798211534fd04
5616e6954edcf0a78e89b5b580c66a825577bc1e
6555 F20101219_AACDZA mehrotra_s_Page_007thm.jpg
de817985798b94a8bb597f6b457bd04c
26d298e85f06daafabf1485a7a4c8e650d8e8da0
18348 F20101219_AACEDR mehrotra_s_Page_074.QC.jpg
6f4d7fa6941f0374d9a89e3e6d6ca50c
012e09102dbdf76b7f890a5ab1817750926510d9
7536 F20101219_AACEEH mehrotra_s_Page_083thm.jpg
3f89b6cf66216f0b07ad35811a2e55be
8648974732248aeae9bf174a72e657277b03c7ed
851 F20101219_AACDYM mehrotra_s_Page_124.txt
dc1dadaaf21449c20c8ec7cd48d0dd00
2ce4709b7315598467a37bcaf79c8f79dc97f661
2008 F20101219_AACDXY mehrotra_s_Page_108.txt
d13e6abd6967ab34526195686a25e8f0
e496abb4a1a36097c3e3fd4a0459bef89c4b8bb2
87884 F20101219_AACDBF mehrotra_s_Page_082.jpg
1664870ac5debfc6634e5b53ca80a1f0
0cf9f52ce9cea0bdddea8f990b8c2d779a23860d
24289 F20101219_AACDAQ mehrotra_s_Page_049.QC.jpg
6b8b696ce4de2ce4beeb6f68327af27d
18461044a88f1622deb9e4d6ee8831f99ff3edb0
25029 F20101219_AACDZB mehrotra_s_Page_008.QC.jpg
721061fb8a1a3d6f63109908116cc03a
fa0791fbd11765244f5a731f980bd723905593fe
5439 F20101219_AACEDS mehrotra_s_Page_074thm.jpg
7765986066cb79fcf2e5c2314c41ad2a
d6ee3f1821ff23b281078a7e389af729f4f28f37
21627 F20101219_AACEEI mehrotra_s_Page_084.QC.jpg
b8b11010ac1d3c8674875cfe6c8f244d
9b1237b2839c6c1680ee85e99ca764ab0c422d71
2421 F20101219_AACDYN mehrotra_s_Page_001thm.jpg
93d340e30ef6d342879fb43f4f989fbc
ad1b802f6502deaf468e3dbf1a6b1f171e156b74
1979 F20101219_AACDXZ mehrotra_s_Page_109.txt
11a3457ae4a5da802c5cf917d8186201
f319063ce250b3eb7accc923ae839c14b463ab39
F20101219_AACDBG mehrotra_s_Page_015.txt
6018e719626d7f1a60bdee05b60ce7b6
88c6ab986c725f96418c49952cfe1e711b8d18b7
7488 F20101219_AACDAR mehrotra_s_Page_047thm.jpg
be8265e58b8b7c521e5255d38b31b0d8
93f20a738c414288bd8f8022d0794a8e5ed87408
6327 F20101219_AACDZC mehrotra_s_Page_008thm.jpg
7ee5ae28fb634800988c4c63f3cf4ef6
f1a3e513dee1e2bf2241e2f98ae66fdee74c373b
31710 F20101219_AACEDT mehrotra_s_Page_075.QC.jpg
0670d5d16c6c714047915735c82544e3
89c400b321f44c9c573a933e72f2421b7d502ae8
5891 F20101219_AACEEJ mehrotra_s_Page_084thm.jpg
541f29b6fd6f7a8961362b621708dbf3
26574404a077ab8d9bae1d331014600267092ed6
419573 F20101219_AACDYO mehrotra_s.pdf
f8618f7f99631504e2c7545bffcbafe1
a7859efcdef41e857f2b23781487fc774de392a6
6446 F20101219_AACDBH mehrotra_s_Page_056thm.jpg
51e452e8109593102a6b4f466174c301
163b625633b3b7139da9e03c755a7ea53a536563
45567 F20101219_AACDAS mehrotra_s_Page_124.jpg
6c130c8b1e98e988d0445ddd28d13212
1b65bdae27a85e18344b57ee49ca1f6dd0d86aed
20813 F20101219_AACDZD mehrotra_s_Page_009.QC.jpg
277f14d8d3f295d35e65a722927114e3
29e1fbed6d8edb2d810cdf9f04560782e2552412
8209 F20101219_AACEDU mehrotra_s_Page_075thm.jpg
0cec6c31cfb84a4157163f54e63fcf7b
1297631da3ee08697e5778fa1adb924edfa0ce90
29799 F20101219_AACEEK mehrotra_s_Page_085.QC.jpg
187f3daefddc50055f623cbd962d3253
b9f4a0b632dd4a63c54a31bee4d85eb5fcc80dab
8382 F20101219_AACDYP mehrotra_s_Page_001.QC.jpg
6f21e40d8bec790bfcbc4e0e5739948d
32b630af0baf3ff8c5466e7e6148d69a357ce8b7
36258 F20101219_AACDBI mehrotra_s_Page_053.pro
4e4c6b8e31171a3c5f07827793dcfabd
1b46849d30435b72da5e3bbf970453e560cb740f
F20101219_AACDAT mehrotra_s_Page_059.tif
db072f6b996be6e0e94726116f559efd
52b7f6f78d36c91e5f6c34cea7d1c173d505f429
5488 F20101219_AACDZE mehrotra_s_Page_009thm.jpg
aa67454a1e4532b21e7b3518aad6a6ce
26ce678fb254d6dd6df489fd5ca3e5cfca29a52b
28583 F20101219_AACEDV mehrotra_s_Page_076.QC.jpg
06beba4d9c59feec1f1a85eeacd74505
d0827f32669be468339624f2833e25f32be6c2c8
7291 F20101219_AACEEL mehrotra_s_Page_085thm.jpg
024b8c772db1d86ba3807ae98bcdf4bb
862a8bcae53a6c70fe453fe072183b2df4c45d96
1672 F20101219_AACDYQ mehrotra_s_Page_002.QC.jpg
058d6dd1281e3b521a037bc2d4922709
0c1fe6c7c0502804690cd95ce422328d91c563e7
28726 F20101219_AACDBJ mehrotra_s_Page_036.pro
6850b4a918927d5d8301b10c1e47a132
e59f23239ac0b545c376697b86b8b5ebde8fb30f
48286 F20101219_AACDAU mehrotra_s_Page_060.pro
dcd709d0cfbcc09e49567689ab6044fb
595e6e7cbc6c867a5d0ada632f0bd2bcb873e30f
F20101219_AACEDW mehrotra_s_Page_076thm.jpg
f951ad714428a036016820972ccb9525
3c04933989edf6ac072542c8d94197c372d942a5
8361 F20101219_AACEFA mehrotra_s_Page_093thm.jpg
8233374e0c8a99e83079f7e927dd5a5c
a192bea8b1b470aa87562108b49a67e0655acd50
18205 F20101219_AACEEM mehrotra_s_Page_086.QC.jpg
a65625e4990ddc552ea684efb60110b0
1fd305b396106357b0e7caa37c4b6606ae1fedd3
636 F20101219_AACDYR mehrotra_s_Page_002thm.jpg
b1e518e0c50ab5fdcf65002ed36fe025
501a01d7d39c2b87bb93610767e1ed8c89dded99
46645 F20101219_AACDBK mehrotra_s_Page_070.pro
26134689d6440bff26dcfe4a6e80cf3b
41c9ffbc63c02cd0cb756224117c78dc231e9aa6
111466 F20101219_AACDAV mehrotra_s_Page_098.jp2
4f830c508f193b4f107e86a8ec90aaae
60614f60ed13ab42b23389cd08312629e224e462
F20101219_AACDZF mehrotra_s_Page_010thm.jpg
7866709b062a070f858edf2db474a1f4
9a5f37171bfefed6afbe1953c8d4a4344f9c4ca0
24950 F20101219_AACEDX mehrotra_s_Page_077.QC.jpg
95cadb1564f1842757bc0b2e7026152a
ba33ee23ab65eaa7e1809083edbe284189c8036c
23198 F20101219_AACEFB mehrotra_s_Page_094.QC.jpg
ec497d643e9890bd204d86c4604c11fe
72f1775103ac5502af5af05db27b7ae83ef5c270
4944 F20101219_AACEEN mehrotra_s_Page_086thm.jpg
0be136b1572f8d5ec1aced6cd023b451
0637bcce093794a89c87a001f6fee7f56fdd9f80
7148 F20101219_AACEDY mehrotra_s_Page_077thm.jpg
1ec3c0474786ecb43add08f6206f88b6
4f4cc1a7cf2c7af9044524c8722cc66e97cc1015
8938 F20101219_AACDYS mehrotra_s_Page_003.QC.jpg
5c8c27b1b8689ed364366508aeacfc82
783c543d9ccb3ba41c974376a85a5b14618fe51f
93666 F20101219_AACDBL mehrotra_s_Page_064.jpg
18f402b87954f7a6c07da811dbc78141
34cac5328e222794bd83a2a726f5f909225690fe
1756 F20101219_AACDAW mehrotra_s_Page_076.txt
fd4213ebc09163a7cc227c82e8fd0c00
f2387fc8a5d3ae20a0db5c97d95051f1b032c1c1
33076 F20101219_AACDZG mehrotra_s_Page_011.QC.jpg
badffb7fabcfc049a4e4027d07c8d8ca
d5402afd61deff8d7ae4e134bea4b4a6ab5df529
6174 F20101219_AACEFC mehrotra_s_Page_094thm.jpg
bdee332d59eb7efa37942ddaaaa3641d
5c676e8f6991f35eec66beef829e49ca7b974a59
7019 F20101219_AACEEO mehrotra_s_Page_087thm.jpg
08739b58997faaea00d2501f6f0078d0
87b2466602308b9993a16b75ab59262b762f9a4d
18754 F20101219_AACEDZ mehrotra_s_Page_078.QC.jpg
14bd66d518b30d8104cc8f50678e5bb0
a00ae14ecfd7dead2aad944bdce4b7faebee97f4
2613 F20101219_AACDYT mehrotra_s_Page_003thm.jpg
a9265c9fcf7b6d93ec8d0dc6bb485c15
f338433788825a1533a5fb404016991940507c53
45254 F20101219_AACDCA mehrotra_s_Page_123.jp2
7ad273e76464453d3783445d294f8b4a
85599950d3ff1cffa9161b8ee25b43999aae00b3
64614 F20101219_AACDBM mehrotra_s_Page_089.pro
1b1b17294cfccda4a5b6da6305f0ed9a
bef5d949bc84181d24d37ea6cf0e0953840a8daf
F20101219_AACDAX mehrotra_s_Page_051.tif
4549a656490e68ab669ce12a9401251f
fb9571b45d59e2049bd5c16d545fa19c3b0b8638
8392 F20101219_AACDZH mehrotra_s_Page_011thm.jpg
4404379be665643fb7e93862a0415d55
2e155497cf043428ec7b2192f966c8e79de46055
27393 F20101219_AACEFD mehrotra_s_Page_095.QC.jpg
a8e84f7119fa7c9eb2ab1df9647df98f
5373508a55adfa27d2cade34028de563b685bc12
23593 F20101219_AACDYU mehrotra_s_Page_004.QC.jpg
562357c8afd8ef1830b64787ce2c28dc
bb6109c0c968b989e4e6fa1a9882c9c88c5ed1bd
F20101219_AACDCB mehrotra_s_Page_066.tif
0ebaa3214bcf4db77a919fd0118010b6
55f724896128f18815b46617d80fe4c5b964ee5d
92043 F20101219_AACDAY mehrotra_s_Page_081.jpg
606351440fce3302cb8d7561166d5ce5
245ca513a8353695bc541e4218fc4ff44c4353f3
34649 F20101219_AACDZI mehrotra_s_Page_012.QC.jpg
31775f58c52c463c21ee76ff436cb1d2
bf81afd732b7b2b206e50afd3b3124cc96f3a9e0
7073 F20101219_AACEFE mehrotra_s_Page_095thm.jpg
154fff1271db25d27e733c6404b57e43
7cb16d67868dee2434e96bc33e1181e2b39b52ec
35908 F20101219_AACEEP mehrotra_s_Page_088.QC.jpg
56ff366667f2bbab7e95aa64bf6536a8
0b2f94d41cf314857c3fb11ae4d680dfcdf1bcef
5540 F20101219_AACDYV mehrotra_s_Page_004thm.jpg
af74f1976181eb400955296330fb51b3
73cc74e1502d206221aeb4d6734e109cc61a426e
F20101219_AACDCC mehrotra_s_Page_014.tif
51fb8da852c734335894431597d773c5
b8ac9e3d0bb6a051c46ea94a455c355aa6164e54
25271604 F20101219_AACDBN mehrotra_s_Page_005.tif
3d04feb0d0c14a3af6e4dab64f20fbfd
04606787b2c944e82682c8b73f2e361e43779191
51155 F20101219_AACDAZ mehrotra_s_Page_027.pro
50e81a50ca0749cb90261bb3e75b19f3
fc1a107a6674842c5d2dd7fe119e068578c37534
8333 F20101219_AACDZJ mehrotra_s_Page_012thm.jpg
17d40b46631a9d9dc566b7a6bf6f3b43
ae96a45bbb520ec2a2b381a62cd9a76c61fd2945
25498 F20101219_AACEFF mehrotra_s_Page_096.QC.jpg
b640b4012efdd622c65c5217aab59960
84b2c08961a4d590717dcb266e37798c3e64f02e
8507 F20101219_AACEEQ mehrotra_s_Page_088thm.jpg
2624ba39b6402226c80bad665bf3a08a
ca992673265101e64fb0af00ab4c7f1e83c6dde8
30261 F20101219_AACDYW mehrotra_s_Page_005.QC.jpg
741b2f95079c1e7743cdcdfa7f55ae0c
2273f776c8e4fb07adcebddc128e33119cec23db
22319 F20101219_AACDCD mehrotra_s_Page_051.QC.jpg
320b91ec1446ecd9a4eaa5391148b6ae
d0830bbe7c16235ddbfcf6e6d2dac89ab6e8e59a
7061 F20101219_AACDBO mehrotra_s_Page_052thm.jpg
350e934d41a395d11197085adcf9ecf3
66da758ee510830272893ac5f8baf77d5328143f
32222 F20101219_AACDZK mehrotra_s_Page_013.QC.jpg
5d7c03077c60599eddf85e682b983d0a
dac27ddc7a7b4f67a15b7efc8525ac064f9daa04
6979 F20101219_AACEFG mehrotra_s_Page_096thm.jpg
2e316845a5b114ab8219f00dd1b9ac26
959ffe9e5dfe4343f25b82e45218046281f53b88
32578 F20101219_AACEER mehrotra_s_Page_089.QC.jpg
9bee5554627e1d46a4903a3dd54d9061
5c2d7e9238270f7f30eddcf0dc5b09b84ab5f4f4
6988 F20101219_AACDYX mehrotra_s_Page_005thm.jpg
8af291827ef75e51ca00394fe796bf16
5fd33281e156e92872b95d3af887341466c048b8
27980 F20101219_AACDCE mehrotra_s_Page_017.pro
09dba5c867fb496cd99b2288013a3dab
0a48e1ef3e5b8396c72afc8afbe1e5997006be02
F20101219_AACDBP mehrotra_s_Page_098.tif
b4020d29a7c2dae6c0510e32768f510c
a076194c3521fc60b2b13de5751e8479d543d528
8009 F20101219_AACDZL mehrotra_s_Page_013thm.jpg
71146b98ab1c1ab08b9c9c5d31e7b972
f0a9d728ebbf2d4229d837e34c8b2c6f6c168b75
22229 F20101219_AACEFH mehrotra_s_Page_097.QC.jpg
66d54e7b7fa3264f5d444cba1af60a6e
7e2b6aa303acd3d77449d4c85e3bbffab4658c7c
7573 F20101219_AACEES mehrotra_s_Page_089thm.jpg
80a7b587a493de0a085be14186b1a5b8
34c3868b83825e1532a2288309326eedf2ce1941
30681 F20101219_AACDYY mehrotra_s_Page_006.QC.jpg
6e9afeef7bb9f99e6fb51efb620797a9
17b54c5a053ca969034ff266468d43c9e5b175de
100471 F20101219_AACDCF mehrotra_s_Page_075.jpg
9360103a00da282cded26a13fa4584ea
b3247180801dc956f21a4670f244a420ac50eac2
128592 F20101219_AACDBQ mehrotra_s_Page_088.jpg
1f0268fcfdb77d6bd356472fe710c55c
745ba6e87833a75db6bdbfe07d4993b6c3e3c2d5
32494 F20101219_AACDZM mehrotra_s_Page_014.QC.jpg
e082664f93c68a657689c2dc22cb6f15
381adff0ea74cea30b0e96291af3afc801302cef
6131 F20101219_AACEFI mehrotra_s_Page_097thm.jpg
25dd9fd3cf1bc4a642e9533fa43a1dbb
d88f24ca8b936552bfcccc61d17bdeedf2aed2df
20091 F20101219_AACEET mehrotra_s_Page_090.QC.jpg
f168d4b2a1848707d812fdc29b8f2142
c17193e77b958564013df01248f8ba7b06151ee3
26045 F20101219_AACDYZ mehrotra_s_Page_007.QC.jpg
8869ce7e81cf9500a926b473f7fd6f92
d29fbbf129f2c154e77f988d49f1c3ee3a663fbf
1051985 F20101219_AACDCG mehrotra_s_Page_119.jp2
1e6f24c054fb422c9025578ca7c2df33
28b367d21bf2ba6d9cc76d595c1bd08acb0643d0
F20101219_AACDBR mehrotra_s_Page_025.tif
7780da7d99e9980edc589d027e76f911
d29405b76e464b2a574e8404c233e42021fb49ed
8054 F20101219_AACDZN mehrotra_s_Page_014thm.jpg
44984a60f05ba4682578a345f6cdfc17
f01ef2a8530eedfb329e8196a192c7d652d2603e
33617 F20101219_AACEFJ mehrotra_s_Page_098.QC.jpg
12ce077a63838f7a91f71d23ebd323f5
5962ddc66cb46b92da50938279518b727b0d7095
5423 F20101219_AACEEU mehrotra_s_Page_090thm.jpg
adc57540d180ca9a1d3234be602fcf32
dd8bac0da8ed351474fbccbfa46f3c28143b473d
82563 F20101219_AACDCH mehrotra_s_Page_046.jpg
2589cc83e5e8f69e6a7231c2312e3193
2e7507b37e017c3a12eba30ae3019ed90157f47f
6412 F20101219_AACDBS mehrotra_s_Page_051thm.jpg
4c4e47d8b23f6f22ad292170812ac78b
1bbeabe04ba8f89bc05e016fe88dfcac0b8cfb40
29834 F20101219_AACDZO mehrotra_s_Page_015.QC.jpg
7c54d1996c1712d845e9cf3a645ccca1
1fdee6ca2e86e99ed9b38b8b546bee42eea2732c
8280 F20101219_AACEFK mehrotra_s_Page_098thm.jpg
06ae1ef42f70f3163d622d084a5f25d7
5d22deb024f3d65427d1e9bce093190f74b85267
25764 F20101219_AACEEV mehrotra_s_Page_091.QC.jpg
a15e734360abb8541370bdbb88a9469a
d0ed162f3e9e1701b84a44470a3167e72f31aba1
7689 F20101219_AACDCI mehrotra_s_Page_006thm.jpg
a2638d0bdef212fb8bbcd5f21b67efff
152191caf86fb1f090d67f54474f801827cce231
F20101219_AACDBT mehrotra_s_Page_083.txt
bda29fbd96cc03332fb0b56b4453ee23
e0373b0c30407a5f3a90079a89c76da206571188
7609 F20101219_AACDZP mehrotra_s_Page_015thm.jpg
d588c998419bdf42cd428c6d9051c393
ef193dbc35f53dc071ada0246957409516e66b7f
29928 F20101219_AACEFL mehrotra_s_Page_099.QC.jpg
c7922df49794a5a34f8e69f95308312e
1420ac5b1e2a0cb283bb08661b9256dea708f535
7206 F20101219_AACEEW mehrotra_s_Page_091thm.jpg
bd7f26e7c3a25f8d180fa52b15a2b722
322147de75a58822a15dc7e70ec00529438b947a
49735 F20101219_AACDCJ mehrotra_s_Page_032.pro
a39267790d1a98df0fbdb0c7f66b6099
a3881286f11ebe7804ed05abbda6ec1f2d7f7880
56469 F20101219_AACDBU mehrotra_s_Page_090.jpg
b2e6c804b1ea29e1e190cebecfc5dda1
6669d1057f673b8d38ac10e24e48f2a9198d90ee
32507 F20101219_AACDZQ mehrotra_s_Page_016.QC.jpg
02cab488d9e71d1a1451a41191499fa5
5e9e13eca242bd360abdb87a3d7f06d999e332c0
7015 F20101219_AACEGA mehrotra_s_Page_106thm.jpg
30736cc5a2210d24b7f12b4757c55aac
d6b2557f967230d32b06d55701a241473e4b0d9c
7910 F20101219_AACEFM mehrotra_s_Page_099thm.jpg
875ed62622ea22431512298415846d55
58cf1121a6e4262a08a26f371b1018ba245d1899
26521 F20101219_AACEEX mehrotra_s_Page_092.QC.jpg
192943ad648495823b3e8b96b53c1721
50d0ecb35d0426f479e70c4c1f4075076066f235
F20101219_AACDCK mehrotra_s_Page_093.tif
0f72f4d557d1c21b45dd179ca008b9d2
228904f153a6d62ab6048afe629954d89482e898
51712 F20101219_AACDBV mehrotra_s_Page_107.pro
3f5cd61d84739eb4da2d95fc7e6a16c5
bdf42bd712782c10178dbc55ddf451c93ba3ce59
8322 F20101219_AACDZR mehrotra_s_Page_016thm.jpg
a60fe2420d160f5f4e3cf32b792eb7b9
5db3db1b7cdc3ec172a73ccede151f6bb5396bbf
34154 F20101219_AACEGB mehrotra_s_Page_107.QC.jpg
21d5764cfe96a84a50fe5f047d3e9435
17158a5585307393e454d228e1d0379730bd295c
28645 F20101219_AACEFN mehrotra_s_Page_100.QC.jpg
77843d28d9a60bf9aad95ed9799550a5
36fc649f67b6fbf745d1dc2e2d25e1933e770988
6678 F20101219_AACEEY mehrotra_s_Page_092thm.jpg
798da1b28559fcc95743ad569c3758b9
77926ef89dde883d1993facbeeb9911ec744b884
100609 F20101219_AACDCL mehrotra_s_Page_032.jpg
62c6bd5b5ad5c7300151b080809269cd
355c440646960a26e8dc2386ccf5c00271adaf5f
35706 F20101219_AACDBW mehrotra_s_Page_049.pro
35b7148e2871d00f3d2aba764ba93a64
031f7aced6dbe11f6f988e7e16a03dbe21a64af1
18532 F20101219_AACDZS mehrotra_s_Page_017.QC.jpg
9a3f22fd685dfc9038df9927f21b458a
40448e083c69573620911f4fda9d839a7d820270
8397 F20101219_AACEGC mehrotra_s_Page_107thm.jpg
dee94cc6a6f0e8e733a4ca9d9fee2772
fe4a54de802958c4e9a32ccfbdf8ad8f8211ff2f
7777 F20101219_AACEFO mehrotra_s_Page_100thm.jpg
82de95e9ac2229fe2c52fb42c70fe14b
84a1f956c03460c4613e464616a89bb2ba517071
32372 F20101219_AACEEZ mehrotra_s_Page_093.QC.jpg
4772ddac0c2c262554c8e888556915ca
cf31ff5d1cf86fae896eec4efcf29c62a542337d
48388 F20101219_AACDCM mehrotra_s_Page_075.pro
ac883052fd2e52c85da2d77652fb4242
eed8fcea6b1675ed987db9c3081d7ebf7cbbca81
8312 F20101219_AACDBX mehrotra_s_Page_110thm.jpg
970e748d63d6a4352d324a618a721c7a
688fc977eec247495ee222db595dc94c0b8c87c8
4669 F20101219_AACDZT mehrotra_s_Page_017thm.jpg
cacf8f5436c9a50e9e4c3cec103a0465
477ac25b64fb0c040b6504d77f1054b185e33947
F20101219_AACDDA mehrotra_s_Page_046.tif
36c570f6b72aa3c18b429a3ea9ff9f0f
de8ceecbe73b9a927ff291ff732a8f986dce7f73
32554 F20101219_AACEGD mehrotra_s_Page_108.QC.jpg
ef11c88c4f3eb3bcb2dc8842c01bf129
fee60e1012a9e869c45e1bb512dad010f679c8b8
23102 F20101219_AACEFP mehrotra_s_Page_101.QC.jpg
bf880923dd7eff1875d1d523f48666c6
cf60981af7c763cfae145ed400859ed613e64fa2
F20101219_AACDCN mehrotra_s_Page_111.tif
96299e588a5357c69b6a2d2a9eae5584
7a022b182380fdfd17dd61396ea878a08dc8820e
1545 F20101219_AACDBY mehrotra_s_Page_044.txt
45be4b9b5c380ee63b45a41e931a5f48
7114b6aeadac10e185d0645db7ea1dc7a831d79d
26925 F20101219_AACDZU mehrotra_s_Page_018.QC.jpg
aca6778d23d2d306e47d095746ce2f7a
314aaf343f83d161f5cdb78a04fe9f579fa56212
2021 F20101219_AACDDB mehrotra_s_Page_027.txt
cf43f941dead4c65c23e0fd03c201053
311074b355b1ec462866c2200123cfafb2da069e
8401 F20101219_AACEGE mehrotra_s_Page_108thm.jpg
450f8fdc9284367e366bdf6a3cd764b6
bf27e448b76b7bf87d00f364bac3ba8f1ed5c727
1008 F20101219_AACDBZ mehrotra_s_Page_090.txt
018371deedc1dc35dde19938a6f7e0d9
08928e8c8503e7041aaa671aa214aecac6b8ab07
6845 F20101219_AACDZV mehrotra_s_Page_018thm.jpg
bf6164d4d85dd8189be96125eddd0f1b
07f23ff9d7ce0bb75579b3461a1618315e4d041d
85011 F20101219_AACDDC mehrotra_s_Page_039.jpg
1a26d43388e54ed121514e49d0376226
581d0fb20332ff516acba703971356c24149c226
32379 F20101219_AACEGF mehrotra_s_Page_109.QC.jpg
a46dff196a91e413acb64cf38ac5e6b1
25eea99b3f76bd23ad76da2e7355583e10a1fc4c
6056 F20101219_AACEFQ mehrotra_s_Page_101thm.jpg
a6df819abf8c1dbadd8e5ffc1581df17
ef8b0406e74f32daaa0dd602b20ddb48219f2641
2004 F20101219_AACDCO mehrotra_s_Page_110.txt
e21cb5bd606e6a96d7c63c0fbb34ba33
28a969ed3f41c352cabd51724b58f45da8e36faa
30038 F20101219_AACDZW mehrotra_s_Page_019.QC.jpg
c61562d4ad47ecb94d16940b660f6e7a
58dcd40a65fdca685e148412f7054f932d51fc21
26790 F20101219_AACDDD mehrotra_s_Page_087.QC.jpg
8453f38924c3cdbc2ee553ef5fd2bb6e
5876a339a2a97ff19ff66b7f8646e2c7b292fcde
8263 F20101219_AACEGG mehrotra_s_Page_109thm.jpg
0042842ae435240b9705f8a1849df5b5
d4c8df53a0a0b7fd45579a5581f46da87031840d
25480 F20101219_AACEFR mehrotra_s_Page_102.QC.jpg
cc290f5558e994b47d55644008fdd33c
6d388e105cd896bb25b444b9c1c55d0e5406e7ee
F20101219_AACDCP mehrotra_s_Page_125.tif
11ed54f7eb62d0536337562c222751ec
5e73e93061ef6953b1f6410803effae8d21ff8a3
7612 F20101219_AACDZX mehrotra_s_Page_019thm.jpg
485046eb06d5c465edf43f923d5f6917
d54c578393a265da5b13991ae50798d886d0028f
32337 F20101219_AACDDE mehrotra_s_Page_062.QC.jpg
38833c1912bab364a04950058e571632
15f86de2d8d1359b8279c018e8e23925491f0442
33184 F20101219_AACEGH mehrotra_s_Page_110.QC.jpg
67cf57f0337d4a42568ca651bbb99a99
a710ab33b607850d1560e2e730097506d4072af8
7033 F20101219_AACEFS mehrotra_s_Page_102thm.jpg
1a34fdf48d80fe79989af7630db9c820
abcf0055c0d44f2977ce9fe2b1c00a2e2c0d2279
F20101219_AACDCQ mehrotra_s_Page_097.tif
4e0855a8db42a0980c0271dff0812c93
a0a39c3f6a5644f4bbbebd1326183658100140b3
32642 F20101219_AACDZY mehrotra_s_Page_020.QC.jpg
9f939adcfda7f2f3ca867bb0e17143a2
a4e5a97dcd7a7139eda2c7e62623f3259a74bed4
188937 F20101219_AACDDF UFE0015611_00001.xml FULL
cf0f7267af49adbb88ca0bcb1c54ec2c
1a64e07479004da1e2f4f17aa5f4bfff0a9f5e6f
BROKEN_LINK
mehrotra_s_Page_001.tif
31390 F20101219_AACEGI mehrotra_s_Page_111.QC.jpg
4c65bf0ab51df0b892d9b4df6d051616
4cdc57d942172a7dee28b3d2c88c278f6f7f85d9
27505 F20101219_AACEFT mehrotra_s_Page_103.QC.jpg
1adcf09a49688ad53ed7096b0a225555
c6a8c772d255bddaaabf5be64116a0d56b3f09d8
F20101219_AACDCR mehrotra_s_Page_013.tif
bae2facf52865f2890a011b3f5f39a0f
f01394be427381e26f05ce08c974be73262744bd
8070 F20101219_AACDZZ mehrotra_s_Page_020thm.jpg
abc9f73c4acc16ecfab9043e123a31c0
47d49432bbe8d3f38fcc88563bedfbf2fc842a9a
7765 F20101219_AACEGJ mehrotra_s_Page_111thm.jpg
600c2b4f4417258180451f59d99a81f0
71f831418a0d6e3660e42a29179e5705dffb03f8
7265 F20101219_AACEFU mehrotra_s_Page_103thm.jpg
89fe5f33e35313dbb0de6114d60ce598
f30feab63495598b9f9b00b087dfa068e925c981
44000 F20101219_AACDCS mehrotra_s_Page_113.pro
a47091384fab281a06cda997190b9c33
8d37ac575c65b40edf166efa39e1e944dbe90ba7
33060 F20101219_AACEGK mehrotra_s_Page_112.QC.jpg
5d51ee97dcb48e2dbf6e64e682072540
26f6c443c159c2eedcb4e07df1fd06c22cf080e0
26069 F20101219_AACEFV mehrotra_s_Page_104.QC.jpg
a523a015b603ddaed10c264a4c5a0c9a
a79928514562845e87453bddf1010070e2139094
7803 F20101219_AACDCT mehrotra_s_Page_022thm.jpg
2a16493aa905ea6ae62ed4070236305f
bc760bedc9fb8df3481cef83bf7baa4807ae93a4
27539 F20101219_AACDDI mehrotra_s_Page_001.jpg
bc1f6aa48ddf6e32a68ef04c780c0e51
3b2d7880edd869a962fb579079106065284e911f
8166 F20101219_AACEGL mehrotra_s_Page_112thm.jpg
d9ee69e66dfde3199423e323d91d290d
b79df2ec029947bab2d392114f6c73f50da2a751
6967 F20101219_AACEFW mehrotra_s_Page_104thm.jpg
493b4112de2869576814a745f60a89bd
cdd65e750edda991745b674d74b5d1032aebfa70
40453 F20101219_AACDCU mehrotra_s_Page_091.pro
488bb63ac78e5af70a7593b7df400cf0
ae4cfacb02d5515437d2b460a2ff9df5c3407b76
4882 F20101219_AACDDJ mehrotra_s_Page_002.jpg
4b0335460d54db9db5e21ba2800204fe
989ac19017155374488d09901ac7552843249d3d
35151 F20101219_AACEHA mehrotra_s_Page_121.QC.jpg
1c62f96003dd6e53037453748a2783a3
ba74737d426f168e1ae973e485bb4b2f1731fca9
26055 F20101219_AACEGM mehrotra_s_Page_113.QC.jpg
4efb9899209643c7a683122243406b1a
26d56ed9b3dfc8dc9293566a1845b5355c6ebfae
32514 F20101219_AACEFX mehrotra_s_Page_105.QC.jpg
ff682d3fd000b17e8807f7105c360d62
d66a24d7bf46d5a8cdc79ac4d694c07de1d6f967
27395 F20101219_AACDDK mehrotra_s_Page_003.jpg
e1abb1ab85a9d9d17774c5c2c97670d3
1d38221d3916dc6232a80a2e21f845ea6be7e82e
F20101219_AACDCV mehrotra_s_Page_091.tif
0603e2c03a33e83c17bcca1240d0f23d
7c3c67b98a1ab6fdcd621f042527cabcbf45deaf
8736 F20101219_AACEHB mehrotra_s_Page_121thm.jpg
c9d8ccd889be1d0f0892c25b9968fb8e
434a1ae50cdd2efe29503ef6c279682b7d976dbb
6792 F20101219_AACEGN mehrotra_s_Page_113thm.jpg
6ffd610f341b8d83c4370c839197822b
9e93fe2c751ede83a74bde46024c9d5d7cfca324
8244 F20101219_AACEFY mehrotra_s_Page_105thm.jpg
d93316c187bb4ba148661bc58ad7ec20
7187704c8c1f285d024ae8b73dfd9631fbf9fdd8
99299 F20101219_AACDDL mehrotra_s_Page_004.jpg
de5993e0a26c6492b005c6039f21b597
c057a60c007f1ad443e3f241af6eabba52cba1c7
88899 F20101219_AACDCW mehrotra_s_Page_018.jp2
68a8d4d453439c7ee469f5af524cff90
73fcf5ff5899058f1b8bd9e7c201aa0c3e29e711
33808 F20101219_AACEHC mehrotra_s_Page_122.QC.jpg
aba70ff95126d85bded6428d3515d51b
2b3a80f40dadf75d4551614fcf55c0a6b9642832
16990 F20101219_AACEGO mehrotra_s_Page_114.QC.jpg
c6a7ede72d80b39f167789b78aa82c62
5d70b918d29b05ba237725266eeae26f03670409
24901 F20101219_AACEFZ mehrotra_s_Page_106.QC.jpg
3359043d071d7d15a365ab40cb111be4
b34f324382287ba09ee61ddd044edf88ec680b6d
93557 F20101219_AACDEA mehrotra_s_Page_019.jpg
5da94f75a891dc8e684f69ca10d8148e
c2e2ff69b675cc0828ece8d0bfed0617e0dec10e
128074 F20101219_AACDDM mehrotra_s_Page_005.jpg
f3990fc4b3751faff52cbdcc9319d24f
5e7d8a29fda0a63238ea3c718f029739c4ea95fb
23366 F20101219_AACDCX mehrotra_s_Page_010.QC.jpg
faffdd8ae8f43067a4374e4dcc7fee6f
b1d003bd1379d53b67f8151735e99a09d0624831
8479 F20101219_AACEHD mehrotra_s_Page_122thm.jpg
9c0a0f35349c53b5dd7c424fa6725059
b8770517844cd046c540c3b984f2c023c10a95f0
5028 F20101219_AACEGP mehrotra_s_Page_114thm.jpg
d2a2b20248934b95206cfa41c1a66657
5d575efef0749f50157ed0afac8f01c5c7381c4f
97948 F20101219_AACDEB mehrotra_s_Page_020.jpg
5bbaff7b764add16d34f8f4782cb2761
20afb806706e001f2f22c6f321ccb79543983b11
113750 F20101219_AACDDN mehrotra_s_Page_006.jpg
4277bfd9cf78b419476927117b9d797d
71a7f327c158b3b3eb56878689f18ac010f8796d
29078 F20101219_AACDCY mehrotra_s_Page_082.QC.jpg
448a2ba6f0821aad71fb285fcae3a560
24325979571735f1ad3c139bde832078a1bc6df8
13715 F20101219_AACEHE mehrotra_s_Page_123.QC.jpg
f5e04d844f1aa4548626cb54498d569e
d104cced8da8d5eefee05900d0e60f99f0b2305b
15497 F20101219_AACEGQ mehrotra_s_Page_115.QC.jpg
d33a4b357d912f914a5309bc0d859698
1dde4dc5cf9192d25de363f918c99db002e05b35
98800 F20101219_AACDEC mehrotra_s_Page_021.jpg
d01fed6d76ba05c0ba63f686c0ffea35
3d892f1d256cd57f4e0d1ba85fca5ebbf05c161b
91067 F20101219_AACDDO mehrotra_s_Page_007.jpg
6304187a9461fd0ab007f8235a224d80
c3bfab0be2c2c6a5cc548a782e5dff29986d944d
25077 F20101219_AACDCZ mehrotra_s_Page_079.QC.jpg
e7e96831d056ea881a21a4934544123b
c6c635bae4bc32bd73c6088525cf00610a0f06a9
3351 F20101219_AACEHF mehrotra_s_Page_123thm.jpg
c36741ba04319fbf0f563e34c4553b47
c34591617b3205fbaba5e30ddc412bd6851d7eb9
95324 F20101219_AACDED mehrotra_s_Page_022.jpg
e85ad425cb194b5fed86e317ec8f1be8
7c3af1f7a41c659b850edd8fb6d8f05a08788aa8
14969 F20101219_AACEHG mehrotra_s_Page_124.QC.jpg
19e0e3a8f6490b9151b577d9cd3bdbab
9846ed4cb2b05f604c95f660210775b5505d7b57
5150 F20101219_AACEGR mehrotra_s_Page_115thm.jpg
d515240429d71fe3332904f7762289d8
2b6575038054d28f4e0f1ac8a6e19732834ae712
103708 F20101219_AACDEE mehrotra_s_Page_023.jpg
eeaa7c22d4cc22e5b30d71cc194f3c5c
ac41a14e5a3b5bbdf34f0e43e437d8e861be29c7
82787 F20101219_AACDDP mehrotra_s_Page_008.jpg
bfa3d266d764c9dba52204d2dd6e00b1
748b7809f55d493eee7811c41659446b80a3f81a
3904 F20101219_AACEHH mehrotra_s_Page_124thm.jpg
22292509ddb881c5838c107314fa46e3
6622977a87e52c692e3dd2744e20bffc5cb10284
31604 F20101219_AACEGS mehrotra_s_Page_116.QC.jpg
c3f403336d56b6fb415e778dd88829c2
bf81c448bbbeff870b93e23663c7e09ebbfe5267
95243 F20101219_AACDEF mehrotra_s_Page_024.jpg
3d1fa8c8bf02dce24c39a5297a747bb8
e943f16b2fbc7d2e5dca807a2bdaf3e9b4bba260
64685 F20101219_AACDDQ mehrotra_s_Page_009.jpg
52a696889981cd84f71c7f9bc7eedbdc
8d2a0757ee7136b09f18417a31aecadce909228f
786 F20101219_AACEHI mehrotra_s_Page_125.QC.jpg
2be47a81992c099610e7acac03b01d86
0d26135607e037bafe40673a3b1f3c65047fc381
7989 F20101219_AACEGT mehrotra_s_Page_116thm.jpg
1ae8c4caace7e50c2f84ee0d636a6f85
7583bb3a969158ab358fa29612684c614603c5e5
102898 F20101219_AACDEG mehrotra_s_Page_025.jpg
1b29a14ed4ff4751a7cc4118940b7036
5e559f1ed20fd48dae089ded47eaabd24ffd9fb0
69995 F20101219_AACDDR mehrotra_s_Page_010.jpg
caa22cdad396f056861a58d23d4eed08
5732cc43e346f00076540360afc69efc088f540c
378 F20101219_AACEHJ mehrotra_s_Page_125thm.jpg
9ac545d057de11d05a32b29e2de8da9a
a9160cdfc3c9e5163eb737c7e970b57e87995d97
33361 F20101219_AACEGU mehrotra_s_Page_117.QC.jpg
ed6f60cdfbf1322e7e054ab7ca9844aa
9d382b02d23667ab27b57a7f415004971cae3c47
103306 F20101219_AACDEH mehrotra_s_Page_026.jpg
9608a5095deff4861a101bc261580f32
adfcb046ca90e93da7c84bb389188c57e13ee1b9
99957 F20101219_AACDDS mehrotra_s_Page_011.jpg
22b95edd8f7bbe5b935f8c49ba7b09da
cba7d56629e08ce75914a36f4c7fef7ef085deec
22 F20101219_AACEHK processing.instr
99ccedd82081b4c3d60b936633e31e18
b8e3adaac2fdccdc68582e2ca4995866232f6077
8275 F20101219_AACEGV mehrotra_s_Page_117thm.jpg
6c8723b7ed2e5790bddb357ff7f49b5e
26bd263620e93669e079fa1d8047ca4e82e893ce
103932 F20101219_AACDEI mehrotra_s_Page_027.jpg
f676697075c6ba835d91f77eecdb1618
74e871aeef0d9b94ea04cafca4ca885d743f8f55
101887 F20101219_AACDDT mehrotra_s_Page_012.jpg
560855be015a8d62cc8e9d04f658d1a9
1f8522a24fefd7f080087c740762d41365bf4ef1
145651 F20101219_AACEHL UFE0015611_00001.mets
680850e12394b8da7039dbd0099903f3
b4a6ce602ec17d822b903d61fdc227753553248b
mehrotra_s_Page_001.tif
35713 F20101219_AACEGW mehrotra_s_Page_118.QC.jpg
e78336bcd08f394e1ec0ad1ea7969a8d
c5f858b863a010d40660061cbce5a6f7866f398a
96484 F20101219_AACDEJ mehrotra_s_Page_028.jpg
c82bc95191a550ef6d14f596d3264779
e0bf9898933465fa450a58ac1e4350366080b076
100229 F20101219_AACDDU mehrotra_s_Page_013.jpg
b88509352a772a58eb7a0b9f155f4968
7cc9eca9f5ad604f88ce0dc51ee6891b764b7738
8911 F20101219_AACEGX mehrotra_s_Page_118thm.jpg
68649c55d46b72bd3a7465188000a5f3
92d2f2af12606e8920a7520f6c157c80906f100a
100036 F20101219_AACDEK mehrotra_s_Page_029.jpg
31b49acda322d71b97017daa37f15989
4248220c2615e6ae44f8955c174514f44d619f75
100802 F20101219_AACDDV mehrotra_s_Page_014.jpg
ecf903cbaa7e71f25ecbe2319b9de683
8a05aade39118ade56681af79de86885804b4094
36042 F20101219_AACEGY mehrotra_s_Page_119.QC.jpg
556ad9e6170a7339452788228cdb06ec
22f4356425d1467164e8d74dc6a8a5bb3e554d9f
97870 F20101219_AACDEL mehrotra_s_Page_030.jpg
81be86e8510be6bcfcbbeaba1c7bdcd4
3888c422494d494b43a863a66077a93f4a6945c6
99202 F20101219_AACDDW mehrotra_s_Page_015.jpg
3c68ac58a82fc4f9585c9eba3dcb84c0
1ea7fae535493fba676fc634b5155d5b4a6b68dc
8896 F20101219_AACEGZ mehrotra_s_Page_119thm.jpg
a84f8aee29e3d3e412d4d1262b5ab958
02028af7d6413a27a05b5571a3137433d5837642
101849 F20101219_AACDEM mehrotra_s_Page_031.jpg
3fd067c2629b833d3846d938be08e8ed
1792a97688f8974dd2ec0f487571f4f75ded40a5
101658 F20101219_AACDDX mehrotra_s_Page_016.jpg
f25e0d42c01073408c735e7a81113809
4d2d064a21f4033c1b66edd7a98c73ce9634d05b
48619 F20101219_AACDFA mehrotra_s_Page_050.jpg
9f3de0db47030d36f69aa8e55d7e1ddb
9efca0e8c33eb72ae5aca4841b2e7efdfddc6d22
99298 F20101219_AACDEN mehrotra_s_Page_033.jpg
9bc0e5016d537bb636a7c49f300baeef
0910150a640e440cfa73fbb54899b5b92c218b4a
59478 F20101219_AACDDY mehrotra_s_Page_017.jpg
435ea14d34d97c9e324acd47f4579d66
773b12cf4828b4c876b2956863a0525b13cc51ff
69161 F20101219_AACDFB mehrotra_s_Page_051.jpg
81f76f0611eff3d36957abd156b72b18
75df54dff5243f2631fc0cda72aff4cb0ec7baee
60440 F20101219_AACDEO mehrotra_s_Page_034.jpg
120db9591bb07e2afa5ccc736fcf0d38
3ddf89d23a68ff940c6ec2d8c8a527395117d759
84101 F20101219_AACDDZ mehrotra_s_Page_018.jpg
4dea3de7aee107969f0af004df034436
3cba5c309701ee67d6970b689157fea25457770c
79178 F20101219_AACDFC mehrotra_s_Page_052.jpg
f98a87f1f7efedbedd7cd6d41eaf0e02
7869ee6a65edee5948f5a686d54a9dac968ff914
91590 F20101219_AACDEP mehrotra_s_Page_035.jpg
214f19f923a09d284696b257912d7005
7b141240d45fe45450189a4e02f3d0e18507eab3
91630 F20101219_AACDFD mehrotra_s_Page_054.jpg
0b2a82b1d4f6ff6ff75b3ff216e7a7ec
e02686b573b8f7da974b48891ffa505adfd5bb8d
92295 F20101219_AACDFE mehrotra_s_Page_055.jpg
f0f4fc23507a5ee7a7b0fba22d315b29
03fa7ad3fbdd7b2f598696bd50a43970275fd274
72363 F20101219_AACDEQ mehrotra_s_Page_036.jpg
1c95bed43364a0c41bec68d80662072c
9ff9bcb47f10577f3ce7208028f384c226063869
74082 F20101219_AACDFF mehrotra_s_Page_056.jpg
99e51e0ce754b22142a3dda21fed961a
48ba5f96b5c7b968e24fc2eefd09a5d79111edb8
86149 F20101219_AACDER mehrotra_s_Page_037.jpg
92f8666d1cd4db0cc2da4cc9ff900f4b
a7fcdddecc99c1fb195ed7a9a36242124b445c0f
104635 F20101219_AACDFG mehrotra_s_Page_057.jpg
222017bba67cce23fd1c0925bebd1b61
24eb710bc976328e35fae14c184fe28984c822d4
86595 F20101219_AACDES mehrotra_s_Page_038.jpg
e8c084ba44ee453383aa9f6a53fe3a33
14ee6b5c81970796dd77e91595ca8775260fe863
100348 F20101219_AACDFH mehrotra_s_Page_058.jpg
bf416fe0652ed1febadc4d7e8841b872
592edfa0f0037ac0db24d74ce25b1895e30a7f56
78033 F20101219_AACDET mehrotra_s_Page_040.jpg
eaa30df8b317317c7402ba39a88e01b8
10d92b51c842aaaef4bef9e558956c7213a44761
106156 F20101219_AACDFI mehrotra_s_Page_059.jpg
d01abb98b9fa917b96fdf3ccbd51f75b
5ae1d0644eadc8b1f8d0c20b3364fa3aad4d1259
92226 F20101219_AACDEU mehrotra_s_Page_041.jpg
6040eaf2e0dfefd6b1ac7170595467af
195bd08747b87694978fb0a773d48b40a82c8a93
95495 F20101219_AACDFJ mehrotra_s_Page_060.jpg
22e295b97b77b6591bffd50af1ba03a4
7bada556639425e4d8ff2f340b4b0982fa6ce81d
76001 F20101219_AACDEV mehrotra_s_Page_042.jpg
f331c12704258ef6bb2dc78521366b04
5f2c0f237d173c21decd4a81d6253fbe509eb768
94629 F20101219_AACDFK mehrotra_s_Page_061.jpg
89f8f0ac3ef38866abac9e5280655ebe
6163ccabbefb3dc31b97f8a381ddbe9b36c6b93a
94169 F20101219_AACDEW mehrotra_s_Page_043.jpg
ea2778e91d9de9cb495f6b392da6a8f3
c5853b4b83705973d86ec3dfc31ba731d69aa1e9
96943 F20101219_AACDFL mehrotra_s_Page_062.jpg
dff5823b781ab11324006bd4821b1535
adabc2187d40982455559365b7518acde172d47c
70680 F20101219_AACDEX mehrotra_s_Page_044.jpg
852c9a245c7b0ec58b253e6949639547
9b9ab21a293d4c4e8cdaa80477fe37bb4a8faaa1
75722 F20101219_AACDGA mehrotra_s_Page_079.jpg
65fa26765bdcc5139079c3f21e6f2c65
a51b611cb4f2732e6376e1be7a274a86d6727759
76958 F20101219_AACDFM mehrotra_s_Page_063.jpg
62e42a63802e90942e6b66d1250a808b
46d800164ddf59ede8498671ffd769f8f72cfc52
76843 F20101219_AACDEY mehrotra_s_Page_045.jpg
e95907b517ab2c607a1edd53920247b7
e1d1002b8f87b07de554ed11783355466e853b03
37071 F20101219_AACCZS mehrotra_s_Page_087.pro
5eb0dc34c1e3c7a447935462d67aff59
91724ab5c05b0a2efff3503f55c381b938642115
62624 F20101219_AACDGB mehrotra_s_Page_080.jpg
cb62d3cee3fc97501af3c9caa7e11dd5
fa130da7fcfa1c02c3f0c42a8f0418481dfe9bf1
104159 F20101219_AACDFN mehrotra_s_Page_065.jpg
7d2d3ca85994292e1917a159bb408336
1d57fb03d337fa363cea5b4cf480d7d8d6b1e37f
57265 F20101219_AACDEZ mehrotra_s_Page_048.jpg
b95311841c357a28f675b7da962f8852
f2dd0feb6b696d239c5e38c1c15588fe8726866b
82291 F20101219_AACCZT mehrotra_s_Page_095.jp2
2f799be975f9390f1c2af27d9cc3bf76
973506bf48770c7f8864e144f879d1cc53611ec4
86946 F20101219_AACDGC mehrotra_s_Page_083.jpg
beb8eff8fa624c9c372c50f739a64d2e
c34f154a5992fd1826baf9227672e66d0b04f971
103172 F20101219_AACDFO mehrotra_s_Page_066.jpg
8cc697e0b59133bd77129356bbc05801
06fede2cd2c4d8e6714b58044b7ad9dc94832e87
7932 F20101219_AACCZU mehrotra_s_Page_041thm.jpg
f064111eb73ac5a1719edb99f7cc7ba8
443265bf471a741a4ac6267fa19be3c370a7d9af
69533 F20101219_AACDGD mehrotra_s_Page_084.jpg
5b44162fc238c11bf197a8ccd205a54d
7c5344741223b545a2994dab9ffc86939f3a0787
111546 F20101219_AACDFP mehrotra_s_Page_067.jpg
31bb10e27feda4f226bf76c21e6c6e2d
f5fabed01c9063ea08852e100754c369f15ebe91
74811 F20101219_AACCZV mehrotra_s_Page_053.jpg
f3cbb9724f6d9bbed7c6d5b1ec911837
4dc6b39e38cff3740ccda32fee43db40dea04d59
92007 F20101219_AACDGE mehrotra_s_Page_085.jpg
68ac9ef7c304c5c964194abe7d948313
b6e0a652d5e3b8950759be477346d242330774e7
92470 F20101219_AACDFQ mehrotra_s_Page_068.jpg
abdf4f400b7b71a0788484db66528274
1bfcf037ce1fc68c21b47b9b195c305ad26fbad9
28540 F20101219_AACCZW mehrotra_s_Page_047.QC.jpg
41998b6e7aa8629df6afa6648298a8ed
525d39d0ce25ca4b80f1918bbd8547dddb7c968f
52930 F20101219_AACDGF mehrotra_s_Page_086.jpg
7fd7c5c54050d1ef335f0b12ad8a379c
d3f5b4c32e261bd4a633c061b30411a3ec411922
33646 F20101219_AACCZX mehrotra_s_Page_067.QC.jpg
ae3958fd6fc496249894ebf02a6fb32c
88e1fe5ed1ce481531aba6915858187ecf98efe9
79399 F20101219_AACDGG mehrotra_s_Page_087.jpg
8b3474263f9e80946919c474896e40aa
552a6b69c0ff119ecd60c46dcace3a80453341d8
90148 F20101219_AACDFR mehrotra_s_Page_069.jpg
7a1f8b24de3f729e2a924597b943a62c
869915eb1fcde7fe4fdf9135b54c186bd8f62e91
1885 F20101219_AACCZY mehrotra_s_Page_024.txt
c2f16caea1c57f8b7517eeaa80fa0e75
280e6ab1317a343995d1405352753a2ae626e2ca
124842 F20101219_AACDGH mehrotra_s_Page_089.jpg
74241ee57c7e9d8cd547c900a16ae1f5
61bdfc7ec2832b433ae3012504244c72bffc4bb8
89885 F20101219_AACDFS mehrotra_s_Page_070.jpg
1194234f3f87be2683b873295e985a8a
5a978a59f36e164074d23bec33973c9b895a2506
74425 F20101219_AACCZZ mehrotra_s_Page_049.jpg
1e68405628f898d3dfd56e9ebbf29f1b
eb499a679b9013da9cb1fa77665cd1ef55860e09
83560 F20101219_AACDGI mehrotra_s_Page_091.jpg
99fb4d7bcf51b95503380a61de2f5794
1d320ec8fc20eaa9e34ec3ae01170ede04e0cf31
98567 F20101219_AACDFT mehrotra_s_Page_071.jpg
fd1e0a3f1e6d199147125a83a1561693
6399a642c2c906fc4fc3a967be7694f5da96d5ca
74981 F20101219_AACDGJ mehrotra_s_Page_092.jpg
f65643089e1af5328a776466a44cafaa
8491bc83c4eb45a579d5587b64cac1814790baf5
88662 F20101219_AACDFU mehrotra_s_Page_072.jpg
70c4f40201b4596a1921251d833abbb9
21834a4ef7faf087fde3b97b9c700ca69f87dc5e
98992 F20101219_AACDGK mehrotra_s_Page_093.jpg
adc829b7373656906bb4f86089394893
c20a2fa7d118f3aa4905977d92cd47193ad37b4f
70027 F20101219_AACDFV mehrotra_s_Page_073.jpg
faff54e7549d1239373b9b4a2a9207a6
c3c0fb3230c07ac0f9726f030af4b3889fcef372
68819 F20101219_AACDGL mehrotra_s_Page_094.jpg
f9d6386fbee2235be812d6545718ecd9
a565b1e6f49719240713b24559f85b09f46fdc48
54117 F20101219_AACDFW mehrotra_s_Page_074.jpg
06c9d77a39aaceb0423eeb0c36b61938
2bd808c04a25d1cf8b6d2251adb97027925f4355
100969 F20101219_AACDHA mehrotra_s_Page_110.jpg
cca0abcdd26cb2e3008ab3c0a43786f1
d3a9947c45b0a0aeeb3446d032b9e8bf44beeb80
82293 F20101219_AACDGM mehrotra_s_Page_095.jpg
ff7fa246e2c6726c5c9feec51339e03b
ac7f74a0b0d393c0ade5b8dfbbff7636cc6c57ab
89117 F20101219_AACDFX mehrotra_s_Page_076.jpg
fba1c3ec3600bd87cb569c2c42148e73
340f81e8f5c32846301e19abe39598cf898374bb
96796 F20101219_AACDHB mehrotra_s_Page_111.jpg
71c7981a95d40a0f257c93335d616b28
dfc189d442497e5284ae34ac43b29bfc932b40d7
67344 F20101219_AACDGN mehrotra_s_Page_097.jpg
2afab72fa26f4b86b0941f45d9997a9d
6186f25bf34f7f9691c5c75bbece2ff315b0b50f
77329 F20101219_AACDFY mehrotra_s_Page_077.jpg
11387314b9e1762bef3a485caea18b7d
21717fb859d7c30c284523c4f708bc9abf74c68b
102603 F20101219_AACDHC mehrotra_s_Page_112.jpg
774c0ef5c7b2c3f61567c01c47cde41b
cedc6788c6434bc472825d0e1961592a94247eb0
105709 F20101219_AACDGO mehrotra_s_Page_098.jpg
af650d111b034350b6badaffddf4893b
7288d99872f085e5065eef02d10e4b4e3687bd45
63248 F20101219_AACDFZ mehrotra_s_Page_078.jpg
fa490d880081d8e38a47529fffae93df
06a954c9e97e34cce65d6456833c42f8e42ac7dd
89014 F20101219_AACDHD mehrotra_s_Page_113.jpg
e4760bb571aef4db0d48e4ce060b806f
89c604d68c68fe3a76b82ac97279fd63ff1726ec
93371 F20101219_AACDGP mehrotra_s_Page_099.jpg
83a07a2f34d0342e971dd43252ec15b5
fb2263b205e717d4708508704f70d062ce7b5129
53470 F20101219_AACDHE mehrotra_s_Page_114.jpg
d869cc702dc18ed14cf91167e88d6c28
60a6c525f0ff5723b63f8f4d8569e3c11ab5e5f4
92093 F20101219_AACDGQ mehrotra_s_Page_100.jpg
cb4abd02b461d5c21502cd72abb861e7
b1e9c2493b82562dafdfd214943f2fd54686e6a2
51127 F20101219_AACDHF mehrotra_s_Page_115.jpg
5a940f6fd7f0979b5650675889cdd3f4
0232120055ebdde8664d64741213c7f20cd0252f
70081 F20101219_AACDGR mehrotra_s_Page_101.jpg
639b143bda2ad239d65598b4a4b4d0c3
34194838f465a08cc688bc37a73e70243d8ecf83
110853 F20101219_AACDHG mehrotra_s_Page_116.jpg
89a02be3b10b230de3e735a4c52de25e
49d35fdf63bbe08c5ef013bdbe69f658749794af
115204 F20101219_AACDHH mehrotra_s_Page_117.jpg
49b7866df9720bc7a02068e778dc90a7
357e3d395e9b12dd7a0170fd99dfb53e5b1dc1db
73797 F20101219_AACDGS mehrotra_s_Page_102.jpg
ee8fe874bc8a33d542935793073ba996
4723ffe7d51452447dd995c0f6217211fba75885
125724 F20101219_AACDHI mehrotra_s_Page_118.jpg
625937007cf0f6af7de04f37da66f5f4
8f5851fcc14fb40ecfd5bc2f8d18b6de22424d58
82436 F20101219_AACDGT mehrotra_s_Page_103.jpg
5f14cad66da98c6a562b9498c780b7ba
64f5d4c249efadcd239ef6d1260d165285187b1b
127329 F20101219_AACDHJ mehrotra_s_Page_120.jpg
315e0f24fa11566b7a4edde7e3c43b92
34f6c94cf62291d46b78278deae7feb8d1fbdf90
77212 F20101219_AACDGU mehrotra_s_Page_104.jpg
905776d8233d9bee8b92905f21c7c3ba
ecb96da25b907e9451be6bee8bd9b720975c7ab8
119315 F20101219_AACDHK mehrotra_s_Page_121.jpg
1b9c7ae059a6fce518040bd0e47de69d
b31483a695b47d12a6b9b08d5dabf59b9c65e1ec
107380 F20101219_AACDGV mehrotra_s_Page_105.jpg
2da0c8430b362211e2808bbc59bf0eb4
02053adc74b627cdea74009f100d37665bccca7b
113638 F20101219_AACDHL mehrotra_s_Page_122.jpg
9d7110654558da04b08f277844df7eef
9a057dc748b58a60f173f79b446a490c6ff6e5c0
75394 F20101219_AACDGW mehrotra_s_Page_106.jpg
1de91e1e5d775052e355c97052207ac8
b4e59c06d2fe4a785f9270d04c552161c282aaf9
46694 F20101219_AACDHM mehrotra_s_Page_123.jpg
c6c7194e7d04be5734b73ecd08328e65
cc5fb19598256a4bf0aba2fb29f79f62e46e15ef
102640 F20101219_AACDGX mehrotra_s_Page_107.jpg
d4a86fc69873a10f1a7cf79ed0b03c90
fbda48113c3a169ee70299f95be56ace41fd0e46
107080 F20101219_AACDIA mehrotra_s_Page_013.jp2
99f4d4bb127950caba613c1ff9c285fd
0b9fecc27f1345348183dd72f302e6a07227b67f
F20101219_AACDHN mehrotra_s_Page_125.jpg
283a2aeba8f60813a2be0fbbc6238c9d
3736054fea28cf761159b5141b4c780faa6c4ffc
101589 F20101219_AACDGY mehrotra_s_Page_108.jpg
e3315aa69f192a5db9a692a9f5793972
4c704d10dba9e743054f1ac3312888ca5f23cd41
107647 F20101219_AACDIB mehrotra_s_Page_014.jp2
23e45c4cd44ac8bc89a6b547f53b3798
7ddb92a8395d9f8884d4d909e871d166c5ffe55a
25576 F20101219_AACDHO mehrotra_s_Page_001.jp2
f88bf02d9c9c1e1423d654d5ea45cdd8
4901a2579b2a4eb16945048c66183960035e5371
100261 F20101219_AACDGZ mehrotra_s_Page_109.jpg
4a68d3762475a271be7e58b9e743d32e
6b5713376b6fb55a17fbf6b18dcb0ad874e02fcc
106457 F20101219_AACDIC mehrotra_s_Page_015.jp2
d94954b4fc3863e75b4051bcdc6d6565
86d26cedbf5cbd208437ac00af59c9df92e298bc
5867 F20101219_AACDHP mehrotra_s_Page_002.jp2
f0a1b6de2439ba719a96613db643e36d
39c7ae99fe4949e6899b81e0f995444b515091d6
109318 F20101219_AACDID mehrotra_s_Page_016.jp2
64d153ce7396f1c6b31b4b611e8c888a
d8023077114f2b012986d09ad75b09b000521b71
28886 F20101219_AACDHQ mehrotra_s_Page_003.jp2
ac87e84a75009e1053607ea5cae6a459
33fa611ee037d8ab95e54ab93ca34b55e01221f7
62521 F20101219_AACDIE mehrotra_s_Page_017.jp2
f4ce3605a9d3f840d9461392ce2edc11
39ae7663556dbb93231ac941b225cce99dea5e28
1051963 F20101219_AACDHR mehrotra_s_Page_004.jp2
bbd44d679032f0436446e80e3dd6cc97
45eaa6d161051ec52da8921f9a9fb78c8d84a9f7
98460 F20101219_AACDIF mehrotra_s_Page_019.jp2
fee54f6a9bb98bc46b2f937403a45c36
d198e334c6ded695060c1e2fe38eb6707165c15e
1051980 F20101219_AACDHS mehrotra_s_Page_005.jp2
bab3ee62c87b3e9c26abb5f17f6e2374
a1e8d24692f3701cd87e974a064647ee7b15aee1
104658 F20101219_AACDIG mehrotra_s_Page_020.jp2
b2c21ef788470911580449a05fd67fdf
cc12562752d798433efd622a664bd2db5b6fd838
105581 F20101219_AACDIH mehrotra_s_Page_021.jp2
f63e0e1b78fe59b282f2fbb4d7a6ed13
ab95cbfc8e0278a5450598cb2ed1ba3e44114757
103423 F20101219_AACDII mehrotra_s_Page_022.jp2
b846de667132d83df8c946987276215e
872093548bf014bd96c0d59f8e3ba1ae6d4a092c
1051959 F20101219_AACDHT mehrotra_s_Page_006.jp2
dc350d3ed7b44610cc1563a163f71c32
e5e48392b38c4c9e0872bd9bdc0e4a4ffecf1243
108856 F20101219_AACDIJ mehrotra_s_Page_023.jp2
8f2564ac43b029b29175f6eafff2e800
d43b52ec64ba7897e393152a32ce4f4620128f87
1051975 F20101219_AACDHU mehrotra_s_Page_007.jp2
18f9ab955f4a795629a5311522911dd9
8e37acb6d008c7547401848028ff499c9957340b
100743 F20101219_AACDIK mehrotra_s_Page_024.jp2
959455acc1cb19c7e14aa81f52ec7536
f7bf432da86823f233fef604d0457f0f9a660838
85616 F20101219_AACDHV mehrotra_s_Page_008.jp2
6980ae0badff6a2f41a00d2cecac45ff
148ee30be38ece89b5af47d5c4f6823ad0919093
109698 F20101219_AACDIL mehrotra_s_Page_025.jp2
bb2d75f315f079cc723b96ae22e08786
81a9f729f73827e273cd5ceaccb4aca7b9357b8c
69374 F20101219_AACDHW mehrotra_s_Page_009.jp2
57b8e36bc235e63fdec02ba9882a085e
a5fe9ed365a99f814f6b67f1678efed42b9bcaab
79258 F20101219_AACDJA mehrotra_s_Page_042.jp2
d8aab1c17b14eed496962c1b734916ec
5d9975c2d4388e6695077a88622d83b1bf7cc1c4
108901 F20101219_AACDIM mehrotra_s_Page_026.jp2
8b0425fb848c860b9d3b203f7bca5972
4f3d1ffb31edb9156167a5d67d225f51b8907cd1
71304 F20101219_AACDHX mehrotra_s_Page_010.jp2
ce49eeb15bec22b61abc20f97cf8a67b
cd1a8f8f1e050a74a496e64b2913fd73d6ebd81c
100798 F20101219_AACDJB mehrotra_s_Page_043.jp2
0e0a54f48a4698e6493fd94113f27f21
9ed19af4150b274354980487ee007fbe36791453
101923 F20101219_AACDIN mehrotra_s_Page_028.jp2
59907a095eefc92d036691e528c7bb00
4e8c668f67b6b41578b5a7f272591be494f3c739
106860 F20101219_AACDHY mehrotra_s_Page_011.jp2
43a40ede237dccafdbcb0d98246b64b0
6879e49876777ea96397bdbb01822141a94b7f70
74367 F20101219_AACDJC mehrotra_s_Page_044.jp2
d2d75231769c3b2f26195c95f0bfdf31
a661d0148a6d6aa92051f8b4b09ca34da47f25a6
107161 F20101219_AACDIO mehrotra_s_Page_029.jp2
e7e22bac75814ecd517fdce2cc15edc1
b3ec60474643f5edf75f8755fee13c22b26e6271
109671 F20101219_AACDHZ mehrotra_s_Page_012.jp2
407e38dde1adb60e66e149b48cd58e4a
c0f3c57ab33256bc674f10fe63e98a6610d52ed0
81565 F20101219_AACDJD mehrotra_s_Page_045.jp2
eedcea9d129bdc40940b64296bb53c3d
852bcb26321b769d8f97074da43ef1c65956163b
108995 F20101219_AACDIP mehrotra_s_Page_031.jp2
c4188787382bea3e6c022b018c36a391
cfd24f1ed5425a7c06b1fb4db10327ae0ccf461c
87044 F20101219_AACDJE mehrotra_s_Page_046.jp2
0d9768243a77dba517c3e236fc0d6472
a5578ffaba3f703b6ca8470b11b5379572c15f29
108566 F20101219_AACDIQ mehrotra_s_Page_032.jp2
06f12e8c5a649f64c390c3baa47f9446
3ed6a78490fd92a62515541ceff81f81885ba92f
93592 F20101219_AACDJF mehrotra_s_Page_047.jp2
282d7be6156e272dde1c4a3a9b8f4f55
e92d1ffc5eeb7ff33c46631e336c4894e4a994f0
105802 F20101219_AACDIR mehrotra_s_Page_033.jp2
775882779cb05798e8ee17c8d464fe49
a21976be9f621b03c1813c6680dd3c71548e27ad
63827 F20101219_AACDJG mehrotra_s_Page_048.jp2
ca581b04ab9a3378b2b4f0f98004987d
5f62d599ba75fc62d0fcef3d5bd6627001742855
64687 F20101219_AACDIS mehrotra_s_Page_034.jp2
f7896100bd2273abae3c247f6a20ac37
d8285d063ba39bb065fd38843b325563b57486f1
50786 F20101219_AACDJH mehrotra_s_Page_050.jp2
9384510012be24d6ef59de57377a83e1
fa1d984926a67cd6bba3d851bacca7ffe91d141b
93135 F20101219_AACDIT mehrotra_s_Page_035.jp2
739c320fc9ee4096140868a42bf85b26
a295e13e14632737ca0ccfb5d46e91704e5470e2
71766 F20101219_AACDJI mehrotra_s_Page_051.jp2
2abb80a74b48eb4f2002076c13321677
126e44bd2de8eebeb59dfd96a90a8a5393c3ce77
82473 F20101219_AACDJJ mehrotra_s_Page_052.jp2
263aa96b4d0c1f0aff8f645174ff6d10
74e71319fb53e790587e9cbdcdef8a26ecb62414
72685 F20101219_AACDIU mehrotra_s_Page_036.jp2
87b8dce28eadacd6749a048d21c634c9
844d1730d7662218e5e1eb8d4e4a6199340f41ae
76551 F20101219_AACDJK mehrotra_s_Page_053.jp2
198698b718d459092de3ca3cdb97cad6
edf373b81c90331b446b7b40034f54f82c994383
90604 F20101219_AACDIV mehrotra_s_Page_037.jp2
76e9f8f1907619202ec5448566883ff4
409e6bd9803f01d9ffcf5c138c6c121dbf19a194
96133 F20101219_AACDJL mehrotra_s_Page_054.jp2
2c34f11ff0aee6c0b4c519baa932ce82
9fd19829d2b6d1b34c865509e82318d261fc206a
91292 F20101219_AACDIW mehrotra_s_Page_038.jp2
db42690a911a11780c143fb79d2d3afa
3632f4c184a81439f1a82bc3ddd726b3d0e45962
96837 F20101219_AACDJM mehrotra_s_Page_055.jp2
c8cfbd345b6b6cba1264eaa3278799cd
613cc4e80b96342259ee9bad4e9e9e827a301bda
90724 F20101219_AACDIX mehrotra_s_Page_039.jp2
3dd520e597d61a13dc2babd134bb1819
68bf53b07d2313f12b18647ed16876f9e76ca0d7
97672 F20101219_AACDKA mehrotra_s_Page_069.jp2
42e176302c391c9da89585a2c00b28f2
3a6c7805477f9dc2a5101bd6ff30a585e71305ba
75401 F20101219_AACDJN mehrotra_s_Page_056.jp2
255761e93ecd3cd7741da7964ebc0773
406386e439b16e204be7eaa72863a479bd664a95
84731 F20101219_AACDIY mehrotra_s_Page_040.jp2
0ec1236ee1d0c33f63143d838812db7a
94df4e77b30ac263b48c42bdbfa192301994c69a
99439 F20101219_AACDKB mehrotra_s_Page_070.jp2
adb18ccc6ba84ca8f4b43d0ce3a88c37
2810b86517b5d36e4947dc0cbdc97a013115b64f
112356 F20101219_AACDJO mehrotra_s_Page_057.jp2
c66b7f840864ca5ef389d5423aa94c34
0c1998b86041c247a20ac4084bbb1242d24ea28b
95900 F20101219_AACDIZ mehrotra_s_Page_041.jp2
a77c5d66cbe02b276664bae08ef68957
8183313a8323ddb90faad5cbc30fdc4cc72d6f9e
105122 F20101219_AACDKC mehrotra_s_Page_071.jp2
efb71928cba6f0415c399ff4f4d55974
53716cbe22810c950b40c57dcf83c6f818055c47
105413 F20101219_AACDJP mehrotra_s_Page_058.jp2
66c6f0e9e8299d9d1d49022123bce2fd
cab95d82b5e262174238afadb0edac105d98733f
94731 F20101219_AACDKD mehrotra_s_Page_072.jp2
8acdada4e8b43a5197e1807226d02f1b
c4ce8f310d54b667337eca0cf8a963ff21b91282
111512 F20101219_AACDJQ mehrotra_s_Page_059.jp2
0e0fde037024fd7ca4ccc42ad375d36f
2e2653ce8f915b92d70cde61495bbfc181b4e404
71875 F20101219_AACDKE mehrotra_s_Page_073.jp2
9abdd3899718e66f224b0fe849cc89b0
3ffb53a34486e24eafd761b3bcff33724a868442
102766 F20101219_AACDJR mehrotra_s_Page_060.jp2
7fb7bbf5ed203f6dd5f71d118b7f067d
fbc5f20f4411351b1e082fef1b2b2cd6bc38064f
58521 F20101219_AACDKF mehrotra_s_Page_074.jp2
8d55d6ce074e4b05d3c32d15aed858b7
0ede41a1b011f223e31f4a0e7413ec93657800df
99807 F20101219_AACDJS mehrotra_s_Page_061.jp2
4b4bf2c6887521d68f01bdb58d924d13
7e0bf6834706fb484bec3049d26ac9dc15a9b58e
105568 F20101219_AACDKG mehrotra_s_Page_075.jp2
64950973c2c19ec81562edead43e8d13
839b22d731f5aec98cf6ad3ff97f687eaacf4092
103027 F20101219_AACDJT mehrotra_s_Page_062.jp2
c2a3e1fbf382075387ee335847093cec
524ae5f64be95b4c60a01d75155f4f0bf73d9108
95240 F20101219_AACDKH mehrotra_s_Page_076.jp2
71e3d18f026ac2ae81d7851f13047cb9
cc2b62e66a3ca426b536ea2a686e53eba5f41d8e
82710 F20101219_AACDJU mehrotra_s_Page_063.jp2
75f4841da163f5727d3ca8758ff09c3f
5dc3478e5cac6be96e047481356fbbf98a4f3d8d
81356 F20101219_AACDKI mehrotra_s_Page_077.jp2
106d6c21c7bfd4678c1f896621994082
3ff13c9abfeac339181adc28f04107cf46831e0b
61641 F20101219_AACDKJ mehrotra_s_Page_078.jp2
1037bde8d45f6bf0983b00adfa9332ae
23c761db4fcc52d5374ace03b98194493d76caf4
97679 F20101219_AACDJV mehrotra_s_Page_064.jp2
cfa21f1b508f7274abbab465467c2de9
75967112a63d0ae16876d99e1c62b3ac43e9a75c
81378 F20101219_AACDKK mehrotra_s_Page_079.jp2
5cac86e64f94446d984c9e2d3c08b0a0
2db8582720e0b37da268dbdd2c90137a170ec5d0
108828 F20101219_AACDJW mehrotra_s_Page_065.jp2
e9e0fc46a4a13fa7311f60522626bff6
fbe1fd0b2a4cf56341554afb508f55fc828a5591
65768 F20101219_AACDKL mehrotra_s_Page_080.jp2
7e27bc7e9985b2d7e66d666f6eff3796
2dfcf412a2e31a18328d7f8f400d76dda15982d8
109445 F20101219_AACDJX mehrotra_s_Page_066.jp2
af2b3932c5d3f6d0e19415fe19d94bc1
b00331f0770e5159f759d4693c5894a4d7a19007
64818 F20101219_AACDLA mehrotra_s_Page_097.jp2
e7ad71d92e84495e315228d1869a803d
a9c82c316f9c0f5bd9bf582cc5a02062b62eaa7f
93852 F20101219_AACDKM mehrotra_s_Page_082.jp2
ca00f8ae72efaff40a261e52d76119c4
390f8a87e10ca5444af84a560bc39ccc90c8ca21
118869 F20101219_AACDJY mehrotra_s_Page_067.jp2
849377101404a8329554f622eacc419a
7d634fe99be4bea50428472c91a64d496a7fa93d
99728 F20101219_AACDLB mehrotra_s_Page_099.jp2
51a14d730bc6f149005d293b7a13f3d1
00d543e6cdd8086bf0030b8d506e8e643c472c3f
94705 F20101219_AACDKN mehrotra_s_Page_083.jp2
3d386021bdd92f47781eb095f9f5fa7e
e5d0305e0d1dbf0c7681c311f6b463d45b0bb441
98092 F20101219_AACDJZ mehrotra_s_Page_068.jp2
398997f867ebbae1b0dbcebc1b1bee73
07252da8f736197a75c9b965b5423faf13c363bd
99240 F20101219_AACDLC mehrotra_s_Page_100.jp2
5a926fef4da88fcc9ce707f4e5c1de27
bbed114b8dbb8cac3cd4784b0b944451c100ebf4
67003 F20101219_AACDKO mehrotra_s_Page_084.jp2
e7de60f1d14a03b4ef1af7e522d2396b
a2cd07d6b3926eb0e056b024873cd4607822b382
67098 F20101219_AACDLD mehrotra_s_Page_101.jp2
7dedb18fe796777c30ca4714a2c85f79
13ae89fe5b96a7e415577de6733b6bce616cb26b
98725 F20101219_AACDKP mehrotra_s_Page_085.jp2
89c4acaf1dd205941570648a0df92bd1
e273aa22d024bd4d95831950d9161d3142028c06
72959 F20101219_AACDLE mehrotra_s_Page_102.jp2
2897ccb0df243bc6c7ac6f215de454c2
6d1b20a6bcf6c1d06540a75d375a0a9199290334
57280 F20101219_AACDKQ mehrotra_s_Page_086.jp2
98805547b496ba3fed7abdd21518d509
a4aac0531c3b57df782e164bf7f3119567b6f17d
90480 F20101219_AACDLF mehrotra_s_Page_103.jp2
82496e97cf321fb2309beb0be58dcfaa
d59aeb4a083e8deb49c25cac392b161c763e1786
84606 F20101219_AACDKR mehrotra_s_Page_087.jp2
55a62c9fcbd426ecaa85dcf9994b0205
159ebe5970081feea11352c52fb392242cccef48
78443 F20101219_AACDLG mehrotra_s_Page_104.jp2
57079870906ff5d14aa7efa375895a83
8e5513485e135f718525684b147fd9135e90ff88
133584 F20101219_AACDKS mehrotra_s_Page_088.jp2
f6d4a95b5c1b296903b94df7df722401
3e526dd90fa1f35ec072bd936496db9d3ca05c61
111476 F20101219_AACDLH mehrotra_s_Page_105.jp2
ee551a1fa49a6b4a8fa1957d7c250a4e
a847fb90c3e690b352e573545c629c18292e7ed1
131005 F20101219_AACDKT mehrotra_s_Page_089.jp2
2c7dd52e1cf5ea223459d6404fe130c0
12f046ee4af20127e1d17c721d79f7c108525bf6
76201 F20101219_AACDLI mehrotra_s_Page_106.jp2
29a53c20113e44289ffbf3f267dc30cd
385d390058befb588a2873b228b7cc9feb94dc8f
53527 F20101219_AACDKU mehrotra_s_Page_090.jp2
5990ade272fdd20a574e43cecacbc430
855fa42efcb508d1c114b0505ab3453b3470ba76
109462 F20101219_AACDLJ mehrotra_s_Page_107.jp2
d41a8876a3cc684eb4c05b1b1f3f818a
2721de85bdd926a7333baeddeb44186e7fdf686e
88604 F20101219_AACDKV mehrotra_s_Page_091.jp2
c74463c0345516caa09d0f54af1e6d83
944057f9a86a23df183222164b9e3e7bb1fa66b3
108998 F20101219_AACDLK mehrotra_s_Page_108.jp2
d0938cde4bf026577505e532436a1799
c61b6bb3c7f2836a0759996feaec46769709bdcd
107942 F20101219_AACDLL mehrotra_s_Page_109.jp2
15bc077287857366302717037e190529
fabdef2600fc71fc5631f3e965f5f6f3bd3f24e2
77556 F20101219_AACDKW mehrotra_s_Page_092.jp2
3c34e30568c01d3f820f69cd50472faf
853e017fc06ea7b0ed947492d9fb31d40c614e54
F20101219_AACDMA mehrotra_s_Page_002.tif
f434c4efa7670fb94b5cca60892ceeef
03cf13226f4e005a683a74d949a2759189111b42
109013 F20101219_AACDLM mehrotra_s_Page_110.jp2
fb5a140f3d288234763d80dd5909cf32
cb85df4f036a3830b9f1be18e465a6899e759d11
106679 F20101219_AACDKX mehrotra_s_Page_093.jp2
7119ed46c40a163fc83df71fe6ad1e8c
a093d315d717e50b9c53c2783ca67987abe84e3c
F20101219_AACDMB mehrotra_s_Page_003.tif
b009bb23975348321a3788b82878564b
56a333952e3d2adb9e736daf3a3fad8849b964a8
103081 F20101219_AACDLN mehrotra_s_Page_111.jp2
5da99040a05dede41b8a570abb9c0bc3
c810835249acaa3fcac177824ac29b10579494fb
69035 F20101219_AACDKY mehrotra_s_Page_094.jp2
4c5b194367786e66465d77d724a460a7
0200174a61708c473c8756f0575343c5fe34944d
F20101219_AACDMC mehrotra_s_Page_004.tif
a9feda9152f5cd6c994e69f3c82385d0
c90e6d05400b2a04845729c8ec8e06bdea21e374
108565 F20101219_AACDLO mehrotra_s_Page_112.jp2
434c2a35c49f02fa8d63f186b9a12a26
e285b4dfff9bb776b1fe5c48d38db49a50533c0e
75217 F20101219_AACDKZ mehrotra_s_Page_096.jp2
4ffcfb78cc70b530d522a417bfa26632
6c58d4d26685052747f32489dbfb1b2ef4e04cfa
F20101219_AACDMD mehrotra_s_Page_006.tif
63d8b41f68495d7b2ec680826443e864
58fe61e32857f474f1afd7567c6bea71568a2692
94424 F20101219_AACDLP mehrotra_s_Page_113.jp2
256e4f2b6fc791e63616774bfdfc5e99
fda956b6652353b3cb578a092ca1234df8a2c70f
F20101219_AACDME mehrotra_s_Page_007.tif
2dae08255cb2d4c26a96903c63f20ace
f70e05b79a11719de8fea964d8dce934cfca5f1b
55173 F20101219_AACDLQ mehrotra_s_Page_114.jp2
b99753ba6c22739e9f039691ab35e499
2fcce022609eff54dbef371f253e198c53d9c178
F20101219_AACDMF mehrotra_s_Page_008.tif
0048d68b6f856daee947b57f1a66b242
52b1d93114b9e2f0f77fec3f15719282cb54260a
51846 F20101219_AACDLR mehrotra_s_Page_115.jp2
4b85fdc08ada1c90c998aed7733885b0
cd69808ee4cadb9c4c2c803521e31fb9b4a10713
F20101219_AACDMG mehrotra_s_Page_010.tif
2b2135434754a1d4b3fd726256095c5f
a3532f32c6728b3dd6d70a50dd53154438ab0fc9
1051972 F20101219_AACDLS mehrotra_s_Page_116.jp2
c421eb023a6c5ee186d422785b7cf28e
98a09821fc1717a52321bd16a24ea0667c2f1561
F20101219_AACDMH mehrotra_s_Page_011.tif
15d7b34d89e6a8511e5b6c356de35a31
bdc4105b98c4146e7435e1e199416c0de6ff1bd4
F20101219_AACDLT mehrotra_s_Page_117.jp2
521e7370a74582cc16e38a89238744e8
88a81ccbe6e34bfae923cd3ae7a7439b32b2dfce
F20101219_AACDMI mehrotra_s_Page_012.tif
3349ed18e3c484781dd588925cd47a64
9dd4ab6a407be1c9a82b18c82390f8cac0639384
1051939 F20101219_AACDLU mehrotra_s_Page_118.jp2
ed5a711a349c1f171cecfa08fb178f1a
faecf251109e4c2c091dfc10648260677ec67393
F20101219_AACDMJ mehrotra_s_Page_016.tif
de9aab11b4ddb89ebd5ce168cd7e3652
d52fff4892ba6be33598504557d009307b44bd2d
F20101219_AACDLV mehrotra_s_Page_120.jp2
0c3534313ea1ca3db825403897c9d45e
c5a4b958c7f9706d8e3c7e50f561716e600258de
F20101219_AACDMK mehrotra_s_Page_017.tif
dd1ee699b09e17e3c85a99ea697a2464
b294d3b8b66e7b1a654b5e96cdc7b18b7ce00ce4
128470 F20101219_AACDLW mehrotra_s_Page_121.jp2
4efcaa185a09b3177c734b4e3e8ead86
8e184e601f411671790f304c3d1441d547f8e8bf
F20101219_AACDML mehrotra_s_Page_018.tif
a0b9a499aafac2a8bd2c0aee5f21d1c9
2c47943f0648f1bad7cd917db32fbb6bc9c45c8e
F20101219_AACDMM mehrotra_s_Page_019.tif
da7009f09729827f768116f77175099e
2be50ba5d576bc0c1b086cafcb9471301f3c86d9
120449 F20101219_AACDLX mehrotra_s_Page_122.jp2
8cc11feb677024a3c1142458694a9048
4447784a7eabff11cda1616ae8e8ef2012626714
F20101219_AACDNA mehrotra_s_Page_034.tif
7f2b3134dfc5569b7a06cd9ca530912e
73573e33aab5be44622089b2a8dd94d0897396bd
F20101219_AACDMN mehrotra_s_Page_020.tif
0ecaf08cb0fe414af6f5dfbfd6e103a0
d8357c07164ccdf1e822e881ec773efc7701a127
47773 F20101219_AACDLY mehrotra_s_Page_124.jp2
7e3cb114754cac8c428e05298aa1ac9f
e6e36ecb58ea1c3f2b65962272d8803e5e508f9f
F20101219_AACDNB mehrotra_s_Page_035.tif
c71b6103264020024aefbaca72d6e1fe
7c71ebf3c52359a909c41c38b8d3f189e0039bdf
F20101219_AACDMO mehrotra_s_Page_021.tif
f95557ca26c202b1d967e48236696566
c38a1f15fee20270317d02bb0280ab8e1a819605
3377 F20101219_AACDLZ mehrotra_s_Page_125.jp2
a1f92426e1c5ffe7db9f3ab8bc3899b8
a62fa426f530237a4912649eb2ad17a60ce87c53
F20101219_AACDNC mehrotra_s_Page_036.tif
01f23f91e1f5a95eb45588623516a735
f6ae9945fcf67a9865feec257479149524eeb497
F20101219_AACDMP mehrotra_s_Page_022.tif
cfee381821300e7693242a3f2c8ecbcc
0357e553b55d1903864994446c628432f2302d62
F20101219_AACDND mehrotra_s_Page_037.tif
15fd1e960d28290dcb0cfed688242313
1d470a2dddb4fa3a1c3af2bf53dd61cc56a1cdc2
F20101219_AACDNE mehrotra_s_Page_038.tif
2a0323698d80f7ab53de28ee5692a2d8
5ce616c2ff5a26e822d57ebc47d17217ef550741
F20101219_AACDMQ mehrotra_s_Page_023.tif
ae0b7b514438c5b7f9b986db34982b45
2419c8425d30c6083352559fbd2d2ed96264cf71
F20101219_AACDNF mehrotra_s_Page_039.tif
b7f062d01e97155b666c00c255b02247
dffe159e0cda66677869a2049ca508f3b1d47a86
F20101219_AACDMR mehrotra_s_Page_024.tif
51d5ff591bd260013969769d0c657d22
73b9b3d7515841840ead23d2f9e7700985288707
F20101219_AACDNG mehrotra_s_Page_040.tif
04fbec3488d96899baf135b4b5cda7da
846f2f52217e1cf4ce85c8a37560e2aa28b295e8
F20101219_AACDMS mehrotra_s_Page_026.tif
49cb55b76628754f1bc0bac723d85332
7cfe7a39fc4f0f7a3890b7a8ea0f0c6dad60bfdd
F20101219_AACDNH mehrotra_s_Page_041.tif
17b4f275fd203021f40508aaa03bb92c
8e3cd89f62ab138fca65bb60db19eb3dad2cc308
F20101219_AACDMT mehrotra_s_Page_027.tif
a10fb6617794941f6fae077a0a3af551
b3571dc230bd9cccdc3ba895d5d580c693a216ea
F20101219_AACDNI mehrotra_s_Page_042.tif
a8cd7d806b0595d423a5603b73f4ef90
b211a27793d73bc711b31b7bf7439f034fe12645
F20101219_AACDMU mehrotra_s_Page_028.tif
b4d847017fb6d7c5e7acb7cd309b8998
9955d877ffad98a1a58d6f456660d531d0fd9bcc
F20101219_AACDNJ mehrotra_s_Page_043.tif
8a482b7d61d469db9bd710c10b33e4ea
ef80678d4a4d07046394b7fc2e3ecb99e956d4a8
F20101219_AACDMV mehrotra_s_Page_029.tif
f4b55098143b46795c7809c646aac716
03ecaeeb2c5c93c03cf463b6060be21a2fb42a7d
F20101219_AACDNK mehrotra_s_Page_044.tif
7de4860b20a46d1dbff3359aea035c0b
aaf6f06765ce5b03d450a51b3041b7965be17d0d
F20101219_AACDMW mehrotra_s_Page_030.tif
898096bf6e2440f14c28198c2ac7f544
e4781f3ce876f1dd09eb566351829b9d5cb01baa
F20101219_AACDNL mehrotra_s_Page_045.tif
af387e0db8f0ef87fd1b5dec4387f46f
ae44e496f31e4aeac2b10236d747e2af34eaa7c1
F20101219_AACDMX mehrotra_s_Page_031.tif
4ec0c9eb6b2802c7e46710a714a7f26c
cce4de5aebeb13174490b027c20b5e10f9b90584
F20101219_AACDOA mehrotra_s_Page_064.tif
83dae81c02e38a431c8d96053b7d59f1
9ca605556a46c28d2b6a558973fca0b78ac7f64f
F20101219_AACDNM mehrotra_s_Page_047.tif
c6e255572bfb59f2707df192e283f4c1
da568c909fddc805c8a1cfcab4089c9817cfc5d2
F20101219_AACDOB mehrotra_s_Page_065.tif
7846ee07f08d5590a6ff305a8c440c51
78f91fff84a5b4734da79d86dd902bc71e9ad6bc
F20101219_AACDNN mehrotra_s_Page_048.tif
f41f2754f1af9e99ccb13e60717647fb
168fe4a54a8fc1a1c059e063b02b853912478fee
F20101219_AACDMY mehrotra_s_Page_032.tif
e5bba1c105305b4b6fef037491cfece1
ad17f6b1cc82d8292f439caff3433113a98efbed
F20101219_AACDOC mehrotra_s_Page_067.tif
c2026f34b13b44e565e9076b31f01936
02ffed21bd6150b9ee468a8e356c6eed2d597645
F20101219_AACDNO mehrotra_s_Page_049.tif
57e795e2d5324c2d357121aaeb31087f
6f8b60afd9dbadbcb20fb71fdd533497360af433
F20101219_AACDMZ mehrotra_s_Page_033.tif
0c2adc56518f7a61369c598d55cca201
e458c2143d0530929f641d9ee7fe3d4a1d79ffeb
F20101219_AACDOD mehrotra_s_Page_069.tif
3ce6c9676ac1335eab7147606e9f3ce9
50d880f8b578f4aa41ac3db9c9c2b0e20b8ce421
F20101219_AACDNP mehrotra_s_Page_050.tif
8335cb44e9726c8536b21bf7972817b9
e59f703f5e641838967da72111d403add8530bbf
F20101219_AACDOE mehrotra_s_Page_070.tif
1a1fe76622193a09c109c45d4feaa969
0735fe514faa2d8bb68a13f08d016f44c135ceeb
F20101219_AACDNQ mehrotra_s_Page_052.tif
617b291bf53cb1ec9ed2a540a0a3bf49
4f24b85529f6f0381441fb55ea597088359cead0
F20101219_AACDOF mehrotra_s_Page_071.tif
fd72047e4aad34727d59c3d23c7ced12
ae7e9827fd829597a7eeec55b5b6be3a41d4fc2d
F20101219_AACDNR mehrotra_s_Page_053.tif
d5e0b1647fb247a7ad565ffbad29d378
bdeffaf6ef302612bc07878e2c244c891d232f07
F20101219_AACDOG mehrotra_s_Page_072.tif
aa67a172372d8480e03c999435419d7e
05e3fe72ad540365fba52173e7e1ed1b38442563
F20101219_AACDNS mehrotra_s_Page_054.tif
f79a79406af60cb517bae9a0776ab841
580c4471aa552df32f5deddd1ba08adda3458e2e
F20101219_AACDOH mehrotra_s_Page_073.tif
5ca29309278dee1967b9fe948ca5aea0
5cf5141972d3271e7f5b4929779f8b61e5913448
F20101219_AACDNT mehrotra_s_Page_055.tif
4c83eb87c2819b5880cb0b6594a434ab
bbba763866c2f533b39c44916f49064072330f7f
F20101219_AACDOI mehrotra_s_Page_074.tif
c0c8cbbd968054f06662fb4d53b10517
4c6a1bf15abe147854b7003aab905c2d19e1dc2d
F20101219_AACDNU mehrotra_s_Page_056.tif
28eba00047ecba45617d123be11306fc
c18acff7fb8e906ee56cf0037bcf839462eff14b
F20101219_AACDOJ mehrotra_s_Page_076.tif
5476f7713ed2ae3f41d7faba4b770929
021a9484adfa1c83c73ce816a395bee55b1f0246
F20101219_AACDNV mehrotra_s_Page_057.tif
653e496d89b23e48ea5da09ade13c246
d7c8f30eebb69d61871b2fa4fc777e400e9ee310
F20101219_AACDOK mehrotra_s_Page_077.tif
d87e245c69f5dfe4618e1cad19457033
dc1f19591ea14d95963767840ebbeba2c9ac0589
F20101219_AACDNW mehrotra_s_Page_058.tif
cd214681db13d04ee365ad0f90868f03
4b9d5f4e2c4951a30ebcbb16ac1897a4bbae49ce
F20101219_AACDOL mehrotra_s_Page_078.tif
2fda9152d1e968d6329d513b0fb625d1
5aa78f4241643a711d34c36e96f4a0ec7cc55ebe
F20101219_AACDNX mehrotra_s_Page_060.tif
b09c43d6d0a3f6295f6aeff268421457
72c2087f6e824c0dabcba7b8fccbaed0bcd80882
F20101219_AACDOM mehrotra_s_Page_079.tif
238884209e9a8b15f8a3450028978fc3
325bb09d6a88f7a275bd504f809627358be7cf28
F20101219_AACDNY mehrotra_s_Page_062.tif
5677222f85df8220dd76023af44cab84
d7c987df7658ed0bcace686b986c5eade10a258a
F20101219_AACDPA mehrotra_s_Page_095.tif
b8a11737f0da0aeb6db06e9dbbd196ff
a64a420a3a0dbaca773e95a6459126b082d49f38
F20101219_AACDON mehrotra_s_Page_080.tif
1fc021203b60569845bf05ad4727f2ae
7be40c9ddf0258f32591a0cc362087e7f4ab42d3
F20101219_AACDPB mehrotra_s_Page_096.tif
057413b8936a45b8269edf56fcd46268
d786a6f936b8acbd499e6a79bfe39e1eb62c0987
F20101219_AACDOO mehrotra_s_Page_081.tif
533054146941bcb41863c5df0bd2ebf6
82ad1cb66ebe4e9cec51f4af432e1babfbe1a118
F20101219_AACDNZ mehrotra_s_Page_063.tif
5e78f33172a71d81c439d06207320eec
62f2e5e22e7c22ffe45c143e9b03c361df18e1cb
F20101219_AACDPC mehrotra_s_Page_099.tif
ff75269722690e9658aaa0d42e34998c
4df87cdea8aabd1d6ec842746042aa6dfd56e259
F20101219_AACDOP mehrotra_s_Page_082.tif
47fa6bd08bc142323eb50ccd279d190f
c64c34552fcfab86d1c69daa802bb7e9bdfb41c8
F20101219_AACDPD mehrotra_s_Page_100.tif
89a4f7deba370e5fcd8101e20f278ab8
d1557b0cb6d11a44a075c9742a6d9b02618f9eb2
F20101219_AACDOQ mehrotra_s_Page_083.tif
c504f3b04a587915fe9115f01877f375
aa93f0209fb7f0bc5c7cfc8d0ac051b0f803f0f2
F20101219_AACDPE mehrotra_s_Page_101.tif
088449c2cc713d3b0469712308209dbb
cf270b098047e1ce75876ffe8f90eeddc9ea86a8
F20101219_AACDOR mehrotra_s_Page_084.tif
5b250531b4f5b606ac96bab6228e5e30
6561d535ecbe31999b441199fa0442cefe3f3984
F20101219_AACDPF mehrotra_s_Page_102.tif
634e3993cfe2b18326950327ae178017
08b940416e3c1da431398260b074b0863878cd6a
F20101219_AACDOS mehrotra_s_Page_085.tif
24c208611086df1a4c383ec9f349dd9c
80e8f7889261001d2275f842d3de56358e22aad9
F20101219_AACDPG mehrotra_s_Page_103.tif
6a1f5cc83e4a9c5021f913457c30f6a2
9a7e99f8915611da5be01596c0fcb63b66f29c6c
F20101219_AACDOT mehrotra_s_Page_086.tif
740b9e79088b1bee84d15b5319b0ec71
c807c8dbb96b59c0aeb7674b15393b022200e83c
F20101219_AACDPH mehrotra_s_Page_104.tif
b5f8942e813ca98bde8ab33a16aef107
b56f592090671fe1926ee6fc35c7daeee4593949
F20101219_AACDOU mehrotra_s_Page_087.tif
a026f207d5f37ce311b823fbea712b48
ac0648581f206be28ed5604e2f6ba60ca26cb5b9
F20101219_AACDPI mehrotra_s_Page_105.tif
51e8a6eaa9de52567635f996fe7fd47f
6f47ca7f96f5f7c153da629649686462483edbea
F20101219_AACDOV mehrotra_s_Page_088.tif
5b8a72d7ceec16aa41219805afc47d8d
ec77bff14109a71abaf0fb5f1ae8106f69f4e563
F20101219_AACDPJ mehrotra_s_Page_106.tif
8aaa50a4b413f472d7e699676b746222
62de93d3ebe54ac36ba5e28cbda7797f200f498a
F20101219_AACDOW mehrotra_s_Page_089.tif
376a5afec08570de78aa7d2ce906589a
3310fee1fb25278cd55e29e1117f18110769a6e1
F20101219_AACDPK mehrotra_s_Page_107.tif
930f8d0bec0472caea06e976e4579095
7687d0abb9fbd93c15b9124fd609231da68e9b67
F20101219_AACDOX mehrotra_s_Page_090.tif
e13cb36d5b6e05396ce29dee15dd23f9
77758d97e9c969651ac648eb1813c8df7a421b02
F20101219_AACDPL mehrotra_s_Page_108.tif
590e2519b6c8ebd4e1c68fd3ec7f3c56
aafb415a4599fbd7aa5b8c57a415bccb1f98e028
F20101219_AACDOY mehrotra_s_Page_092.tif
897f585b9a5631fa425b4bb8e3ed7cbd
bb3905ab9587b833057ee5461ad52ccde405ca0d
F20101219_AACDQA mehrotra_s_Page_124.tif
b91d6f6b0d165db07d7c4da16fdb173d
dfd492a47b58f86e160fe740fbb1b32ba2d27209
F20101219_AACDPM mehrotra_s_Page_109.tif
863fa454c9fc4def75e2212a5a01edae
878e0dbc6318f63d1d7b99d0f473f096fa1202f8
F20101219_AACDOZ mehrotra_s_Page_094.tif
8da9593ffc5f3c860490d0a2b9e7952d
e95b02de53b1e913faf7ffd9ee9f3d4661ea5030
8663 F20101219_AACDQB mehrotra_s_Page_001.pro
d22d54c07e429181a4f8b50c49180768
f6587989433490e34de082113592c3855a4534fa
F20101219_AACDPN mehrotra_s_Page_110.tif
d39de6424226347899296db2c628e1fa
13b2285062bf7882678219d2fb764f4fa1162ba0
1252 F20101219_AACDQC mehrotra_s_Page_002.pro
eae29258ba2e8464c4102b8c065f2ea6
58b846de6b387003740abf349f4ae4ca21509742
F20101219_AACDPO mehrotra_s_Page_112.tif
4cccd2931b43ac870de2d64996bb3a0b
d49e4d36161bad8e01bef94267f74f0ada1581af
11608 F20101219_AACDQD mehrotra_s_Page_003.pro
fc32d23a39b1976f573fc14950e8c966
a12193993c1c3b2afcc8654c2263029ff9f5dfc7
F20101219_AACDPP mehrotra_s_Page_113.tif
155c0ca876d1a6dd59a6ee4cf8464f9f
de489b5a0034290a7e2425d3f4fdc9bbd7312cbe
58230 F20101219_AACDQE mehrotra_s_Page_004.pro
dad30cc4d9f58c8525df1ae1299f869b
d6dbe4627d6e2b4ab4e51558f3e6084e6f92e3cd
F20101219_AACDPQ mehrotra_s_Page_114.tif
4a8cd0cbb3776d5bedaba7571c726da1
8f74eff7f7a2015e8e7ecba7b8c5f4e879427ffb
68595 F20101219_AACDQF mehrotra_s_Page_005.pro
61bd3db9985271dc8ca7753088bf8b76
6b2772be8e31f6a5af3965b53ba256e2349d0b94
F20101219_AACDPR mehrotra_s_Page_115.tif
f2c41b489407a69a6532674ad1e90fa6
09669c39660b1ccbef72ae457d4e82fa30a9b88a
53886 F20101219_AACDQG mehrotra_s_Page_006.pro
940bbed5bad940837b6aa1349e2109bd
2fe068abd965ac1b1a4c3b317f791da30a0c1b0b
F20101219_AACDPS mehrotra_s_Page_116.tif
b8efc5884719830c85e32491948ba903
db46b5546f12ec59b5dc6c1921f0ddff5bf28c7e
45584 F20101219_AACDQH mehrotra_s_Page_007.pro
3c0f33f3a48b0a0e786459671cdafe30
b872228bd836ba0166ccedbf871a78257b259f69
F20101219_AACDPT mehrotra_s_Page_117.tif
f4aa5bc13279ab830deafaaa9ec86d26
0dcbad9c4c05d5b6f0fa5019fca23d83d645fbc1
38140 F20101219_AACDQI mehrotra_s_Page_008.pro
38749aca5aa035e15573f64688e95876
040c6e584e4be593d17af5e273f05611655b8089
F20101219_AACDPU mehrotra_s_Page_118.tif
24c44938577a7c199e62f338e18ce89a
fa2b7ed0b38fc0d1fd5af10ecb51b405ac0594e0
30734 F20101219_AACDQJ mehrotra_s_Page_009.pro
bd7d63201618b8cda780fd108e71d89e
e62c6eb0e7ecc70ef557c6f773673c7e53cc11ba
F20101219_AACDPV mehrotra_s_Page_119.tif
4c94e9de4d39310597b559826430410a
2d9b43eb582d4429ce16cf47e07c834eac81ba6b
20609 F20101219_AACDQK mehrotra_s_Page_010.pro
3b1faad359bd6586f2f48e3521c0bd6d
b8777a14053b06aab939e26fda50c5f8380aeddf
F20101219_AACDPW mehrotra_s_Page_120.tif
93397067d7400316de0f61d41e9f02a6
0c9d90ec07220bc9dc3172812156ced994c0b52c
48700 F20101219_AACDQL mehrotra_s_Page_011.pro
a5e379f2ffda7b28fb6796321c6c710c
b5baa42f9ce7e5d41462d965d708be26fbc7597b
F20101219_AACDPX mehrotra_s_Page_121.tif
750a8a4e63bf68d8c6ed3cb17bbc6ac7
9c8202a50ada61323ae8a90f6093fe38d4ca9c93
49900 F20101219_AACDRA mehrotra_s_Page_029.pro
43e7228975ebf59a15980bc228cbfec4
d0106cdd6e7ac662b1d7c0c1dee043b04c2214f9
50687 F20101219_AACDQM mehrotra_s_Page_012.pro
5f541f75b05ec441f15f02a7c64c35a5
058e37f35d5f07af101a9a80d1a670320e8a1de6
F20101219_AACDPY mehrotra_s_Page_122.tif
aa0f590daba5f224342fbed4c4544cac
b0a1e7be1b3d8c57ce2211c2023f12d20f1f5ea9
47795 F20101219_AACDRB mehrotra_s_Page_030.pro
7ed4714b6736a4d72436a9a1cc83dff4
f55897ea59c434d84a28455c4d76fd983815e414
50310 F20101219_AACDQN mehrotra_s_Page_013.pro
eef469b4a1240559bcf2ec96abb40045
21bc5c372a13aff6903b991716f72ec93c73985e
F20101219_AACDPZ mehrotra_s_Page_123.tif
fe23b2ae65e9ed146b388b2c721be160
3587cd09f1eb928119b5de8acb0427bac05b2814
49974 F20101219_AACDRC mehrotra_s_Page_031.pro
adc07b5f276acca10e7d5d175c0d00d0
cd7769ea8d7a287541b6df8f29af0a9c1417875f
50404 F20101219_AACDQO mehrotra_s_Page_014.pro
d618ab3886728db16e5dab0e50d432da
0842397349176570162b7d86d7ac39d7241c72be
49323 F20101219_AACDRD mehrotra_s_Page_033.pro
cd74027cb15e9e7a0e00983a81c66338
7893f467fc40b09ed2f67d2b33b10b4d3f51c37a
53505 F20101219_AACDQP mehrotra_s_Page_015.pro
88020cb35bf150a1cb5c943707c01dc9
d120ce04fef7aa16ed778f354b043b1f078dec74
28491 F20101219_AACDRE mehrotra_s_Page_034.pro
d73219a7b9e0ba9a1705da9a7006fae0
9c9b174341910f829fcd58f97f31bf5d076c1572
50729 F20101219_AACDQQ mehrotra_s_Page_016.pro
13d51c962f7145eeb82e16a75a1855ac
bf964250aca10089d66c7cfa971752e10cf08223
43986 F20101219_AACDRF mehrotra_s_Page_035.pro
6746b562562006b57ddef68b00478b28
fde9b598109c672f9aeb6665b3194511d6280cf7
40545 F20101219_AACDQR mehrotra_s_Page_018.pro
37a354afb52a6648050e0127063b0579
3e6f0508aa8512f991dfeabcdcb7162f89bc9bcf
42373 F20101219_AACDRG mehrotra_s_Page_037.pro
27f94248faa6b3db928500321855dfc2
ce0a05697a70fb0fde7dfe06fc6eeb25f9890045
44845 F20101219_AACDQS mehrotra_s_Page_019.pro
b121ef1dd21737a363c94ae707e8d5a7
9d4edcc3d09e0d46d614287969f4f0d0b3c8f0a8
42839 F20101219_AACDRH mehrotra_s_Page_038.pro
18f76e32f8e46ec05378adaa13f07dbb
2548c0978f0420da04f355c7f0627ab05f7df757
48174 F20101219_AACDQT mehrotra_s_Page_020.pro
96b829c9c97ccb4dfe4181666fedd107
2075e6d09a19f7d8d47e4fc06204a109c90dac43
42923 F20101219_AACDRI mehrotra_s_Page_039.pro
82f257c46161f7cca9f6931ea124d86a
29c94fa928ec92b60e6e3dc91f001c9ee1bec8bc
48197 F20101219_AACDQU mehrotra_s_Page_021.pro
b2201b23016b59f710b3398ebbe03bdd
9e0ad2bfda81a60b0c18525bb97f0408a8f287f8
39096 F20101219_AACDRJ mehrotra_s_Page_040.pro
42f9ddc8d4f0b426846a100acf978c9b
248e2a87d601e833f5d8d9ff7e846157a85fa43d
48305 F20101219_AACDQV mehrotra_s_Page_022.pro
f5830e6dbef6d6a7854cf884b52690c3
51ba2e074b833f2d2680343322e32d5bcc5c12c6
45235 F20101219_AACDRK mehrotra_s_Page_041.pro
e7f3f8ed90cb5a6785c1fe17bd519ad3
cd4a030249b7d338efca63b3183e04fe39c1abca
47701 F20101219_AACDQW mehrotra_s_Page_024.pro
0bf40a8ba55184dba951af50ac52c011
1fe17936284ce6b372526e28f359372506c58587
38047 F20101219_AACDRL mehrotra_s_Page_042.pro
2b08d422b56d544bd31d9613d94e79d8
3f15b978d5a2a9ddfe4948a14db2735b035f18c3
51734 F20101219_AACDQX mehrotra_s_Page_025.pro
f940f2494d39dc029d8fc8a500fc5202
2d3b9a7cd0e0ddca6e28b72974cba3e562e2361a
48623 F20101219_AACDRM mehrotra_s_Page_043.pro
c39a4af2ea59f169029f6ae8b967c59b
03af190a83eb7ccfe645811cfda34e8df9775130
51118 F20101219_AACDQY mehrotra_s_Page_026.pro
6f6ccd8490c8036873f5e6f9586d478f
5770869a9b3c01146747aa7843efe3d9e74eef6b
47316 F20101219_AACDSA mehrotra_s_Page_061.pro
409fcfe887170a3cb7747da25c1ed644
93a1d9651f4303f4493e1be4a6256a6ea3729b34
48013 F20101219_AACDQZ mehrotra_s_Page_028.pro
31ea40a7fb738e00786bfc9d02554443
bc2eb0c749fd4eb9c93db86538c2c661029bda0f
48588 F20101219_AACDSB mehrotra_s_Page_062.pro
4b793999ee8ef7f375b2deb714a21018
e81322eff138616bd4d9469ce55115ad5ead5d87
34969 F20101219_AACDRN mehrotra_s_Page_044.pro
e0ba4c11d2f60908aa40abe667472826
1347e475ec33ee329fd053e4f0707a9d3dcbc838
38209 F20101219_AACDSC mehrotra_s_Page_063.pro
fd7ebabd7f4b52928766e5dcdf43f1e8
5d137436ddd29d3cf112c5d4f9ed5adfff9ee2dd
38111 F20101219_AACDRO mehrotra_s_Page_045.pro
b0c27e4f2de97bc2b9050afa0d4856f4
02856482325be7fd95423a983a722116013e132b
45245 F20101219_AACDSD mehrotra_s_Page_064.pro
6c337ae05e42c2985b23abde8cf8367d
b888d4eaab437c33b0a8e43ce5b72c58c55e7737
40792 F20101219_AACDRP mehrotra_s_Page_046.pro
b27da18103cdd8c6db08034873be22c1
156f98a052bac303ec61ce12ba40591377ec2c2b
52441 F20101219_AACDSE mehrotra_s_Page_065.pro
9dd9ae5d9f23abf93c8764f01e6a0a24
a575276fdacec1699f9078eb5455e9744448fc77
43048 F20101219_AACDRQ mehrotra_s_Page_047.pro
c79fa61d939136e61bb095516555be97
52edd1792b69baa07d18f3636d836f53061bf50a
51895 F20101219_AACDSF mehrotra_s_Page_066.pro
e3096f62b60b9ac83c48c33875323e00
79e6aa1d9106bede1858af88215444997f54c24a
26883 F20101219_AACDRR mehrotra_s_Page_048.pro
e7a05989a7f63c18b034bc162b56847a
94075728b01f2d2ef7f2b490e4a7738b2aaa7de1
47376 F20101219_AACDSG mehrotra_s_Page_068.pro
2a68eedebc819f42f9ef52f02370cf75
9c0f6fc73982b723ca0a92b6e1f6309cd938115a
24017 F20101219_AACDRS mehrotra_s_Page_050.pro
d660525863796c7ca6c0b85561b2f72a
6fdca3612265dc8e6841d63072b2dbfc6c3a791e
44215 F20101219_AACDSH mehrotra_s_Page_069.pro
1299488c2bf57d49d4d45c65e011cd6f
9c77dc141179691109b731a5ee28c77bf7eccce3
33969 F20101219_AACDRT mehrotra_s_Page_051.pro
0d976c2910db80f78b040ccd6d8207b3
1a1c4119d5e5bfca8d0703c1dcea6616b3f34f00
48223 F20101219_AACDSI mehrotra_s_Page_071.pro
c19fc1577553c1f4a55199f020cda78f
d3a55993581a9cbe41dd48cc2bb41feb2342bcc1
44448 F20101219_AACDRU mehrotra_s_Page_054.pro
3e2f585a53dd7866a291e6523a9f4f89
9848c0e1c4d747e9c3911f2bcab7f10848c949ba
43589 F20101219_AACDSJ mehrotra_s_Page_072.pro
3d3e52bdf2c51ad2b5ea809daafb965c
642d128069fff6c1f4d618607a74017a8b25dc61
44433 F20101219_AACDRV mehrotra_s_Page_055.pro
e5cbd14441e868dc81b16e7eb004c763
1e00bc5381da7e3dded15a3aad7c70e5de340b1b
33378 F20101219_AACDSK mehrotra_s_Page_073.pro
ad85ec8c3d7015cac42b0b00540b6550
b6c4e9ff2a4915191c03348a2fd91910982f38f3
34447 F20101219_AACDRW mehrotra_s_Page_056.pro
2925648ce2f29f6c183abda6f9b498e0
7ca3a10c6aa5ebea382ede28e59b49dce29dea7f
26282 F20101219_AACDSL mehrotra_s_Page_074.pro
471c5d4f180e5261c1558a6762627430
21cecf4ba54a4dd1d4726e27ac1896e10e85adda
52230 F20101219_AACDRX mehrotra_s_Page_057.pro
a9d7ff50471309a464b62a91962b5b67
aea3e6689e8997d49a81148de3fdafbb19ff45e2
48742 F20101219_AACDTA mehrotra_s_Page_093.pro
8a46cb468be1fb05f54a2e161dd2723a
ef886e174c301a6cb02a484ad79016147712139b
43989 F20101219_AACDSM mehrotra_s_Page_076.pro
efba5788b0bb72df448cdb4e351223d6
6902579dbdd519dff63e562b681e1c27d43a28e5
49069 F20101219_AACDRY mehrotra_s_Page_058.pro
31edf43a1399d9c640e85a9167adea99
e0693ada0759ef2a6ab0d2606168ab9259be00c6
29685 F20101219_AACDTB mehrotra_s_Page_094.pro
445711f0d763ad1e5e16d446a8d781d6
5192c9d4657ee43a259ea904dba8454d61f13647
31928 F20101219_AACDSN mehrotra_s_Page_077.pro
36dcb3ba650506b4ccbddfdd8ac2b8c8
56a30a718debd752bd38169b30e91b59a3cd471e
53582 F20101219_AACDRZ mehrotra_s_Page_059.pro
3bbaca137a5ff143daa52e9f5f48d09f
a9def1b2228c30909b414a262a45cb97d26f502e
34269 F20101219_AACDTC mehrotra_s_Page_095.pro
641e00223dc8e817689bbdcd53cc48c9
046e38bdb9d25ff338658547b4b72ec40558d495
25321 F20101219_AACDSO mehrotra_s_Page_078.pro
121ba30fb2d937ff85963e815c722398
d00efc03568807901504742fdbdd52596d1e2fe5
32799 F20101219_AACDTD mehrotra_s_Page_096.pro
6f11c9e501e185dc5d9be7a9b63d8bcf
e5200499ef6270f1cd4dea4b727ba4ad4f92a9b4
35760 F20101219_AACDSP mehrotra_s_Page_079.pro
d521ac90d2e1df8b7ce7cf0fbbee1c07
a9988e610b02f87e14045e8855e86571016ceb61
26620 F20101219_AACDTE mehrotra_s_Page_097.pro
dbc6914e12ae79f3ee295073f0f4bc83
0855c0935514eeb6b62ac50cdff14e43721c594e
26961 F20101219_AACDSQ mehrotra_s_Page_080.pro
a918de0696ef84461a1aad301e681ff3
c85635fa87eb64e4acd6e5366427f0b12f51568c
51300 F20101219_AACDTF mehrotra_s_Page_098.pro
8c9df2f70aa0913a7c29106448993742
90de61639b4457de9770160259747931ccce9c35
45127 F20101219_AACDSR mehrotra_s_Page_081.pro
9cff695bced82d570c437a4c0f47fbdd
073ac77db3dfd7c9a8088704ca7cd616bee428c4
45805 F20101219_AACDTG mehrotra_s_Page_099.pro
7c6229abb68740daf94e6575dd7a21b8
012bd0f84dc55490091a450f48aa9547ec626135
42259 F20101219_AACDSS mehrotra_s_Page_082.pro
c09b4adfb0e08db0151e3e19111c1896
838a0e3103f0802edb8532d22d3647e7f8aecdfc
46377 F20101219_AACDTH mehrotra_s_Page_100.pro
b46bb27efe3e0ec105fbc60690df615e
aa85fc5a97a0f4d8046da0aa328db90b326ce9c9
43090 F20101219_AACDST mehrotra_s_Page_083.pro
5571fbebbbfeb71a4a82f722cdd82129
f6e2c9ab0b9a13ff7fd7c577cbdd8d35117b90d1
27629 F20101219_AACDTI mehrotra_s_Page_101.pro
3e80d80f7731fdc4130209d8e90225d9
b8fe3b6fbdcfe38b4c676ebdfa4ad67541ce10f6
21894 F20101219_AACDSU mehrotra_s_Page_084.pro
45516753948a5197f78090e96bf45380
b414ed978c4de0abefccb8483fbff9ba284012ad
25878 F20101219_AACDTJ mehrotra_s_Page_102.pro
4cbee0295b25745faaab097bfd67c44d
575335c0ab0916eb7634000989aaee280d6916ab
45273 F20101219_AACDSV mehrotra_s_Page_085.pro
c5a8c03be12c102cabe6f52cc4507996
61d41fc9d2fb202fc0aa87d78860018fa4bd4210
42460 F20101219_AACDTK mehrotra_s_Page_103.pro
7d7c66bc53da11fb3c359d8bb00466f3
adf9b20c6902bfd9079f09d73251f609a8f2ccd4
25000 F20101219_AACDSW mehrotra_s_Page_086.pro
c443da99ef46ef8d21c660695339d956
8c3ddb02239906cb31df3fe39c26ad8b81134649
32940 F20101219_AACDTL mehrotra_s_Page_104.pro
697b2e32cbbf7cdefce647691bb8aae0
951d58499e8011578cef95090fd5bf15eb1c321e
65541 F20101219_AACDSX mehrotra_s_Page_088.pro
f55b5f9463916ce5071e11fb4922c4b0
9013246984180b3bbaf20d6a7f97b2a11d23cc95
54227 F20101219_AACDTM mehrotra_s_Page_105.pro
08db0dc22c5f1a80eb69bf49f000fa6f
ba1ca0681fb575e45a113910f7b9a6c120f5a3f4
19180 F20101219_AACDSY mehrotra_s_Page_090.pro
a5c12cca2b1fdaa4cd11ccb57103af82
31efcb0827c07b758beb684a55cd78a30035c34c
60927 F20101219_AACDUA mehrotra_s_Page_121.pro
f1d1f931b97bb079d1e3d5ff76c3149c
4f336e5ec26ed76ff0d33c7d2487cbc9899baa58
29411 F20101219_AACDTN mehrotra_s_Page_106.pro
b0b213905266fb68ed09f535acdcdcde
b5bfa575b979d91baa08f800a865432870809b34
35452 F20101219_AACDSZ mehrotra_s_Page_092.pro
923cf3c323fdec04b0608c3fede87093
56525adbae52c2881565c3c94619a49923604e47
55575 F20101219_AACDUB mehrotra_s_Page_122.pro
3be10d5beebbf80fd47dba9fef89b0f7
3a84712329760bad0333e27176f0cb8ea4737cb9
50957 F20101219_AACDTO mehrotra_s_Page_108.pro
0893b94b43e6cc5f6f6b31afb3a875b0
cfbbc0eeeed112ae62cc59043f2858403d2505f6
19848 F20101219_AACDUC mehrotra_s_Page_123.pro
0ebe6595afb72635f641162ee6126b96
ba407124d393b2e26b2a589dad395f93fe91e36d
50012 F20101219_AACDTP mehrotra_s_Page_109.pro
d8054fa1171eeeeef29e042c50e71493
95aabece9096f5c476f0b08738a6a8fc00a16244
20182 F20101219_AACDUD mehrotra_s_Page_124.pro
caa5b750d49822ae7ad0da140c5da38d
36140779f41df7cf6164685df1cfec7a6d20c0b7
50859 F20101219_AACDTQ mehrotra_s_Page_110.pro
5aec6d0d26d683a849063ca62a1f0911
d7bfe4f5337ba5d8fe669f634c3a2a14a615f5fd
468 F20101219_AACDUE mehrotra_s_Page_001.txt
b67079f9a165e21280dce4902fac2926
6508ee64d3e8080dc84934942ec74dd6c5819ac3
48501 F20101219_AACDTR mehrotra_s_Page_111.pro
c288bd7eaba6f0c3bca319ff9dcd7c50
b4a8b3736dde7700fb38bf7f611e8c291a919418
31784 F20101219_AACEAA mehrotra_s_Page_021.QC.jpg
fd111d4423cd6191591901ca58d0af75
d997ad167eedb9bfb685767bee5a7d5a24ef8b46
114 F20101219_AACDUF mehrotra_s_Page_002.txt
e9511090e8439501df31898507ace530
39378dc9f20345168a719dbf78ecf7ebf33a59d0
50511 F20101219_AACDTS mehrotra_s_Page_112.pro
9476d6b9d568e5bb296d3e3bdb2389bd
b3f62206e820d4590c541f86157f484fcaa7f21e
8065 F20101219_AACEAB mehrotra_s_Page_021thm.jpg
615d37474110eea80a96a8ee73224688
d11cdaf192baed8465f5a438d34b79f2256a0220
521 F20101219_AACDUG mehrotra_s_Page_003.txt
de91bf778dafddba347df225e54df167
ca0610f313ed6e9c02e6e2dbeb95855a7d16bb75
21969 F20101219_AACDTT mehrotra_s_Page_114.pro
54662ecfebaf3b3140693dae50445407
c8a4b0620891c96f659ef0d57608f7ea0d699dad
32174 F20101219_AACEAC mehrotra_s_Page_022.QC.jpg
e14d90bb2706181e95e0f36eb927d1c0
f142cce392d203cc0d7fce14b5b18440bdb7b906
2570 F20101219_AACDUH mehrotra_s_Page_004.txt
38a09a3d1235835482397ad44e5eebba
9497a0a0fc05a56319cc2b483e5757ddcf3a0cec
21200 F20101219_AACDTU mehrotra_s_Page_115.pro
1eb8ed34cffc1c682229cda27d4ea549
feb12448f0562a26c0dc476e43481850f0bc24a7
33919 F20101219_AACEAD mehrotra_s_Page_023.QC.jpg
1e061dad6611f5d4e4ea2469cfab2316
39deb424550433ee1cee2269dbd8181634dbb2aa
2909 F20101219_AACDUI mehrotra_s_Page_005.txt
67fc9e0bb0f4bdf92f6cc9409e144d52
82d7be6bc2b54b5497842be5f75b9321f7fb3a80
53626 F20101219_AACDTV mehrotra_s_Page_116.pro
dcf5258a76e67236d42ebace0bd56edd
4e5cce9dddabe758acd50d4867eeada7e39d0f72
F20101219_AACEAE mehrotra_s_Page_023thm.jpg
57b5a06e5720d73efd1e750c6953b465
7e2bc9e93ce3a6b97ef4e973c22401319482619c
2263 F20101219_AACDUJ mehrotra_s_Page_006.txt
b4bc052a80440bdb400f376e9cfdb6d4
31f16d7ee8d0177bddc9475e323178f7bb7865fc
55843 F20101219_AACDTW mehrotra_s_Page_117.pro
b0dda274c0b57651abd3a62e6957c852
d025140e14c69bb2eea3674ecab4911f229ae9ba
30285 F20101219_AACEAF mehrotra_s_Page_024.QC.jpg
a06590b32891f1bbc91816303f0d0be0
b449e189e8a7af169d1f2242e44ab8202cf06057
1681 F20101219_AACDUK mehrotra_s_Page_008.txt
af9224a50316d7ad600c9ad6935aabbf
2ba274f79bd99ef704a1f4e11de76d8a99953caa
61135 F20101219_AACDTX mehrotra_s_Page_118.pro
847c7a7ba43188edd2a68d466cdbfb61
af96260526676a498883717fb9113f9d368981c6
7779 F20101219_AACEAG mehrotra_s_Page_024thm.jpg
28b078024eef53d6275e8c5641856bf1
3baffc2ac1b7990ca3e9aebeaf09d9e124c27e2e
1903 F20101219_AACDVA mehrotra_s_Page_028.txt
c204d5b173724072ab1b3eab1a834bde
283cb49e0acba50fbdef5d5bddb1a0f1454eca24
1236 F20101219_AACDUL mehrotra_s_Page_009.txt
d3b7a93156de50fd998ff4ebc74e99e5
3afc5695e71b0b1149eb5fa43e8fb9e677dd7f44
61215 F20101219_AACDTY mehrotra_s_Page_119.pro
e3ef0dfc645d7b48bc6c78aa059202f1
8a095e56dcde697ce08b0be0e7908bf55d17590b
33195 F20101219_AACEAH mehrotra_s_Page_025.QC.jpg
7216e14c5efb57b5e8db2404ae5beada
8237ab7b9d890b5b6404d5bd77b5818f475b837f
1040 F20101219_AACDUM mehrotra_s_Page_010.txt
3cac02d83fef612e272d07d65fd48e1d
8e0b9a0e0da2e8deae1e032a14195e7ee5e42c67
57705 F20101219_AACDTZ mehrotra_s_Page_120.pro
580944aa368f33ef6c984df8f612e465
b4049d7ce015ec8939565f4dd6bbe67e47171fa3
8353 F20101219_AACEAI mehrotra_s_Page_025thm.jpg
bcbc775fb9ac51418d6b426c2b063330
abfb04b54ef7db5c6ffa58e94c9c1fd40e9fb15f
1976 F20101219_AACDVB mehrotra_s_Page_029.txt
c1fb57a385d31793496c55b3b0d49bb4
601b583445a3d4b52d50a0f199cbc114f8f86093
1962 F20101219_AACDUN mehrotra_s_Page_011.txt
10b820602661a00556dce380f467a9d7
873d8da5107928b1818dee4c2f15d48faf198235
33477 F20101219_AACEAJ mehrotra_s_Page_026.QC.jpg
133864dd2d5ca2bc68977cf001eae968
bf9009ce7e3d629974ce48bf73ba0dddc5535ddb
1888 F20101219_AACDVC mehrotra_s_Page_030.txt
30d00a477978f50511282a22b6918c57
a19709f0e4ff0b4014addb6076c0db02de09068c
2029 F20101219_AACDUO mehrotra_s_Page_012.txt
58d26c4ca5c7fa604d9cc4d06ca4574b
a8339808282ecce050b04ec21967b22d4d66369f
8162 F20101219_AACEAK mehrotra_s_Page_026thm.jpg
74c683de307abc744b5dbb02b1078b8f
346dc34d479fce9c0eb3e0b51a288851b8a27ad9
1973 F20101219_AACDVD mehrotra_s_Page_031.txt
69099594f4cd21a504fdc64df5a54b1c
d1b4dbf36d1f4c31322403075bbc3075366c3db4
1980 F20101219_AACDUP mehrotra_s_Page_013.txt
e55b0e7e3016460bebb899429f476723
88ea69af6898ed0a39a674d70497deecec4aeb17
1960 F20101219_AACDVE mehrotra_s_Page_032.txt
0ae85a2219101e5ddd01e7e629628c4e
caaea1b6a889c2179420e12ab252863295b12593
1986 F20101219_AACDUQ mehrotra_s_Page_014.txt
7c211060009298a68faa9c770a1e6e85
d368a30d2012a0ae35c3da11eca32a7940066252
35053 F20101219_AACEAL mehrotra_s_Page_027.QC.jpg
2bad43c3ac0a4b73430d8bf23a81d28a
c15d4b6576a93e092339c1aa24937b4a14b4284e
F20101219_AACDVF mehrotra_s_Page_033.txt
e935d2f48d14d97a6c008770377551d6
613b74dd0d49b0ab27edaaf2f23333ddaf65c484
2002 F20101219_AACDUR mehrotra_s_Page_016.txt
c1c1e5eadc2111565ac22b73b0ecafdf
2ceb366ac8305644e79b8fefa7f656c5f3377d55
4764 F20101219_AACEBA mehrotra_s_Page_034thm.jpg
10b794947d4a7aa31f8d66544fd40f10
2c46d2a3a4fe72d12a27aef3743723d8cb806291
8378 F20101219_AACEAM mehrotra_s_Page_027thm.jpg
a464c782f12a8c32a691347ea555ea50
943b3008c49184cbb99048f5de4f49fd156a0362
1137 F20101219_AACDVG mehrotra_s_Page_034.txt
64ab25aa8540037f36aa61ee86a3dd98
eaafb880b74f9d2858e2a6c81444580aca1e260e
1202 F20101219_AACDUS mehrotra_s_Page_017.txt
36ce8341c2ab81b6bc33fb158c8b67d2
0e2a06143f4d69b1056587c3747f23dd591296cd
29087 F20101219_AACEBB mehrotra_s_Page_035.QC.jpg
b6573606a62e262870a78ec476ee3f91
b88068a66a5e87cbab518735a568e73c2d6b8f07
30588 F20101219_AACEAN mehrotra_s_Page_028.QC.jpg
0747e8052037a2af7cc71786576196a1
b8535bd032c9b08821ebe86edc5fdd87800295a4
1811 F20101219_AACDVH mehrotra_s_Page_035.txt
369efb0a5cd1f54b853ee8eb2b12276f
92e406c3c06f284d4cf2720ffb8a36830c362c5a
1720 F20101219_AACDUT mehrotra_s_Page_018.txt
a0b6ad43965dfcaa527ffe39c767cda8
45d6704e82267e2340f7e072cd0bc642e0ca9409
F20101219_AACEBC mehrotra_s_Page_035thm.jpg
5ed4f2e8e2368486800adbb7d45889f9
58660a562ee3bb5fb881599b1fd4aee5322333a3
7867 F20101219_AACEAO mehrotra_s_Page_028thm.jpg
674c3ce550974681cfde8eed357d5504
946b6362e28184c579917f53e57c9315e651e6aa
1402 F20101219_AACDVI mehrotra_s_Page_036.txt
2657fb33f1e0f2bd139e4a380d9f457f
4dbaa04da3f08317db8a34eb1dbbd38f220b9f46
1827 F20101219_AACDUU mehrotra_s_Page_019.txt
f159deac79714570f7c2f4ffa6d0097f
25c6fa566a7a9817b85e174f3153b82510ce08a4
24173 F20101219_AACEBD mehrotra_s_Page_036.QC.jpg
ef6b01efb68e5a131dd22fa0b055a2c8
c9d70f99bf1a4e32a97ecd41a8f7172e9c887e55
32324 F20101219_AACEAP mehrotra_s_Page_029.QC.jpg
99489e09444aa4404322ac0186dc400e
6f195149c07e4f8f2a58317aae7647db2d50039b
1776 F20101219_AACDVJ mehrotra_s_Page_037.txt
202a4431809dcddd51e4d4b1ad2379bb
b8f063860d2c7098f00dbe0200a4a9883ddb6cdb
F20101219_AACDUV mehrotra_s_Page_020.txt
b8dc53f1134a4bf8a50400b722d3515e
075cb9c7836da2ab8e4f27728aff49d3b4fcab50
6653 F20101219_AACEBE mehrotra_s_Page_036thm.jpg
8434781ed12bc83346b98a4790b9e566
ba4d64ff31cc0006f331b0fbc39d303f13a2d707
8142 F20101219_AACEAQ mehrotra_s_Page_029thm.jpg
926afede3a99d7b6ee526ac09f206c57
4a4920f36d6092f8192ffbafb405428ca8cb0e34
1742 F20101219_AACDVK mehrotra_s_Page_038.txt
3b691f2497a625a662a15c89f3a0741c
113df8043fe7789ed0944398c7debe9d9a76d108
1902 F20101219_AACDUW mehrotra_s_Page_021.txt
411247fde6c9b639555a797a0b206c1a
4a53d9646cd5c970b829ae74207e74ba3f5c0088
27173 F20101219_AACEBF mehrotra_s_Page_037.QC.jpg
82fe5da47f5c350a55796f39f205d40f
560ddb0117d6940ce6beaf422271b03742bddfff
1864 F20101219_AACDWA mehrotra_s_Page_055.txt
7e60f1be80e0ce06c5ee6c55ca9ada96
81eb8a2706d15dd32b838487b6837a50a79bf601
31415 F20101219_AACEAR mehrotra_s_Page_030.QC.jpg
779cd245ae72a587495e882df1f87d7f
16f0a9d6dcd20cd7bcaa22bbd12c83432d7c5466
1766 F20101219_AACDVL mehrotra_s_Page_039.txt
3abcdaa1a5dc93e87906b30a262c3f99
30d880d5b36a8b6b40249890cd1e51377bc6deee
2049 F20101219_AACDUX mehrotra_s_Page_023.txt
48e6f86c6a0aac4146212aeef1e30cb4
f9be2f0ecc618c5766cbdc878fee8a129fb3b15d
7499 F20101219_AACEBG mehrotra_s_Page_037thm.jpg
faa7a00050a4f6a1eb4e5d5c274a44b1
4361bda72577e887f83b6926fd35dd0ab41e05aa
1596 F20101219_AACDWB mehrotra_s_Page_056.txt
c07fea03d23330c7ce04e4d32212e086
a727cdc059aa82104d4c083933a7df8723fb412c
7919 F20101219_AACEAS mehrotra_s_Page_030thm.jpg
fd790e58c02baec9452a2d04a5f11e3f
09baac1594ab83db7179a7e834bfe2208708d987
1597 F20101219_AACDVM mehrotra_s_Page_040.txt
4cb316194cf4f7db269985be95b68b23
150e7625cd955ba1a37a8377ad4210401b134c6f
2036 F20101219_AACDUY mehrotra_s_Page_025.txt
dbfc64ebdfc42143ed2ed89649283edb
c794e4593fefa95446ac991132525b781c752a51
28718 F20101219_AACEBH mehrotra_s_Page_038.QC.jpg
6a1ee8ec18ce38da49ccfbe07d674594
1551831ebfb144d49073f5ec0a78a5e81a426912
32342 F20101219_AACEAT mehrotra_s_Page_031.QC.jpg
94a7e14872277b693a4cea1ac6e3aa05
da64bdfd0e4671cff9856f91d54f999478fff062
1851 F20101219_AACDVN mehrotra_s_Page_041.txt
e8cfef2fce9512f59e0c3cdace2a2630
05139a76588899d5486c96cc13e83b2c33a1224b
2013 F20101219_AACDUZ mehrotra_s_Page_026.txt
1ceaacf06ae67061ad661a4d42903d43
9ec9c945826ae2658544b0aaed985403a51b517e
7257 F20101219_AACEBI mehrotra_s_Page_038thm.jpg
2268aea15905bbe29630bc7b4b329247
405aec9fd078eb0af823361c7e24e46195fd8168
2050 F20101219_AACDWC mehrotra_s_Page_057.txt
eebd300b211dc89d06527b7cd28ad648
73fb06dc99fea5da98157ced73ade30fc6ef2a43
F20101219_AACEAU mehrotra_s_Page_031thm.jpg
db0e31757ac27964afa29e86f5378f68
d813501417893c16531eeeda9ca9fa11f906bbd5
1593 F20101219_AACDVO mehrotra_s_Page_042.txt
ef4a31d8dd8835de1050947be47eb44a
27e471940850a6d368e3f2d1aaaf366fcafccbea
27616 F20101219_AACEBJ mehrotra_s_Page_039.QC.jpg
68442785782282bd15bf135562a3f2bf
43ccae120033ccf92fb05e804dc3abc005064d5b
1939 F20101219_AACDWD mehrotra_s_Page_058.txt
8878b5f1a2b87f087fd8464d0ee4da1c
1d5bd413ac793f277434fc25cf7878bab2ead7a3
32852 F20101219_AACEAV mehrotra_s_Page_032.QC.jpg
7f4def88c8f28ae3993e41deb549beef
1dae000a581ccb49b5de165986c364366c33390b
1942 F20101219_AACDVP mehrotra_s_Page_043.txt
b1abc38efb12740e3ee326c031eeb9a8
3bd21b1932404bc84a7bb48df5186301f1ff62a9
7012 F20101219_AACEBK mehrotra_s_Page_039thm.jpg
018333a18e358d67835423dbcb912064
5eb19318b41307762ad0146bf256316342e7d727
2123 F20101219_AACDWE mehrotra_s_Page_059.txt
e0edbc47e7fb75114067b449d2ca0f61
194e3516fa4e6ad139dea517a02a4a1f615a3544
8348 F20101219_AACEAW mehrotra_s_Page_032thm.jpg
dc495e58e062ced31b1fc4c6128df2fe
4cc5ddf6111235e70644283322dad840c2da742e
1579 F20101219_AACDVQ mehrotra_s_Page_045.txt
75c897a791898b67de83d0ea5c520096
4935597b5e928d31c9036a325493ef7b43ffb750
24280 F20101219_AACEBL mehrotra_s_Page_040.QC.jpg
d9614642c4e5ecf037e23f7af27cb5e8
19ebf40e46d0658e8bde3b6c7003994c1e6975ad
1945 F20101219_AACDWF mehrotra_s_Page_060.txt
eee077d48488609681e13fe4a151bd9a
75a2d5ee82a6d12323583706f190ed04f6ba03c3
32674 F20101219_AACEAX mehrotra_s_Page_033.QC.jpg
29a053d1601f430225ac2960a9407edc
7c0dcee09265f144845fddb988a53b1532e8519a
1693 F20101219_AACDVR mehrotra_s_Page_046.txt
0900b82ab87f708f7636056b3c9aee18
ce9d99abaf9e37f032d1a04eb13a3ec24b7a6660
6539 F20101219_AACECA mehrotra_s_Page_049thm.jpg
ff23ff9ca3d1ca93941751089b59c681
d3540123e29499d241b65b3b0e64835a0840a066
1876 F20101219_AACDWG mehrotra_s_Page_061.txt
e64e08941cb96b3cded8710616ff86f4
ab9da3df80a43329a47fcc5d7ad3357fccc73deb
8354 F20101219_AACEAY mehrotra_s_Page_033thm.jpg
2e3b34a48a3f982a9cb169c6b9734d1b
b6d2bfe748a5f5f8f0790a57c4ccd5d95b84270f
1739 F20101219_AACDVS mehrotra_s_Page_047.txt
8f938273191edb04be9c0af875532420
a788961d35cbbbcaf4681c64fcbc9b0d06669a72
16106 F20101219_AACECB mehrotra_s_Page_050.QC.jpg
b30cf6da163c829187ffed7d889ec9ae
7f4bdc96cbec65d9241f6cfa4ca76dcf3bbff1bb
6738 F20101219_AACEBM mehrotra_s_Page_040thm.jpg
b09e4247278542feb2f4eb9dd715078a
32c37b9d9be611331a21b912fe3e6abbc3112cc3
1918 F20101219_AACDWH mehrotra_s_Page_062.txt
6ce74e35ec393c55b79b65c26a48367a
e4783fc541f75f6ac77286f18dfe3110dbeb6ac6
19427 F20101219_AACEAZ mehrotra_s_Page_034.QC.jpg
59b55b9fa38ea172ff0f91242cfc07c7
9e139c124f49ea762481ce18ccab39d2cf664c05
1134 F20101219_AACDVT mehrotra_s_Page_048.txt
c827c5baf0382bb401de6cf8941c311b
33e7296ad94ae19c6e2edabd36954034ce6c168d
4964 F20101219_AACECC mehrotra_s_Page_050thm.jpg
f3c4743d0656976219350c61d3849667
b3101a8a61a5e4bfebb282bd61e1a136fc056fb5
31083 F20101219_AACEBN mehrotra_s_Page_041.QC.jpg
5585144f8e4723a28456bb7ad18ae782
57ad6fddcd545b13e726f3ebb6168444023ba584
1561 F20101219_AACDWI mehrotra_s_Page_063.txt
ed28b1d34427bd1532f6bc4306e0452e
cef14cbcf64ac4818b076f98042b48f65ffa4f87
1474 F20101219_AACDVU mehrotra_s_Page_049.txt
bdfb502c029adfe177ca95542e1e2250
0b0742e3de394126bc1d57dbaefa093208be934a
25217 F20101219_AACECD mehrotra_s_Page_052.QC.jpg
d4583fbcaad3f0e27ab9242ca34118c2
d3190cda82ae23d7ba450dfb4180e461602ba550
24125 F20101219_AACEBO mehrotra_s_Page_042.QC.jpg
3bbe09cb3c2c508cd361579dee37f604
2193f7742fee154bb250e365fbbecc0f6ca6ab17
1823 F20101219_AACDWJ mehrotra_s_Page_064.txt
5820a73642734b88e68b1f09ae150ff8
3f8b6f1088927ebdd628f3ceeed76e1dff8eeae2
1124 F20101219_AACDVV mehrotra_s_Page_050.txt
ae18a0e22aa58cd7d06163089a0310cd
bb4f4c18aba9afeed5024b187f8c5b1d0cb01cf1
25645 F20101219_AACECE mehrotra_s_Page_053.QC.jpg
97f0ceb95cf8a66c69c2f84444f889ed
33acce4716f037e12c1c39052ea397e1317c4a96
6714 F20101219_AACEBP mehrotra_s_Page_042thm.jpg
21e10b6761bebbebc249482876daf19d
ad49dcee7ba3530ad090f57108fb654a0f0717a3
1506 F20101219_AACDVW mehrotra_s_Page_051.txt
884dd2d77416184c7706aa741e1fae9e
da7a3efcd425b9effd16827bf36a13bc3f12aa12
6507 F20101219_AACECF mehrotra_s_Page_053thm.jpg
95604ea6f430d1b1a460099b93d70ed8
0c46072ca3655b17a59228a998105413b6660109
30753 F20101219_AACEBQ mehrotra_s_Page_043.QC.jpg
f4267b00da151354f7dc37fce66ecfc1
b8d4352e27b1f3c6a324454ce4cefbd1a6c0e40d
F20101219_AACDWK mehrotra_s_Page_065.txt
59dbf0df45f9343181ed5f17147c2494
fbeb746d9f1a1702407fc1f38e26adfdd39b4cfa



PAGE 1

CONTINGENT CLAIMS ANALYSIS OF OPTIMAL INVESTMENT DECISION MAKING IN THE MANAGEMENT OF TIMBER STANDS By SHIV NATH MEHROTRA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

PAGE 2

Copyright 2006 by Shiv Nath Mehrotra

PAGE 3

iii ACKNOWLEDGMENTS I am grateful to my supervisory committee chair, Dr. Douglas R. Carter, co-chair, Dr. Janaki R. Alavalapati, and Drs. Donald L. Rockwood, Alan J. Long and Charles B. Moss for their academic guidance and support. I particularly wish to thank Dr. Charles Moss for always finding time to help with th e finance theory as well as for aiding my research in many ways. I thank my family for their support and encouragement.

PAGE 4

iv TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT.....................................................................................................................vi ii CHAPTER 1. INTRODUCTION........................................................................................................1 Economic Conditions in Timber Markets.....................................................................1 The Forest Industry in Florida......................................................................................2 Outline of the Investment Problem...............................................................................3 Research Objectives......................................................................................................8 2. PROBLEM BACKGROUND......................................................................................9 Introduction to Slash Pine.............................................................................................9 Slash Pine as a Commercial Plantation Crop........................................................9 Slash Pine Stand Density.....................................................................................11 Thinning of Slash Pine Stands.............................................................................12 Financial Background.................................................................................................13 The Nature of the Harvesting Decision Problem................................................14 Arbitrage Free Pricing.........................................................................................17 Review of Literature on Uncertainty and Timber Stand Management.......................20 3. THE CONTINGENT CLAIMS MODEL AND ESTIMATION METHODOLOGY.....................................................................................................26 The One-Period Model...............................................................................................26 The Deterministic Case.......................................................................................26 The Stochastic Case.............................................................................................29 Form of the Solution for the Stochastic Value Problem......................................31 The Contingent Claims Model....................................................................................31 The Lattice Estimation Models...................................................................................38 The Binomial Lattice Model...............................................................................38

PAGE 5

v The Trinomial Lattice Model fo r a Mean Reverting Process..............................42 The Multinomial Lattice Model for Tw o Underlying Correlated Stochastic Assets...............................................................................................................43 4. APPLICATION OF THE CONTINGENT CLAIMS MODEL.................................45 Who is the Pulpwood Farmer?...................................................................................45 The Return to Land in Timber Stand Investments......................................................50 On the Convenience Yield and the Timber Stand Investment...................................57 Dynamics of the Price Process...................................................................................60 Modeling the Price Process.................................................................................63 The Geometric Brownian Motion Process..........................................................65 Statistical Tests of the Geometric Brownian Motion Model...............................67 The Mean Reverting Process...............................................................................70 Statistical Tests of the Mean Reverting Process Model......................................74 Instantaneous Correlation....................................................................................75 The Data......................................................................................................................7 6 Growth and Yield Equations...............................................................................76 Plantation Establishment Expenses.....................................................................78 Risk-Free Rate of Return.....................................................................................79 The Model Summarized.............................................................................................79 5. RESULTS AND DISCUSSION.................................................................................81 A Single Product Stand and the Geometri c Brownian Motion Price Process............81 Sensitivity Analysis.............................................................................................84 Comparison with the Dyna mic Programming Approach....................................89 A Single Product Stand and the M ean Reverting Price Process.................................90 The Multiple Product Stand and Geometri c Brownian Motion Price Processes........93 Thinning the Single Product Stand and th e Geometric Brownian Motion Price Process....................................................................................................................96 Discussion...................................................................................................................98 Recommendations for Further Research..................................................................104 APPENDIX CORRELATION OF FIRST DIFFERENCES OF AVERAGES OF TWO RANDOM CHAINS......................................................................105 LIST OF REFERENCES.................................................................................................107 BIOGRAPHICAL SKETCH...........................................................................................115

PAGE 6

vi LIST OF TABLES Table page 1-1. Comparison of applied Dynamic Programming and Contingent Claims approaches..................................................................................................................6 2-1. Area of timberland classified as a sl ash pine forest type by ownership class, 1980 and 2000 (Thousand Acres ) ............................................................................10 3-1. Parameter values for a three dimensional lattice.......................................................44 4-1. Florida statewide nomi nal pine stumpage average product price difference and average relative prices (1980-2005).........................................................................46 4-2. The effect of timber product price di fferentiation on optimal Faustmann rotation...47 4-3. The effect of timber product relative prices on optimal Faustmann rotation............47 4-4. Estimated GBM process parameter values for Florida statewide nominal quarterly average pulpwood prices..........................................................................66 4-5. Results of Jarque-Bera test applied to GBM model for Florida statewide nominal quarterly average pulpwood stumpage prices..........................................................70 4-6. Inflation adjusted regression and MR model parameter estimates............................73 4-7. Results of Jarque-Bera test applied to MR model residuals for Florida statewide nominal quarterly average pulpwood stumpage prices............................................75 4-8. Average per acre planta tion establishment expenses for with a 800 seedlings/acre planting density........................................................................................................78 5-1. Parameter values used in analysis of harvest decision for single product stand with GBM price process...........................................................................................82 5-2. Parameter values used in analysis of harvest decision for single product stand with MR price process..............................................................................................91 5-3. Parameter values used in analysis of harvest decision for multiproduct stand with GBM price processes...............................................................................................93

PAGE 7

vii LIST OF FIGURES Figure page 1-1. Florida statewide nominal quarterly average pine stumpage prices (1976-2005 II qtr)........................................................................................................................... ...1 3-1. Typical evolution of even-aged stand and stumpage values for the Faustmann analysis.....................................................................................................................27 4-1. Sample autocorrelation function plot for nominal Florid a statewide pulpwood stumpage instantaneous ra te of price changes..........................................................69 4-2. Sample autocorrelation function plot for nominal Florid a statewide pulpwood stumpage price MR model regression residuals.......................................................75 5-1. Total per acre merchantable yield curve for slash pine stand....................................81 5-2. Crossover price line for single product stand with GBM price process....................83 5-3. Crossover price lines for different levels of intermediate expenses..........................85 5-4. Crossover price line for differe nt levels of standard deviation.................................86 5-5. Crossover price lines for varying levels of positive constant convenience yield......87 5-6. Crossover price lines for different levels of current stumpage price.........................88 5-7. Crossover price line for single product stand with MR price process.......................92 5-8. Merchantable yield curves for pulpwood and CNS...................................................93 5-9. Crossover price lines for multiproduct stand.............................................................95 5-10. Single product stand merchantable yield cu rves with single thinning at different ages........................................................................................................................... 97

PAGE 8

viii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CONTINGENT CLAIMS ANALYSIS OF OPTIMAL INVESTMENT DECISION MAKING IN THE MANAGEMENT OF TIMBER STANDS By Shiv Nath Mehrotra August 2006 Chair: Douglas R. Carter Cochair: Janaki R. Alavalapati Major Department: Forest Resources and Conservation The treatment of timber stand investment problems involving stochastic market prices for timber and multiple options can be considerably improved by the application of real options analysis. The an alysis is applied to the d ilemma of mature slash pine pulpwood crop holders in Florida facing depr essed markets for their product. Using a contingent claims approach an arbitrage fr ee market enforced value is put on the option of waiting with or without commercial thi nning, which when compared with the present market value of stumpage allows an optimal decision to be taken. Results for two competing models of tim ber price process su pport the decision to wait for a representative unthinned 20-year-old cutover slash pine pulpwood stand with site index 60 (age 25) and in itial planting density 800 trees per acre. The present (III Qtr 2005) value of stumpage is $567/acre as compar ed to the calculated option value for the Geometric Brownian motion price proce ss of $966/acre and $1,290/ acre for the Mean

PAGE 9

ix Reverting price process. When the analysis differentiates the merchantable timber yield between products pulpwood and chip-n-saw wi th correlated Geometric Brownian motion price processes the option value rises to $1,325/acre for a stumpage market value of $585/acre. On the other hand the commercial thinning option holds no value to the single product stand investment when the poor response of the slash pine spec ies to late rotation thinning is accounted for. The analysis shows that the measurement of option values embedded in the timber stand asset is hampered by the lack of availa bility of market information. The absence of a market for the significant catastrophic risk associated with the asset as well other nonmarketed risks also hampers the measurement of option values. The analysis highlights the importance of access to market information for optimal investment decision making for timber stand management. It concludes that stand owners can realize the full value of the signifi cant managerial flexibility in their stands only when access to market information im proves and markets for trading in risks develop for the timber stand investment.

PAGE 10

1 CHAPTER 1 INTRODUCTION Economic Conditions in Timber Markets Pine pulpwood prices in Flor ida have been declining si nce the peaks of the early 1990’s (Figure 1-1). After reachi ng levels last seen in the early 1980’s, in 2005 the prices have shown signs of a weak recovery. The trend in pulpwood markets reflects the impact of downturn in pulp and paper manufacturing resulting from several factors (Ince 2002) like: 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.001976 1978 1979 1980 1981 1983 1984 1985 1986 1988 1989 1990 1991 1993 1994 1995 1996 1998 1999 2000 2001 2003 2004Year Stumpage Price O.B. ($/Ton) Saw Timber Price Chip-n-saw Price Pulpwood Prices Source: Timber Mart-South Figure 1-1. Florida statewide nominal quarterly average pi ne stumpage prices (1976-2005 II qtr) 1. A strong US dollar, rising imports and weakness in export markets since 1997. 2. Mill ownership consolidation and closures.

PAGE 11

2 3. Increased paper recyclin g along with continued e xpansion in pulpwood supply from managed pine plantations, particularly in the US South. In a discussion of the findings and projecti ons of the Resource Planning Act (RPA), 2000 Timber Assessment (Haynes 2003), Ince (2 002) has noted that the pulp and paper industry sector has witnessed a fall in capacity growth since 1998 with capacity actually declining in 2001. The report pr ojects that US wide pulpwood stumpage prices would stabilize in the near term w ith a gradual recovery, but woul d not increase appreciably for several decades into the futu re. With anticipated expansi on in southern pine pulpwood supply from maturing plantations, pine stumpage prices are projected to further subside after 2015. Pine pulpwood stumpage prices are not projected to return to the peak levels of the early 1990’s in the foreseeable future (Adams 2002). Nevertheless, the US South is projected to remain the dominant region in production of fiber products and pulpwood demand and supply. The Forest Industry in Florida Florida has over 16 million acres of forests, representing 47% of the state’s land area. Non-industrial private forest (NIPF) owners hold approximat ely 53% of the over 14 million acres of timberland in the state (Carter and Jokela 2002). The forest based industry in Florida has a larg e presence with close to 700 manufacturing facilities. The industry produces over 900,000 tons of pa per and over 1,700,000 tons of paperboard annually apart from hardwood and softwood lumber and structur al panels (AF&PA 2003). Pulpwood and sawlogs are the principa l roundwood products in Florida accounting for up to 80% of the output by volume. Pulpwo od alone accounted for more than 50% of the roundwood output in 1999. NIPF land contri buted 45% of the to tal roundwood output

PAGE 12

3 while an equal percent came from industry held timberlands. Slash and longleaf pine provided 78% of the softwood roundw ood output (Bentley et al. 2002). Forest lands produce many benefits for th eir owners who express diverse reasons for owning them. A survey of private forest land owners in the US South by Birch (1997) found that nearly 38% of the private forestland owners hold forestland primarily because it is simply a part of the farm or residen ce. Recreation and esthetic enjoyment was the primary motive for 17% while 9% of the owners stated farm or domestic use as the most important reason for owning forest land. Among st commercial motives, land investment was the primary motive for 12% of the owners At the same time expected increase in land value in the following 10 years was listed as the most important benefit from owning timberland by 27% of landowners accoun ting for 21% of private forests listed. Significantly, timber production was the prim ary motive for only 4% of the private forestland owners, but these owners control 35% of the private fo restland. Similarly, only 7% of the owners have listed income from the sale of timber as the most important benefit in the following 10 y ears, but they control 40% of the private forest. Outline of the Investment Problem Timberland is defined as land that either bears or has the potential to bear merchantable quality timber in economic quantities. The US has nearly 740 million acres of forestland, of which 480 million acres is cla ssified as timberland and the rest are either preserves or lands too poor to produce ade quate quality or quantity of merchantable timber (Wilson 2000). Small private woodlot ownership (<100 acr es) accounts for more than 90% of NIPF timberland holdings in the US and remain s a significant part of the investment pattern (Birch 1996). The prolonged depressi on in pulpwood prices poses a dilemma for

PAGE 13

4 NIPF small woodlot timber cultivators in Florida who are holding a mature pulpwood crop. These pulpwood farmers must decide abou t harvesting or extending the rotation. The option to extend the rotation and wait out the depressed markets brings further options like partial realiza tion of revenues immediately through commercial thinnings. These decisions must be made in the face of uncertainty over the futu re market price(s) for their timber product(s). Slash pine pulpwood stand owners must also contend with the fact that the species does not respond well to late rotati on thinnings, limiti ng the options for investing in late rota tion products (Johnson 1961). The timber stand investment is subject to several risks, mark eted as well as nonmarketed (e.g., risk of damage to the physic al assets in the absence of insurance). Understanding and incorporating these risks in to management decisions is crucial to increasing the efficiency of the investment The asset value/price risk is the most common form of risk encountered by all i nvestors. For most forms of investments markets have developed several financial in struments for trading in risk. Insurance products are the most common while others su ch as forwards, futures and options are now widely used. Unfortunately, timberland investments lag behind in this respect. Institutional timberland investors, with their la rger resources, deal with specific risk by diversification (geographic, product). Small woodlot owne rs must contend with the greatest exposure to risk. Investment risk in timber markets has b een long recognized and extensively treated in literature. As a result, on the one hand, ther e is a better apprecia tion of the nature and importance of correctly modeling the stochastic variables, and on th e other hand, there is improved insight into the nature of the inve stment problem faced by the decision maker.

PAGE 14

5 Despite the considerable progress, no single universally acceptable approach or model has yet been developed for analyzing and so lving these problems. Due to the financial nature of the problem, developments in financial literature have mostly preceded progress in forest economics research. In the last decades, the most important and influential development in financial theory has been that of the option pricing theory. Several timber investment problems are in the nature of contingent claims and best treated by the application of option pricing theo ry or what is described as real options analysis (since the investments are real as opposed to financial instruments). It is known that for investment d ecisions characterized by uncertainty, irreversibility, and the ability to postpone, investors set a higher hurdle rate. Stand management decisions like commercial thinning and final harvest share these characteristics. Options analysis provides a means for valuing the flexibility in these investments. There are two approaches to options analysis, namely, the dynamic programming (DP) approach and the conti ngent claims (CC) approach. Almost all treatment of investment problems in forestry literature uses the DP approach to options analysis. Despite its popularity in research, the applied DP approach has some drawbacks which limit its utility for rese arch or empirical applicati ons. The CC valuation is free from these limitations. Some important features of the application of the two approaches are compared in Table 1.1. The most critical problem is that application of the DP approach requires the determination of an appropriate discount rate. In the absen ce of theoretical guidance on the subject studies are forced to use arbitrary discount rates with little relation to the risk of the asset. For example, Insley (2002) us es a discount rate of 5%, Insley and Rollins

PAGE 15

6 (2005) use 3% and 5% real di scount rates alternately, while Plantinga (1998) uses a 5% “real risk-free” discount rate even though the analysis uses subjective probabilities. No justification is offered for the choice of the discount rate (P lantinga (1998) cites Morck et al. (1989) for providing a rate “typical” to timber investment ). Hull (2003) illustrates the difference between the discount rate applic able to the underlying instrument and the option on it. For a 16% discount rate applic able to the underlying, the illustration shows that the discount rate on the option is 42.6%. Explaining the hi gher discount rate required for the option, Hull (2003) mentions that a position on the option is riskier than the position on the underlying. Another problem with the use of arbitrar y discount rates is that the results of different studies are not comparable. Table 1-1. Comparison of applied Dynami c Programming and Contingent Claims approaches _____________________________________________________________________________ Dynamic Programming Approach Contingent Claims Approach _____________________________________________________________________________ 1. Requires the use of an externally Uses a risk-free discount rate that determined discount rate. This is reliably estimated from existing discount rate is unobservable market instruments. (unless the option itself is traded). The discount rates used in published forestry literature bear no relation to the risk of the asset. 2. Published forestry literature does Distinguishes between marketed and not specify whether the marketed, non-marketed components of the the non-marketed or both components assets risk. Applies only to marketed of the asset’s risk are being treated. risk. Extensions have been proposed to account for non-marketed risk 3. Risk preferences are treated It is a risk neutral analysis. inconsistently in published forestry literature. 4. Requires use of historical estimates Replaces the drift with the risk-free of mean return or drift which is rate of return. Estimates of susceptible to large statistical erro rs. historical variance are relatively stable. ________________________________________________________________________

PAGE 16

7 Similarly, none of the published research on options analysis in forestry specifies whether the marketed, the non-marketed or bo th risks are being tr eated. Since the only stochasticity allowed is in the timber price, it may be possible to infer that the marketed risk is the object of the analysis. But such inference would challeng e the validity of some of their conclusions. For example, Plantinga (1998) concludes th at reservation price policies, on an average, increase rotation lengths in comparison to the Faustmann rotation, while management costs decrease rota tion lengths. By includ ing a notional cost of hedging against non-marketed risks (insur ance purchase) in the analysis as a management cost any conclusion regarding th e rotation extension e ffect of reservation prices policies would be cast in doubt without better market data on the size of these hedging costs. Failure to highlight the treatment of risk preferences in the analysis is another source of confusion. Some studies like Brazee and Mendelsohn (1988) specify that the decision maker is risk neutral. Knowing this helps individuals to interpret the results according to their risk preferences. But when risk preferences are not specified, as in Insley (2002) for example, and there is c onfusion over the discount rate applied, the results produced by the analysis lose interpretative value. Real options analysis as it is applied through contingent claims valuation is itself a nascent branch of the option pricing theory which has developed principally by extending option pricing concepts to the valuation of real assets. Ther e is increasing recognition of the shortcomings of the techniques develope d for pricing financial asset options when applied to real assets and several modified approaches have been proposed. Nevertheless, application of real options an alysis to timber investment decisions offers an opportunity

PAGE 17

8 to take advantage of a unified financial theory to treat the su bject and thus obtain a richer interpretation of the results. Research Objectives The general objective of this study is to apply contingent claims analysis to examine typical flexible investment decisi ons in timber stand management, made under uncertainty. The analysis is applied to th e options facing the NIPF small woodlot owner in Florida holding a mature even aged sl ash pine pulpwood crop. Th e specific objectives are 1. To analyze and compare the optimal clear-cut harvesting decision for a single product, i.e., pulpwood, producing stand with Geometric Brownian Motion (GBM) and Mean Reverting (MR) price process alternately. 2. To analyze the optimal clear-cut harvesting decision for a multiple product, i.e. pulpwood and chip-n-saw, producing stand w ith their prices following correlated GBM processes. 3. To analyze the optimal clear-cut harvesting decision with an option for a commercial thinning for a single product, i.e., pulpwood, producing stand with a GBM price process.

PAGE 18

9 CHAPTER 2 PROBLEM BACKGROUND Introduction to Slash Pine Slash pine ( Pinus elliottii var. elliottii ) is one of the hard yellow pines indigenous to the southeastern United States. Other o ccasional names for the specie are southern pine, yellow slash pine, swamp pine, pitch pine, and Cuban pine. Along with the most frequently encountered variety P. elliottii var. elliottii the other recognized variety is P. elliottii var. densa which grows naturally only in the s outhern half of peninsula Florida and in the Keys (Lohrey and Kossuth 1990). The distribution of slash pine within its natural range (8 latitude and 10 longitude) was initially determined by its suscep tibility to fire injury during the seedling stage. Slash pine grew thr oughout the flatwoods of north Fl orida and south Georgia as well as along streams and the edges of swamps and bays. Within these areas either ample soil moisture or standing water protected young seedlings from frequent wildfires in young forests (Lohrey and Kossuth 1990). Slash pine is a frequent and abundant seed producer and is characterized by rapid early growth. After the sapling stage it can withstand wildfires a nd rooting by wild hogs which has helped it to spread to drier sites (Lohrey and Kossuth 1990). Slash Pine as a Commercial Plantation Crop Florida has the largest area of timberland (B arnett and Sheffield 2004) classified as slash pine forest type (49%) while noni ndustrial private landowners hold the largest portion of slash pine tim berland (Table 2-1)

PAGE 19

10 Table 2-1. Area of timberland classified as a slash pine forest type, by ownership class, 1980 and 2000 (Thousand Acres ) _____________________________________________________ Ownership Class 1980 2000 _____________________________________________________ National Forest 522 493 Other Public 569 684 Forest Industry 4,649 3,719 Nonindustrial Private 7,039 5,479 _____________________________________________________ Total 12,779 10,375 _____________________________________________________ Source: Barnett and Sheffield, 2004 Slash pine makes rapid volume growth at early ages and is adaptable to short rotations under intensive mana gement. Almost three-fourths of the 50-year yield is produced by age 30, regardless of stand basal area. Below age 30, maximum cubic volume yields are usually produced in unt hinned plantations, so landowners seeking maximum yields on a short ro tation will seldom find commercial thinning beneficial. Where sawtimber is the objective, commercia l thinnings provide early revenues while improving the growth and quality of the sa wtimber and maintaining the stands in a vigorous and healthy conditi on (Lohrey and Kossuth 1990). A study by Barnett and Sheffi eld (2004) found that a majority (59%) of the slash pine inventory volume in plantations and natu ral stands was in the <10” dbh class while about 25% of the stands were less than 8 years old. The study concluded that this confirmed the notion that slash pine rotations are typically le ss than 30 years and that the stands are intensively managed. Plantation yields are influenced by previ ous land use and interspecies competition. Early yields are usually hi ghest on recently abandoned fields where the young trees apparently benefit from the residual effects of tillage or fertilizer and the nearly complete lack of vegetative competiti on. Plantations established after the harvest of natural stands

PAGE 20

11 and without any site treatment other than burning generally have lower survival and, consequently, lower basal area and volume than stands on old fields. Yields in plantations established after timber harvest and intensive site preparation such as disking or bedding are usually intermediate. Comparing slash pine to loblolly pine ( Pinus taeda L. ), Shiver (2004) notes that slash pine may be preferred over loblolly pi ne for reasons other than wood yields. For instance, slash pine would be the favored sp ecies for landowners who want to sell pine straw. Slash pine also prunes itself much bett er than loblolly, and for solid wood products the lumber grade will probably be higher for slash pine. Slash pine is more resistant to southern pine beetle ( Dendroctonus frontalis Zimmermann) attack than loblolly and it is rarely bothered with pine tip moth ( Rhyacionia frustrana (Comstock)), which can decimate young loblolly stands. Slash Pine Stand Density Dickens and Will (2004) discuss the eff ects of stand density choices on the management of slash pine stands. The c hoice of initial planting density and its management during the rotation depends on landowner objectives like maximizing revenues from pine straw, obtaining intermed iate cash flows from thinnings or growing high value large diameter class timber produc ts. High planting dens ity in slash pine stands decreases tree diameter growth as well as suppresses the tree height growth to a lesser extent, but total volume production pe r unit of land is increased. However, the volume increment observed for early rotation ages soon peaks and converges to that of lower density stands as the growth rate of high density stands reach a maximum earlier. Citing a study at the Plantation Management Research Cooperative, Georgia, Dickens

PAGE 21

12 and Will (2004) remark that management intensity does not change the effects of stand density. Dickens and Will (2004) mention that higher density plantings achieve canopy closure, site utilization, a nd pine straw production earlier than lower density plantings under the same level of management. Higher pl anting densities also may be beneficial on cut-over sites with low site preparation and management inputs. The higher planting densities help crop trees occupy the site, wh ereas the lower planting densities may permit high interspecific competition until much late r during stand development, reducing early stand volume production. Thinning of Slash Pine Stands Mann and Enghardt (1972) describe the resu lts of subjecting slash pine stands to three levels of thinnings at ages 10, 13 & 16. Early thinnings removed the diseased trees while later thinnings concentrat ed on release of better stem s. Their study concluded that early and heavy thinnings increased diamet er growth but reduced volume growth. The longer thinnings were deferred, the slower wa s the response in diameter growth. They concluded that age 10 was too early for a thi nning as most of the timber harvested was not merchantable and volume growth was lost, even though the diameter increment results were the best. The decision between thinning at ages 13 and 16 depended on the end product, the ability to realize merchant able volumes in thinnings and the loss of volume growth. They recommend that short rotation pulpwood crops were best left unthinned as the unthinned stands had good volume growth. Quoting Mann and Enghardt (1972) “volume growth is good, no costs are in curred for marking, there are fewer small trees to harvest and stand dist urbances that may attract bark beetle are avoided” (Mann and Enghardt 1972, p.10).

PAGE 22

13 Johnson (1961) has discussed the results of a study of thinning conducted on heavily stocked industrial slash pine stands of merchantable size. The study found that slash pine does not respond well to late release i.e., if it ha s been grown in moderately dense stands for the first 20 to 25 years of its life. It does not sta gnate, except perhaps on the poorest sites, but it cannot be expected to respond to cultural treatments such as thinnings as promptly or to the degree desired. Johnson (1961) observes that the typical thinning operation that removes four to six cords of wood from well-stocked stands is nothing more than an interim recovery of capital from the forestry enterprise. These thinnings do not stimulate growth of the residual stand or total production The study found no real increase in total volume produc tion or in average size of trees from commercial thinnings in slash pine stands being managed on short rotations for small products. Johnson (1961) concludes that silvicultura l considerations for commercial thinning in small product slash pine forest ma nagement are secondary to commercial considerations because of its re sponse to intermediate cuttings. Financial Background The timber farming investment exposes the investor to the risks that the asset carries. These risks come in the form of mark eted risks like the volatile market price for the timber products or non-marketed risks that also effect the value of the investment such as hazards that threaten the investment in the form of fire, pests, adverse weather etc. Usually, investors separate the spectrum of risks taken on by them from an investment into core and non-core risks. The core risk could be the market price of the investments output or product. Th is is the risk the investor expects to profit out of and

PAGE 23

14 likes to retain. The non-core risk like the non-marketed risks listed above are undesirable and the investor would ideally like to transf er such risks. A common market instrument for risk transfer is the insurance produc t. By paying a price one can transfer the undesirable risk to the market. If the non-ma rketed risks associated with the timber investment were marketed, the market data av ailable can be incorpor ated into investment analysis. In the absence of markets for a part or all of an assets risk, the common asset pricing theories are no t applicable and altern ate methods have to be applied. The analysis in this study is restricted to the marketed risk in the form of timber price risk only. The Nature of the Harvesting Decision Problem Following a price responsive harvesting regime, the slash pine pulpwood farming investor holding a mature crop and facing a stochastically ev olving pulpwood market price would like to know the best time for se lling his crop. From his knowledge of past movements of market price for pulpwood the investor knows that th e present price is lower than the average of prices in the r ecent past. He may sell the crop at the present price but significantly he ha s the option to hold the crop. Th e crop is still growing, both in size and possibly in value, and that pr ovides incentive to hold the harvest. But the market price is volatile. The future market price for pulpwood cannot be predicted with certainty. How does the investor decide his immediate action; sell or hold? While equilibrium asset values are determ ined by their productiv e capacities their instantaneous market values are determined by the ever changing market forces. Asset holders would like to earn a fair compensation on their investment i.e., the principal plus a return for the risk undertaken by holding the investment over time. But there is no guarantee to earning a ‘fair’ retu rn in the market place. Usually investors have a finite

PAGE 24

15 time frame for holding an asset and must reali ze the best value for their asset in this period. The decision to hold the asset for a futu re sale date is a gamble, an act of speculation. It carries the risk of loss as well as the lure of profit. But a ll investments in risky assets are speculative activities. One i nvestment may be more risky than another but one market equilibrium theory in the form of the Capital Asset Pricing Model (CAPM) assures us that their expected returns are pr oportional to their ris k, specifically to the systematic or non-diversifiabl e portion of their risk. The CAPM theory, development of which is simultaneously attributed to Sh arpe (1963, 1964) and Lintner (1965a, 1965b) amongst others, has it that at any point in ti me each marketed asset has an associated equilibrium rate of return which is a function of its covariance with the market portfolio and proportional to the market pr ice of risk. The expression ‘rat e of return’ refers to the capital appreciation plus cash payout, if any, ove r a period of time, expressed as a ratio to the asset value at the co mmencement of the period. If all risky investments are gambles, how does one choose amongst the enormous variety of gambles that are available in the market place? Once again, financial theory informs us that the choice amongst risky assets depends on the risk attitudes of individuals. Individuals w ould apportion their wealth am ongst a portfolio of assets (which serves to eliminate the non-systematic risk of the assets). The portfolio is constructed to match the risk-return tradeo ff sought by the individual. Once chosen, how does one decide how long to hold an asset? Th e risk associated with every asset as well as its expected return ch anges over time. Over a peri od of time the risk-return

PAGE 25

16 characteristic of a particular asset may lose its appeal to the indivi dual’s portfolio which itself keeps changing with maturing of risk attitudes over time. Returning to the pulpwood farmer’s deci sion problem, the question boils down to this: How does the pulpwood farmer decide whether his investment is worth holding anymore? It follows from the arguments a bove that the crop would be worth holding as long it can be expected to earn a return comm ensurate with its risk. But, how is the comparison between the expected rate of return and the required rate of return achieved? The usual financial technique is to subjectively estimate the expected cash flows from the asset, discount them to the present using a risk-adjusted discount rate, and compare the resulting value to the present market value of the asset. If the expected discounted value is higher, then the expected rate of re turn over the future relevant period under consideration is higher than th e required rate of return. A nd how does this work? It works because the required rate of re turn and the risk-adjusted discount rate are different names for the same value. The expected equilibri um rate of return generated by the CAPM represents the average return for all assets shar ing the same risk characteristics or in other words, the opportunity cost. When we use th e risk-adjusted discount rate to calculate the present value of the future cash flows, we ar e in effect accounting for the required rate of return. The discounting apportions the future cash flows between the required rate of return and residual value, if any. Can discounted cash flow (DCF) analysis be used to solve the pulpwood farmer’s harvesting problem? The pulpwood farmer’s valuation problem is compounded by the ability to actively manage the investment (fle xibility) or more specifically, the ability to postpone the harvest decision should the need arise. Not only do decision makers have to

PAGE 26

17 deal with an uncertain future market va lue for the pulpwood crop but they must also factor in the response to the possible values. The termination date or harvest date of the timber stand investment and thus its payoff is not fixed or predetermined. Traditional DCF analysis can deal with the price un certainty by the technique of subjective expectations but has no answer for flexibility of cash flow timings. This shortcoming has been overcome by decision analysis tools like decision trees or simulation to account for the state responsive future cash flows. So, are tools like decision trees or simulation techniques the answer to the pulpwood fa rmer’s dilemma? Almost, except that the appropriate discount rate sti ll needs to be determined. Arbitrage Free Pricing Despite widespread recogniti on of its shortcomings, the CAPM generated expected rate of return is most commonly used as the risk-adjusted discount ra te appropriate to an investment. It turns out that while the mean -variance analysis led school of equilibrium asset pricing does a credible job of explaining expected returns on assets with linear risk they fail to deal with non-linear risk of the type associated with assets whose payoffs are contingent. Hull (2003) provides an illustration to show that the risk (and hence discount rates) of contingent claims is much highe r than that of the underlying asset. The pulpwood farmer holds an asset with a contingent claim because the payoff from his asset over any period is contingent on a favorable price being offered by the market for his crop. There are two alternate though equivalent techniques for valuing a risky asset by discounting its expected future cash flows. One, as already described involves an adjustment to the discount rate to account fo r risk. The other method adjusts the expected cash flows (or equivalently, the probability distribution of futu re cash flows) and uses the

PAGE 27

18 risk-free rate to discount the resulting certainty equivalent of the future cash flows. The CC valuation procedure follows this certain ty equivalent approach. The argument is based on the Law of One Price (LOP). The LOP argues that in a perfect market, in equilibrium, only one price for each asset, irre spective of individual risk preferences, can exist as all competing prices woul d be wiped out by arbitrageurs. Baxter and Rennie (1996) illustrate the difference between expectation pricing and arbitrage pricing using the example of a fo rward trade. Suppose one is asked by a buyer to quote today a unit price for selling a commodity at a future dateT. A fair quote would be one that yields no sure pr ofit to either party or in ot her words provides no arbitrage opportunities. Using expectation pr icing, the seller may believe th at the fair price to quote would be the statistical average or expected price of the commodity, TS where TSis the unit price of the commodity at timeTand Eis the expectation operator. But a statistical average would turn out to be the true price only by coincidence and thus could be the source of significant loss to the seller. The market enforces an arbitrage free price for such trades using a different mechanism. If the borrowing/lending rate isr, then the market enforced price for the forward trade is0 rTSe. This price follows the logic that it is the cost that either party would incur by borrowing funds at the rate r to purchase the commodity today and store it for the necessary duration (assuming no storag e costs). This price would be different from the expected price, yet offer no arbitrage opportunities. The arbitrage free approach to the problem of valuing financial options was first solved by Black and Scholes (1973) using a replicating portfolio technique. The replicating portfolio technique involves finding an asset or combination of assets with

PAGE 28

19 known values, with payoffs that exactly match the payoffs of the contingent claim. Then, using the LOP it can be argued that the continge nt claim must have the same value as the replicating portfolio. Financial options are contingent claims whose payoffs depend on some underlying basic financial asset. These instruments are very popular with hedgers or risk managers. The underlying argument to the equilibriu m asset pricing methods is the no arbitrage condition. The no arbitrage condition requires that the equi librium prices of assets should be consistent in a way that there is no possibility of riskless profit. A complete market offers no arbitrage opportuni ties as there exists a unique probability distribution under which the prices of all marketed assets are proportional to their expected values. This unique distribution is called a risk neutral pr obability distribution of the market. The expected rate of return on every risky asset is equal to the risk-free rate of return when expectations are calcula ted with respect to the market risk neutral distribution. Copeland et al. (2004) define a complete ma rket as one in which for every future state there is a combination of traded assets that is equivalent to a pure state contingent claim. A pure state contingent claim is a securi ty with a payoff of one unit if a particular state occurs, and nothing otherw ise. In other words, when th e number of unique linearly independent securities equals the total number of alternative future states of nature, the market is said to be complete. Equilibrium asset pricing theories have been developed with a set of simplifying assumptions regarding the market. In addition to completeness and pure competition, CC analysis theory assumes that the market is perfect i.e., it is characterized by

PAGE 29

20 1.An absence of transa ction costs & taxes 2.Infinite divisibility of assets. 3.A common borrowing and lending rate. 4.No restrictions on short sales or the use of its proceeds. 5.Continuous trading. 6.Costless access to full information. Review of Literature on Uncertainty and Timber Stand Management The published literature on treatment of uncer tainty in timber stand management is reviewed here from an evolutionary perspec tive. A selected few papers are reviewed as examples of a category of research. The literature dealing with sta tic analysis of financial ma turity of timber stands is vast and diverse. Including the seminal anal ysis of Faustmann (1849) several approaches to the problem have been developed. The early work on static analysis has been summarized by Gaffney (1960) and Bentley a nd Teeguarden (1965). These approaches range from the zero interest rate models to pr esent net worth models and internal rate of return models. The Soil Rent/Land Expecta tion Value (LEV) model, also known as the Faustmann-Ohlin-Pressler model, is now accepted as the correct static financial maturity approach. However, the static models are bui lt on a number of critical assumptions which erode the practical value of the analysis. Fail ure to deal with the random nature of stand values is a prominent shortcoming. Uncertain fu ture values mean that the date of optimal harvest cannot be determined in advance but must be price responsive i.e., it must depend on the movement of prices and stand yield am ongst other things. The harvest decision is local to the time of decision and it is now recognized that a dynamic approach to address the stochastic nature of timb er values is appropriate. Amongst the first to treat stochasticity in stand management, Norstom (1975) uses DP to determine the optimal harvest with a stochastic timber market price. The stochastic

PAGE 30

21 variable was modeled using tr ansition matrices as in Ga ssmann (1988), who dealt with harvesting in the presence of fire risk. The us e of transition matrices has persisted with Teeter et al. (1993) in the determination of the economic strategies for stand density management with stochastic prices. However, much advance followed in mode ling stochasticity with the introduction of the use of diffusion processes in investment theory. Brock et al. (1982) illustrated the optimal stopping problem in stochastic fi nance using the example of a harvesting problem over a single rotation of a tree with a value that grows according to a diffusion process. Miller and Voltair e (1980, 1983) followed up, extending the analysis to the multiple rotation problems. Clarke and Reed (1989) obtained an analytical solution using the Myopic Look Ahead (MLA) approach, allo wing for simultaneous stochasticity in timber price and yield. These papers illu strate the use of stochastic dynamic programming for stylized problems which ar e removed from the pr actical problems in forestry e.g., they ignore the costs in forestry. Modeling the empirical forestry problem, Yin and Newman (1995) modified Clarke and Reed (1989) to incorporate annual administrative and land rental costs as exogenous parameters. However, while acknowledging opti on costs, they chose to ignore them for simplicity. Also, as noted by Gaffney (1960) th e solution to the optimal harvest problem is elusive because the land use has no predetermined cost and the solution calls for simultaneous determination of site rent and financial maturity. Since land in forestry investment is typically owned, not leased or rented, accounting for the unknown market land rental has been one objective of financial maturity analysis since Faustmann (1849).

PAGE 31

22 In the meanwhile, the use of search models to develop a reservation price approach gained popularity with papers by Brazee and Mendelsohn (1988) and others. The technique of the search models is not unlike the DP approach to contingent claims. The approach differs from the CC approach in solution methodology and in the interpretation of the results. Fina et al. ( 2001) presents an extension of the reservation price approach using search models to consider de bt repayment amongst other things. Following the landmark Black and Scholes (1973) paper the development of methodology for the valuation of contingent claims has progresse d rapidly. A useful simplification in the form of the discrete time binomial lattice to approximate the stochastic process was presented by Cox et al. (1979). Other tec hniques for obtaining numerical approximations have been developed including the trinomial approximation, the finite difference methods, Monte Carlo si mulations and numerical integration. Geske and Shastri (1985) provide a review of th e approximation techniques developed for valuation of options. An important simultaneous line of research has been the study of the nature of stochasticity in timber prices. Washburn a nd Binkley (1990a) tested for weak form efficiency in southern pine stumpage ma rkets and reported that annual and quarterly average prices display efficiency, but also poi nt out that monthly averages display serial correlation. Yin and Newman (1996) found evid ence of stationarity in monthly and quarterly southern pine time series price data Since reported prices for timber are in the form of period averages, researchers have to contend with unrav eling the effect of averaging on the statistical properties of the price series. Working (1960) demonstrated the introduction of serial correla tion in averaged price series, not present in the original

PAGE 32

23 series. However, Haight and Holmes (1991) demonstrated that serially correlated averaged price series tends to behave as a random walk. The lack of conclusive data on the presence or absence of sta tionarity in timber price data is because of the imperfections of the data available for analysis. Desp ite the lack of unanimity on the empirical evidence there is some theoretical su pport for the mean reversion (negative autoregression) arising from the knowledge that commodity prices could not exhibit arbitrarily large deviations from long term marginal cost of production without feeling the effects of the forces of demand and supply (Schwartz 1997). The use of contingent claim analysis is a relatively recent development in stand management literature. Morck et al. (1989) use real options analysis to solve for the problem of operating a fixed term lease on a st anding forest with the option to control the cut rate. Zinkhan (1991, 1992) and Thomson ( 1992b) used option analysis to study the optimal switching to alternate land use (agriculture). Thom son (1992a) used the binomial approximation method to price the option value of a timber stand with multiple rotations for a GBM price process. The paper demonstrates a comprehensive treatment of the harvest problem, incorporating the option value of abandonment and switching to an alternate land use. Plantinga (1997) illustrated the valuation of a contingent claim on a timber stand for the mean-reverting and drif tless random walk price processes, using a DP approach attributed to Fisher and Ha nemann (1986). Yoshimoto and Shoji (1998) use the binomial tree approach to model a GBM process for timber prices in Japan and solve for the optimal rotation ages. Insley (2002) advocated the mean-re verting process for price stochasticity. The paper incorporates amenity values and uses harvesting costs as an

PAGE 33

24 exercise price to model the harvesting problem over a single rotation as an American call option. In order to obtain a numerical solu tion, the paper uses a discretization of the linear complementarity formulation with an implicit finite difference method. All these studies use a stochastic DP approach with an arbitrary discount rate. Hughes (2000) used the Black-Scholes call option valuation equa tion to value the forest assets sold by the New Zealand Fo restry Corporation in 1996. The option value estimated by him was closer to the actual sa le value than the alternate discounted cash flow analysis. It is a unique case of a study ap plying real options analysis to value a real forestry transaction. Insley and Rollins (2005) solve for the la nd value of a public forest with mean reverting stochastic timber pr ices and managerial flexibility. They use a DP approach to show that by including managerial flexib ility, the option value of land exceeds the Faustmann value (at mean prices) by a fact or of 6.5 for a 3% discount rate. The land value is solved endogenously for an infinite rotation framework. In a break from analysis devoted to th e problems of a single product timber stand Forboseh et al. (1996) study the optimal cl ear cut harvest problem for a multiproduct (pulpwood and sawtimber) stand w ith joint normally distribut ed correlated timber prices. The study extends the reservation price a pproach of Brazee and Mendelsohn (1988) to multiple products and looks at the effect of various levels of prices and correlation on the expected land value and the pr obability of harvest at differe nt rotation ages. A discrete time DP algorithm is used to obtain the solutions. In a similar study, Gong and Yin (2004) st udy the effect of incorporating multiple autocorrelated timber products into the optim al harvest problem. The paper models the

PAGE 34

25 timber prices (pulpwood and sawtimber) as disc rete first order autoregressive processes. Dynamic programming is used to solve for reservation prices. Teeter and Caulfied (1991) use dyna mic programming to demonstrate the determination of optimal density management with stochastic prices using a first order autoregressive price process modeled using a transition probability matrix. The study uses a fixed rotation age and allows multiple thinnings. Brazee and Bulte (2000) analyze an optimal even-aged stand management strategy with the option to thin (fixed intensity) with stochastic timber prices. Using a random draw mechanism for the price process and a backward recursive DP algorithm for locati ng the reservation pri ces, the study finds the existence of an optimal reservation pri ce policy for the thinning option. Lu and Gong (2003) use an optimal stocking level function to determine the optimal thinning as well as a reservation price function to determine th e optimal harvest strategy for a multiproduct stand with stochastic product prices without autocorrelations.

PAGE 35

26 CHAPTER 3 THE CONTINGENT CLAIMS MOD EL AND ESTIMATION METHODOLOGY The One-Period Model In order to develop the application of opti ons analysis to investment problems it is helpful to first examine the nature of one-p eriod optimization models. One-period models for investment decision making operate by comp aring the value of the investment in the beginning of period with its value at the end of the period. The model is first explained in the context of the deterministic Faustmann pr oblem. This is followed by an extension of the logic to the stochastic problem. The Deterministic Case The problem of finding the optimal financ ial stand rotation age is an optimal stopping problem. In the deterministic Faustmann framework, the optimal rotation age is achieved by holding the stand as long as th e (optimal) investment in the stand is compensated by the market at the required rate of return. The value of the immature stand is the value of all net investments in the st and up to the present in cluding the land rental costs and the cost of capital. This means that the value of all investments in the stand (adjusted for positive intermediate cash flows like revenue from thinnings) up to the present compounded at the required rate of retu rn represents the stand value. This value represents fair compensation to the stand owne r for his investment and fair cost to the purchaser who would incur an identical amount in a deterministic world. Therefore, this value represents the fair market value of th e pre-mature stand. The market value of the merchantable timber in the stand, if any, is less than the stand market value in this period.

PAGE 36

27 The stand owner continues to earn the re quired return on his (optimal) investments only till the rotation age is reached when th e value of the merchantable timber in the stand exactly equals the compounded value of investments. Beyond this rotation age the market will only pay for the value of the merchantable timber in the stand. If the stand is held longer than this rotation age, even if no fresh investments other than land rent are made, the market compensation falls short of the compounded value of investments as the value of merchantable timber grows at a lowe r rate. The optimal ro tation age represents the unique point of financial maturity of the st and. Before this age the stand is financially immature and after this age the stand is fi nancially over mature. A typical evolution of the two values is depicted in Figure 3-1. 0 500 1000 1500 2000 2500 3000 3500 4000 4500Yea r s 3 7 11 15 19 23 27 31 35 39 43 47Rotation age (Years)Stand Value ($/Acre) Value of Merchantable Timber Present Value of net investments Figure 3-1. Typical evolution of even-aged stand and stumpage values for the Faustmann analysis

PAGE 37

28 Equivalently, a more familiar way of frami ng this optimization problem is to let the stand owner compare the value of harvesting the stand in the present period to the net (of cost of waiting) discounted values of harvests at all possible future rotation ages. The cost of waiting includes land rent a nd all other intermediate cash flows. More specifically, the comparison is between the value of a harves t decision today and th e net discounted value of the stand in the next period assuming that similar optimal decisions are taken in the future. In this case the stand value represents the discounted value of a future optimal harvest which exactly equals the earlier de fined stand market value consisting of net investment value. Thus, the proble m is cast as a one-period problem. The one-period deterministic Faustmann op timization problem in discrete time can be summarized mathematically by Equation 3-1. () ()max(),() 1 Ft Fttt (3-1) Here, () F= Stand Value function t = Rotation age = Stand termination value or the market va lue of the merchantable timber in the stand = Rate of cash flow (land re ntal expenses, thinnings etc) = Constant discount rate = A discrete interval of time For the period that the decision to hold the stand dominates, the second expression in the bracket is relevant and we ha ve for the holding period Equation 3-2. () ()() 1 Ftt Fttt t (3-2) It may be noted that the only decision requi red of the decision maker is whether to hold the stand or to harvest it. In the standard deterministic case, any intervention

PAGE 38

29 requiring new investments like thinnings is assumed optimally predetermined and the resulting cash flows are only a function of rotation age. This holding expression can be simplified to yield Equation 3-3 for the continuous time 1 ()()() FttdFt dt (3-3) Here, the limit of 0 has been taken. Equation 3-3 clearly expresses the holding condition in perfect competition as one in which the yield (Right Hand Side (RHS)) in the form of the dividend and the capital appr eciation/depreciation or change in market value over the next infinitesimal period equals the required rate of return on the current market value of the asset (Left Hand Side (LHS)). The optimal stopping conditions are ()() FTT (3-4) ()()ttFTT (3-5) In Equation 3-5 the subscript t denotes the derivative of the respective function with respect to the time variable. The first c ondition is simply that at the optimal rotation age T the market value should equal the terminat ion value and the second condition is the tangency or the smooth pasting condition (D ixit and Pindyck 1994) requiring that the slopes of the two functions should be equal. The Stochastic Case In the stochastic value framework, the problem of optimal rotation is equivalent to holding the asset as long as it is expected to earn the required return. With stochastic parameter values, not only are future asset va lues dependent on the realizations of the parameters but the ability to actively ma nage the asset by responding to revealed parameter values induces an option value. Dixit and Pindyck (1994) derive the holding

PAGE 39

30 condition for the stochastic framework using the Bellman equation, which expresses the value as 1'(,)max(,,)(1)(,)|,uFxtxutFxtxu (3-6) Here, () F = Stand value function x = The (vector of) stochastic variable(s). For this analysis it represents the timber price(s) t = Rotation age u = The control or decision variable (opti on to invest) = The rate of cash flow = The discount rate E = Expectation operator = A discrete interval of time This relation means that the present value(,) Fxt from holding the asset is formed as a result of the optimal decisionu taken at the present, which determines the cash flow in the next period and the expected discounted valu e resulting from taking optimal decisions thereon. Distinct from the deterministic case, in this case, the value (and possibly cash flows) depends on the stochastic timber price. Also, the decision can be expanded to include the decisi ons to make new investments in the stand (like thinning) which effects the immediate cash flows as well as expectations of future market values. Similar to the deterministic case, the holding condition can be re-expressed as 1 (,)max(,,)(,)uFxtxutdFxt dt (3-7) To quote Dixit and Pindyck (1994): The equality becomes a no arbitrage or equilibrium condition, expressing the investor’s willingness to hold the asse t. The maximization with respect toumeans the current operation of the asset is be ing managed optimally, bearing in mind not only the immediate payout but also the consequences for future values. (Dixit and Pindyck 1994, p.105)

PAGE 40

31 Form of the Solution for th e Stochastic Value Problem In general the solution to the problem ha s the form of ranges of values of the stochastic variable(s) x Continuation is optimal for a ra nge(s) of values and termination for other(s). But as elaborated by Dix it and Pindyck (1994), economic problems in general have a structured soluti on where there is a single cutoff x with termination optimal on one side and continuation on the ot her. The threshold its elf is a continuous function of time, referred to as the crossover line The continuation optimal side is referred to as the continuation region and the termination optimal side as the termination region As pointed out by Plantinga (1998) the values of the crossover stumpage price line for timber harvesting problems are equivalent to the concept of reservation prices popular in forestry literature. Consequently, the optimal stopping conditi ons for the stochastic case for all t are (Dixit and Pindyck 1994) **((),)((),) Fxttxtt (3-8) **((),)((),)xxFxttxtt (3-9) In Equation 3-9 the subscript x denotes the derivative of the respective function with respect to the variable x The Contingent Claims Model In this section the general theory of CC valuation is developed in the context of the harvest problem. The CC valuation approach is also built on a one-period optimization approach and the discussion of the last sec tion should help to put the following discussion into perspective.

PAGE 41

32 The simplest harvest problem facing the decision maker is as follows: Should the stand be harvested immediately, accepting th e present market value of the timber or should the harvest decision be postponed in e xpectation of a better outcome? That is, the possibility for all optimal in terventions other than harv est is ignored. In a dynamic programming formulation of the problem, us ing the Bellman equation, the problem can be expressed mathematically as follows (Dixit and Pindyck 1994) 1 (,)max(,),(,)(,1)| 1 FxtxtxtFxtx (3-10) Here (,) Fxt is the expected net present value of all current and future cash flows associated with the investment at time t when the decision maker makes all decisions optimally from this point onwards. The stocha stic state variable, timber price in the present problem, is represented by x The immediate cash flow from a decision to hold the investment is denoted by(,) x t The result of optimal deci sions taken in the next period and thereafter will yield value (,1) Fxt which is a random variable today. The expected value of (,1) Fxtis discounted to the pres ent at the discount rate Finally, (,) x t represents the present value of termin ation or the value realized when the investment is fully disposed off today. While we know the present termination valu e, we are interested in learning the value of waiting or the conti nuation value. If the decision to wait is optimally taken then the continuation value is given by 1 (,)(,)(,1)| 1 FxtxtFxtx (3-11) If the increments of time are represented by and 0 the continuation value expressed in continuous time after algebraic manipulation will be

PAGE 42

33 1 (,)(,) FxtxtdF dt (3-12) If it is assumed that the state variable x (timber price) follows a general diffusion process of the form (,)(,) dxxtdtxtdz (3-13) then, using Ito’s Lemma, after algebraic ma nipulation and simplification we obtain the partial differential equation (PDE) 21 0 2xxxtFFFF (3-14) Here,(,) x t (,) x t and (,) x t In typical economic problems the continuation equation will hold for the value of the asset for all x x where x is a critical value of the state variable x with the property that continuation is optimal when the state variable value is on one side of it and stopping or termination is optimal when the state variable value is on its other side This yields the boundary conditions for all t given by Equations 3-8 and 3-9, which the valu e of the asset must m eet at the critical value of the state variable The DP formulation of the problem assu mes that the appropriate discount rate is known or can be determined by some means. An equivalent formulation of the problem can be found using CC valuation. In this fo rm the PDE for the continuation region value is given by 21 ()0 2xxxtFrFFrF (3-15) Here r represents the risk-fr ee rate of return and represents the rate of return shortfall which could be a dividend and/or convenience yi eld. Dixit and Pindyck (1994)

PAGE 43

34 illustrate the derivation of the contingent claim PDE by using the replicating portfolio method. In an alternate general derivation the procedure is to first show that under certain assumption all traded derivative assets must satisfy the no-arbitrage equilibrium relationii ir Here is the expected return on the derivative security, i represents the component of its volatility attributable to an un derlying stochastic variable i and i represents the market price of risk fo r the underlying stochastic variable. Where there is only one underlyi ng stochastic variable the relation simplifies tor Constantinides (1978) derived the cond ition for changing the asset valuation problem in the presence of market risk to one where the market price of risk was zero. The derivation, presented below, proceeds fr om Merton’s (1973) proof of equilibrium security returns satisfying the CAPM relationship pm p mr (3-16) where ()m mr is the market price of risk, the subscript p refers to the project (asset, option etc) and subscript mrefers to the market portfolio which forms the single underlying stochastic variable. Merton (1973) assumed that 1. The markets are perfect with no transaction costs, no ta xes, infinitely divisible securities and continuous trad ing of securities. Investor s can borrow and lend at the same interest rate and short sale of secu rities with full use of proceeds is allowed. 2. The prices of securities are lognormally di stributed. For each security, the expected rate of return per unit time i and variance of return over unit time 2i exist and are finite with 20i The opportunity set is non-st ochastic in the sense that i ,2i and the covariance of returns per unit time ij and the riskless borrowing-lending rate r, are all non-stochastic functions of time.

PAGE 44

35 3. Each investor maximizes his strictly con cave and time-additive utility function of consumption over his lifespan. Investors have homogenous exp ectations regarding the opportunity set. Let (,)Fxt denote the market value of a project. The market value is completely specified by the state variable x and timet, and represents the time and risk-adjusted value of the stream of cash flows generated fr om the project. Let the change in the state variable x be given by dxudtdz (3-17) The drift u and variance 2 may have the general form (,)uuxt and 22(,) x t .Let dt denote the cash flow generated by the project in time interval (,)ttdt with(,) x t Then, the return on the project in the time interval (,)ttdt is the sum of the capital appreciation (,)dFxt and the cash returndt Assuming that the function (,)Fxtis twice differentiable w.r.t. x and atleast once differentiable w.r.t.t, Ito’s Lemma can be used to expand (,)dFxt as 2(,) 2txxxxdFxtFuFFdtFdz (3-18) The rate of return on the project is 2(,)1 (,)2x txxxdFxtdtF FuFFdtdz FxtFF (3-19) with expected value per unit time p and covariance with the market per unit time pm given by 21 2ptxxxFuFF F (3-20)

PAGE 45

36 x pmmF F since pmpm x mp mF F where (,) x t is the instantaneous correlation coefficient between dz and the return on the market portfolio. By substitution in the Equation 3-16 we obtain the PDE 21 ()0 2xxxtFuFFrF (3-21) First, it may be noted that is the correlation coefficient between dzand the return on the market portfolio. Since dzis the only source of stochast icity in the project and the underlying, is also equal to the correlation coefficient between return on the underlying and the return on the market portfolio. Second, when compared with the DP formulation using the discount rate it can be seen that the CC analysis modifies the total expected rate of return by a factor of which allows the use of the risk-free rate of returnr. In this manner the CC analysis converts the problem of valuing a risky asset to one of valuing its certainty equivalent. It does away with the need to determine the discount rate but does require an additional assumption regarding the completeness of the market or in other words only the marketed risk of the asset can be valued. Further, as shown in Hull and White (1988), if the state variable is a traded security and pays a continuous proportional dividend at rate then in equilibrium, the total return provided by the security in exce ss of the risk-free ra te must still be so that; r (3-22) or

PAGE 46

37 r (3-23) Substituting in Equation 3-21 we obtain the PDE derived by Dixit and Pindyck (1994) using the replic ating portfolio i.e., 21 ()0 2xxxtFrFFrF (3-24) Hull (2003) differentiates betw een the investment and the consumption asset. An investment asset is one that is bought or sold purely for the purpose of investment by a significant number of investor s. Conversely, a consumption asset is held primarily for consumption. Commodities like timber are c onsumption assets and can earn a below equilibrium rate of return. Lund and Oksendal (1991) discuss that generally investors will not like to hold an asset that earns a belowequilibrium rate of return. But empirically commodities that earn a below equilibrium rate of return are stored in some quantities. To quote Lund and Oksendal (1991): In order to explain storage of commodities whose prices are below-equilibrium, it is assumed that the storers have an advant age from the storage itself. This is known as gross convenience yield of the commod ity. The net convenience yield (or simply the convenience yield) is defined as th e difference between the marginal gross convenience yield and the marginal cost of storage. (Lund and Oksendal 1991, p.8) If we assume a continuous proportional convenience yield then the assumption is completely analogous to an assumption of a continuous proportio nal dividend yield. Therefore, the can represent the continuous prop ortional convenience yield from holding the timber and the PDE will hold.

PAGE 47

38 The Lattice Estimation Models The Binomial Lattice Model In order to determine the holding value of the asset i.e., the value in the continuation region, it is necessary to solve the PDE. As it is not always possible to obtain an analytical solution, several numerical procedures have been devised. Amongst the popular methods for obtai ning a numerical solution are the lattice or tree approximations (that work by approximating the stochastic process) and the finite difference methods, explicit and implicit (that work by discretizing the partial differential equation). Monte Carlo simu lations and numerical inte gration are other popular techniques. This study uses the lattice approximation ap proach for its simplicity and intuitive appeal. Depending on the nature of the problem the binomial or higher dimension lattice models were used. The binomial approximati on approach is suitable for valuation of options on a single underlying st ochastic state variable and was first presented by Cox et al. (1979). For an underlying asset that follows a GBM process of the form dx dtdz x (3-25) where the drift and the variance 2 are assumed constant, the binomial approach works by translating the continuous time GB M process to a discrete time binomial process. The price of a non-divi dend paying underlying asset denoted by P is modeled to follow a multiplicative binomial generating process. The current asset price is allowed to either move up over the next period of length by a multiplicative factor u to uP with subjective probability p or fall by the multiplicative factor dto dPwith probability

PAGE 48

39 (1) p To prevent arbitrage the relation 1 urd must hold where rrepresents the risk-free interest rate. The asset price follows the same process in every period thereafter. Following Ross (2002) it can be shown that the binomial model approximates the lognormal GBM process as becomes smaller. Let iYequal 1 if the price goes up at time i and 0 otherwise. Then, in the first nincrements the number of times the price goes up is 1n i iY and the asset price would be 1 0 n Y i i n nu PPd d Letting t n gives 10t i iY t tP u d Pd Taking logarithms we obtain 1 0lnlnlnt t i iP tu dY Pd (3-26) The iY are independent, identically distribu ted (iid) Bernoulli random variables with mean p and variance(1) p p Then, by the central limit theorem, the summation 1 t i iY which has a Binomial di stribution, approximates a normal distribution with mean t p and variance (1)t p p as becomes smaller (and t grows larger). Therefore, the distribution of 0lntP P converges to the normal distribution as t grows.

PAGE 49

40 Following the moment matching procedure Luenberger (1998) shows that the derived expressions for the parametersu,d and p are 211 2 22 p (3-27) ue (3-28) de (3-29) The DP procedure for analysis of an option on an underlying asset that follows GBM process would proceed by using a binomial lattice parameterized by these expressions. The DP procedure would obtain the option value by r ecursively discounting the next period values using th e subjective probability value p and an externally determined discount rate. In contrast the contingent analysis pro cedure is illustrated using the replicating portfolio argument as follows. In addition to the usual assumptions of frictionless and competitive markets without arbitrage opportunitie s, as noted earlier, it is assumed that the price of a non-divide nd paying asset denoted by P follows a multiplicative binomial generating process. The asset price is allowe d to either move up in the next period by a multiplicative factor u or fall by the multiplicative factor d.If there exists an option on the asset with an exercise price of X then the present value of the option denoted by c would depend on the contingent payo ffs in the next period denoted by 00,ucMAXuPX and 00,dcMAXdPX where 0P denotes the current price of the asset.

PAGE 50

41 In order to price the option a portfolio consisting of one unit of the asset and munits of the option written against the asset is constructed such that the end of the period payoff on the portfolio are equal i.e., 00uduPmcdPmc (3-30) Solving for m we get 0()udPud m cc (3-31) If the end of the period payoff is equal th e portfolio will be risk free and if we multiply the present value of the portfolio by1r we should obtain the end of period payoff 00(1)()urPmcuPmc (3-32) or 0(1) (1)uPrumc c mr (3-33) Substituting Equation 3-31 for m in Equation 3-33 yields (1)(1) (1)udrdur cccr udud (3-34) Letting (1)rd q ud (3-35) where qis known as the risk-neutral probability, we can express the present value of the option as (1)(1)udcqcqcr (3-36)

PAGE 51

42 From Equations 3-28 and 3-29 we have ue and de To find the value of the risk-neutral probability q these values of u and dcan be substituted in Equation 3-35 to obtain 2(1)11 2 22r re q ee (3-37) Compared with the expression for the subjectiv e probability p in Equation 3-27, it can be seen that under the risk-neutral valuation the drift of the GBM process is replaced by the risk-free rater. In general, if the asset pays out a continuous proportional dividend then, under CC analysis the drift is modified tor (Equation 3-24). The corresponding risk neutral probability is 21 2 22 r q (3-38) For the treatment of previsible non-stochast ic intermediate cash flows (costs) with a fixed value ( ) the Equation 3-36 is modified to (1)(1)udcqcqcr (3-39) It is implicit that represents the discounted net present value of all such cash flows in the period. The CC procedure for a single period outlin ed above is easily extended to multiple periods and the option value is derived by recursively solving through the lattice. The Trinomial Lattice Model for a Mean Reverting Process For an asset that follows a MR process of the form

PAGE 52

43 _dxxxdtdz (3-40) the contingent claims PDE is given by 21 ()0 2xxxtFrxFFrF (3-41) where _()() x xx x is a function of the underlying asset x Hull (2003) describes a general two-stage pr ocedure for building a trinomial lattice to represent a MR pro cess for valuation of an option on a single underlying state variable. For trinomial lattice the state variable can move up by a multipleu, down by a multiple dor remain unchanged represented bym. Since MR processes tend to move back to a mean when disturbed, the trinomial latti ce has three kinds of branching. Depending on the current value of the state variable the next period movements can follow one of the three branching patterns ( ,,,,,,,, mddumduum) with associated probabilities. The parameters of the lattice are determined by matching the moments of the trinomial and MR processes. The procedure can be adapted for most forms of the MR process. Details of the procedure can be found in Hull (2003). The Multinomial Lattice Model for Two Unde rlying Correlated Stochastic Assets When the problem is to find the value of an option on two underlying assets with values that follow the GBM processes iiiiiidxxdtxdz 1,2i (3-42) which are correlated with instantaneous correlation coefficient given by ( i.e., they have a joint lognormal distribution) th e contingent claim PDE has the form

PAGE 53

44 111222 1 22222 111212221 1 2 21 2 2 0xxxxxx x xtxFxxFxFrxF rxFFrF (3-43) A multinomial lattice approach is used to value such options, also called rainbow options. The development of the multinomial pr ocess for the correlated assets is similar to that described for the binomial lattice with a single underlying asset. The parameters of the multinomial lattice are derived by matc hing the moments of the underlying asset value processes. Hull (2003) discusses alternate lattice parameterization methods developed for the multinomial lattice valu ation approach. This study uses the method discussed in Hull and White (1988). At each node on the lattice the assets can move jointly to four states in the next period. The resulting parameter values for a three dimensional lattice are summarized in Table 3-1. Table 3-1. Parameter values for a three dimensional lattice _______________________________________________ Period 1 state Risk neutral probability _______________________________________________ 1,2uu 0.25(1) 12, ud 0.25(1) 12, du 0.25(1) 12, dd 0.25(1) ________________________________________________ Here 22i i ir iue (3-44) 22i i ir ide (3-45) represent, respectively, the constant up and down movement multiplicands for asseti. Parameter i represents the volatility and i represents the dividend /convenience yield of asset i while rrepresents the risk-free rate and the size of the discrete time step

PAGE 54

45 CHAPTER 4 APPLICATION OF THE CONTINGENT CLAIMS MODEL Who is the Pulpwood Farmer? Before applying the CC model to the pulpwood farmer’s dilemma, it is necessary to establish a mathematical description of a pulpwood farmer. For a commercial timber production enterprise, the choice of timber pr oduct(s) to be produced (or rotation length chosen) is guided by the prevailing and expected future timber market prices amongst other things. The following discus sion describes the role of relative timber product prices in this decision. A slash pine stand will produce multiple ti mber products over its life. For products that are principally differentia ted by log diameter, the early part of the rotation produces the lowest diameter products like pulpwood. As the rotation progresses the trees gain in diameter resulting in production of higher diameter products like sawtimber. Since individual tree growth rates vary there is no en bloc transition of the stand from the lower to a higher diameter product, but rather, for most part of the merchantable timber yielding rotation ages the stand would contain a mix of products with the mix changing in favor of the higher diameter products w ith increasing rotation age. The average pine stumpage price data seri es reported by Timber Mart South (TMS) for different timber products reveal that on an average the large diam eter products garner prices that are significantly higher than lower diameter pr oduct prices (Table 4-1). This implies that the value of merchantable timber in the stand increases sharply with rotation age from the combined effects of larger merc hantable yields and increasing proportion of

PAGE 55

46 higher diameter timber. More important, it al so implies that short rotation farming may be difficult to justify using the TMS reported prices. Table 4-1. Florida statewide nominal pine stumpage average product price difference and average relative prices (1980-2005) _______________________________________________________________________ Timber Products Average absolute Average relative price difference prices ($/Ton) ______________________________________________________________________ Sawtimber vs. CNS 7.09 1.35 CNS vs. Pulpwood 9.79 1.99 _______________________________________________________________________ Source: Timber Mart-South In general, the cultivation of early rotati on products is differentiable from that of the late rotation produc ts by the silvicultural choices. Hi gh density planting and absence of pre-commercial thinnings are some choices that could characteri ze the cultivation of pulpwood. For slash pine, the decision to plan t dense and not resort to pre-commercial thinnings limits the stand owner’s choices wi th respect to switching to higher diameter product farming by prolonging the rotation. For a general slash pine stand with two products (pulpwood and sawtimber) the results of price differentiation on the optimal Faustmann rotation age are shown in Table 4-2. The illustration us es a year 0 establishment cost of $120/acre, no intermediate cash flows, a 5% constant annual discount rate, a cutover site index of 60 and 600 surviving trees per acre (tpa) at age 2 with the Pienaar and Rheney (1995) slash pine growth and yield equations. Pulpwood was defined as merc hantable timber from trees with minimum diameter at breast height (dbh) of 4 inches up to a diameter 2 inches outside bark and sawtimber as trees with minimum dbh 8 inches to 6 inches outside bark. The undifferentiated single timber pr oduct price was assumed $10/ton.

PAGE 56

47 Table 4-2. The effect of timber product pr ice differentiation on optimal Faustmann rotation ___________________________________________________________________ Price difference Optimal rotation age Absolute Relative $/Ton Years ___________________________________________________________________ 0 1.0 21 5 1.5 23 10 2.0 25 20 3.0 27 30 4.0 28 ___________________________________________________________________ Similarly, Table 4-3 shows that it is the relative product prices (for the purpose of this study, relative product price was define d as the price of the late rotation product expressed as a proportion of th e price of the early rotation pr oduct) that are important to the determination of the optimal rotation changes. Table 4-3 maintains the absolute increments while changing the size of the re lative increments. For this illustration the initial common timber product market price was assumed to be $20/ton. Table 4-3. The effect of timber product rela tive prices on optimal Faustmann rotation _______________________________________________________________ Price difference Optimal rotation age Absolute Relative $/Ton Years _______________________________________________________________ 0 1.0 20 5 1.25 21 10 1.50 23 20 2.00 24 30 2.50 26 _______________________________________________________________ Economic theory has it that relative pric ing of goods is an important market signal which allows the efficient allocation of res ources. In the context of the timber stumpage markets, relative product pricing serves as a signal to the timber producers to produce (more/less of) one or the other timber product. In order to induce producers to increase

PAGE 57

48 the production of late rotation pr oducts (which involve greater investment and/or risk) the market must offer a higher relative price. Since relative prices are not constant, an investment decision based on these prices must consider an average or mean of relativ e prices over an appropriate period of time. A timber land owner who bases his investment decision on the averag e relative prices deduced from the prices reported by TMS w ould never choose the lower rotation ages associated with pulpwood farming (19-25 year s for slash pine from Yin et al. 1998). Yet pulpwood farming is chosen by substantial numbers of timber land owners. Certainly, the average relative price of produc ts could not be the only re ason for choosing the pulpwood rotation. The practice of pulpw ood farming with slash pine c ould be the result of several considerations. Short rotations are attractive in themselves for the early realization of timber sale revenues (capital constraint cons ideration). Other considerations like earning regular income from the sale of pine stra w in denser stands with no thinnings also influence the choice. However, the altern ate considerations do not diminish the importance of relative product prices. The stum page prices applicable to a particular stand can be vastly different from the average prices reported by TMS. Some stands can experience greater relative pric es at the same point in tim e than others. This varying relative prices experienced by stands can be easily explained by th e nature of timber markets. Once the maximum FOB price that a timber purchaser can offer is determined for a period of time, the stumpage price appli cable to prospective suppliers is determined by the cost of harvesting and transporting th e timber to the location of the purchaser’s consumption/storage facility. From the average difference between TMS reported FOB and stumpage prices, it can be seen that these costs form a very high (as much as 2/3 for

PAGE 58

49 pulpwood) portion of the FOB price. At a point in time harvesting co sts may vary little from one stand location to another in a re gion but the transportation costs can vary significantly. For a pulpwood stand located clos e to a purchaser (pulp mill) the relative product prices would always be lower than thos e for other distant stands (say with respect to a sawtimber purchaser in the region), justifying the pulpwood farming decision. This argument implies that a significant number of th e stands located close to pulp mills would be choosing pulpwood farming and this should be empirically borne out. It also implies that once multiple products are considered there can be no single Faustmann rotation age that suits all even-aged single same specie sta nds even if their site quality was the same; rather, there would be a continuum of op timal rotation ages depending on the average relative stumpage prices applicable for the stand. For the present analysis it was assumed th at the slash pine pulpwood plantation was located close to a pulpwood purchaser (who was not expected to stop operations) resulting in experiencing low average (long ru n) relative prices. For sufficiently small average relative prices it may also justify treating the entire merchantable timber output, irrespective of diameter size, as pulpwood. Despite the location advantage, in the s horter run, a stand w ould still experience wide differences in relative product prices from fluctuating market conditions. In the present conditions where pulpw ood prices have been depressed for several years while other products have fared relatively better, th ere is a market signal in favor of higher diameter products to all sta nds irrespective of location. Therefore, the pulpwood stand under analysis would be experiencing higher than normal relative pr ices. This situation

PAGE 59

50 was analyzed as a multiproduct option problem though with modest relative prices as compared to TMS reported prices. The Return to Land in Timber Stand Investments This section deals with the calculation of return to timberland. Land serves as a store of value as well as a f actor of production. As a fact or of production used for the timber stand investment, land must earn a retu rn appropriate to the investment. For the pulpwood farmer’s harvest problem land rent is a cost that will be incurred if the option to wait is chosen. In the contingent claim anal ysis the land rent is modeled as a parameter observed by the decision maker and hence ha ving a known present value. If land is not owned but rented/leased the explic it portion of this return is in the form of rent charged by the renter/leaser. However, whether explicit or implicit, there is very little useful data available on either timber land values or l ease/rent values. Most decision makers do not have access to a reliable estimat e of even the present value of their timber land. This makes it necessary to determine the appropria te return to be charged to land for the purpose of the analysis. The following discussi on uses the term ‘timberland value’ to refer to the value of the bare land, unle ss it is specifically stated otherwise. In its report on large timberl and transactions in the US the TMS newsletter (2005) reports a weighted average tr ansaction price in 2005 for the southern US of $1160/acre. Smaller timberland transactions at $2000/acre or higher in Fl orida are routinely reported. A part of these valuations must arise from the value of the land itself while some of the balance could be for the standing trees (if any). Recent literatu re discusses other important sources of the valuation like high nontimber values in the form of leisure and recreation values etc. and expectations of future demand for alternative higher uses. Aronsson and Carlen (2000) st udies empirical forest land pr ice formation and notes that

PAGE 60

51 non-timber services, amongst other reasons, ma y explain the divergen ce of the valuation from present value of future timber sale incomes. Wear and Newm an (2004) discuss the high timber land values in the context of us ing empirical timberla nd prices to predict migration of forest land to alternate uses. Zhang et al. (2005) look at the phenomena of timber land fragmentation or ‘retailization’ through sales to purchasers looking for aesthetic/recreation values and its implications for forestry. Since this analysis assumes that timber sales is the only major source of value the appropriate timberland value is the value of bare land the present best use of which is timber farming and for which non-timber valu es are insignificant. Assuming that the market price of such timberland could be obs erved, the question is: Can this value be used for the purpose of analysis? Is informa tion on the traded price of bare timber land appropriate for analysis? Chang (1998) has proposed a modified vers ion of the Faustmann model suggesting that empirical land values could be used with the Faustmann op timality condition to determine optimal rotations. Chang (1998) di scusses a generalized Faustmann formula that allows for changing parameters (stumpag e price, stand growth function, regeneration costs and interest rate) from rotation to ro tation. The form of the optimal condition derived by him is 1() ()kk kkkkk kRT R TLEV t (4-1) Here, () R T is the net revenue from a clear-cut sa le of an even aged timber stand at the optimal rotation age T and is the required rate of return. The subscript k refers to the rotation. The condition is interpreted to m ean that instead of the constant LEV of the standard Faustmann condition, the discounted value of succeeding harvest net revenues

PAGE 61

52 (1 kLEV) must be substituted. Chang (1998) interpre ts this to mean that the market value of bare land existing at the time of taking th e harvest decision can replace the standard constant Faustmann LEV. But, if the observed la nd value is very high as compared to the LEV the RHS of the equation increases signifi cantly, resulting in a drastic lowering of the optimal rotation age T In the state of Florida, whic h is experiencing high rates of urbanization, it is not unusual to find timber land valued at several multiples of the LEV. Failure to account for non-market values like aes thetic or recreational values in the model alone may not explain the failure to observe the rotation shortening effect. Klemperer and Farkas (2001) discuss this effect of using empirical land values while using Chang’s (1998) version of the Faustmann model. By definition, the value of any asset is the discounted value of net surpluses that it is expected to provide over its economic lifetime in its best use. This suggests that the market value of land may be differentiable into two parts. One part of the market value is derived from the current best use and the other is the speculative or expected future best use (Castle and Hoch 1982). This means that th e present market valu e of timber land, if known, does not provide information on the valu e in current use without the separation of the speculative value component. The critical fact is that the land rent ch argeable to current best use cannot exceed the expected net surplus in current best us e. No investor would pay a land rent higher than the net surplus he exp ects to earn by putting it to use. Using empirical land values could result in overcharging rents as the la nd values may be inflated by the speculative value component.

PAGE 62

53 This gives rise to the question: What about the opportunity cost to the speculative component of land value? Does the landowner lo se on that account? The answer is that if a parcel of land is being held by the landow ner despite its current market value being higher than its valuation in cu rrent best use, an investment or speculation motive can be ascribed to the landowner. Th e landowner treats the land not only as a productive factor in the timber stand investment but also as a speculative asset. The landowner could earn a capital gain over and above the value of future rents in the current best use by selling the land in such a market. If the investor chooses to hold the land, it is because he expects to profit from doing so. And this profit is in the form of expected capital appreciation. It is this expected capital appreciation that co mpensates the landowner for the opportunity cost on the speculative component of land value A formal derivation of this argument follo ws from economic theory. According to the economic theory of capital, in a competitiv e equilibrium, an asset holder will require compensation for the opportunity cost on the curr ent market value of a capital asset plus the depreciation cost for allowing the use of his asset (Nicholson 2002). Representing the present market price of the capital asset byP, the required compensation v will be () vPd (4-2) where is the percent oppor tunity cost and dis the assumed proportional depreciation on the asset value. When the asset market value is not constant over time the required compensation will be a function of time()vt. The present value of the asset would equal the discounted value of future compen sation incomes. At the present time t the present discounted value (PDV) of the compensation received at time s ( ts ) would be

PAGE 63

54 ()() s tvse and the present discounted value of all future compensation incomes would be ()()()()stts ttPDVPtvsedsevseds (4-3) Differentiating ()Ptwith respect to t and ignoring depreciation we have () ()()()()tstt tdPt evsedsevtePtvt dt (4-4) Therefore, () ()() dPt vtPt dt (4-5) So, the required compensation income at any time is equal to the opportunity cost on the current market value of the asset less th e expected change in the market value of the asset. The interpretation is that the ‘fair’ or competitive compensation for leasing an asset consist of both the interest cost as well as the expected change in the value of the asset. If the expected change in the value is positive the rental charges are decreased to that extent since the value appreciation compensates the as set owner for a part of the interest cost. The net compensation () vt is the opportunity cost for the asset value in its current best use. It cannot be more th an this cost as prospective re nters cannot afford to pay more as already argued. It cannot be less because a lower charge would tran sfer a surplus to the renter attracting competition amongst renters. Therefore, to find the amount to be appr opriated as return to timberland it is required that its value in current (best) use be determined and then the return would be given by the opportunity cost of holding the land in its current (best) use.

PAGE 64

55 The static Faustmann framework determines the timber land value or Land Expectation Value (LEV) as the present va lue of net harvest re venues arising from infinite identical rotations in timber farming us e. In contrast, in the stochastic framework, the ability to actively manage the investme nt adds an option value which must be incorporated in the valuation method. As argued and shown by Plantinga (1998), Insley (2002, 2005), and Hughes (2000) a price responsi ve harvest strategy adds a significant option value to the investment. In this study the land value was determined within the CC analysis assuming that timber farming was the current best use. The parameters for the valuation are the current values of timber price and pl antation establishment cost as well as annual maintenance costs. In the risk neutral anal ysis the current risk-free rate se rves as the discount rate. The infinite identical rotations methodology was used to capture the tradeoff with future incomes meaning that the net expected surplu s value over the first rotation was used as the expected average value for future rota tions. This may not effect the land value significantly since, as observed by Bright and Price (2000), the present value of net surplus in the first rotation forms most of (>80%) the estimated timberland value when calculated in this way, for a sufficiently l ong rotation and high disc ount rate. Therefore, the land value in current use can be estimated with information available to the decision maker. And the land rent is the opportunity cost of this value. The mathematical formulation of the land value estimati on problem is given by Equation 4-6. 1 00 0|() max 1t rtri qti i rt tEPPQteaeC LV e (4-6) Here,

PAGE 65

56 L V= Present value of land q E = Risk neutral expectation operator tP = Stochastic timber price at t period from present time 0 ()Qt= Deterministic merchantable timber yield function (of rotation age t ) ta = Annual recurring plantation administrati on expenses treated as risk-free asset 0C = Value of plantation establishment expens es to be incurred today (at year 0) r = Present risk-free interest rate assumed constant in future Then, the present value of estimated land rent isrLV. There are some points to note about the above argume nts and methodology outlined for determining the land value in current best use. First, it is implied that the rent value is calculated afresh by the decision maker every period. This is empirically true for shorter duration uses like agri culture farming and there is no reason why it should not be so for timber farming if decision makers are e fficient information processors as normally assumed and information is easily and freel y accessible. If market information on comparable land rents was available, it would be stochastic and th e decision maker would utilize the new information availabl e every period for decision making. It is also important that a stochastic rent value calcul ated as argued above captures and transfers fresh information about the exp ected future to the decision making process. That is, if the estimated land/rent value is high, it will increase the cost of rotation extension and vice versa. For example, if the stand owner learns of a demonstrable technological advance improving the financial returns to stan d investments, in the midst of the rotation, the stand owne r will seek to apply the techno logy to the present rotation, thereby adopting the ‘best use’. However, if the improved technology cannot be applied to the current rotation then there should be pressure on the decision maker to shorten the present rotation so that the improved technology could be applied to the next rotation.

PAGE 66

57 There is no empirical evidence known to suppor t this result regarding timberland owner behavior but it can be argued that timberla nd owners never have free and easy access to the necessary information. It is also importa nt to note that market prices of timberland themselves provide no valuable input to the st and decision making proces s but rather it is the value in current best use that is relevant Thus, in periods of speculative inflation of land prices one may not expect to observe any appreciable change s in stand decision making behavior. It is the direction of change s in real input costs and output values which result in changes in land rent. Second, it is implied that the rent value is a function of the current timber price(s). However, it need not be perfectly correlated with timber prices(s) since other parameters of the valuation (the costs and discount ra tes) would be expected to follow (largely) independent stochastic processes. Third, the method outlined for estimation of land rent provides an estimate for a single period i.e., for the present period only. Ideally, the rent value should be modeled as a stochastic variable. But that would require information rega rding the stochastic process defining the plantation expenses (or non-timber sources of ca sh flow) and discount rate. In the absence of data on the stochastic process for the other flows, in the following analysis, land rent was assumed to behave like a risk-free asset. On the Convenience Yield and the Timber Stand Investment To solve the harvesting problem using the la ttice approach the c onstant volatility of the underlying variable is estimated from hist orical price data. Th e risk-free rate is estimated from yields on treasury bills of matching maturity. However, the estimation of the convenience yield poses a problem. The concept of convenience yield, as it is popularly interpreted, was first propos ed by Working (1948, 1949) in a study of

PAGE 67

58 commodity futures markets. The phenomena of “prices of deferred futures….below that of the near futures” (Working 1948, p.1) wa s labeled an inverse carrying charge. The carrying charge or storage cost is the cost of physically ho lding an asset over a period. The concept can be illustrated as follows: ignoring physical storage costs, the arbitrage free forward price F for future delivery of a commodity is determined by the relation rt oPe where 0P is the current unit price of the commodity, ris the borrowing/lending rate while t is the period of the contract. Therefore, the forward price should be proportional to the length of the contract. The inverse carrying ch arge or convenience yield discussed by Working (1948, 1949) is said to accrue to the contract writer when the no arbitrage relation does not hold for some contract lengths andrt oFPe Even though an opportunity for arbitrage exists, arbitrag eurs are unable to take advantage as nobody that is holding the commodity in inventory is willing to lend the commodity for shorting. Inventory holder may be unwilling to le nd the commodity when markets are tight (Luenberger, 1998) i.e., supply shortage is anticipated. Brennan (1991) defines convenience yield of a commodity as: ...the flow of services which accrue to th e owner of a physical inventory but not to the owner of a contract for future delive ry. ....the owner of the physical commodity is able to determine where it will be stored and when to liquidate the inventory. Recognizing the time lost and the cost s incurred in ordering and transporting a commodity from one location to another, the marginal convenience yield includes both the reduction in costs of acquiring i nventory and the value of being able to profit from temporary local shortages of the commodity through ownership of a larger inventory. The profit may arise from either local price variations or from the ability to maintain a production process despite local shortages of a raw material. (Brennan 1991, p.33-34) The convenience yield is not constant but would vary with the gross inventory of the commodity in question, amongst other things.

PAGE 68

59 If there exists a futures market for the co mmodity then the futures prices represent the risk neutral expected values of the commodity. The risk neutral drift() t which will be a function of time since the convenience yield () t and forward risk free rate () rt are empirically stochastic, can be calculated from the futures prices as (Hull 2003) ln() (1) ()ln () Ft Ft t tFt (4-7) Here, () Ft is the futures price at time t. In the absence of a futures market, theore tically it should be possible to estimate the convenience yield by comparing wi th equilibrium returns on an investment asset that spans the commodity’s risk (replicating portf olio).As discussed by McDonald and Siegel (1985), the difference between the equilibrium rate of return on a financial asset that shares the same covariance as the asset and expected rate of return on the asset will yield But, empirically, such an asset is diffi cult to locate or construct from existing traded assets. Similarly, we could estimate r from the equivalent Usually, the Capital Asset Pricing model (CAPM) for timbe r stands is estimated by regressing excess returns on the historical timber price agains t the excess returns on the market portfolio. Thus, this methodology suffers from the failure to incorporate the convenience yield in total returns on timber stands. Using the estimated by this method will only yield r i.e., a value of zero. To the best of this authors’ knowledge no method for estimating convenience yield for timber is available in published li terature. Therefore, this study proceeds by assuming that the convenience yield0 and r The results are tested for sensitivity to different levels of constant

PAGE 69

60 Dynamics of the Price Process Modeling the empirical price process is th e key to the development and results of the real options analysis. Beginning with Wa shburn and Binkley (1990a) there has been debate over whether the empiri cal stumpage price returns pr ocess is stationary (meanreverting) or non-stationary (random walk). Th e debate has remained inconclusive due to the conflicting evidence on the distorting eff ect of period averaging on prices. Working (1960) was the first to show that the first differences of a period averaged random chain would exhibit first orde r serial correlation of the magnit ude of 0.25 (approximated as the number of regularly spaced observations in the averaged period increased). Washburn and Binkley (1990a) found consis tent negative correlation at the first lag for several quarterly and annual averaged stumpage pri ce series though most were less than 0.25 and statistically significant only for prices in one case. On the other hand, Haight and Holmes ( 1991) have provided heuristic proof to the effect that a stationary first order autoregr essive process, when averaged over a period, would behave like a random walk as the size of the averaging period was increased. They used this proof to explain away the observed non-stationarity in the quarterly averaged stumpage prices. The stationarity of the price process has im plications for the efficiency of stumpage markets. “A market in which prices always “fully reflect” available information is called “efficient”” (Fama 1970, p.383). U tilizing the expected rate of return format, market efficiency is described as ~~ ,1,1 ,|1|jtjt ttjtPrP (4-8)

PAGE 70

61 Here, E is the expectation operator, ,jtP is the price of security j at time t ~ ,1 jtP its random price at time 1 t with intermediate cash flows reinvested, ~ ,1 jtr is the random one-period percent rate of return ~ ,1 , jt jt jtPP P, t represents the information set assumed to be fully reflected in the price at t The information set t is further characterized accordi ng to the form of efficiency implied i.e., weak form efficiency which is lim ited to the historical data set, semi-strong form efficiency which includes other publicly available information and strong form efficiency that also includes the privat ely available information. As Fama (1970) discusses, the hypothesis that asset prices at any point fully reflect all available information is extreme. It is more common to use historical data to test prices for weak form efficiency in support of th e random walk model of prices. Washburn and Binkley (1990a) tested for the weak form efficiency using the equilibrium model of expected returns with alternate form s of Sharpe’s (1963) singleindex market models. Ex-post returns to st umpage were regressed on a stock market index and an inflation index. The residuals from the regressions were then tested for serial correlation the presence of which woul d lead to rejection of the weak form efficiency hypothesis. Since these tests requ ired the assumption of a normal distribution for the residuals, this was tested using th e higher moments (skewness and kurtosis). The non-parametric turning points test was also conducted as an alternate test for serial dependence. They found evidence of stationa rity in returns generated from monthly averaged data but returns generated from quart erly and annually averaged data displayed

PAGE 71

62 non-stationarity. Sign ificantly, they did not find ev idence to support the normal distribution assumption of the residuals. Haight and Holmes (1991) used an Au gmented Dickey-Fuller test and found stationarity in instantaneous returns on monthly and quarterly spot stumpage prices and non-stationarity in instanta neous returns on quarterly averaged stumpage prices. Hultkrantz (1993) contended th at the stationarity found in returns generated from monthly averaged price series by Washburn and Binkley (1990a) could be consistent with market efficiency when producers were risk averse. He used a panel data approach to Dickey-Fuller tests and found that southern st umpage prices were stationary. Washburn and Binkley (1993) in reply ar gued that the results of Hultk rantz’s analysis were by and large similar to their analysis and point out th at if Haight and Holmes (1991) proof of the behavior of averaged prices is consider ed, then both (Hultk rantz 1993 and Washburn & Binkley 1990) their analyses could be biased away from rejection of the weak form market efficiency. Yin and Newman (1996) used the Augmented Dickey-Fuller and arrived at conclusions similar to Hultkrantz’s (1993). Gjolberg and Guttormsen (2002) applied the va riance ratio test to timber prices to check the null hypothesis of a random walk fo r the instantaneous returns. Their tests could not reject the random walk hypothesis in the shorter periods (1 month and 1 year) but over longer horizons, they f ound evidence of mean reversion. Prestemon (2003) found that most southern pi ne stumpage price series returns were non-stationary. He noted that te sts of time series using altern ate procedures may not agree regarding stationarity or market informational efficiency as time series of commodity asset prices may not be martingales.

PAGE 72

63 McGough et al. (2004) argue that a first or der autoregressive process for timber prices is consistent with efficiency in th e timber markets. They advocate the use of complex models (VARMA) that include dynami cs of the timber inventory while noting that such models would be difficult to estimate and apply to harvesting problems. In summary, in the absence of better data and models or stronger tests, it is difficult to conclusively establish the efficiency or otherwise of stumpage markets and or choose between the random walk or autoregressive models. This study considered both, the stationary and non-stationary models, for the price process alternately. Modeling the Price Process Two alternate models for the stochastic price process were applied to the real options model. The first model is the Geom etric Brownian motion which a form of the random walk process that incorporates a drif t and conforms with the efficient market hypothesis. Expressed mathematically it is dPPdtPdz (4-9) Here, P=Price of the asset at time t = Constant drift = Constant volatility dz= Increment of a Weiner process Geometric Brownian motion processes tend to wander far away from their starting points. This may be realistic for so me economic variables like investment asset prices. It is argued th at commodity prices (Schwartz 1997 ) must be related to their longrun marginal cost of production. Such a sset prices are modeled by Mean Reverting processes, which is the second model used fo r the stochastic process in this analysis. While in the short run the price of a comm odity may fluctuate randomly, in the long run

PAGE 73

64 they are drawn back to their marginal co st of production. The Ornstein-Uhlenbeck process is a simple form of the MR process expressed as _dPPPdtdz (4-10) Here, = Coefficient of reversion _P = Mean or normal level ofP The is interpreted as the speed of reversion. Higher values of correspond to faster mean reversion. _P is the level to which P tends to revert. _P may be the long run marginal cost of production .. The expected change in Pdepends on the difference between Pand_P If Pis greater (less) than_P it is more likely to fall (rise) over the next short interval of time. Hen ce, although satisfying the Mar kov property, the process does not have independent increments. The Weiner process in discre te time is expressed as ttttzzt (4-11) Here, t = Realization of a Normal Random variable with mean 0 variance 1 and (,)0ttjCov for 0 j In continuous time, the process is ttdzdt. A Weiner process tz is a random walk in continuous time with the properties (Luenberger 1998) i. For any st the quantity ()() z tzs is a normal random variable with mean zero and variance ts ii. For any 12340 tttt the random variables 21()() ztzt and 43()() ztzt are uncorrelated.

PAGE 74

65 iii. 0()0 zt with probability 1. The Geometric Brownian Motion Process Applying Ito’s lemma, the Geometric Br ownian motion (GBM) process can be expressed in logarithmic form as 2ln 2tdPdtdz (4-12) In discrete logarithmic form the equation becomes 2 1lnln 2ttPPtz (4-13) Thus, the log-difference or the instantane ous rate of price change is normally distributed. In order to model the GBM process an es timate of the volatility was required. Following Tsay (2002), let1lnlntttrPP Then, tr is normally distributed with mean 21 2 t and variance2t where t is a finite time interval. If rs denotes the sample standard deviation i.e., 2 11n t t rrr s n (4-14) then ^ rs t (4-15) Here ^ denotes the estimated values of from the data. For the nominal F.O.B. and stumpage statewide pulpwood quarterly pr ice data for Florid a, using the above methodology we obtain the estimates listed in Table 3-4.

PAGE 75

66 However, as the TMS data is availabl e in period average form while the GBM process models the behavior of spot prices, it is necessary to account for any distortion to the statistical properties of the data from averaging. Working (1960) has demonstrated that to an approximation, the variance of ra tes of change calculated from arithmetic averages of n consecutive regular spaced valu es of a random chain will be 2 3 of the variance of first difference of correspondingly positioned terms in the unaveraged chain, as n increases. The prices reported by TMS are calc ulated as an arithmetic average of all reported prices in a quarter. As discusse d by Washburn and Binkley (1990b), the price averages will be unbiased estimates of the arithmetic mean of prices at anynregular intervals within the period so long as the likelihood of a timber sale occurring and the expected transaction size are cons tant throughout each period. Making the necessary correction to the es timated variance we obtain the revised estimate of the variance listed in Table 4-4. Table 4-4. Estimated GBM process paramete r values for Florida statewide nominal quarterly average pulpwood prices ______________________________________________________________________ Estimated Parameter FOB Stumpage ______________________________________________________________________ Uncorrected Values Standard Deviation 0.10 0.24 Corrected Values Standard Deviation 0.12 0.29 ______________________________________________________________________ It may be noted that the calculated sta ndard deviation for the F.O.B. price was significantly lower than the st andard deviation of the st umpage price. One possible explanation is that pulp mills revise their mill delivered prices relatively infrequently, whether they are gate purchase prices or supplie r contracted prices. It is also possible that while gate purchase prices are public knowledge, mill delivered price of pulpwood purchased from other sources may be incompletely reported due to mill concerns with

PAGE 76

67 strategic competitive disadvantage from revealing prices. On the other hand harvesting and transportation costs change drastically from one stand to another, resulting in higher volatility of reported stumpage prices. The st umpage prices reporte d are not the prices experienced by a particular stand or a common price experienced by all stands but prices experienced by different stands that reported selling timber in the period. The harvesting and transportation costs are themselves vola tile and likely imperfectly correlated with FOB prices but it is possible that they do not account for th e entire difference in the reported standard deviations. Since stand ow ners experience the stumpage price and not the FOB price, in the absence of data on volat ility of harvesting and transportation costs, this study uses the estimated standard deviat ion of reported stumpage prices to replace the estimated volatility of F.O.B. prices wh ile treating the harvesting and transportation costs as non-stochastic. To account for the pos sibility of overestimation of timber price variance the analysis was subjected to te sts of sensitivity to price volatility. Statistical Tests of the Geom etric Brownian Motion Model The GBM process in discrete logarithmic fo rm is a discrete random walk with drift i.e., it has the general form 1tttyy where 2(0,)tNt and (,)0ttjCov for 0j (4-16) The process is clearly non-st ationary with a unit root. But if we take the first difference we obtain a stationary process tty (4-17) The first difference process has mean and variance2t Further, the covariance (,)0ttsCovyy for 0 s

PAGE 77

68 To see how well the empirical data fits the GBM model, the sample autocorrelation function (ACF) at several lags was calculated and plotted for the di fferenced logarithmic form of the price data series. The sample ACF () h at lag hwas calculated using the formula || __ || 1 ^ 2 1()nh tht t n t tyyyy n h yy n nhn (4-18) where 11n t tyy n is the sample mean. For largen, the sample autocorrelations of an independent identically distributed (iid) sequence with finite variance ar e approximately iid with distribution 1 (0,) N n (Brockwell and Davis 2003). Hence, for the iid sequence, about 95% of the sample autocorrelations should fall between the bounds 1.96 n For the GBM process the instan taneous rate of price change1lnlntttrPP is stationary with mean 21 2 t variance2t and covariance (,)thtCovrr equaling zero for all 0 h If the empirical price data is m odeled by the GBM process, then the sequence tr should be white noise i.e., it shoul d be a sequence of uncorrelated random variables. A plot of the sample autocorrela tions for the instantaneous rate of price changes of the reported nominal pulpwood statew ide stumpage prices along with the 95% confidence intervals are presented in Figure 4-1, plotted using th e ITSM 2000 statistical software (Brockwell and Davis 2003).

PAGE 78

69 -1.00 -.80 -.60 -.40 -.20 .00 .20 .40 .60 .80 1.00 0 5 10 15 20 25 30 35 40 Sample ACF Figure 4-1. Sample autocorrelation function plot for nominal Flor ida statewide pulpwood stumpage instantaneous rate of price changes The dashed lines on either side of the cen tre plot the 95% conf idence interval. If the sequence is stationary, for the 40 lags plotted, 2 or less ACF’s should fall beyond the 95% confidence bounds. For the stumpage price series, no more than 1 ACF beyond lag 0 fell outside the 95% confidence bounds. Signifi cantly, as proved by Working (1960), the ACF at lag 1 for stumpage price instantaneous rate of change sequence was approx. 0.25 (^(1)0.27 ). This could be the effect of the averaging process. To check if the trsequence was Gaussian i.e., if all of its joint distributions are normal the Jarque-Bera test was used. The Jarque-Bera test statistic is given by (Brockwell and Davis 2003) 2 4 2 2 2 3 3 23 624 m m m n m distributed asymptotically as 2(2) (4-19)

PAGE 79

70 if 2 (,)tYIIDN where 1r j n r jYY m n The results of the Jarque-Ber a test applied to the stumpa ge prices, given in Table 45, indicate that the normality hypothesis wa s weakly supported by the empirical data at the 5% level of significance. Table 4-5. Results of Jarque-Bera test a pplied to GBM model fo r Florida statewide nominal quarterly average pulpwood stumpage prices _______________________________________________________ Test Value Stumpage _______________________________________________________ Jarque-Bera Test Statistic 6.0984 P-value 0.0474 _______________________________________________________ The ACF test indicates that the GBM pro cess can be used to model the empirical data. However, this does not exclude the possibility of the true price process having a non-constant drift and/or variance. Lutz (1999) tested stumpage price series for constant variance. He found that the vari ance for stumpage price series examined was not constant for the early parts of the series i.e., up to 1920. From 1920 onwards, the examined series were found to display constant variance. Even if stumpage price data is heteroskedastic, it was implicitly assumed that the logarithmic transformation rendered the data ho mescedastic. The test results also did not exclude the possibility of an alternate model providing a better fit. On the basis of the ACF test it was only possible to conclude that there was insufficient evidence to reject the GBM model. The Mean Reverting Process The simple MR process is given by

PAGE 80

71 _ttdPPPdtdz Hence, tP is normally distributed with 00__ |t tEPPPPPe and 2 02 var|1 2t tPPe Using the expected value and variance we can express tP as 2 0_ 1 10,1 2t tt te PPePeN 1_ 1tttttPPPePPe 1_ttttPPPP when 1 e (4-20) where 2 0,tN The last equation provides a discrete time first order autoregressive equivalent of the continuous time Ornstein-Uhlenbeck proc ess. In order to estimate the parameters an OLS regression of the form 1 ttttPPabP (4-21) with aP and b was run. Then, the estimated parameters are given by ^ ^ ^a P b ^^b and ^ One problem with using this simple form of the MR process is that it allows negative values for the stochastic variable. Pl antinga (1998) justifies the choice of this model for timber stumpage price by referr ing to the possibility of harvesting and transporting costs exceeding the FOB timber pric e. In such a case the effective stumpage price would be negative. However, it can be argued that the ne gative stumpage price

PAGE 81

72 would still be bound by the harvesting and transportation costs i.e., if the FOB price were zero, the negative stumpage pr ice cannot be larger than the cost for harvesting and removal. But the MR process described abov e is unbounded in the negative direction. Hull (2003) describes an alternate lo g normal form of the MR process _lnlnlnttdPPPdtdz (4-22) This model restricts the price process to positive values. Thus, lntP given 0ln P is normally distributed with mean __ 0lnlnlntPPPe and variance 22 1 2te The deviations from the long-run mean are ex pected to decay following an exponential decline. This analysis uses this form of the MR process to model the FOB prices. When the harvesting and transportation costs are dedu cted from the stochastic values of the FOB price the magnitude of resulting negative stumpage price is restricted to these costs. However, adopting Equation 4-21 for estimation of _P implies that the mean to which the process reverts is constant over any period of time. Considering that _P is interpreted as the long run cost of production, over a short interval of a few days or weeks, it may be feasible to assume that the value is constant. But when the analysis must cover several years, this assumption is questionable. One common correction method employed (Smith and McCardle 1999) is to re gress the inflated values (present) of the historical asset price, which yields an inflation adjusted estimate of_P It also implies that for an analysis conducted in nomina l terms, the future values of _P must be inflated at an estimated average inflation rate. The average rate of annual inflation computed from the PPI (1921-2005) was approx.3.0%.

PAGE 82

73 The possibility of a constant real or inflation adjusted nominal_P for pulpwood prices was corroborated by the historical performance of pulpwood prices over the 30 years or so of TMS reporting period as we ll as the RPA (2003) projections of future performance. This phenomenon can be partly attribut ed to technological advances and in some measure to adverse demand and supply movements. Considering that the other parameter estimates are only marginally effected this analysis uses the inflation adjusted parameter values. To check for the effect of period averaging on the estimated parameter values, simulation was carried out. The simulation re vealed that regression of period averaged data generated consistent estimates of _P while was consistently underestimated by a factor of approx. 0.67 or the Working’s correc tion. The result of regressing inflated past values of the pulpwood prices using the Pr oducers Price Index-All Commodities (PPI) on estimated _P and other parameters are listed in Table 4-6. Table 4-6. Inflation adjusted regressi on and MR model parameter estimates _____________________________________________________________________________ ^a ^b ^ _P ^ ^ _____________________________________________________________________________ Stumpage Price 0.2979 -0.1245 2.3922 0.1245 0.2230 Standard Error 0.3285 0.1278 FOB Price 0.5694 -0.1781 3.1963 0.1781 0.0945 Standrad Error 0.4338 0.1350 _____________________________________________________________________________ Estimates corrected for period averaging effect. Of particular importance are the reversion coefficient values. For both price series the reversion coefficient values are low indicat ing that the annual price series exhibit low or insignificant reversion behavior. The ‘half life’ of the MR process or the time it takes

PAGE 83

74 to revert half way back to the long run mean, given by ln0.5 was approximately 2.6 years for stumpage price, illustrating the extr emely slow reversion process. Regarding the low values of mean reversion coefficients Dixit and Pindyck (1994) observe that this seems to be the case for many economic variable s and that it is usually difficult to reject the random walk hypothesis using just 30 or 40 years data. Secondly, the estimated variance for the FO B price process was sharply lower than that for the stumpage price. Once again, this difference can be attributed to the stochastic harvesting and transportation costs but may also partly be the result of the unsuitable data. As in the GBM process case, the an alysis was conducted by attributing the stumpage price process variance to the FOB price process and usi ng a non-stochastic harvesting and transportation cost. Finally, it must be noted that the lattice mo del for MR process used in this analysis was based on the existence of futures mark ets for the commodity and hence knowledge of futures prices, which represent the risk neutra l expected future values. In the absence of futures markets for timber, the value of the inflation adjusted estimated _Pwas used. This was justified for a long interval since mean re verting prices (and henc e futures prices) are expected to converge to _Pin the long run. However, in the short run this only serves as an approximation. Statistical Tests of the Mea n Reverting Process Model Examination of the stumpage price regres sion residuals shows first order serial correlation (Figure 4-2) as shown by Working (1964).

PAGE 84

75 -1.00 -.80 -.60 -.40 -.20 .00 .20 .40 .60 .80 1.00 0 5 10 15 20 25 30 35 40 Sample ACF Figure 4-2. Sample autocorrelation function plot for nominal Flor ida statewide pulpwood stumpage price MR model regression residuals Also, the results of Jarque-Bera test for normality do not support the normality hypothesis (Table 4-7) Table 4-7. Results of Jarque-Bera test ap plied to MR model residuals for Florida statewide nominal quarterly aver age pulpwood stumpage prices _______________________________________________________________ Test Statistic Stumpage Price _______________________________________________________________ Jarque-Bera Test Statistic 9.6299 P-value 0.0081 _______________________________________________________________ Instantaneous Correlation In order to model the simultaneous stochas tic evolution of two correlated stochastic processes following the GBM, an estimate of the instantaneous correlation between the two time series was required. The estimation of the instantaneous correlation of two period averaged GBM processes is not eff ected by period averaging (Appendix). The estimated instantaneous correlation for th e TMS reported Florida statewide average stumpage quarterly prices of pulpwood an d chip-n-saw assuming GBM processes was 0.43.

PAGE 85

76 The Data Time series data on prices of the timber products was acquired from Timber MartSouth (TMS). Price data for Florida extending from the last quarter of 1976 for pulpwood and the first quarter of 1980 for chip-n-saw to the second quarter of 2005 are used for the analysis. The stumpage price data are re ported by Timber Mart-South as quarterly average of final sale prices recorded in auctions for timber products in the reporting region. The data was used to represent spot timber prices in the analysis. However, due to the nature of data generation, collection and reporting processes, the validity of the data for this purpose is suspect. For example, the process starting from bidding for the timber to removal of the timber from the stand is usually a few months long. This means that the auction bid prices are a reflection of the bi dder’s expectation rega rding future prices when the timber will actually reach the ma rket, not the immediat e price. Errors in recording, approximations etc also undermin e the data. Other shortcomings have been discussed in various contexts above. Harvesting and transportation cost was calculated using the difference between reported F.O.B. and stumpage prices of tim ber. The appropriateness of this method is questionable because of the time difference between auctions and actual movement of timber from the stand to the market. Growth and Yield Equations Slash pine growth and yield equations deve loped by Pienaar and Rheney (1996) are used. These equations for cutover forest land were developed using da ta from plantations sites in Georgia. The average site index for the sites was 60 ft (at age 25). The equations used in the analysis are

PAGE 86

77 i. Expected Average dominant height (Hin ft) 0.073451.804 0.0691 123131.3679(1)(0.6780.5461.3950.412)* A ge AgeHSeZZZZZAgee where S = Site Index 1 Z =1 if fertilized, zero otherwise 2 Z =1 if bedded, zero otherwise 3 Z =1 if herbicided, zero otherwise ii. Survival after the second growing season (in trees/acre) 1.3451.345 210.0041() 21 AgeAgeNNe where 1Nand 2N are trees per acre surviving at 1Age and 2Age respectively21()AgeAge iii. Basal area ( B in ft2 /acre) 35.6686.2053.155 3.3941.3360.366 0.09 1312 (0.5570.4362.1340.354)*AgeAgeAge Age BBeHN ZZZZZagee where B Z = 1 if burned, zero otherwise iv. Stem Volume outside bark (V in ft3/acre) 0.320.501 0.0171.016 0.82 A geAgeVHNB v. Merchantable volume prediction (, dtV in ft3/acre) 3.845.72 0.120.520.69 td N DD dtVVe where ,dtV=per acre volume of trees with dbh>d inches to a merchantable diameter t inches outside bark D = quadratic mean dbh in inches 0.005454 B N = pi

PAGE 87

78 The merchantable yield output from the gr owth and yield models is in units of ft3 outside bark/acre. To convert the yield to tons/acre conversion factors of 90 ft3/cord and 2.68 tons/cord (Timber-Mart South) were used. These equations were developed from experimental plantations reaching an age of 16 growing seasons. For this reason, their us e for extrapolating growth and yield to higher rotation ages is questionable (Yin et al.1998) and may not represent the true stand growth. Nevertheless, for the purpose of this analysis, these equations are the best source for modeling the growth and yield of slash pine. Plantation Establishment Expenses Average plantation establishment expenses for cutover land in the US South reported by Dubois et al. (2003) were used. Th e relevant reported costs are listed in Table 4-8. Table 4-8. Average per acre plantation establishment expenses for with a 800 seedlings/acre planting density _______________________________________________________________________ Expense Head 2002 2005 ________________ ________________ $/acre $/seedling $/acre $/seedling _______________________________________________________________________ Mechanical Site preparation* 166.50 195.82 Burning** 15.02 17.66 Planting cost* 49.99*** 58.79 Seedling cost 0.04 0.05 _______________________________________________________________________ Total Cost for 800 seed lings/acre 280. 00 329.21 _______________________________________________________________________ All Types ** Others *** Planting cost for average 602 seedlings/acre The Producers Price Index-All Commodities was obtained from the Federal Reserve Economic data and used to extrapolate the nominal plantation expense data

PAGE 88

79 reported for 2002 to 2005. The index stood at 132.9 in December 2002 and rose to 156.3 by July 2005. For an acre planted with 800 s eedlings the total planting cost under the above listed expense heads in July 2005 was estimated at $329.21 or approx. $330/acre. Risk-Free Rate of Return The yield on Treasury bills with 1 year maturity (Federal Reserve Statistical Release) was used as the estimated risk-free ra te of return. The reported risk-free rate for July 2005 was 3.64%. The Model Summarized The value of options available to the d ecision maker were analyzed using a CC valuation procedure. The analysis also highlig hted the form of the optimal strategy. The following are the important points of the model 1. The model considers an even-aged mature (20 year age) slash pine pulpwood plantation in 2005. Only revenues from sale of timber are considered significant for the analysis. Since the analysis focuses on the pulpwood crop, the plantation was assumed to have been planted dense (800 tr ees/acre initial planting density) with no thinnings up to the present age. The planta tion was assumed to be cutover with site index 60 ft (rotation age 25). Site preparat ion activities assumed are mechanical site preparation (shear/rake/pile) and burning only. A clear-cut harvest was considered for the final harvest. When the thinning opti on was the subject of analysis only a single thinning in the form of a row thinning that removes every third row of trees was considered. 2. For a stand with the chosen initial planting density and site index on a cutover site, the growth and yield equations produce a single product yield curve that peaks approximately at age 43. Rotation age 43 was selected as the terminal age for the options on the stand in this study. This terminal age was applied uniformly to all models for comparability of results. Even though later stand products would have later yield peaks, current empirical practi ces and unreliability of the yield curve for higher rotation ages were arguments in favor of the lower terminal age. 3. Only the timber price (prices for multiple product analysis) was modeled as a stochastic variable. It was assumed that th e stand growth and yield models provide a reliable forecast of the future merchantable timber yields. 4. The present values of other parameters of the valuation model like the risk-free interest rate, the land rent and the interm ediate expenditure/cash flows on plantation

PAGE 89

80 were assumed known to the decision maker. Some intermediate cash flows could be positive in the form of regular realizatio ns of amenity values or sale of some minor/non-timber products while others coul d be negative in the form of annual taxes and overhead expenditures associated with maintenance activities. The basic analysis assumes that the net result from a combination of both positive and negative cash flows was a negative cash flow of $10/acre/year. For the purpose of consistency, all intermediate cash flows are treated as occu rring at the beginning of a period. This arrangement does not effect the analysis since the intermediate cash flows are assumed non-stochastic. Nonstochastic variables are una ffected by the expectation operator but are effected by discounting. So, regardless of where they occur in the period their value at the beginning of the period can be considered as the appropriately discounted value. These known values were extrapolated like risk-free variables i.e., with close to zero varian ce (and no correlation with the stochastic variables). Harvesting and transportation costs per unit merchantable timber were assumed constant i.e., the effect of economi es of scale observed for older or larger stands was ignored for want of data. 5. The unit FOB price of the timber product was modeled as the stochastic variable and the unit harvesting and transportation costs de duced from empirical data served as the strike price for the option on the stand. The estimated empirical values of variance for the timber stumpage price were used to model the variance of the FOB price. 6. The GBM and MR models applied were assume d to have constant parameters i.e., the drift and variance for the GBM model and the reversion coefficient and variance parameters for the MR models were assumed constant. 7. Land rent was estimated for the stochastic price process using the CC valuation as detailed earlier. 8. Taxes are not specifically treated in the analysis. 9. Ideally the term structure of interest rates should be used to model the risk-free rate. For simplicity, a single constant risk-free interest rate was used instead. 10. An assumption was made that the pulpwood stand was located so as to experience low/moderate relative timber product prices. 11. For the basic model the convenience yield was assumed to be zero. Sensitivity analysis to consider the effect of pos itive values of the convenience yield was conducted.

PAGE 90

81 CHAPTER 5 RESULTS AND DISCUSSION A Single Product Stand and the Geometric Brownian Motion Price Process In the following section the entire merchantable output of the stand at any rotation age was treated as a single undifferentiated product, in this case pulpwood. As argued earlier, this would be the case for a stand expe riencing low relative timber product prices. Figure 5-1 plots the per acre merchantable timber yield curve for a cutover slash pine stand in Florida with the following si te description and management history 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.002 9 16 23 30 37 44 51 58 65 72 79 86 93 10Rotation age (Years)Merchantable Yield (Tons/Acre) Total Merchantable Wood Figure 5-1. Total per acre merchantab le yield curve for slash pine stand

PAGE 91

82 Site Index -60 (age 25) Site PreparationBurning only Initial planting density800 Trees per acre Thinnings – None Parameter values used for the anal ysis are listed in Table 5-1. Table 5-1. Parameter values used in analysis of harvest decision for single product stand with GBM price process _________________________________________________________________________ Parameter Effective Date/ Unit Value Period _________________________________________________________________________ FOB price II Qtr 2005 $/Ton 21.96 Stumpage price II Qtr 2005 $/Ton 7.42 Harvesting and transportation cost II Qtr 2005 $/Ton 14.54 Initial plantation expenses II Qtr 2005 $/acre 330.00 Estimated land rent II Qtr 2005 $/acre/year 34.00 Other annual expenses II Qtr 2005 $/acre/year 10.00 Estimated standard deviatio n 07-01-2005 Annual 0.29 of GBM price process Risk free rate 07-01-2005 %/annum 3.64 Constant convenience yield Annual 0.00 Present age of stand 07-01-2005 Years 20.00 ____________________________________________________________________ In order to value the option to postpone the clear-cut harvest the FOB price for pulpwood was modeled as a stochastic variable following a GBM process with a constant standard deviation of 0.29. A binomial latt ice was constructed usi ng Equations 3-28, 3-29 and 3-37 for this stochastic variable with a one year period. The backward recursive option pricing procedure was then implemented to determine the option value. The GAUSS Light version 5.0 (Aptech Systems, Inc.) software was used for finding solutions. The per acre pre-tax value of an immediate harvest an d sale as pulpwood of the entire merchantable yield at rotation age 20 at current stumpage price of $7.42/ton was

PAGE 92

83 $567. The maximum or terminal rotation age considered was 43 years. At $966/acre or $12.64/ton the calculated option value was higher than the value of immediate harvest. Figure 5-2 plots the upper bounds of the st umpage prices for the harvest region or the crossover price line. Since a discrete time approximation with large period values (annual) was used continuity wa s sacrificed i.e., the reported values of crossover prices display large jumps. The crossover line has also been smoothened to remove the incongruities in the data recovered from the discre te lattice structure. 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 180.00 200.00 2021222324252627282930313233343536373839404142 Rotation Age (Years)Stumpage Price ($/Ton) Optimal cross-over prices Figure 5-2. Crossover price line for sing le product stand with GBM price process The region to the RHS of the line is th e harvesting region and to its LHS is the continuity region. The form of the crossover line suggests that the optimal strategy will comprise of harvesting only if the rotati on age approaches the terminal age and the stumpage prices decrease to zero. As th e rotation age approaches the terminal age harvesting at higher stumpage prices becomes feasible. These results conform to the

PAGE 93

84 findings of Thomson (1992a) and the discussi on in Plantinga (1998) on the results of a Geometric Brownian motion price process. Th e form of the optimal harvesting strategy implies that harvesting was only feasible to avoid uneconomic outcomes or when there was a low probability of improving returns by waiting any further in the time left to the terminal date. This result for the GBM price process is al so confirmed from the results for plain financial (American) options on non-dividend bearing stocks that are always optimally held to the maturity/terminal date. The cro ssover line for stand harvesting is observed because of the presence of the intermediate expenses. Sensitivity Analysis Sensitivity of the results to changes in values of various parameters was considered next. The land rent was re-estimated to reflec t the change in value of the parameter under consideration. First, the respon se of the results to changes in intermediate expenses was considered. The option value corresponding to an increase in intermediate expenses by $10/annum/acre was $859/acre, a decrease of mo re than $100/acre. On the other hand the option value for an increase in intermedia te expenses by $40/annum/acre decreased the option value to $617/acre a drop of about $350/acre. If the higher intermediate expenses are considered to arise from payments for purchase of insurance against non-marketed un desirable risks, it is possible to see the effect that catastrophic risks have on the ha rvesting strategy and option values. Thus, the observed empirical rotations of less than 30 years could be partly explained by the presence of non-marketed undesirable risks. On the other hand, lowering intermediate expenses by $10/annum/acre increased the option value to $1,088/acre, an increase of more than $100/acre. Thus, positive and

PAGE 94

85 previsible cash flows in the form of, say, non-timber incomes or aesthetic values would lead to longer optimal rotations. 0 50 100 150 200 250 300 350 400 2021222324252627282930313233343536373839404142 Rotation age (Years)Stumpage Price ($/Ton) Unchanged Intermediate Expenses Less $5 Less $10 Less $20 Figure 5-3. Crossover price lines for different levels of intermediate expenses Figure 5-3 illustrates the effect of ch anging the magnitude of intermediate cash flows. As the intermediate cash flows in th e form of expenses or negative cash flows increase the crossover line shifts to the left towards lower rotation ages From the option pricing theory it is known that option value is directly related to the magnitude of the variance of the underlyi ng stochastic asset value. The variance for stumpage prices estimated from the TMS data may be higher than the variance experienced by individual pulpwood stand ow ners for reasons discussed earlier. Higher variances mean the possibility of higher pos itive payoffs even while the effect of the higher negative values is limited to zero.

PAGE 95

86 The results of the sensitivity analysis for different levels of variances confirmed the known behavior of option values. The option va lue for a standard deviation value of 0.20 was $765/acre as compared to $966/acre for the base standard deviation of 0.29. The option value dropped further to $658/acr e for a standard deviation of 0.10. Figure 5-4 shows that when the variance leve l is lower the crossover lines lie to the left of higher variance models so that optimal harvesting at lower rotation ages as well as lower stumpage prices becomes feasible. This im plies that in a situation of large expected variances arising, say, from an unpredictable regulatory environment, harvesting should be optimally postponed. 0 20 40 60 80 100 120 140 160 180 20020 22 24 26 28 30 32 34 36 38 40 42Rotation age (Years)Stumpage Prices ($/Ton) Unchanged Standard Deviation 0.29 Standard Deviation 0.2 Standard Deviation 0.1 Figure 5-4. Crossover price line for di fferent levels of standard deviation Instead of using a convenience yield value of zero, the use of a positive constant convenience yield will alter the risk-neutral expected drift of the process (Equation 3-38). For a constant convenience yield of 0.005 the option value dropp ed to $874/acre, dropping further to $803/acre for convenien ce yield value 0.01 and to $755/acre for

PAGE 96

87 convenience yield value 0.015. Since higher levels of convenience yield are associated with low levels of inventory and associated hi gher market prices, it suggests that optimal rotations should be shorter when the markets are tight. Figure 5-5 plots the effect of different le vels of constant convenience yield on the crossover price lines. It show s the leftward shift of the crossover lines in response to higher levels of constant positive convenience yields. 0 20 40 60 80 100 120 140 160 180 200 2021222324252627282930313233343536373839404142 Rotation age (Years)Stumpage Price ($/Ton) Convenience Yield =0 Convenience Yield = 0.005 Convenience Yield = 0.01 Convenience Yield = 0.015 Figure 5-5. Crossover price lines for vary ing levels of positiv e constant convenience yield It iz also of interest to know if the opt imal decision changes for a different current price i.e., does a higher or lower current stumpage price induce earlier harvesting. The per acre option value corresponding to a pres ent stumpage price of $1/ton ($76/acre) was $7/ton ($548/acre). On the other hand the pe r acre option value for a present stumpage price of $20/ton ($1,529/acre) was $25/ton ($1,933/acre). The po ssibility of higher

PAGE 97

88 payoffs as a result of higher current prices inflates the land rent reducing the relative option values. Figure 5-6 plots the results of consideri ng different levels of current stumpage prices. The plots show that the cross-over price lines shift to the left for a price increase and vice versa. This results pa rtly from the effect of a di rect relation between land rent and current prices. All other things being cons tant, a higher current timber price increases the present land value which increases the cost of waiting through the land rent. At the same time higher present stumpage price al so means lower possibility of unfavorable outcomes but this effect is overwhelmed by the increase in land values. 0 20 40 60 80 100 120 140 160 180 2002 0 22 24 2 6 28 3 0 3 2 34 3 6 38 40 4 2Rotation Age (Years)Stumpage Price ($/Ton) Unchanged Stumpage Price = $7.42/Ton Stumpage Price = $1.00/Ton Stumpage Price = $20/Ton Figure 5-6. Crossover price lines for different levels of current stumpage price

PAGE 98

89 Next, by changing the present rotation age of the stand from 20 to 25 and 30 we can observe the drop in option values commonl y associated with financial options as the time remaining till the terminal date is reduced This is due to the lower probability of higher payoffs in the remaining time. For the timber stand, for a present rotation age of 25 the associated option value was $9.97/ton ($999/acre). Similarly, for a present rotation age of 30 the option value was $8.88/ton ($1,027/acre). Finally, the effect of a change in the initial planting density was studied. The current plantation establishment expenses were adjusted to reflect the cost of planting less plants which effects the estimated land rent, though only marginally. The important observation is that lower initial planting de nsities did not change option values which were $12.62/ton ($909/acre) for 700 tpa an d $12.64/ton ($781/acre) for 500 tpa. The option value calculated earlier for a 800 tpa initial planting dens ity was $12.64/ton. Comparison with the Dynamic Programming Approach This section applies the DP approach to the single product slash pine pulpwood stand with timber prices following a GBM pro cess. The binomial lattice was set up using Equations 3-28 and 3-29 with the subjective probability given by Equation 3-27 instead of the risk-neutral probabili ty given by Equation 3-37. The estimated value of the drift for pulpwood stumpage prices was 0.05 (with a standard error of n =0.053 or >100%). A variety of discount rates have been used in published forestry literature using the DP approach, the most common being a real rate of 5%. Since this analysis was conducted in nominal terms and the average inflation estima ted from the PPI series was 3%, a nominal discount rate of 8% was used in this DP analysis. Further, some of the published literature assumes the intermediate costs are constant in real terms. Therefore, for

PAGE 99

90 comparability, future values of intermediate expenses including the estimated land rent and harvesting and transportation cost were in flated at the average inflation rate of 3% computed from the PPI series. The land rent was estimated using the DP procedure. All other parameter values used were unchanged from Table 5-1. The option value derived from the DP approach, parameterized as above, was $2,393/acre. This value was more than tw ice the option value derived using the CC approach i.e., $966/acre. The use of a discount rate of approximately 12.5% brought down the estimated option value using the DP approach close to the option value estimated using the CC approach. As noted and illustrated in Hull (2003) the appropriate discount rate for options is much higher than the discount rate applicable to the underlying asset. First, it should be noted that at 12.5% th e discount rate is much higher than typical rates considered in forestry l iterature on options an alysis. Second, this discount rate is not a constant but would vary according to the parameter values of the problem. This is evident from the sensitivity of the option values to parameters exhibited above. This illustration serves to highlight the problems associated with using the DP approach in the absence of a method for determining the appropriate discount rate. A Single Product Stand and the Mean Reverting Price Process In this section the optima l harvesting strategy for th e single product (pulpwood) stand is analyzed with a mean reverting FO B price process. The stand description and management history were identical to th ose considered for the GBM price process analysis. The parameters used in the ba sic analysis are listed in Table5-2.

PAGE 100

91 The problem was modeled by consideri ng only the FOB price for pulpwood as stochastic following a MR process of the fo rm given by Equation 4-22 with a constant standard deviation of 0.22 and constant reversion coefficient with value 0.18. Table 5-2. Parameter values used in analysis of harvest decision for single product stand with MR price process _________________________________________________________________________ Parameter Effective Date/ Unit Value Period _________________________________________________________________________ FOB price II Qtr 2005 $/ton 21.96 Stumpage price II Qtr 2005 $/ton 7.42 Harvesting and transportation cost II Qtr 2005 $/ton 14.54 Mean FOB price level II Qtr 2005 $/ton 24.44 Initial plantation expenses II Qtr 2005 $/acre 330.00 Estimated land rent II Qtr 2005 $/acre/year 24.00 Other annual expenses II Qtr 2005 $/acre/year 10.00 Estimated standard deviatio n 07-01-2005 Annual 0.22 of MR price process Estimated constant reversi on 07-01-2005 Annual 0.18 coefficient Risk free rate 07-01-2005 %/annum 3.64 Constant convenience yield Annual 0.00 Present age of stand 07-01-2005 Years 20.00 Estimated average inflation rate %/annum 3.00 ____________________________________________________________________ The option value at $1,290 was higher than present stumpage value of $567. From the form of the crossover price lin e (drawn after smoothing) for the mean reverting FOB prices (Figure 5-7) it is evident that the strategy for the optimal harvest is significantly different than that for the GB M prices. The form of the crossover line suggests that the optimal strategy would be to harvest if a sufficiently high stumpage was received at each rotation age, the crossover price declining with the rotation age. These results are consistent with those reported for the reservation prices obtained using search algorithms and for other studies with first or der autoregressive or mean reverting prices.

PAGE 101

92 0 2 4 6 8 10 12 14 16 18 20 2021222324252627282930313233343536373839404142 Rotation Age (Years)Stumpage Prices ($/Ton) Crossover Price line Figure 5-7. Crossover price line for sing le product stand with MR price process The form of the crossover price line for the MR price process is a result of the characteristics of the process. By definiti on the MR process has a higher probability of moving in the direction of the mean value in the following period. Therefore, when the present stumpage price is higher than the mean the probability is higher that the price will fall in the following period and vice versa. This implies the optimal strategy suggested by the form of the crossover line, i.e., to harvest if the stumpage price is high as it is more likely to fall if the option to wait is chosen The crossover line is downward sloping as it approaches the terminal period since the po ssibility of profiting from waiting is lower and immediate harvest at lower prices is justifie d. The dropping rate of yield increase of the stand also influences the shape similarly.

PAGE 102

93 The Multiple Product Stand and Geomet ric Brownian Motion Price Processes Allowing for the presence of multiple prod ucts and assuming that their individual prices follow the GBM process with correla tion between the two price processes should reflect the empirical problem better than th e single product stand case. The case of two products i.e., pulpwood and ch ip-n-saw were considered.. The yield curves for the two timber pro ducts are plotted in Figure 5-8. The parameters used for the analysis are listed in Table 5-3. 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.002 7 12 17 22 27 32 37 42 47 52 57 62 67 72 77 82Rotation Age (Years)Merchantable Yield (Ton/acre) Pulp wood yield CNS Yield Figure 5-8. Merchantable yiel d curves for pulpwood and CNS The present stumpage price value for the CNS product was selected so that it was closer to the present stumpage for pulpwood than the price reported by TMS, to reflect the low relative price phenomena. The vari ance parameter for CNS was calculated from

PAGE 103

94 TMS data as illustrated above for pulpwood. The CNS stumpage variance was imputed to the CNS FOB variance while a common harves ting and transportation cost was used. Table 5-3. Parameter values used in analys is of harvest decision for multiproduct stand with GBM price processes _________________________________________________________________________ Parameter Effective Date/ Unit Value Period _________________________________________________________________________ Pulpwood FOB price II Qtr 2005 $/ton 21.96 Stumpage price II Qtr 2005 $/ton 7.42 Harvesting and transportation cost II Qtr 2005 $/ton 14.54 Estimated standard deviatio n 07-01-2005 Annual 0.29 of GBM price process C-n-S FOB price II Qtr 2005 $/ton 26.54 Stumpage price II Qtr 2005 $/ton 12.00 Harvesting and transportation cost II Qtr 2005 $/ton 14.54 Estimated standard deviatio n 07-01-2005 Annual 0.24 of GBM price process Initial plantation expenses II Qtr 2005 $/acre 330.00 Estimated land rent II Qtr 2005 $/acre/year 40.00 Other annual expenses II Qtr 2005 $/acre/year 10.00 Risk free rate 07-01-2005 %/annum 3.64 Constant convenience yield Annual 0.00 Present age of stand 07-01-2005 Years 20.00 ____________________________________________________________________ The model allowed the decision maker to sell differentiated products as long as the stumpage price for CNS was greater than the pulpwood stumpage price. But if the CNS price fell below the pulpwood price, the st and owner could sell the entire output as pulpwood. The option price was $1,325 as compared to the present market value of $585. The crossover lines (after smoothing) for rotation ages 34 to 39 are plotted in Figure 5-9. Compared to the single product stand analysis harvesting is optimal at higher

PAGE 104

95 rotation ages when the second timber produc t is introduced, even though the relative prices considered were half the TMS reported average. The optimal strategy suggested is the same i.e., to harvest when the stumpage prices are sufficiently low and to hold otherwise. Crossover Stumpage Price lines by Rotation ages for Pulpwood and CNS0 10 20 30 40 50 60 70 80 0102030405060708090100110120130140 CNS Stumpage Price ($/Ton)Pulpwood Stumpage Price ($/Ton) Rotation age 34 35 36 37 38 39 Figure 5-9. Crossover price lines for multiproduct stand The results obtained for the multiproduct stand with correlated price processes are due to several factors. First, the yield of th e late rotation product wh ich is higher valued, increases in quantity at a high rate as the rotation increases in length. This increases the size of the net harvest revenues per period. Second, the presence of positive autocorre lation between the two price processes means that their joint variance is higher th an the variance of th e single product stand. This can be interpreted from Equation 3-43 the terms in the first box bracket. The positive correlation between variance and op tion values has already been shown above.

PAGE 105

96 Finally, the stand owner has an additional option to sell the crop at the price of the lower diameter product should the price of the higher diameter product fall below it. This option increases future payoffs and adds further value to the stand. Thinning the Single Product Stand and the Geometric Brownian Motion Price Process In order to analyze the commercial thinning option for the single product (pulpwood) stand with a GBM price proce ss, the following assumptions were made i. A single commercial thinning in the form of a row thinning is planned involving the removal of every third row of trees from the stand. No selection is involved. It is assumed that this one in three row thinning yields one third of the existing merchantable yield in the stand as harvest. ii. The residual stand continues to grow fo r the balance of the rotation and yields merchantable timber which equals the unthinned stand yield less the quantity removed at thinning. That is, the total me rchantable yield of the stand from thinning plus clear-cut harvest equals the merchantable yield from clear-cut harvest of the unthinned stand iii. The stumpage price for thinnings is half that for a clear-cut harvest at any time on account of the higher per unit harvesting and transportation cost. The failure to obtain significant improvem ent in total yield from a late rotation thinning was modeled on the empirical observations of Johnson (1961) discussed above. Figure 5-10 depicts the merchantable yiel d curves after the a pplication of a single thinning at different rotation ages. The para meters used in the analysis were unchanged from Table. 5.1 including the estimated land rent. The following three options were available to the decision maker at each age 1. Clear-cut harvest now. 2. Postpone clear-cut harvest without thinning. 3. Postpone clear-cut harvest after thinning. The decision maker chooses amongst the th ree options on the ba sis of the highest present value. The results obtained were iden tical to the case of the single product stand

PAGE 106

97 with GBM price process without the thinning option, indicating that thinning was not optimal at any age and the thinning option adds no value. This case serves to show that the presence of an option does not always add value to the asset. In this particular case the value of flexibility was not sufficient to make up for the loss of revenues on account of the lower thinning stumpage price. 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.002 5 8 1 1 14 1 7 20 2 3 2 6 2 9 3 2 3 5 3 8 41 4 4 47 5 0 53 5 6 59Rotation Age (Years)Merchantable Yield (Tons/Acre) Unthinned Stand Thinning age 20 Thinning age 25 Figure 5-10. Single product stand merchantable yield curves with single thinning at different ages If the structure of the slash pine stand’s response to late thinning was maintained the results did not change for higher/lower thinning intensities. This further confirmed that commercial thinning added no value to the investment and the option could be disregarded by stand owners. The sensitivity of the results to higher levels of thinning stumpage prices was also analyzed. The result remains unchanged for higher thinning stumpage prices as long as

PAGE 107

98 they remain lower than the clea r-cut harvest stumpage price. (up to nine tenths the clearcut harvest stumpage was used). Discussion In all cases considered, the option value calculated was higher than the present stumpage value of the stand. This means that the optimal decision was to postpone harvest for a later date, i.e., the option should be retained and immediate harvest was not optimal policy. But do the results imply that the decision to postpone harvest was optimal for all decision makers? To answer this question it is necessary to look at the nature of results obtained through options analysis. An insight into the re sults of the options analysis can be gained by treating investment decision making unde r risk as gambling. The no-arbitrage condition that underlies the option pricing method essentially means finding a price for the gamble that makes it fair. A fair gamble is one that does not favor either party to the gamble. This means that the expected value to either party from the gamble is zero. In a competitive market all risky assets/investment opportunities/gambles would be fairly priced. Ross (2002) uses the gambling analogy to introduce the arbitrage pricing theorem which states that either there exists a probabi lity vector on the set of possible outcomes of an experiment under which the expected return of each possible wager on the outcomes is equal to zero or there exists a betting strategy that yields a positive win for each outcome of the experiment. The probabilities that result in all bets being fair are called risk neutral probabilities. The option pricing method uses risk neutral probabilities to produce an arbitrage free price for an asset. When this arbitrage free price is compared to the current market value, a decision can be made to hol d or dispose off the asset. If the current market value is higher than the arbitrage free price, it means that a profit can be earned by

PAGE 108

99 cashing in the market value. On the other hand if the asset market value is lower than the arbitrage free price the gamble on the asset is under priced. This is because if one decides to hold the asset one exchanges a lower market value asset for a higher valued asset. If the decision to accept the gamble and hold the asset is taken, option pricing does not guarantee any profits. The option pricing theory only asserts that the gamble is favorably priced or in other words a gamble with similar risk can be only had in the competitive market for a higher price. But, is it necessary that the asset holder should be inclined to take even this favorably priced gamble? It could be argue d that an individual that chose to invest in the asset in the first place and thus take on the risks associated with the asset would be likely to take this fa vorable gamble. But, the actual decision would depend on the individual’s utility function at the time of making the decision along with other factors like the size of wealth at stake. Some empiri cal studies (Dennis1989, 1990 and Jamnick and Beckett 1987) of NIPF ha rvesting behavior have used econometric models to determine that stand owner characte ristics like age & wealth effect the harvest decision. Practical decision making would also be gu ided by factors like taxes, the ability to avail of government subsidies fo r regeneration, the ability to borrow, etc. Fina et al. (2001) study the effect of debt principa l repayment obligation for NIPF landowners on harvest scheduling. The paper quotes Birch (1996) to argue that NIPF landowners may be less endowed financially and dependent on the credit market for carrying out their operations. The paper demonstrates that rese rvation prices are a pos itive function of the time to debt principal payments, i.e., immine nt repayment of debt obligations leads to timber land owners accepting lower reservation prices.

PAGE 109

100 Moreover, before any conclusions regardin g optimal decisions are drawn from the analysis for empirical use it must be considered that the analysis itself is incomplete because it does not treat the non-marketed risks. The exclusion of non-marketed risks from the analysis does not lessen its im portance to the decision making process. Catastrophic risks like damage from ex treme weather conditions are capable of destroying most of the value of a stand. Stan d investors would be reluctant to retain such risks and would be willing to pay to transfer them to the market place through the use of market instruments like insurance products we re they available. When this payment is added to the cost of holding, the waiting decision becomes less appealing and the option value decreases. This has been shown through th e analysis of sensitivity of the results to increased intermediate expenses. The failure to provide a comprehensive tr eatment for non-marketed risks together with market price risk is common to all options analysis research in forestry, unrelated to the CC approach. As shown earlier, in the abse nce of information on the market cost of insurance against catastrophic risk the CC analysis is incomplete and the option values derived are on the higher side. But when a market for these risks does not exist other methods have been suggested to factor th e non-marketed risks into the analysis. Luenberger (1998) and Smith and Nau (1995) de scribe an integrated approach to treating the public (marketed) and private (non-marketed) risks together in the analysis. The approach involves using subjective probabilit ies for the private risks and risk-neutral probabilities for the marketed risks. There are other reasons to discount the re sults of the analysis. The assumptions underlying the CC analysis are cr itical to the empirical validity of the prescriptions. For

PAGE 110

101 example the absence of a common rate for borrowing and lending can effect the analysis. Commonly, the borrowing rate available to i ndividuals is signifi cantly higher than the lending rate. The effect of the adverse spread is to reduce the fair value of the option to the purchaser. Hughes (2000) incorporates this adverse spread into the real option valuation of the assets of the New Zealand Forest Corporation and the study provides an illustration of this effect. Tahvonen et al. (2001) studies the Faustmann problem under conditions of borrowing constraints and conc ludes that borrowing cons traints in the form of high borrowing costs l ead to shorter rotations. Next, the timber markets are characteri zed by an absence of freely available information. Haight and Holmes (1991) point ou t that using the reserv ation price policies for harvesting requires the monitoring of stum page prices and readiness to complete a sale contract. Assuming that the cost of information is of th e same magnitude as the cost of timber cruising, the study found that as the fixed costs increased harvesting is acceptable at lower prices (hence earlier) to avoid paying the additional costs of price monitoring. The study concludes that a fixed ro tation harvest may be preferred as it does not require stumpage price monitoring. The same cost of information can be readily applied to yield determin ation, input costs etc. Timber markets also operate with subs tantial friction or transaction costs. Washburn and Binkley (1990a) observe that th e weak-form efficiency test implicitly assumes that movement of stumpage in and out of storage is frictionless; that is, that timber sale plans can be instantaneously adju sted at no cost. But they question this assumption, arguing that the time and cost involved in consummating a timber sale might produce short-run friction in the stumpage market. In this condition, the failure of

PAGE 111

102 stumpage prices to adjust instantaneously to new information might i ndicate that the costs of adjustment exceed the possible economic gains. Similarly, the failure to empirically observ e the other critical assumptions regarding continuous trading, short sales, etc., also undermine the results of the analysis. Empirically, values of parameters like vari ance, risk-free rates (term structure) and convenience yield evolve with time. Some pa rameter values used for the real options analysis are previsible like the risk-free ra te or the convenience yield (where a futures market of sufficient term exists). Others li ke the variance have to be estimated from historical data. Historical volatility is an impe rfect substitute for expe cted volatility. It is known from the operation of financial markets that the volatility implicit in actual market trades in options is seldom accurately predicte d by historical data. It is the perception of future volatility that determines optio n values rather than its history. Another important observation is that there are no fixed reservation prices that can be predetermined and used for decision making by stand owners. The crossover prices derived from the analysis are not fixed a nd are sensitive to evolving market based parameter values like the variance, convenie nce yield and the present timber price (and hence the estimated land rent) as shown above. The form or shape of the crossover price lines does suggest the nature of the optimal strategy but even that is not useful information unless the debate over the nature of stochasticity of timber prices could be settled. As illustrated earlier, the optimal stra tegy suggested by the form of the crossover price line for the two popular st ochastic processes for timber price considered in this analysis is diametrically opposite.

PAGE 112

103 The one key conclusion from the analysis is the importance of market information to the optimal stand management and invest ment decision making processes in the presence of uncertainty. It is widely ackno wledged that timber markets operate with a woeful lack of information, with the stand ow ners being the lowest in the hierarchy of the informed. This inadequacy is manifest in the importance of consultants for the stand sale process and the significant transaction costs imposed thereby. It is common for stand owners to be unaware of the market price of their product. Determining a useful estimate for the unobserved land rent is still an unreso lved issue. In the absence of futures markets the determination of convenience yields remains a problem. The absence of markets for trading in presently non-marketed risks m eans that their market values are unknown. Without access to critical information required for investment decision making the significant value of flexibility in management of stands cannot be measured. Inability to measure the option value means that stand owne rs cannot fully realize this value which in turn implies that investment decision ma king for timber stand is not optimal. Recently, some timber purchasers have in troduced innovation to the marketplace by using the internet to disseminate inform ation about their purchasing practices and provide a transparent auction site for the selle rs to bid their selling prices. Perhaps the greatest gain of this innovation will come in the form of the flow of information to the stand investors. Greater transparency should redress seller concerns about being on the losing side of the transaction and enco urage informed decision making resulting in increased efficiency. With the increasing presence of corporate timberland managers like TIMO’s ( Timber Investment Management Organizatio ns) and REIT’s (Real Estate Investment

PAGE 113

104 Trusts), it is conceivable that the demand fo r financial innovations will increase and will result in the creation of markets for trading in presently non-marketed risks. The same developments should spur the creation of fo rward/futures markets. These markets will create tremendous information for the decisi on makers and should increase efficiencies all around. Recommendations for Further Research A vast number of studies have researched timber stand investment decisions with a similarly large number of approaches. Howe ver, the treatment of decision making under risk from the perspective of an investment analysis is a relatively new subject with a number of inadequately researched asp ects. Some areas recommended for further research are i. The simultaneous production of multiple tim ber products in sta nds effects decision making in ways that are inadequately unders tood at present. Research on modeling the complexities of dealing with multiple prod ucts in conjunction with commercial thinning or flexible silvicultural investme nt options could provide insight into risk management at the stand le vel amongst other things. ii. Non-marketed sources of risk are ignored or insufficiently treated in the analysis of investment decision making. Application of some of the available models for dealing with non-marketed risk can improve the va lue of results obtained from investment analysis. iii. The role of stochastic land rent or the su rplus assigned to land in the real options analysis has never been researched. Different mathematical methods have been used by researchers to determine land value but the equivalence of these methods remains to be shown.

PAGE 114

105 APPENDIX CORRELATION OF FIRST DIFFERENCES OF AVERAGES OF TWO RANDOM CHAINS The correlation of two period averaged random chains can be calculated by extending Working (1960). Following Working (1960) let the two random chains be represented by 1 iiiXX ()0,var()1,(,)0iiiijEcor for 0 j 1 iiiYY ()0,var()1,(,)0iiiijEcor for 0j Then, from Working (1960) 2 ()()212 ()() 3xy imimmm VarVar m as mgets larger Here mis the number of evenly spaced cons ecutive time series data averaged and ()111111 (.....)(.....)x imiiimimimiXXXXXX mm is the difference of consecutive averages. The instantaneous correlation to be estimated is ()() ()() ()()(,) (,) ()()xy imim xy imim xy imimCov Cor VarVar ()()(,) 22 33xy imimCov mm ()()(,) 2 3xy imimCov m Or in the general case where 2()ixVar and 2()iyVar

PAGE 115

106 ()() ()() 22(,) (,) 2 3xy imim xy imim xyCov Cor m To solve for()()(,)xy imimCov let(,)iiCovd From the Markov property of i X and iY and assumptions regardi ng the random nature of i and i it follows that (,)0iijCov for 0 j We can express ()121111 (1)(2).....(1).....x imiiimiiimmmmm m ()121111 (1)(2).....(1).....y imiiimiiimmmmm m Therefore, 22 ()()112211 21 (,)(1)(,)(2)(,).......(,)xy imimiiiiimimCovmCovmCovCov m 2222 2(1)(2)...1(1)....1 d mmmm m 221 3 m d m 2 3 md as mgets larger So, ()() ()() 22(,) (,) 2 3xy imim xy imim xyCov Cor m 222 3 2 3xymd m 22 xyd Therefore, the correlation of the first differences of the two averaged random chains would equal the correlation of th e unaveraged random chains and requires no correction.

PAGE 116

107 LIST OF REFERENCES ADAMS, D. 2002. Harvest, Inventory, and Stumpage Prices: Consumption Outpaces Harvest, Prices Rise Slowly. J ournal of Forestry. 100(2):26-31. AF&PA (AMERICAN FOREST AND PAPER ASSOCIATION). 2003. Florida : Forest and Paper Industry at a Glance. 2 p. Retrieved 03-15-2006 from www.afandpa.org ARONSSON, T., AND O. CARLEN.2000. The Determinants of Forest Land Prices. An Empirical Analysis. Canadian Journa l of Forest Research. 30(4):589-595. BARNETT, J.P. AND R.M. SHEFFIELD.2004. Slash Pine: Characteri stics, History, Status, and Trends. In Dickens, E.D.; Barnett, J.P.; Hubbard, W.G.; Jokela, E.J., eds. 2004. Slash Pine: Still Growing and Growing! Pr oceedings of the Slash Pine Symposium. Gen. Tech. Rep. SRS-76. Asheville, NC: U. S. Department of Agriculture, Forest Service, Southern Research Station. 1-6. BAXTER, M. AND A. RENNIE.1996.Financial Calculus: An Introduction to Derivative Pricing. Cambridge University Press. New York, NY.233 p BENTLEY, J.W., T.G. JOHNSON, AND E. FORD.2002. Florida’s Timber Industry—An Assessment of Timber Product Output a nd Use, 1999. Resource Bulletin. SRS–77. Asheville, NC: U.S. Department of Agricu lture, Forest Service, Southern Research Station.37 p. BENTLEY, W.R., AND D.E. TEEGUARDEN.1965.Financial Maturity: A Theoretical Review. Forest Science. 11(1):76-87. BIRCH, T.W.1996. Private Forest Land Owners of the United States, 1994. USDA Forest Service, Northeastern Forest Experiment Station Research Bulletin NE-134.183 p. BIRCH, T.W. 1997. Private Forest-Land Owners of the Southern United States, 1994. Northeastern Forest Experiment Stat ion. Research Bulletin NE-138. 147 p. BLACK, F., AND M. SCHOLES.1973. The Pricing of Options and Corporate Liabilities. Journal of Political Economy. 81 (3):637-654. BRAZEE, R.J., AND R. MENDELSOHN.1988.Timber Harvesting w ith Fluctuating Prices. Forest Science.34:359-372. BRAZEE, R.J., AND E. BULTE.2000. Optimal Harvesting and Thinning with Stochastic Prices. Forest Science. 46(1):23-31.

PAGE 117

108 BRENNAN, M.J. 1991. The Price of Convenience and the Valuation of Commodity Contingent Claims. In D. Lund and B. Oksendal (eds) Stochastic Models and Option Values (Contribution to Economic Analysis # 200 ). North-Holland. Amsterdam, The Netherlands. 33-71. BRIGHT, G., AND C. PRICE. 2000. Valuing Forest Land unde r Hazards to Crop Survival. Forestry. 73(4):361-370. BROCK, W.A., M. ROTHSCHILD, AND J.E. STIGLITZ. 1982. Stochastic Capital Theory. in: G. Feiwel, ed..Joan Robinson and Modern Economic Theory. Macmillan. London. 591-622. BROCKWELL, P.J., AND R.A. DAVIS. 2003. Introduction to Time Series and Forecasting. 2nd Edition. Springer-Verlag, New York, NY. 434 p. CARTER, D.R., AND E.J. JOKELA. 2002. Florida’s Renewable Fo rest Resources. School of Forest Resources and Conservation, Univer sity of Florida, Florida Cooperative Extension Service Document CIR14 33. 10 p. Retrieved 05-03-2006 from http://edis.ifas.ufl.edu/. CASTLE, E.N., AND I. HOCH. 1982. Farm Real Estate Price Components, 1920-78. American Journal of Agricult ural Economics. 64(1):8-18. CHANG, S.J. 1998. A Generalized Faustmann Model for the Determination of Optimal Harvest Age. Canadian Journal of Forest Research. 28(5):652-659. CLARKE, H.R., AND W.J. REED.1989. The Tree-Cutting Problem in a Stochastic Environment: The Case of Age Dependent Growth. Journal of Economic Dynamics and Control.13:569-595. CONSTANTINIDES, G.M. 1978. Market Risk Adjustment in Project Valuation. The Journal of Finance. 33(2):603-616. COPELAND, T.E., J.F. WESTON, AND K. SHASTRI.2004.Financial Theory and Corporate Policy. 4th Edition. Pearson Addison Wesley. New York, NY. 1000 p. COX, J.C., S.A. ROSS, AND M. RUBENSTEIN.1979. Option Pricing: A Simplified Approach. Journal of Financial Economics.7(3):229-263. DENNIS, D.F.1989. An Econometric Analysis of Harvest Behavior: Integrating Ownership and Forest Characteristic s. Forest Science. 35(4):1088-1104. DENNIS, D.F. 1990. A Probit Analysis of Harves t Decisions using Pooled Time-Series and Cross-Sectional Data. Journal of Environmental Economics and Management. 18(2):176-187.

PAGE 118

109 DICKENS, E.D., AND R.E. WILL.2004. Planting Density Impacts on Slash Pine Stand Growth, Yield, Product Class Distributi on, and Economics. In Dickens, E.D.; Barnett, J.P.; Hubbard, W.G.; Jokela, E.J ., eds. 2004. Slash Pine: Still Growing and Growing! Proceedings of the Slash Pine Symposium. Gen. Tech. Rep. SRS-76. Asheville, NC: U.S. Department of Agricu lture, Forest Service, Southern Research Station. 36-44. DIXIT, A.K., AND R.S. PINDYCK.1994. Investment under Uncertainty. Princeton University Press. Princeton, New Jersey. 468 p. DUBOIS, M. R., T.J. STRAKA, S.D. CRIM, AND L.J. ROBINSON.2003. Costs and Cost Trends for Forestry Practices in the S outh. Forest Landowner. 60(2):3-8. FAMA, E.F. 1970. Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance. 25(2):383-417. FAUSTMANN, M. 1849. Calculation of the Value which Forest Land and Immature Stands Possess for Forestry. Reprinted in Journa l of Forest Economics.1995. 1(1):7-44. FEDERAL RESERVE STATISTICAL RELEASE. H. 15. Selected Interest Rates. Retrieved 0315-2006 from http://www.federalreserve.gov FEDERAL RESERVE ECONOMIC DATA. Producers Price Index. Retrieved 03-15-2006 from http://research.stlouisfed.org/fred2/series/PPIACO FINA, M., G.S. AMACHER, AND J. SULLIVAN. 2001. Uncertainty, Debt, and Forest Harvesting: Faustmann Revisited. Forest Science. 47(2):2001. FISHER, A.C., AND W.M. HANEMANN. 1986. Option Value and the Extinction of the Species. Published in Advances in Applied Micro-Economics. 4:169-190. FORBOSEH, P.F., R.J. BRAZEE, AND J.B. PICKENS.1996. A Strategy for Multiproduct Stand Management with Uncertain Future Prices. Forest Science. 42(1):58-66. GAFFNEY, M.M. 1960. Concepts of Financial Matur ity of Timber and Other Assets. A.E. Information Series No. 62. North Ca rolina State College, Raleigh. 105 p. GASSMANN, H.I. 1988. Optimal Harvest of a Forest in the Presence of Risk. Canadian Journal of Forest Research. 19:1267-1274. GESKE, R., AND K. SHASTRI.1985. Valuation by Approxi mation: A Comparison of Alternative Option Valuation Technique s. The Journal of Financial and Quantitative Analysis. 20(1):45-71. GJOLBERG, O., AND A.G. GUTTORMSEN.2002. Real Options in the Forest: What if Prices are Mean-reverting? Forest Policy and Economics. 4:13-20

PAGE 119

110 GONG, P., AND R.YIN.2004. Optimal Harvest Strategy for Slash Pine Plantations: The Impact of Autocorrelated Prices for Multiple Products. Forest Science.50(1):10-19. HAIGHT, R.G. AND T.P. HOLMES. 1991. Stochastic Price Models and Optimal Tree Cutting: Results for Loblolly Pine Natural Resource Modeling 5(4):423-443. HAYNES, R.W. 2003. An Analysis of the Timber Situation in the United States: 19522050. General Technical Report PNW-GTR560. USDA, Forest Service, Pacific Northwest Research Station, Portland, Oregon. 254 p. HUGHES, W.R. 2000. Valuing a Forest as a Call Option: The Sale of Forestry Corporation of New Zealand. Forest Science. 46(1):32-39. HULL, J.C. 2003. Options, Futures, and Other Derivatives. 5th Edition. Prentice Hall. Upper Saddle River, New Jersey. 744 p. HULL, J.C., AND A. WHITE. 1988. An Overview of Continge nt Claims Pricing. Canadian Journal of Administrative Services. 5:55-61. HULTKRANTZ, L.1993. Informational Efficiency of Markets for Stumpage: Comment. American Journal of Agricult ural Economics. 75(1):234-238. INCE, P.J. 2002. Recent Economic Downturn and Pulpwood Markets. Paper presented at Southern Forest Economics Workers (SOFEW) Conference. 26 p. Retrieved 03-152006 from http://sofew.cfr.msstate.edu/index.html INSLEY, M.2002. A Real Options Approach to th e Valuation of a Forestry Investment. Journal of Environmental Economics and Management.44: 471-492. INSLEY, M., AND K. ROLLINS. 2005. On Solving the Multir otational Timber Harvesting Problem with Stochastic Prices: A Linear Complementarity Formulation. American Journal of Agricultural Economics. 87(3):735-755. JAMNICK, M., AND D. BECKETT.1987. A Logit Analysis of Private Woodlot Owners Harvest Decisions in New Brunswick. Ca nadian Journal of Forest Research 18(3):330-336. JOHNSON, J.W. 1961. Thinning Practices in S hort-Rotation Stands. Published in Advances in Management of Southern Pine: Proceedings of the 10th Annual Forestry Symposium. A.B. Crow (ed.).L ouisiana State University Press. Baton Rouge, LA. 50-60. KLEMPERER, D.W., AND D.R. FARKAS. 2001. Impacts on Economically Optimal Timber Rotations when Future Land Use Change s. Forest Science. 47(4):520-525. LINTNER, J. 1965a. Security Prices and Maximal Ga ins from Diversification. Journal of Finance. 20(4):587-615.

PAGE 120

111 LINTNER, J. 1965b. The Valuation of Risky Assets and the Selection of Risky Investment in Stock Portfolios and Capital Budgets. Review of Economics and Statistics. 47(1):13-37. LOHREY, R.E., AND KOSSUTH, S.V. Slash Pine. In Silvics of North America. 1990. Vol.1. Conifers. R.M. Burns and B.H. Honkala, tech. coords. Agriculture Handbook 654. U.S. Department of Agriculture, Fo rest Service, Washington, DC. 677-698. LU, F., AND P. GONG. 2003. Optimal Stocking Level and Final Harvest Age with Stochastic Prices. Journal of Forest Economics. 9:119-136 LUENBERGER, D. 1998. Investment Science. Oxford University Press. New York, NY. 494 p. LUND, D., AND B. OKSENDAL. 1991. Stochastic Models and Option Values: Applications to Resources, Environment and Investme nt Problems. North Holland. Amsterdam, The Netherlands. 301 p. LUTZ, J. 1999. Do Timber Prices Follow a Ra ndom Walk or Are They Mean Reverting? Paper presented at SOFEW conference (1999). 13 p. Retrieved 03-15-2006 from http://sofew.cfr.msstate.edu MANN, W. F., JR., AND H.G. ENGHARDT. 1972. Growth of Planted Slash Pine under Several Thinning Regimes. South. Forest Exp. Station., New Orleans, LA. USDA Forest Service. Research Paper SO-761. 10 p. MCDONALD, R.L., AND D.R. SIEGEL. 1985. Investment and the Valuation of Firms when there is an Option to Shut Down. Inte rnational Economic Review. 26(2):331-349 MCGOUGH, B., A.J. PLANTINGA, AND B. PROVENCHER. 2004. The Dynamic Behavior of Efficient Timber Prices. Land Economics. 80(1):95-108. MERTON, R.C. 1973. An Intertemporal Capital Asset Pricing Model. Econometrica. 41:867-887. MILLER, R.A., AND K. VOLTAIRE.1980. A Sequential Stochastic Tree Problem. Economic Letters.5:135-140. MILLER, R.A., AND K. VOLTAIRE.1983. A Stochastic Analys is of the Tree Paradigm. Journal of Economic Dynamics and Control 6:371-386. MORCK, R., E. SCHWARTZ, AND D. STANGELAND.1989. The Valuation of Forestry Resources under Stochastic Prices and Inventories. Journal of Financial and Quantitative Analysis. 24(4):473-487. NICHOLSON, W. 2002. Microeconomic Theory: Basic Principles and Extensions. 8th Edition. Thomson Learning, Inc. Amherst, Massachusetts. 748 p.

PAGE 121

112 NORSTROM C.J. 1975. A Stochastic Model for the Growth Period Decision in Forestry. Swedish Journal of Economics. 77(3):329-337. PIENAAR, L.V., AND J.W. RHENEY. 1995. An Evaluation of the Potential Productivity of Intensively Managed Pine Plan tations in Georgia. Final reported submitted to the Georgia Consortium for Technological Competitiveness in Pulp and Paper. 41 p. PLANTINGA, A.J. 1998.The Optimal Timber Rotation: An Option Value Approach. Forest Science. 44(2):192-202. PRESTEMON, J.P. 2003. Evaluation of U.S. Southern Pine Stumpage Market for Informational Efficiency. Canadian Jour nal of Forest Research. 33(4):561-572. ROSS, S.M. 2002. An Elementary Introduction to Mathematical Finance: Options and Other Topics. Cambridge University Press. New York, NY. 270 p. SCHWARTZ, E.S.1997. The Stochastic behavior of Commodity Prices: Implications for Valuation and Hedging Journal of Finance. 52(3):923-973. SHARPE, W.F.1963. A Simplified Model for Portfolio Analysis. Management Science. 9(2):277-293. SHARPE, W.F.1964. Capital Asset Prices: A Th eory of Market Equilibrium under Conditions of Risk. Journal of Finance. 19(3):425-442. SHIVER, B. D. 2004. Loblolly versus Slash Pine Gr owth and Yield Comparisons. In Dickens, E.D.; Barnett, J.P.; Hubbard, W.G.; Jokela, E.J., eds. 2004. Slash Pine: Still Growing and Growing! Proceedings of the Slash Pine Symposium. Gen. Tech. Rep. SRS-76. Asheville, NC: U.S. Depart ment of Agriculture, Forest Service, Southern Research Station. 45-49. SMITH, J.E., AND R. NAU. 1995. Valuing Risky Projects: Option Pricing Theory and Decision Analysis. Manageme nt Science. 41(5):795-816. SMITH J.E., AND K.F. MCCARDLE. 1999. Options in the Real World: Lessons Learned in Evaluating Oil and Gas Investments. Operations Research. 47(1):1-15. TAHVONEN, O., S. SALO, AND J. KUULUVAINEN. 2001. Optimal Forest Rotation and Land Values under a Borrowing Constraint. Jour nal of Economic Dynamics and Control. 25:1595-1627. TEETER, L.D., AND J.P. CAULFIELD. 1991. Stand Density Management Strategies under Risk: Effects of Stochastic Prices. Cana dian Journal of Forest Research. 21:13731379. TEETER, L.D., G. SOMERS AND J. SULLIVAN. 1993. Optimal Forest Harvest Decisions: A Stochastic Dynamic Programming Appro ach. Agricultural Systems.42(1):73-84.

PAGE 122

113 THOMSON, T.A. 1992a. Optimal Forest Rotation when Stumpage Prices follow a Diffusion Process. Land Ec onomics. 68(3):329-42. THOMSON, T.A. 1992b. Option Pricing and Timberland’s Land-Use Conversion Option: Comment. Land Economics. 68(4):462-466. TIMBER MART SOUTH. Warnell School of Forest Resour ces, Center for Forest Business, Warnell School of Forest Resources, University of Georgia, Athens, GA. TIMBER MART SOUTH MARKET NEWS QUARTERLY.2005. The Journal of Southern Timber Market News. Vol. 10. No.4 rev. Center for Forest Business, Warnell School of Forest Resources, University of Georgia, Athens, GA. 30 p. TSAY, R.S. 2002. Analysis of Financial Time Series. John Wiley & Sons, New York, NY. 448 p. WASHBURN, C.L., AND C.S. BINKLEY. 1990a. Informational Efficiency of Markets for Stumpage. American Journal of Agri cultural Economics 72(2):394-405. WASHBURN, C.L., AND C.S. BINKLEY. 1990b. On the Use of Period-Average Stumpage Prices to Estimate Forest Asset Pric ing Models. Land Economics. 66(4):379-393. WASHBURN, C.L., AND C.S. BINKLEY. 1993. Informational Efficiency of Markets for Stumpage: Reply. American Journal of Agricultural Economics. 75(1):239-242. WEAR, D.N., AND D.H. NEWMAN. 2004. The Speculative Shadow over Timberland Values in the US South. Journal of Forestry. December: 25-31. WILSON, J.D. 2000. Timberland Investments. In Modern Real Estate Portfolio Management. Frank J. Fabozzi Series edited by Susan Hudson-Wilson Wiley. New Hope, Pennsylvania. 149-164. WORKING, H. 1948. Theory of the Inverse Carrying Charge in Futures Markets. Journal of Farm Economics. 30:1-28 WORKING, H. 1949. The Theory of the Price of Storage. American Economic Review. 39:50-166 WORKING, H. 1960. Note on the Correlation of First Differences of Averages in a Random Chain. Economet rica. 28(4):916-918. YIN, R., AND D.H. NEWMAN. 1995. A Note on the Tree Cutting Problem in a Stochastic Environment. Journal of Fore st Economics. 1(2):181-190. YIN, R., AND D.H. NEWMAN. 1996. Are Markets for Stumpage Informationally Efficient? Canadian Journal of Fore st Research. 26:1032-1039.

PAGE 123

114 YIN, R., L.V. PIENAAR, AND M.E. ARONOW. 1998. The Productivity a nd Profitability of Fiber Farming Journal of Forestry 96(5):13-18. YOSHIMOTO, A., AND I. SHOJI. 1998. Searching for an Optimal Rotation Age for Forest Stand Management under Stoc hastic Log Prices. European Journal of Operational Research. 105:100-112. ZHANG, Y., D. ZHANG, AND J. SCHELHAS. 2005. Small-scale Non-indus trial Private Forest Ownership in the United States: Rati onale and Implications for Forest Management. Silva Fennica. 39(3):443–454. ZINKHAN, C. F. 1991. Option Pricing and Timber land’s Land-Use Conversion Option. Land Economics. 67(3):317-325. ZINKHAN, C. F. 1992. Option Pricing and Timber land’s Land-Use Conversion Option: Reply. Land Economics. 68(4):467-469.

PAGE 124

115 BIOGRAPHICAL SKETCH Shiv Nath Mehrotra was born in Vrindaba n, India, in 1965. After earning a Post Graduate Diploma in Forestry Management (P GDFM) from the Indian Institute of Forest Management, India, in 1991, he joined M/s. Century Pulp & Paper, India, in the Raw Materials department. In 1992 he earned a Ma ster of Arts (MA) degree in economics from Agra University, India. Serving M/s. Ce ntury Pulp & Paper in various capacities, he managed the fiber procurement operations and a farm forestry development program till June, 2002. In 2002 he was awarded a fellowshi p to pursue the docto ral program at the School of Forest Resources and Conservation, University of Florida. He joined the doctoral program in the fall of 2002, completing it in August, 2006.

PAGE 125

116


Permanent Link: http://ufdc.ufl.edu/UFE0015611/00001

Material Information

Title: Contingent Claims Analysis of Optimal Investment Decision Making in the Management of Timber Stands
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0015611:00001

Permanent Link: http://ufdc.ufl.edu/UFE0015611/00001

Material Information

Title: Contingent Claims Analysis of Optimal Investment Decision Making in the Management of Timber Stands
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0015611:00001


This item has the following downloads:


Full Text











CONTINGENT CLAIMS ANALYSIS OF OPTIMAL INVESTMENT DECISION
MAKING IN THE MANAGEMENT OF TIMBER STANDS














By

SHIV NATH MEHROTRA


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006
































Copyright 2006

by

Shiv Nath Mehrotra
















ACKNOWLEDGMENTS

I am grateful to my supervisory committee chair, Dr. Douglas R. Carter, co-chair,

Dr. Janaki R. Alavalapati, and Drs. Donald L. Rockwood, Alan J. Long and Charles B.

Moss for their academic guidance and support. I particularly wish to thank Dr. Charles

Moss for always finding time to help with the finance theory as well as for aiding my

research in many ways.

I thank my family for their support and encouragement.




















TABLE OF CONTENTS


page

ACKNOWLEDGMENT S ................. ................ iii....... ....


LIST OF TABLES ........._.._... ..............vi..._.._........


LIST OF FIGURES .............. ....................vii


AB S TRAC T ......_ ................. ..........._..._ viii..


CHAPTER


1. INTRODUCTION ................. ...............1.......... ......


Economic Conditions in Timber Markets ................. ...............1............ ...
The Forest Industry in Florida ................ ...............2............ ...
Outline of the Investment Problem ................. ...............3............ ...
Research Objectives............... ...............

2. PROBLEM BACKGROUND .............. ...............9.....


Introduction to Slash Pine....................... .... ............
Slash Pine as a Commercial Plantation Crop .............. ...............9.....
Slash Pine Stand Density ................. ...............11................
Thinning of Slash Pine Stands............... ...............12.
Financial Background ............... ... ........... ............ .............1
The Nature of the Harvesting Decision Problem ................. .......................14
Arbitrage Free Pricing .............. ... .... ... ... ... .. .......... ...........1
Review of Literature on Uncertainty and Timber Stand Management. .................. ....20

3. THE CONTINGENT CLAIMS MODEL AND ESTIMATION
METHODOLOGY .............. ...............26....


The One-Period Model .............. ...............26....
The Deterministic Case .............. ...............26....
The Stochastic Case....................... ........................2
Form of the Solution for the Stochastic Value Problem. ........._..._.._ ........_.......3 1
The Contingent Claims Model ................. ...............31................
The Lattice Estimation Models............... ...............38.
T he B inomi al Latti ce M od el .............. ...............3 8....












The Trinomial Lattice Model for a Mean Reverting Process..............................42
The Multinomial Lattice Model for Two Underlying Correlated Stochastic
Assets ........._.___..... .__ ...............43....


4. APPLICATION OF THE CONTINGENT CLAIMS MODEL ................ ...............45


Who is the Pulpwood Farmer? ............ .... ...............45
The Return to Land in Timber Stand Investments................ ..............5
On the Convenience Yield and the Timber Stand Investment .............. ..................57

Dynamics of the Price Process ................. ......... ...............60.....
Modeling the Price Process .............. ...............63....
The Geometric Brownian Motion Process .............. ........... ...............6
Statistical Tests of the Geometric Brownian Motion Model ............... .... ...........67
The Mean Reverting Process............... .. .... ................7
Statistical Tests of the Mean Reverting Process Model .............. ................74
Instantaneous Correlation ............ .....___ ......__ ............7
The D ata..................... ... .... ..........7
Growth and Yield Equations .............. ...............76....
Plantation Establishment Expenses .............. ...............78....
Risk-Free Rate of Return ............ .....___ ...............79..
The Model Summarized .............. ...............79....


5. RE SULT S AND DIS CU SSION............... ..............8


A Single Product Stand and the Geometric Brownian Motion Price Process ............81
Sensitivity Analysis............... .... ... .. ...........8
Comparison with the Dynamic Programming Approach .................. ...............89
A Single Product Stand and the Mean Reverting Price Process ............... .............90
The Multiple Product Stand and Geometric Brownian Motion Price Processes........93
Thinning the Single Product Stand and the Geometric Brownian Motion Price
Process .............. ...............96....
D discussion .................. .. ....... .... ........... .............9
Recommendations for Further Research .............. ...............104....


APPENDIX CORRELATION OF FIRST DIFFERENCES OF AVERAGES OF
TWO RANDOM CHAINS................ ...............105


LI ST OF REFERENCE S ................. ...............107................


BIOGRAPHICAL SKETCH ................. ...............115......... ......

















LIST OF TABLES


Table pg

1-1. Comparison of applied Dynamic Programming and Contingent Claims
approaches ................. ...............6.................

2-1. Area of timberland classified as a slash pine forest type, by ownership class,
1980 and 2000 (Thousand Acres) .............. ...............10....

3-1. Parameter values for a three dimensional lattice ......____ ... ......_ ...............44

4-1. Florida statewide nominal pine stumpage average product price difference and
average relative prices (1980-2005) ...._.. ................ ............... 46 ....

4-2. The effect of timber product price differentiation on optimal Faustmann rotation...47

4-3. The effect of timber product relative prices on optimal Faustmann rotation ............47

4-4. Estimated GBM process parameter values for Florida statewide nominal
quarterly average pulpwood prices .............. ...............66....

4-5. Results of Jarque-Bera test applied to GBM model for Florida statewide nominal
quarterly average pulp wood stumpage prices .............. ...............70....

4-6. Inflation adjusted regression and MR model parameter estimates............._._... .........73

4-7. Results of Jarque-Bera test applied to MR model residuals for Florida statewide
nominal quarterly average pulpwood stumpage prices ................ ........._ ......75

4-8. Average per acre plantation establishment expenses for with a 800 seedlings/acre
planting density .............. ...............78....

5-1. Parameter values used in analysis of harvest decision for single product stand
with GBM price process............... ...............82

5-2. Parameter values used in analysis of harvest decision for single product stand
with MR price process............... ...............91

5-3. Parameter values used in analysis of harvest decision for multiproduct stand with
GBM price processes .............. ...............93....


















LIST OF FIGURES


Figure pg

1-1. Florida statewide nominal quarterly average pine stumpage prices (1976-2005 II
qtr) .............. ...............1.....

3-1. Typical evolution of even-aged stand and stumpage values for the Faustmann
analy si s............... ............... 2

4-1. Sample autocorrelation function plot for nominal Florida statewide pulpwood
stumpage instantaneous rate of price changes.. .........._..._ ................. ....._._.69

4-2. Sample autocorrelation function plot for nominal Florida statewide pulpwood
stumpage price MR model regression residuals ................. .....___ .........._.....75

5-1. Total per acre merchantable yield curve for slash pine stand............... ..................8

5-2. Crossover price line for single product stand with GBM price process...................83

5-3. Crossover price lines for different levels of intermediate expenses ........................85

5-4. Crossover price line for different levels of standard deviation .............. .................86

5-5. Crossover price lines for varying levels of positive constant convenience yield......87

5-6. Crossover price lines for different levels of current stumpage price.........................88

5-7. Crossover price line for single product stand with MR price process.......................92

5-8. Merchantable yield curves for pulpwood and CNS ................. ........................93

5-9. Crossover price lines for multiproduct stand ................. ...............95......_._. .

5-10. Single product stand merchantable yield curves with single thinning at different
ages ........._._. ._......_.. ...............97.....
















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CONTINGENT CLAIMS ANALYSIS OF OPTIMAL INVESTMENT DECISION
MAKING IN THE MANAGEMENT OF TIMBER STANDS


By

Shiv Nath Mehrotra

August 2006

Chair: Douglas R. Carter
Cochair: Janaki R. Alavalapati
Maj or Department: Forest Resources and Conservation

The treatment of timber stand investment problems involving stochastic market

prices for timber and multiple options can be considerably improved by the application of

real options analysis. The analysis is applied to the dilemma of mature slash pine

pulpwood crop holders in Florida facing depressed markets for their product. Using a

contingent claims approach an arbitrage free market enforced value is put on the option

of waiting with or without commercial thinning, which when compared with the present

market value of stumpage allows an optimal decision to be taken.

Results for two competing models of timber price process support the decision to

wait for a representative unthinned 20-year-old cutover slash pine pulpwood stand with

site index 60 (age 25) and initial planting density 800 trees per acre. The present (III Qtr

2005) value of stumpage is $567/acre as compared to the calculated option value for the

Geometric Brownian motion price process of $966/acre and $1,290/acre for the Mean









Reverting price process. When the analysis differentiates the merchantable timber yield

between products pulpwood and chip-n-saw with correlated Geometric Brownian motion

price processes the option value rises to $1,325/acre for a stumpage market value of

$585/acre. On the other hand the commercial thinning option holds no value to the single

product stand investment when the poor response of the slash pine species to late rotation

thinning is accounted for.

The analysis shows that the measurement of option values embedded in the timber

stand asset is hampered by the lack of availability of market information. The absence of

a market for the significant catastrophic risk associated with the asset as well other non-

marketed risks also hampers the measurement of option values.

The analysis highlights the importance of access to market information for

optimal investment decision making for timber stand management. It concludes that stand

owners can realize the full value of the significant managerial flexibility in their stands

only when access to market information improves and markets for trading in risks

develop for the timber stand investment.

















CHAPTER 1
INTTRODUCTION

Economic Conditions in Timber Markets

Pine pulpwood prices in Florida have been declining since the peaks of the early

1990's (Figure 1-1). After reaching levels last seen in the early 1980's, in 2005 the prices

have shown signs of a weak recovery. The trend in pulpwood markets reflects the impact

of downturn in pulp and paper manufacturing resulting from several factors (Ince 2002)

like:


50.00-

45.00






O -*Saw Timber Price
S25.00 -a-Chip-n-saw Price
P- -Pulpwood Prices





5.00



Year

Source: Timber Mart-South


Figure 1-1. Florida statewide nominal quarterly average pine stumpage prices (1976-2005
II qtr)

1. A strong US dollar, rising imports and weakness in export markets since 1997.

2. Mill ownership consolidation and closures.









3. Increased paper recycling along with continued expansion in pulpwood supply
from managed pine plantations, particularly in the US South.

In a discussion of the findings and proj sections of the Resource Planning Act (RPA),

2000 Timber Assessment (Haynes 2003), Ince (2002) has noted that the pulp and paper

industry sector has witnessed a fall in capacity growth since 1998 with capacity actually

declining in 2001. The report proj ects that US wide pulpwood stumpage prices would

stabilize in the near term with a gradual recovery, but would not increase appreciably for

several decades into the future. With anticipated expansion in southern pine pulpwood

supply from maturing plantations, pine stumpage prices are proj ected to further subside

after 2015. Pine pulpwood stumpage prices are not proj ected to return to the peak levels

of the early 1990's in the foreseeable future (Adams 2002). Nevertheless, the US South is

proj ected to remain the dominant region in production of fiber products and pulpwood

demand and supply.

The Forest Industry in Florida

Florida has over 16 million acres of forests, representing 47% of the state' s land

area. Non-industrial private forest (NIPF) owners hold approximately 53% of the over 14

million acres of timberland in the state (Carter and Jokela 2002). The forest based

industry in Florida has a large presence with close to 700 manufacturing facilities. The

industry produces over 900,000 tons of paper and over 1,700,000 tons of paperboard

annually apart from hardwood and softwood lumber and structural panels (AF&PA

2003).

Pulpwood and sawlogs are the principal roundwood products in Florida accounting

for up to 80% of the output by volume. Pulpwood alone accounted for more than 50% of

the roundwood output in 1999. NIPF land contributed 45% of the total roundwood output









while an equal percent came from industry held timberlands. Slash and longleaf pine

provided 78% of the softwood roundwood output (Bentley et al. 2002).

Forest lands produce many benefits for their owners who express diverse reasons

for owning them. A survey of private forest land owners in the US South by Birch (1997)

found that nearly 3 8% of the private forestland owners hold forestland primarily because

it is simply a part of the farm or residence. Recreation and esthetic enj oyment was the

primary motive for 17% while 9% of the owners stated farm or domestic use as the most

important reason for owning forest land. Amongst commercial motives, land investment

was the primary motive for 12% of the owners. At the same time expected increase in

land value in the following 10 years was listed as the most important benefit from owning

timberland by 27% of landowners accounting for 21% of private forests listed.

Significantly, timber production was the primary motive for only 4% of the private

forestland owners, but these owners control 35% of the private forestland. Similarly, only

7% of the owners have listed income from the sale of timber as the most important

benefit in the following 10 years, but they control 40% of the private forest.

Outline of the Investment Problem

Timberland is defined as land that either bears or has the potential to bear

merchantable quality timber in economic quantities. The US has nearly 740 million acres

of forestland, of which 480 million acres is classified as timberland and the rest are either

preserves or lands too poor to produce adequate quality or quantity of merchantable

timber (Wilson 2000).

Small private woodlot ownership (<100 acres) accounts for more than 90% of

NIPF timberland holdings in the US and remains a significant part of the investment

pattern (Birch 1996). The prolonged depression in pulpwood prices poses a dilemma for









NIPF small woodlot timber cultivators in Florida who are holding a mature pulpwood

crop. These pulpwood farmers must decide about harvesting or extending the rotation.

The option to extend the rotation and wait out the depressed markets brings further

options like partial realization of revenues immediately through commercial thinnings.

These decisions must be made in the face of uncertainty over the future market prices)

for their timber productss. Slash pine pulpwood stand owners must also contend with the

fact that the species does not respond well to late rotation thinnings, limiting the options

for investing in late rotation products (Johnson 1961).

The timber stand investment is subj ect to several risks, marketed as well as non-

marketed (e.g., risk of damage to the physical assets in the absence of insurance).

Understanding and incorporating these risks into management decisions is crucial to

increasing the efficiency of the investment. The asset value/price risk is the most

common form of risk encountered by all investors. For most forms of investments

markets have developed several Einancial instruments for trading in risk. Insurance

products are the most common while others such as forwards, futures and options are

now widely used. Unfortunately, timberland investments lag behind in this respect.

Institutional timberland investors, with their larger resources, deal with specific risk by

diversification (geographic, product). Small woodlot owners must contend with the

greatest exposure to risk.

Investment risk in timber markets has been long recognized and extensively treated

in literature. As a result, on the one hand, there is a better appreciation of the nature and

importance of correctly modeling the stochastic variables, and on the other hand, there is

improved insight into the nature of the investment problem faced by the decision maker.










Despite the considerable progress, no single universally acceptable approach or model

has yet been developed for analyzing and solving these problems. Due to the Einancial

nature of the problem, developments in Einancial literature have mostly preceded progress

in forest economics research. In the last decades, the most important and influential

development in Einancial theory has been that of the option pricing theory. Several timber

investment problems are in the nature of contingent claims and best treated by the

application of option pricing theory or what is described as real options analysis (since

the investments are real as opposed to Einancial instruments).

It is known that for investment decisions characterized by uncertainty,

irreversibility, and the ability to postpone, investors set a higher hurdle rate. Stand

management decisions like commercial thinning and final harvest share these

characteristics. Options analysis provides a means for valuing the flexibility in these

investments. There are two approaches to options analysis, namely, the dynamic

programming (DP) approach and the contingent claims (CC) approach. Almost all

treatment of investment problems in forestry literature uses the DP approach to options

analysis. Despite its popularity in research, the applied DP approach has some drawbacks

which limit its utility for research or empirical applications. The CC valuation is free

from these limitations. Some important features of the application of the two approaches

are compared in Table 1.1.

The most critical problem is that application of the DP approach requires the

determination of an appropriate discount rate. In the absence of theoretical guidance on

the subj ect studies are forced to use arbitrary discount rates with little relation to the risk

of the asset. For example, Insley (2002) uses a discount rate of 5%, Insley and Rollins










(2005) use 3% and 5% real discount rates alternately, while Plantinga (1998) uses a 5%

"real risk-free" discount rate even though the analysis uses subj ective probabilities. No

justification is offered for the choice of the discount rate (Plantinga (1998) cites Morck et

al. (1989) for providing a rate "typical" to timber investment). Hull (2003) illustrates the

difference between the discount rate applicable to the underlying instrument and the

option on it. For a 16% discount rate applicable to the underlying, the illustration shows

that the discount rate on the option is 42.6%. Explaining the higher discount rate required

for the option, Hull (2003) mentions that a position on the option is riskier than the

position on the underlying. Another problem with the use of arbitrary discount rates is

that the results of different studies are not comparable.

Table 1-1. Comparison of applied Dynamic Programming and Contingent Claims
approaches


Dynamic Programming Approach


1. Requires the use of an externally
determined discount rate. This
discount rate is unobservable
(unless the option itself is traded).
The discount rates used in published
forestry literature bear no relation to
the risk of the asset.

2. Published forestry literature does
not specify whether the marketed,
the non-marketed or both components
of the asset's risk are being treated.


3. Risk preferences are treated
inconsistently in published forestry
literature .

4. Requires use of historical estimates
of mean return or drift which is
susceptible to large statistical errors.


Contingent Claims Approach


Uses a risk-free discount rate that
is reliably estimated from existing
market instruments.






Distinguishes between marketed and
non-marketed components of the
assets risk. Applies only to marketed
risk. Extensions have been proposed to
account for non-marketed risk

It is a risk neutral analysis.



Replaces the drift with the risk-free
rate of return. Estimates of
historical variance are relatively stable.









Similarly, none of the published research on options analysis in forestry specifies

whether the marketed, the non-marketed or both risks are being treated. Since the only

stochasticity allowed is in the timber price, it may be possible to infer that the marketed

risk is the obj ect of the analysis. But such inference would challenge the validity of some

of their conclusions. For example, Plantinga (1998) concludes that reservation price

policies, on an average, increase rotation lengths in comparison to the Faustmann

rotation, while management costs decrease rotation lengths. By including a notional cost

of hedging against non-marketed risks (insurance purchase) in the analysis as a

management cost any conclusion regarding the rotation extension effect of reservation

prices policies would be cast in doubt without better market data on the size of these

hedging costs.

Failure to highlight the treatment of risk preferences in the analysis is another

source of confusion. Some studies like Brazee and Mendelsohn (1988) specify that the

decision maker is risk neutral. Knowing this helps individuals to interpret the results

according to their risk preferences. But when risk preferences are not specified, as in

Insley (2002) for example, and there is confusion over the discount rate applied, the

results produced by the analysis lose interpretative value.

Real options analysis as it is applied through contingent claims valuation is itself a

nascent branch of the option pricing theory which has developed principally by extending

option pricing concepts to the valuation of real assets. There is increasing recognition of

the shortcomings of the techniques developed for pricing financial asset options when

applied to real assets and several modified approaches have been proposed. Nevertheless,

application of real options analysis to timber investment decisions offers an opportunity










to take advantage of a unified financial theory to treat the subject and thus obtain a richer

interpretation of the results.

Research Objectives

The general obj ective of this study is to apply contingent claims analysis to

examine typical flexible investment decisions in timber stand management, made under

uncertainty. The analysis is applied to the options facing the NIPF small woodlot owner

in Florida holding a mature even aged slash pine pulpwood crop. The specific obj ectives

are

1. To analyze and compare the optimal clear-cut harvesting decision for a single
product, i.e., pulpwood, producing stand with Geometric Brownian Motion
(GBM) and Mean Reverting (MR) price process alternately.

2. To analyze the optimal clear-cut harvesting decision for a multiple product, i.e.
pulpwood and chip-n-saw, producing stand with their prices following correlated
GBM processes.

3. To analyze the optimal clear-cut harvesting decision with an option for a
commercial thinning for a single product, i.e., pulpwood, producing stand with a
GBM price process.















CHAPTER 2
PROBLEM BACKGROUND

Introduction to Slash Pine

Slash pine (Pinus elliottii var. elliottii) is one of the hard yellow pines indigenous

to the southeastern United States. Other occasional names for the specie are southern

pine, yellow slash pine, swamp pine, pitch pine, and Cuban pine. Along with the most

frequently encountered variety P. elliottii var. elliottii the other recognized variety is P.

elliottii var. densa, which grows naturally only in the southern half of peninsula Florida

and in the Keys (Lohrey and Kossuth 1990).

The distribution of slash pine within its natural range (80 latitude and 100

longitude) was initially determined by its susceptibility to fire injury during the seedling

stage. Slash pine grew throughout the flatwoods of north Florida and south Georgia as

well as along streams and the edges of swamps and bays. Within these areas either ample

soil moisture or standing water protected young seedlings from frequent wildfires in

young forests (Lohrey and Kossuth 1990).

Slash pine is a frequent and abundant seed producer and is characterized by rapid

early growth. After the sapling stage it can withstand wildfires and rooting by wild hogs

which has helped it to spread to drier sites (Lohrey and Kossuth 1990).

Slash Pine as a Commercial Plantation Crop

Florida has the largest area of timberland (Barnett and Sheffield 2004) classified as

slash pine forest type (49%) while nonindustrial private landowners hold the largest

portion of slash pine timberland (Table 2-1)









Table 2-1. Area of timberland classified as a slash pine forest type, by ownership class,
1980 and 2000 (Thousand Acres)

Ownership Class 1980 2000

National Forest 522 493
Other Public 569 684
Forest Industry 4,649 3,719
Nonindustrial Private 7,039 5,479

Total 12,779 10,375

Source: Barnett and Sheffield, 2004

Slash pine makes rapid volume growth at early ages and is adaptable to short

rotations under intensive management. Almost three-fourths of the 50-year yield is

produced by age 30, regardless of stand basal area. Below age 30, maximum cubic

volume yields are usually produced in unthinned plantations, so landowners seeking

maximum yields on a short rotation will seldom find commercial thinning beneficial.

Where sawtimber is the obj ective, commercial thinnings provide early revenues while

improving the growth and quality of the sawtimber and maintaining the stands in a

vigorous and healthy condition (Lohrey and Kossuth 1990).

A study by Barnett and Sheffield (2004) found that a maj ority (59%) of the slash

pine inventory volume in plantations and natural stands was in the <10" dbh class while

about 25% of the stands were less than 8 years old. The study concluded that this

confirmed the notion that slash pine rotations are typically less than 30 years and that the

stands are intensively managed.

Plantation yields are influenced by previous land use and interspecies competition.

Early yields are usually highest on recently abandoned fields where the young trees

apparently benefit from the residual effects of tillage or fertilizer and the nearly complete

lack of vegetative competition. Plantations established after the harvest of natural stands









and without any site treatment other than burning generally have lower survival and,

consequently, lower basal area and volume than stands on old fields. Yields in plantations

established after timber harvest and intensive site preparation such as disking or bedding

are usually intermediate.

Comparing slash pine to loblolly pine (Pinus taeda L.), Shiver (2004) notes that

slash pine may be preferred over loblolly pine for reasons other than wood yields. For

instance, slash pine would be the favored species for landowners who want to sell pine

straw. Slash pine also prunes itself much better than loblolly, and for solid wood products

the lumber grade will probably be higher for slash pine. Slash pine is more resistant to

southern pine beetle (Dendroctonus frontalis Zimmermann) attack than loblolly and it is

rarely bothered with pine tip moth (Rhyacionia frustr anar~rtrt~t~r (Comstock)), which can

decimate young loblolly stands.

Slash Pine Stand Density

Dickens and Will (2004) discuss the effects of stand density choices on the

management of slash pine stands. The choice of initial planting density and its

management during the rotation depends on landowner obj ectives like maximizing

revenues from pine straw, obtaining intermediate cash flows from thinnings or growing

high value large diameter class timber products. High planting density in slash pine

stands decreases tree diameter growth as well as suppresses the tree height growth to a

lesser extent, but total volume production per unit of land is increased. However, the

volume increment observed for early rotation ages soon peaks and converges to that of

lower density stands as the growth rate of high density stands reach a maximum earlier.

Citing a study at the Plantation Management Research Cooperative, Georgia, Dickens









and Will (2004) remark that management intensity does not change the effects of stand

density.

Dickens and Will (2004) mention that higher density plantings achieve canopy

closure, site utilization, and pine straw production earlier than lower density plantings

under the same level of management. Higher planting densities also may be beneficial on

cut-over sites with low site preparation and management inputs. The higher planting

densities help crop trees occupy the site, whereas the lower planting densities may permit

high interspecific competition until much later during stand development, reducing early

stand volume production.

Thinning of Slash Pine Stands

Mann and Enghardt (1972) describe the results of subj ecting slash pine stands to

three levels of thinnings at ages 10, 13 & 16. Early thinnings removed the diseased trees

while later thinnings concentrated on release of better stems. Their study concluded that

early and heavy thinnings increased diameter growth but reduced volume growth. The

longer thinnings were deferred, the slower was the response in diameter growth. They

concluded that age 10 was too early for a thinning as most of the timber harvested was

not merchantable and volume growth was lost, even though the diameter increment

results were the best. The decision between thinning at ages 13 and 16 depended on the

end product, the ability to realize merchantable volumes in thinnings and the loss of

volume growth. They recommend that short rotation pulpwood crops were best left

unthinned as the unthinned stands had good volume growth. Quoting Mann and Enghardt

(1972) "volume growth is good, no costs are incurred for marking, there are fewer small

trees to harvest and stand disturbances that may attract bark beetle are avoided" (Mann

and Enghardt 1972, p.10).










Johnson (1961) has discussed the results of a study of thinning conducted on

heavily stocked industrial slash pine stands of merchantable size. The study found that

slash pine does not respond well to late release i.e., if it has been grown in moderately

dense stands for the first 20 to 25 years of its life. It does not stagnate, except perhaps on

the poorest sites, but it cannot be expected to respond to cultural treatments such as

thinnings as promptly or to the degree desired. Johnson (1961) observes that the typical

thinning operation that removes four to six cords of wood from well-stocked stands is

nothing more than an interim recovery of capital from the forestry enterprise. These

thinnings do not stimulate growth of the residual stand or total production. The study

found no real increase in total volume production or in average size of trees fr~om

commercial thrinning\ in slash pine stands being managed on short rotations for small

products.

Johnson (1961) concludes that silvicultural considerations for commercial thinning

in small product slash pine forest management are secondary to commercial

considerations because of its response to intermediate cuttings.

Financial Background

The timber farming investment exposes the investor to the risks that the asset

carries. These risks come in the form of marketed risks like the volatile market price for

the timber products or non-marketed risks that also effect the value of the investment

such as hazards that threaten the investment in the form of fire, pests, adverse weather

etc.

Usually, investors separate the spectrum of risks taken on by them from an

investment into core and non-core risks. The core risk could be the market price of the

investments output or product. This is the risk the investor expects to profit out of and









likes to retain. The non-core risk like the non-marketed risks listed above are undesirable

and the investor would ideally like to transfer such risks. A common market instrument

for risk transfer is the insurance product. By paying a price one can transfer the

undesirable risk to the market. If the non-marketed risks associated with the timber

investment were marketed, the market data available can be incorporated into investment

analysis. In the absence of markets for a part or all of an assets risk, the common asset

pricing theories are not applicable and alternate methods have to be applied. The analysis

in this study is restricted to the marketed risk in the form of timber price risk only.

The Nature of the Harvesting Decision Problem

Following a price responsive harvesting regime, the slash pine pulpwood farming

investor holding a mature crop and facing a stochastically evolving pulpwood market

price would like to know the best time for selling his crop. From his knowledge of past

movements of market price for pulpwood the investor knows that the present price is

lower than the average of prices in the recent past. He may sell the crop at the present

price but significantly he has the option to hold the crop. The crop is still growing, both

in size and possibly in value, and that provides incentive to hold the harvest. But the

market price is volatile. The future market price for pulpwood cannot be predicted with

certainty. How does the investor decide his immediate action; sell or hold?

While equilibrium asset values are determined by their productive capacities their

instantaneous market values are determined by the ever changing market forces. Asset

holders would like to eamn a fair compensation on their investment i.e., the principal plus

a return for the risk undertaken by holding the investment over time. But there is no

guarantee to earning a 'fair' return in the market place. Usually investors have a finite









time frame for holding an asset and must realize the best value for their asset in this

period.

The decision to hold the asset for a future sale date is a gamble, an act of

speculation. It carries the risk of loss as well as the lure of profit. But all investments in

risky assets are speculative activities. One investment may be more risky than another but

one market equilibrium theory in the form of the Capital Asset Pricing Model (CAPM)

assures us that their expected returns are proportional to their risk, specifically to the

systematic or non-diversifiable portion of their risk. The CAPM theory, development of

which is simultaneously attributed to Sharpe (1963, 1964) and Lintner (1965a, 1965b)

amongst others, has it that at any point in time each marketed asset has an associated

equilibrium rate of return which is a function of its covariance with the market portfolio

and proportional to the market price of risk. The expression 'rate of return' refers to the

capital appreciation plus cash payout, if any, over a period of time, expressed as a ratio to

the asset value at the commencement of the period.

If all risky investments are gambles, how does one choose amongst the enormous

variety of gambles that are available in the market place? Once again, financial theory

informs us that the choice amongst risky assets depends on the risk attitudes of

individuals. Individuals would apportion their wealth amongst a portfolio of assets

(which serves to eliminate the non-systematic risk of the assets). The portfolio is

constructed to match the risk-return tradeoff sought by the individual. Once chosen, how

does one decide how long to hold an asset? The risk associated with every asset as well

as its expected return changes over time. Over a period of time the risk-return









characteristic of a particular asset may lose its appeal to the individual's portfolio which

itself keeps changing with maturing of risk attitudes over time.

Returning to the pulpwood farmer' s decision problem, the question boils down to

this: How does the pulpwood farmer decide whether his investment is worth holding

anymore? It follows from the arguments above that the crop would be worth holding as

long it can be expected to earn a return commensurate with its risk. But, how is the

comparison between the expected rate of return and the required rate of return achieved?

The usual financial technique is to subj ectively estimate the expected cash flows from the

asset, discount them to the present using a risk-adjusted discount rate, and compare the

resulting value to the present market value of the asset. If the expected discounted value

is higher, then the expected rate of return over the future relevant period under

consideration is higher than the required rate of return. And how does this work? It works

because the required rate of return and the risk-adjusted discount rate are different names

for the same value. The expected equilibrium rate of return generated by the CAPM

represents the average return for all assets sharing the same risk characteristics or in other

words, the opportunity cost. When we use the risk-adjusted discount rate to calculate the

present value of the future cash flows, we are in effect accounting for the required rate of

return. The discounting apportions the future cash flows between the required rate of

return and residual value, if any.

Can discounted cash flow (DCF) analysis be used to solve the pulpwood farmer' s

harvesting problem? The pulpwood farmer' s valuation problem is compounded by the

ability to actively manage the investment (flexibility) or more specifically, the ability to

postpone the harvest decision should the need arise. Not only do decision makers have to









deal with an uncertain future market value for the pulpwood crop but they must also

factor in the response to the possible values. The termination date or harvest date of the

timber stand investment and thus its payoff is not fixed or predetermined. Traditional

DCF analysis can deal with the price uncertainty by the technique of subj ective

expectations but has no answer for flexibility of cash flow timings. This shortcoming has

been overcome by decision analysis tools like decision trees or simulation to account for

the state responsive future cash flows. So, are tools like decision trees or simulation

techniques the answer to the pulpwood farmer's dilemma? Almost, except that the

appropriate discount rate still needs to be determined.

Arbitrage Free Pricing

Despite widespread recognition of its shortcomings, the CAPM generated expected

rate of return is most commonly used as the risk-adjusted discount rate appropriate to an

investment. It turns out that while the mean-variance analysis led school of equilibrium

asset pricing does a credible job of explaining expected returns on assets with linear risk

they fail to deal with non-linear risk of the type associated with assets whose payoffs are

contingent. Hull (2003) provides an illustration to show that the risk (and hence discount

rates) of contingent claims is much higher than that of the underlying asset. The

pulpwood farmer holds an asset with a contingent claim because the payoff from his asset

over any period is contingent on a favorable price being offered by the market for his

crop.

There are two alternate though equivalent techniques for valuing a risky asset by

discounting its expected future cash flows. One, as already described involves an

adjustment to the discount rate to account for risk. The other method adjusts the expected

cash flows (or equivalently, the probability distribution of future cash flows) and uses the









risk-free rate to discount the resulting certainty equivalent of the future cash flows. The

CC valuation procedure follows this certainty equivalent approach. The argument is

based on the Law of One Price (LOP). The LOP argues that in a perfect market, in

equilibrium, only one price for each asset, irrespective of individual risk preferences, can

exist as all competing prices would be wiped out by arbitrageurs.

Baxter and Rennie (1996) illustrate the difference between expectation pricing and

arbitrage pricing using the example of a forward trade. Suppose one is asked by a buyer

to quote today a unit price for selling a commodity at a future date T A fair quote would

be one that yields no sure profit to either party or in other words provides no arbitrage

opportunities. Using expectation pricing, the seller may believe that the fair price to quote

would be the statistical average or expected price of the commodity, E [S, ], where S, is

the unit price of the commodity at time T and E is the expectation operator. But a

statistical average would turn out to be the true price only by coincidence and thus could

be the source of significant loss to the seller.

The market enforces an arbitrage free price for such trades using a different

mechanism. If the borrowing/lending rate is r then the market enforced price for the

forward trade is Sne'T This price follows the logic that it is the cost that either party

would incur by borrowing funds at the rate r to purchase the commodity today and store

it for the necessary duration (assuming no storage costs). This price would be different

from the expected price, yet offer no arbitrage opportunities.

The arbitrage free approach to the problem of valuing financial options was first

solved by Black and Scholes (1973) using a replicating portfolio technique. The

replicating portfolio technique involves finding an asset or combination of assets with









known values, with payoffs that exactly match the payoffs of the contingent claim. Then,

using the LOP it can be argued that the contingent claim must have the same value as the

replicating portfolio. Financial options are contingent claims whose payoffs depend on

some underlying basic Einancial asset. These instruments are very popular with hedgers

or risk managers.

The underlying argument to the equilibrium asset pricing methods is the no

arbitrage condition. The no arbitrage condition requires that the equilibrium prices of

assets should be consistent in a way that there is no possibility of riskless profit. A

complete market offers no arbitrage opportunities as there exists a unique probability

distribution under which the prices of all marketed assets are proportional to their

expected values. This unique distribution is called a risk neutral probability distribution

of the market. The expected rate of return on every risky asset is equal to the risk-free

rate of return when expectations are calculated with respect to the market risk neutral

di stributi on.

Copeland et al. (2004) define a complete market as one in which for every future

state there is a combination of traded assets that is equivalent to a pure state contingent

claim. A pure state contingent claim is a security with a payoff of one unit if a particular

state occurs, and nothing otherwise. In other words, when the number of unique linearly

independent securities equals the total number of alternative future states of nature, the

market is said to be complete.

Equilibrium asset pricing theories have been developed with a set of simplifying

assumptions regarding the market. In addition to completeness and pure competition, CC

analysis theory assumes that the market is perfect i.e., it is characterized by









1.An absence of transaction costs & taxes
2.Infinite divisibility of assets.
3.A common borrowing and lending rate.
4.No restrictions on short sales or the use of its proceeds.
5.Continuous trading.
6.Costless access to full information.


Review of Literature on Uncertainty and Timber Stand Management

The published literature on treatment of uncertainty in timber stand management is

reviewed here from an evolutionary perspective. A selected few papers are reviewed as

examples of a category of research.

The literature dealing with static analysis of financial maturity of timber stands is

vast and diverse. Including the seminal analysis of Faustmann (1849) several approaches

to the problem have been developed. The early work on static analysis has been

summarized by Gaffney (1960) and Bentley and Teeguarden (1965). These approaches

range from the zero interest rate models to present net worth models and internal rate of

return models. The Soil Rent/Land Expectation Value (LEV) model, also known as the

Faustmann-Ohlin-Pressler model, is now accepted as the correct static financial maturity

approach. However, the static models are built on a number of critical assumptions which

erode the practical value of the analysis. Failure to deal with the random nature of stand

values is a prominent shortcoming. Uncertain future values mean that the date of optimal

harvest cannot be determined in advance but must be price responsive i.e., it must depend

on the movement of prices and stand yield amongst other things. The harvest decision is

local to the time of decision and it is now recognized that a dynamic approach to address

the stochastic nature of timber values is appropriate.

Amongst the first to treat stochasticity in stand management, Norstom (1975) uses

DP to determine the optimal harvest with a stochastic timber market price. The stochastic









variable was modeled using transition matrices as in Gassmann (1988), who dealt with

harvesting in the presence of Gire risk. The use of transition matrices has persisted with

Teeter et al. (1993) in the determination of the economic strategies for stand density

management with stochastic prices.

However, much advance followed in modeling stochasticity with the introduction

of the use of diffusion processes in investment theory. Brock et al. (1982) illustrated the

optimal stopping problem in stochastic Einance using the example of a harvesting

problem over a single rotation of a tree with a value that grows according to a diffusion

process. Miller and Voltaire (1980, 1983) followed up, extending the analysis to the

multiple rotation problems. Clarke and Reed (1989) obtained an analytical solution using

the Myopic Look Ahead (MLA) approach, allowing for simultaneous stochasticity in

timber price and yield. These papers illustrate the use of stochastic dynamic

programming for stylized problems which are removed from the practical problems in

forestry e.g., they ignore the costs in forestry.

Modeling the empirical forestry problem, Yin and Newman (1995) modified Clarke

and Reed (1989) to incorporate annual administrative and land rental costs as exogenous

parameters. However, while acknowledging option costs, they chose to ignore them for

simplicity. Also, as noted by Gaffney (1960) the solution to the optimal harvest problem

is elusive because the land use has no predetermined cost and the solution calls for

simultaneous determination of site rent and financial maturity. Since land in forestry

investment is typically owned, not leased or rented, accounting for the unknown market

land rental has been one obj ective of Einancial maturity analysis since Faustmann (1849).









In the meanwhile, the use of search models to develop a reservation price approach

gained popularity with papers by Brazee and Mendelsohn (1988) and others. The

technique of the search models is not unlike the DP approach to contingent claims. The

approach differs from the CC approach in solution methodology and in the interpretation

of the results. Fina et al. (2001) presents an extension of the reservation price approach

using search models to consider debt repayment amongst other things.

Following the landmark Black and Scholes (1973) paper the development of

methodology for the valuation of contingent claims has progressed rapidly. A useful

simplification in the form of the discrete time binomial lattice to approximate the

stochastic process was presented by Cox et al. (1979). Other techniques for obtaining

numerical approximations have been developed including the trinomial approximation,

the finite difference methods, Monte Carlo simulations and numerical integration. Geske

and Shastri (1985) provide a review of the approximation techniques developed for

valuation of options.

An important simultaneous line of research has been the study of the nature of

stochasticity in timber prices. Washburn and Binkley (1990a) tested for weak form

efficiency in southern pine stumpage markets and reported that annual and quarterly

average prices display efficiency, but also point out that monthly averages display serial

correlation. Yin and Newman (1996) found evidence of stationarity in monthly and

quarterly southern pine time series price data. Since reported prices for timber are in the

form of period averages, researchers have to contend with unraveling the effect of

averaging on the statistical properties of the price series. Working (1960) demonstrated

the introduction of serial correlation in averaged price series, not present in the original









series. However, Haight and Holmes (1991) demonstrated that serially correlated

averaged price series tends to behave as a random walk. The lack of conclusive data on

the presence or absence of stationarity in timber price data is because of the imperfections

of the data available for analysis. Despite the lack of unanimity on the empirical

evidence there is some theoretical support for the mean reversion (negative

autoregression) arising from the knowledge that commodity prices could not exhibit

arbitrarily large deviations from long term marginal cost of production without feeling

the effects of the forces of demand and supply (Schwartz 1997).

The use of contingent claim analysis is a relatively recent development in stand

management literature. Morck et al. (1989) use real options analysis to solve for the

problem of operating a fixed term lease on a standing forest with the option to control the

cut rate. Zinkhan (1991, 1992) and Thomson (1992b) used option analysis to study the

optimal switching to alternate land use (agriculture). Thomson (1992a) used the binomial

approximation method to price the option value of a timber stand with multiple rotations

for a GBM price process. The paper demonstrates a comprehensive treatment of the

harvest problem, incorporating the option value of abandonment and switching to an

alternate land use.

Plantinga (1997) illustrated the valuation of a contingent claim on a timber stand

for the mean-reverting and driftless random walk price processes, using a DP approach

attributed to Fisher and Hanemann (1986). Yoshimoto and Shoji (1998) use the binomial

tree approach to model a GBM process for timber prices in Japan and solve for the

optimal rotation ages. Insley (2002) advocated the mean-reverting process for price

stochasticity. The paper incorporates amenity values and uses harvesting costs as an









exercise price to model the harvesting problem over a single rotation as an American call

option. In order to obtain a numerical solution, the paper uses a discretization of the

linear complementarity formulation with an implicit finite difference method. All these

studies use a stochastic DP approach with an arbitrary discount rate.

Hughes (2000) used the Black-Scholes call option valuation equation to value the

forest assets sold by the New Zealand Forestry Corporation in 1996. The option value

estimated by him was closer to the actual sale value than the alternate discounted cash

flow analysis. It is a unique case of a study applying real options analysis to value a real

forestry transaction.

Insley and Rollins (2005) solve for the land value of a public forest with mean

reverting stochastic timber prices and managerial flexibility. They use a DP approach to

show that by including managerial flexibility, the option value of land exceeds the

Faustmann value (at mean prices) by a factor of 6.5 for a 3% discount rate. The land

value is solved endogenously for an infinite rotation framework.

In a break from analysis devoted to the problems of a single product timber stand

Forboseh et al. (1996) study the optimal clear cut harvest problem for a multiproduct

pulpwoodd and sawtimber) stand with joint normally distributed correlated timber prices.

The study extends the reservation price approach of Brazee and Mendelsohn (1988) to

multiple products and looks at the effect of various levels of prices and correlation on the

expected land value and the probability of harvest at different rotation ages. A discrete

time DP algorithm is used to obtain the solutions.

In a similar study, Gong and Yin (2004) study the effect of incorporating multiple

autocorrelated timber products into the optimal harvest problem. The paper models the









timber prices pulpwoodd and sawtimber) as discrete first order autoregressive processes.

Dynamic programming is used to solve for reservation prices.

Teeter and Caulfied (1991) use dynamic programming to demonstrate the

determination of optimal density management with stochastic prices using a first order

autoregressive price process modeled using a transition probability matrix. The study

uses a Eixed rotation age and allows multiple thinnings. Brazee and Bulte (2000) analyze

an optimal even-aged stand management strategy with the option to thin (fixed intensity)

with stochastic timber prices. Using a random draw mechanism for the price process and

a backward recursive DP algorithm for locating the reservation prices, the study finds the

existence of an optimal reservation price policy for the thinning option. Lu and Gong

(2003) use an optimal stocking level function to determine the optimal thinning as well as

a reservation price function to determine the optimal harvest strategy for a multiproduct

stand with stochastic product prices without autocorrelations.















CHAPTER 3
THE CONTINTGENT CLAIMS MODEL AND ESTIMATION METHODOLOGY

The One-Period Model

In order to develop the application of options analysis to investment problems it is

helpful to first examine the nature of one-period optimization models. One-period models

for investment decision making operate by comparing the value of the investment in the

beginning of period with its value at the end of the period. The model is first explained in

the context of the deterministic Faustmann problem. This is followed by an extension of

the logic to the stochastic problem.

The Deterministic Case

The problem of finding the optimal financial stand rotation age is an optimal

stopping problem. In the deterministic Faustmann framework, the optimal rotation age is

achieved by holding the stand as long as the (optimal) investment in the stand is

compensated by the market at the required rate of return. The value of the immature stand

is the value of all net investments in the stand up to the present including the land rental

costs and the cost of capital. This means that the value of all investments in the stand

(adjusted for positive intermediate cash flows like revenue from thinnings) up to the

present compounded at the required rate of return represents the stand value. This value

represents fair compensation to the stand owner for his investment and fair cost to the

purchaser who would incur an identical amount in a deterministic world. Therefore, this

value represents the fair market value of the pre-mature stand. The market value of the

merchantable timber in the stand, if any, is less than the stand market value in this period.











The stand owner continues to earn the required return on his (optimal) investments

only till the rotation age is reached when the value of the merchantable timber in the

stand exactly equals the compounded value of investments. Beyond this rotation age the

market will only pay for the value of the merchantable timber in the stand. If the stand is

held longer than this rotation age, even if no fresh investments other than land rent are

made, the market compensation falls short of the compounded value of investments as the

value of merchantable timber grows at a lower rate. The optimal rotation age represents

the unique point of financial maturity of the stand. Before this age the stand is financially

immature and after this age the stand is financially over mature. A typical evolution of

the two values is depicted in Figure 3-1.


4500-

4000

3500

3000

S- -Value of Merchantable limber
t 2500

-* Present Value of net
S2000
investments

gj 1500

1000

500





Rotation age (Years)



Figure 3-1. Typical evolution of even-aged stand and stumpage values for the
Faustmann analysis










Equivalently, a more familiar way of framing this optimization problem is to let the

stand owner compare the value of harvesting the stand in the present period to the net (of

cost of waiting) discounted values of harvests at all possible future rotation ages. The cost

of waiting includes land rent and all other intermediate cash flows. More specifically, the

comparison is between the value of a harvest decision today and the net discounted value

of the stand in the next period assuming that similar optimal decisions are taken in the

future. In this case the stand value represents the discounted value of a future optimal

harvest which exactly equals the earlier defined stand market value consisting of net

investment value. Thus, the problem is cast as a one-period problem.

The one-period deterministic Faustmann optimization problem in discrete time can

be summarized mathematically by Equation 3-1.


F(t)= m;lnr, xlax ~ O+tr8) (3-1)


Here,

F()= Stand Value function
t = Rotation age
0Z = Stand termination value or the market value of the merchantable timber in the stand
ri = Rate of cash flow (land rental expenses, thinnings etc)
B = Constant discount rate
A = A discrete interval of time

For the period that the decision to hold the stand dominates, the second expression

in the bracket is relevant and we have for the holding period Equation 3-2.

F(t + At) 32



It may be noted that the only decision required of the decision maker is whether to

hold the stand or to harvest it. In the standard deterministic case, any intervention









requiring new investments like thinnings is assumed optimally predetermined and the

resulting cash flows are only a function of rotation age. This holding expression can be

simplified to yield Equation 3-3 for the continuous time


OF~t) rt+-Ftl) (3-3)


Here, the limit of A 4 0 has been taken. Equation 3-3 clearly expresses the holding

condition in perfect competition as one in which the yield (Right Hand Side (RHS)) in

the form of the dividend and the capital appreciation/depreciation or change in market

value over the next infinitesimal period equals the required rate of return on the current

market value of the asset (Left Hand Side (LHS)).

The optimal stopping conditions are

F(T) = OZ(T) (3 -4)

F,(T)= O,(T) (3-5)

In Equation 3-5 the subscript t denotes the derivative of the respective function

with respect to the time variable. The first condition is simply that at the optimal rotation

age Tthe market value should equal the termination value and the second condition is the

tangency or the smooth pasting condition (Dixit and Pindyck 1994) requiring that the

slopes of the two functions should be equal.

The Stochastic Case

In the stochastic value framework, the problem of optimal rotation is equivalent to

holding the asset as long as it is expected to eamn the required return. With stochastic

parameter values, not only are future asset values dependent on the realizations of the

parameters but the ability to actively manage the asset by responding to revealed

parameter values induces an option value. Dixit and Pindyck (1994) derive the holding









condition for the stochastic framework using the Bellman equation, which expresses the

value as


F(x,t) =max z~(x,u~,t)A(+(1+A) l-EF(x~t+ A)l |x~u) (3-6)

Here,

F()= Stand value function
x = The (vector of) stochastic variable(s). For this analysis it represents the timber
prices)
t = Rotation age
u = The control or decision variable (option to invest)
xi = The rate of cash flow
B = The discount rate
E = Expectation operator
A = A discrete interval of time

This relation means that the present value F(x, t) from holding the asset is formed

as a result of the optimal decision taken at the present, which determines the cash flow

ai in the next period A and the expected discounted value resulting from taking optimal

decisions thereon. Distinct from the deterministic case, in this case, the value (and

possibly cash flows) depends on the stochastic timber price. Also, the decision can be

expanded to include the decisions to make new investments in the stand (like thinning)

which effects the immediate cash flows as well as expectations of future market values.

Similar to the deterministic case, the holding condition can be re-expressed as


OF(x, t) = max zcx,u~~t)+ E FxL ) (3 -7)


To quote Dixit and Pindyck (1994):

The equality becomes a no arbitrage or equilibrium condition, expressing the
investor' s willingness to hold the asset. The maximization with respect tou means
the current operation of the asset is being managed optimally, bearing in mind not
only the immediate payout but also the consequences for future values. (Dixit and
Pindyck 1994, p.105)









Form of the Solution for the Stochastic Value Problem

In general the solution to the problem has the form of ranges of values of the

stochastic variable(s) x Continuation is optimal for a range(s) of values and termination

for otherss. But as elaborated by Dixit and Pindyck (1994), economic problems in

general have a structured solution where there is a single cutoff x* with termination

optimal on one side and continuation on the other. The threshold itself is a continuous

function of time, referred to as the crossover line. The continuation optimal side is

referred to as the continuation region and the termination optimal side as the termination

region. As pointed out by Plantinga (1998) the values of the crossover stumpage price

line for timber harvesting problems are equivalent to the concept of reservation prices

popular in forestry literature.

Consequently, the optimal stopping conditions for the stochastic case for all t are

(Dixit and Pindyck 1994)

F(x* (t), t) = O(x*(t), t) (3-8)

Fx (x* (t), t) = 2x (x*(t), t) (3-9)

In Equation 3-9 the subscript x denotes the derivative of the respective function

with respect to the variable x .

The Contingent Claims Model

In this section the general theory of CC valuation is developed in the context of the

harvest problem. The CC valuation approach is also built on a one-period optimization

approach and the discussion of the last section should help to put the following discussion

into perspective.









The simplest harvest problem facing the decision maker is as follows: Should the

stand be harvested immediately, accepting the present market value of the timber or

should the harvest decision be postponed in expectation of a better outcome? That is, the

possibility for all optimal interventions other than harvest is ignored. In a dynamic

programming formulation of the problem, using the Bellman equation, the problem can

be expressed mathematically as follows (Dixit and Pindyck 1994)

I 1
F~(x,ti)=max O(x,t), r(x,ti)+-18E[F(x,ti+1) |x] (3-10)

Here F(x, t) is the expected net present value of all current and future cash flows

associated with the investment at time t, when the decision maker makes all decisions

optimally from this point onwards. The stochastic state variable, timber price in the

present problem, is represented by x The immediate cash flow from a decision to hold

the investment is denoted by zi(x, t) The result of optimal decisions taken in the next

period and thereafter will yield value F(x, t + 1) which is a random variable today. The

expected value of F(x, t + 1) is discounted to the present at the discount rate B Finally,

OZ(x, t) represents the present value of termination or the value realized when the

investment is fully disposed off today.

While we know the present termination value, we are interested in learning the

value of waiting or the continuation value. If the decision to wait is optimally taken then

the continuation value is given by

_I 1
F(x, t) =z(x,t)+-+E [F(x,t +1)I |x] (3-11)

If the increments of time are represented by A and A 4 0, the continuation value

expressed in continuous time after algebraic manipulation will be










OF(x,ta)= z(x, t)+ -E[dF] (3- 12)


If it is assumed that the state variable x (timber price) follows a general diffusion

process of the form

dx~ = pU(x, t)dt + a(x, t)dz (3-13)

then, using Ito's Lemma, after algebraic manipulation and simplification we obtain the

partial differential equation (PDE)


-a2FXY+ pUFx + Ft BF + z= 0 (3-14)


Here, pu = pu(x, t), a = o(x, t) and ai = zi(x, t) In typical economic problems the

continuation equation will hold for the value of the asset for all x > x*, where x* is a

critical value of the state variable x with the property that continuation is optimal when

the state variable value is on one side of it and stopping or termination is optimal when

the state variable value is on its other side. This yields the boundary conditions for all t,

given by Equations 3-8 and 3-9, which the value of the asset must meet at the critical

value of the state variable

The DP formulation of the problem assumes that the appropriate discount rate B is

known or can be determined by some means. An equivalent formulation of the problem

can be found using CC valuation. In this form the PDE for the continuation region value

is given by


-G2FXY + (r 3)FX + Ft -rF + = 0 (3-15)


Here r represents the risk-free rate of return and 3 represents the rate of return

shortfall which could be a dividend and/or convenience yield. Dixit and Pindyck (1994)









illustrate the derivation of the contingent claim PDE by using the replicating portfolio

method. In an alternate general derivation the procedure is to first show that under certain

assumption all traded derivative assets must satisfy the no-arbitrage equilibrium

relation a-r = A re, Here a is the expected return on the derivative security, a,


represents the component of its volatility attributable to an underlying stochastic variable

i and ii, represents the market price of risk for the underlying stochastic variable. Where

there is only one underlying stochastic variable the relation simplifies to a r = Aso.

Constantinides (1978) derived the condition for changing the asset valuation

problem in the presence of market risk to one where the market price of risk was zero.

The derivation, presented below, proceeds from Merton' s (1973) proof of equilibrium

security returns satisfying the CAPM relationship


a -r =i 2pm (3-16)

where ii= (s-)is the market price of risk, the subscript p refers to the proj ect (asset,


option etc) and subscript m refers to the market portfolio which forms the single

underlying stochastic variable. Merton (1973) assumed that

1. The markets are perfect with no transaction costs, no taxes, infinitely divisible
securities and continuous trading of securities. Investors can borrow and lend at the
same interest rate and short sale of securities with full use of proceeds is allowed.

2. The prices of securities are lognormally distributed. For each security, the expected
rate of return per unit time as and variance of return over unit time 0z2 OXiSt and are
finite with 0,2 > 0 The opportunity set is non-stochastic in the sense that az >"22
and the covariance of returns per unit time o, and the riskless borrowing-lending
rate r are all non-stochastic functions of time.









3. Each investor maximizes his strictly concave and time-additive utility function of
consumption over his lifespan. Investors have homogenous expectations regarding
the opportunity set.

Let F(x, t) denote the market value of a proj ect. The market value is completely

specified by the state variable x and time t, and represents the time and risk-adjusted

value of the stream of cash flows generated from the proj ect. Let the change in the state

variable x be given by

dre = udt + odz (3-17)

The drift u and variance 02 may have the general form u = u(x, t) and

02 __ 2(x, t) .Let aidt denote the cash flow generated by the proj ect in time interval

(t, t + dt) with ai = zi(x, t) Then, the return on the proj ect in the time interval (t, t + dt) is

the sum of the capital appreciation dF(x, t) and the cash retuma~idt Assuming that the

function F(x, t) is twice differentiable w.r.t. x and atleast once differentiable w.r.t. t, Ito's

Lemma can be used to expand dF(x, t) as



dFi(xt)=( F+uF +-F,; dt + Fxdz (3-18)


The rate of return on the proj ect is

dF(x, t) +zidt__ 1 2 F
z+,+~ +-F dt+ dz (3-19)
F (x, t) F 2 : Fto

with expected value per unit time a,, and covariance with the market per unit time a,

given by

1 a2
a = F +F uF +-F ,; (3-20)
F 2










J, = pa, smnce p =
FF


where p = p(x, t) is the instantaneous correlation coefficient between &z and the return

on the market portfolio.

By substitution in the Equation 3-16 we obtain the PDE


- Fxx + (u-_ Alp)Fx + Ft -rF + 7r = 0 (3 -21)


First, it may be noted that p is the correlation coefficient between &z and the return

on the market portfolio. Since &z is the only source of stochasticity in the proj ect and the

underlying, p is also equal to the correlation coefficient between return on the

underlying and the return on the market portfolio.

Second, when compared with the DP formulation using the discount rate B it can

be seen that the CC analysis modifies the total expected rate of return pu by a factor of

Alpo which allows the use of the risk-free rate of return r In this manner the CC analysis

converts the problem of valuing a risky asset to one of valuing its certainty equivalent. It

does away with the need to determine the discount rate B but does require an additional

assumption regarding the completeness of the market or in other words only the marketed

risk of the asset can be valued.

Further, as shown in Hull and White (1988), if the state variable is a traded security

and pays a continuous proportional dividend at rate 3, then in equilibrium, the total

return provided by the security in excess of the risk-free rate must still be Alpo, so that;

pu + 3- r = Alpo (3 -22)











pu Alpe = r 3 (3-23)

Substituting in Equation 3-21 we obtain the PDE derived by Dixit and Pindyck

(1994) using the replicating portfolio i.e.,


cr2F, + (r 3)Fx + F rF + 7r = 0 (3 -24)


Hull (2003) differentiates between the investment and the consumption asset. An

investment asset is one that is bought or sold purely for the purpose of investment by a

significant number of investors. Conversely, a consumption asset is held primarily for

consumption. Commodities like timber are consumption assets and can earn a below

equilibrium rate of return. Lund and Oksendal (1991) discuss that generally investors will

not like to hold an asset that earns a below-equilibrium rate of return. But empirically

commodities that earn a below equilibrium rate of return are stored in some quantities. To

quote Lund and Oksendal (1991):

In order to explain storage of commodities whose prices are below-equilibrium, it
is assumed that the stores have an advantage from the storage itself. This is known
as gross convenience yield of the commodity. The net convenience yield (or simply
the convenience yield) is defined as the difference between the marginal gross
convenience yield and the marginal cost of storage. (Lund and Oksendal 1991, p.8)

If we assume a continuous proportional convenience yield then the assumption is

completely analogous to an assumption of a continuous proportional dividend yield.

Therefore, the 3 can represent the continuous proportional convenience yield from

holding the timber and the PDE will hold.









The Lattice Estimation Models

The Binomial Lattice Model

In order to determine the holding value of the asset i.e., the value in the

continuation region, it is necessary to solve the PDE. As it is not always possible to

obtain an analytical solution, several numerical procedures have been devised. Amongst

the popular methods for obtaining a numerical solution are the lattice or tree

approximations (that work by approximating the stochastic process) and the finite

difference methods, explicit and implicit (that work by discretizing the partial differential

equation). Monte Carlo simulations and numerical integration are other popular

techniques.

This study uses the lattice approximation approach for its simplicity and intuitive

appeal. Depending on the nature of the problem the binomial or higher dimension lattice

models were used. The binomial approximation approach is suitable for valuation of

options on a single underlying stochastic state variable and was first presented by Cox et

al. (1979). For an underlying asset that follows a GBM process of the form


= pudt + odz (3-25)


where the drift pu and the variance 02 are assumed constant, the binomial approach

works by translating the continuous time GBM process to a discrete time binomial

process. The price of a non-dividend paying underlying asset denoted by P is modeled to

follow a multiplicative binomial generating process. The current asset price is allowed to

either move up over the next period of length A by a multiplicative factor u to uP with

subjective probability p or fall by the multiplicative factor dto dP with probability









(1- p) To prevent arbitrage the relation u > 1+ r > d must hold where r represents the

risk-free interest rate. The asset price follows the same process in every period thereafter.

Following Ross (2002) it can be shown that, the binomial model approximates the

lognormal GBM process as A becomes smaller. Let Y equal 1 if the price goes up at time

iA and 0 otherwise. Then, in the first n increments the number of times the price goes up



is [Y and the asset price would be P = (d" u I


Letting n = gives




',P = d^

Taking logarithms we obtain


In( =,, In d + Y I n (3-26)


The Y are independent, identically distributed (iid) Bernoulli random variables

with mean p and variance p(1 p) Then, by the central limit theorem, the


summation I Y, which has a Binomial distribution, approximates a normal distribution

t t t
with mean p and variance p(1 p) as Abecomes smaller (and grows larger).


Therefore, the distribution of In converges to the normal distribution as ~hgrows.









Following the moment matching procedure Luenberger (1998) shows that the

derived expressions for the parameters ,d and p are



p =2 +1 Io 2 :" (3-27)




u =e" (3-28)

d =e "J (3-29)

The DP procedure for analysis of an option on an underlying asset that follows

GBM process would proceed by using a binomial lattice parameterized by these

expressions. The DP procedure would obtain the option value by recursively discounting

the next period values using the subj ective probability value p and an externally

determined discount rate.

In contrast the contingent analysis procedure is illustrated using the replicating

portfolio argument as follows. In addition to the usual assumptions of frictionless and

competitive markets without arbitrage opportunities, as noted earlier, it is assumed that

the price of a non-dividend paying asset denoted by P follows a multiplicative binomial

generating process. The asset price is allowed to either move up in the next period by a

multiplicative factor u or fall by the multiplicative factor d .If there exists an option on

the asset with an exercise price of X, then the present value of the option denoted by c

would depend on the contingent payoffs in the next period denoted by

cl = M4lX [0,ugq -X] and cd = M4X [0,d~o X] where 4 denotes the current price of

the asset.









In order to price the option a portfolio consisting of one unit of the asset and

na units of the option written against the asset is constructed such that the end of the

period payoff on the portfolio are equal i.e.,

upo -nac,, = dP, -nacd (3-30)

Solving for na we get


nz= 4(-)(3-31)
c,, cd

If the end of the period payoff is equal the portfolio will be risk free and if we

multiply the present value of the portfolio by l +r we should obtain the end of period

payoff

(1 + r)(P, mc) = uP, nac, (3-32)



P, [(1 +r) uj +nc
c = (3-33)
nz(1+r)

Substituting Equation 3-31 for na in Equation 3-33 yields


C='((1+ r)-d 1 edu-(1+r): (r 3-4
u-d u-d

Letting

(1+ r)- d
q = (3-35)
u-d

where q is known as the risk-neutralprobability/, we can express the present value of the

option as

c = [qc, + (1 -q)cd j+t(1 +r) (3 -3 6)









From Equations 3-28 and 3-29 we have u = e"i and d = e-" To find the value

of the risk-neutral probability q these values of u and d can be substituted in Equation

3-35 to obtain


(1+ r)- en 1 1 2
q~ = +- 0 (3-37)


Compared with the expression for the subjective probability p in Equation 3-27, it

can be seen that under the risk-neutral valuation the drift of the GBM process pu is

replaced by the risk-free rater .

In general, if the asset pays out a continuous proportional dividend 6 then, under

CC analysis the drift is modified tor 3 (Equation 3-24). The corresponding risk neutral

probability is


q=1 2 (3-3 8)
2 20

For the treatment of previsible non-stochastic intermediate cash flows (costs) with a

fixed value (si) the Equation 3-36 is modified to

c = [qcu + (1-q4)cd j-t(1+ r)+ zi (3-39)

It is implicit that i represents the discounted net present value of all such cash

flows in the period.

The CC procedure for a single period outlined above is easily extended to multiple

periods and the option value is derived by recursively solving through the lattice.

The Trinomial Lattice Model for a Mean Reverting Process

For an asset that follows a MR process of the form











dx= 9 x- x dt + odz (3 -40)

the contingent claims PDE is given by


-aF~U + [r- 3(x)]F~ + ,- rF + z = 0 (3-41)


where 3(x) = pu (x- x) i s a function of the underlying asset x .


Hull (2003) describes a general two-stage procedure for building a trinomial lattice

to represent a MR process for valuation of an option on a single underlying state variable.

For trinomial lattice the state variable can move up by a multiple u, down by a multiple

d or remain unchanged represented by na Since MR processes tend to move back to a

mean when disturbed, the trinomial lattice has three kinds of branching. Depending on

the current value of the state variable the next period movements can follow one of the

three branching patterns ((na, d, d), {u, na, d), {u, u, na) with associated probabilities. The

parameters of the lattice are determined by matching the moments of the trinomial and

MR processes. The procedure can be adapted for most forms of the MR process. Details

of the procedure can be found in Hull (2003).

The Multinomial Lattice Model for Two Underlying Correlated Stochastic Assets

When the problem is to find the value of an option on two underlying assets with

values that follow the GBM processes

dxC = pU,xldt +a~xldZ i = 1, 2 (3 -42)

which are correlated with instantaneous correlation coefficient given by p ( i.e., they

have a joint lognormal distribution) the contingent claim PDE has the form











12 1F' 2ea FI2 F22 3 (3-43)

+[r-32 2Fx2+F, rF+7t=0

A multinomial lattice approach is used to value such options, also called rainbow

options. The development of the multinomial process for the correlated assets is similar

to that described for the binomial lattice with a single underlying asset. The parameters of

the multinomial lattice are derived by matching the moments of the underlying asset

value processes. Hull (2003) discusses alternate lattice parameterization methods

developed for the multinomial lattice valuation approach. This study uses the method

discussed in Hull and White (1988). At each node on the lattice the assets can move

jointly to four states in the next period. The resulting parameter values for a three

dimensional lattice are summarized in Table 3-1.

Table 3-1. Parameter values for a three dimensional lattice

Period 1 state Risk neutral probability

ugu2 0.25(1+ p)
uz,d2 0.25(1- p)
dz,u2 0.25(1- p)
dz, d2 0.25(1+ p)


Here

uI =e 2 (3-44)


d. = e 2~ (3-45)

represent, respectively, the constant up and down movement multiplicands for asseti .

Parameter o, represents the volatility and 3, represents the dividend/convenience yield of

asseti while r represents the risk-free rate and A the size of the discrete time step















CHAPTER 4
APPLICATION OF THE CONTINTGENT CLAIMS MODEL

Who is the Pulpwood Farmer?

Before applying the CC model to the pulpwood farmer' s dilemma, it is necessary to

establish a mathematical description of a pulpwood farmer. For a commercial timber

production enterprise, the choice of timber products) to be produced (or rotation length

chosen) is guided by the prevailing and expected future timber market prices amongst

other things. The following discussion describes the role of relative timber product prices

in this decision.

A slash pine stand will produce multiple timber products over its life. For products

that are principally differentiated by log diameter, the early part of the rotation produces

the lowest diameter products like pulpwood. As the rotation progresses the trees gain in

diameter resulting in production of higher diameter products like sawtimber. Since

individual tree growth rates vary there is no en bloc transition of the stand from the lower

to a higher diameter product, but rather, for most part of the merchantable timber yielding

rotation ages the stand would contain a mix of products with the mix changing in favor of

the higher diameter products with increasing rotation age.

The average pine stumpage price data series reported by Timber Mart South (TMS)

for different timber products reveal that on an average the large diameter products garner

prices that are significantly higher than lower diameter product prices (Table 4-1). This

implies that the value of merchantable timber in the stand increases sharply with rotation

age from the combined effects of larger merchantable yields and increasing proportion of










higher diameter timber. More important, it also implies that short rotation farming may

be difficult to justify using the TMS reported prices.

Table 4-1. Florida statewide nominal pine stumpage average product price difference and
average relative prices (1980-2005)


Timber Products Average absolute Average relative
price difference prices
($/Ton)


Sawtimber vs. CNS 7.09 1.35
CNS vs. Pulpwood 9.79 1.99

Source: Timber Mart-South

In general, the cultivation of early rotation products is differentiable from that of

the late rotation products by the silvicultural choices. High density planting and absence

of pre-commercial thinnings are some choices that could characterize the cultivation of

pulpwood. For slash pine, the decision to plant dense and not resort to pre-commercial

thinnings limits the stand owner' s choices with respect to switching to higher diameter

product farming by prolonging the rotation.

For a general slash pine stand with two products pulpwoodd and sawtimber) the

results of price differentiation on the optimal Faustmann rotation age are shown in Table

4-2. The illustration uses a year 0 establishment cost of $120/acre, no intermediate cash

flows, a 5% constant annual discount rate, a cutover site index of 60 and 600 surviving

trees per acre (tpa) at age 2 with the Pienaar and Rheney (1995) slash pine growth and

yield equations. Pulpwood was defined as merchantable timber from trees with minimum

diameter at breast height (dbh) of 4 inches up to a diameter 2 inches outside bark and

sawtimber as trees with minimum dbh 8 inches to 6 inches outside bark. The

undifferentiated single timber product price was assumed $10/ton.










Table 4-2. The effect of timber product price differentiation on optimal Faustmann
rotation

Price difference Optimal rotation age
Absolute Relative
$/Ton Years

0 1.0 21
5 1.5 23
10 2.0 25
20 3.0 27
30 4.0 28


Similarly, Table 4-3 shows that it is the relative product prices (for the purpose of

this study, relative product price was defined as the price of the late rotation product

expressed as a proportion of the price of the early rotation product) that are important to

the determination of the optimal rotation changes. Table 4-3 maintains the absolute

increments while changing the size of the relative increments. For this illustration the

initial common timber product market price was assumed to be $20/ton.

Table 4-3. The effect of timber product relative prices on optimal Faustmann rotation

Price difference Optimal rotation age
Absolute Relative
$/Ton Years

0 1.0 20
5 1.25 21
10 1.50 23
20 2.00 24
30 2.50 26


Economic theory has it that relative pricing of goods is an important market signal

which allows the efficient allocation of resources. In the context of the timber stumpage

markets, relative product pricing serves as a signal to the timber producers to produce

(more/less of) one or the other timber product. In order to induce producers to increase










the production of late rotation products (which involve greater investment and/or risk) the

market must offer a higher relative price.

Since relative prices are not constant, an investment decision based on these prices

must consider an average or mean of relative prices over an appropriate period of time. A

timber land owner who bases his investment decision on the average relative prices

deduced from the prices reported by TMS would never choose the lower rotation ages

associated with pulpwood farming (19-25 years for slash pine from Yin et al. 1998). Yet

pulpwood farming is chosen by substantial numbers of timber land owners. Certainly, the

average relative price of products could not be the only reason for choosing the pulpwood

rotation. The practice of pulpwood farming with slash pine could be the result of several

considerations. Short rotations are attractive in themselves for the early realization of

timber sale revenues (capital constraint consideration). Other considerations like earning

regular income from the sale of pine straw in denser stands with no thinnings also

influence the choice. However, the alternate considerations do not diminish the

importance of relative product prices. The stumpage prices applicable to a particular

stand can be vastly different from the average prices reported by TMS. Some stands can

experience greater relative prices at the same point in time than others. This varying

relative prices experienced by stands can be easily explained by the nature of timber

markets. Once the maximum FOB price that a timber purchaser can offer is determined

for a period of time, the stumpage price applicable to prospective suppliers is determined

by the cost of harvesting and transporting the timber to the location of the purchaser' s

consumption/storage facility. From the average difference between TMS reported FOB

and stumpage prices, it can be seen that these costs form a very high (as much as 2/3 for










pulpwood) portion of the FOB price. At a point in time harvesting costs may vary little

from one stand location to another in a region but the transportation costs can vary

significantly. For a pulpwood stand located close to a purchaser (pulp mill) the relative

product prices would always be lower than those for other distant stands (say with respect

to a sawtimber purchaser in the region), justifying the pulpwood farming decision. This

argument implies that a significant number of the stands located close to pulp mills would

be choosing pulpwood farming and this should be empirically borne out. It also implies

that once multiple products are considered there can be no single Faustmann rotation age

that suits all even-aged single same specie stands even if their site quality was the same;

rather, there would be a continuum of optimal rotation ages depending on the average

relative stumpage prices applicable for the stand.

For the present analysis it was assumed that the slash pine pulpwood plantation was

located close to a pulpwood purchaser (who was not expected to stop operations)

resulting in experiencing low average (long run) relative prices. For sufficiently small

average relative prices it may also justify treating the entire merchantable timber output,

irrespective of diameter size, as pulpwood.

Despite the location advantage, in the shorter run, a stand would still experience

wide differences in relative product prices from fluctuating market conditions. In the

present conditions where pulpwood prices have been depressed for several years while

other products have fared relatively better, there is a market signal in favor of higher

diameter products to all stands irrespective of location. Therefore, the pulpwood stand

under analysis would be experiencing higher than normal relative prices. This situation










was analyzed as a multiproduct option problem though with modest relative prices as

compared to TMS reported prices.

The Return to Land in Timber Stand Investments

This section deals with the calculation of return to timberland. Land serves as a

store of value as well as a factor of production. As a factor of production used for the

timber stand investment, land must earn a return appropriate to the investment. For the

pulpwood farmer' s harvest problem land rent is a cost that will be incurred if the option

to wait is chosen. In the contingent claim analysis the land rent is modeled as a parameter

observed by the decision maker and hence having a known present value. If land is not

owned but rented/leased the explicit portion of this return is in the form of rent charged

by the renter/leaser. However, whether explicit or implicit, there is very little useful data

available on either timber land values or lease/rent values. Most decision makers do not

have access to a reliable estimate of even the present value of their timber land. This

makes it necessary to determine the appropriate return to be charged to land for the

purpose of the analysis. The following discussion uses the term 'timberland value' to

refer to the value of the bare land, unless it is specifically stated otherwise.

In its report on large timberland transactions in the US, the TMS newsletter (2005)

reports a weighted average transaction price in 2005 for the southern US of $1160/acre.

Smaller timberland transactions at $2000/acre or higher in Florida are routinely reported.

A part of these valuations must arise from the value of the land itself while some of the

balance could be for the standing trees (if any). Recent literature discusses other

important sources of the valuation like high non-timber values in the form of leisure and

recreation values etc. and expectations of future demand for alternative higher uses.

Aronsson and Carlen (2000) studies empirical forest land price formation and notes that









non-timber services, amongst other reasons, may explain the divergence of the valuation

from present value of future timber sale incomes. Wear and Newman (2004) discuss the

high timber land values in the context of using empirical timberland prices to predict

migration of forest land to alternate uses. Zhang et al. (2005) look at the phenomena of

timber land fragmentation or 'retailization' through sales to purchasers looking for

aesthetic/recreation values and its implications for forestry.

Since this analysis assumes that timber sales is the only maj or source of value the

appropriate timberland value is the value of bare land the present best use of which is

timber farming and for which non-timber values are insignificant. Assuming that the

market price of such timberland could be observed, the question is: Can this value be

used for the purpose of analysis? Is information on the traded price of bare timber land

appropriate for analysis?

Chang (1998) has proposed a modified version of the Faustmann model suggesting

that empirical land values could be used with the Faustmann optimality condition to

determine optimal rotations. Chang (1998) discusses a generalized Faustmann formula

that allows for changing parameters (stumpage price, stand growth function, regeneration

costs and interest rate) from rotation to rotation. The form of the optimal condition

derived by him is

8Rk (Tk >
S= BR(Rk k)+ BLEYk+1 (4-1)


Here, R(T) is the net revenue from a clear-cut sale of an even aged timber stand at

the optimal rotation age T and 6 is the required rate of return. The subscript k refers to

the rotation. The condition is interpreted to mean that instead of the constant LEV of the

standard Faustmann condition, the discounted value of succeeding harvest net revenues










(LEYk+1) must be substituted. Chang (1998) interprets this to mean that the market value

of bare land existing at the time of taking the harvest decision can replace the standard

constant Faustmann LEV. But, if the observed land value is very high as compared to the

LEV the RHS of the equation increases significantly, resulting in a drastic lowering of

the optimal rotation age T In the state of Florida, which is experiencing high rates of

urbanization, it is not unusual to find timber land valued at several multiples of the LEV.

Failure to account for non-market values like aesthetic or recreational values in the model

alone may not explain the failure to observe the rotation shortening effect. Klemperer and

Farkas (2001) discuss this effect of using empirical land values while using Chang' s

(1998) version of the Faustmann model.

By definition, the value of any asset is the discounted value of net surpluses that it

is expected to provide over its economic lifetime in its best use. This suggests that the

market value of land may be differentiable into two parts. One part of the market value is

derived from the current best use and the other is the speculative or expected future best

use (Castle and Hoch 1982). This means that the present market value of timber land, if

known, does not provide information on the value in current use without the separation of

the speculative value component.

The critical fact is that the land rent chargeable to current best use cannot exceed

the expected net surplus in current best use. No investor would pay a land rent higher

than the net surplus he expects to earn by putting it to use. Using empirical land values

could result in overcharging rents as the land values may be inflated by the speculative

value component.









This gives rise to the question: What about the opportunity cost to the speculative

component of land value? Does the landowner lose on that account? The answer is that if

a parcel of land is being held by the landowner despite its current market value being

higher than its valuation in current best use, an investment or speculation motive can be

ascribed to the landowner. The landowner treats the land not only as a productive factor

in the timber stand investment but also as a speculative asset. The landowner could earn a

capital gain over and above the value of future rents in the current best use by selling the

land in such a market. If the investor chooses to hold the land, it is because he expects to

profit from doing so. And this profit is in the form of expected capital appreciation. It is

this expected capital appreciation that compensates the landowner for the opportunity

cost on the speculative component of land value

A formal derivation of this argument follows from economic theory. According to

the economic theory of capital, in a competitive equilibrium, an asset holder will require

compensation for the opportunity cost on the current market value of a capital asset plus

the depreciation cost for allowing the use of his asset (Nicholson 2002). Representing the

present market price of the capital asset by P, the required compensation v will be

v = P(6 + d) (4-2)

where 6 is the percent opportunity cost and d is the assumed proportional depreciation on

the asset value. When the asset market value is not constant over time the required

compensation will be a function of time v(t) The present value of the asset would equal

the discounted value of future compensation incomes. At the present time t the present

discounted value (PDV) of the compensation received at time s (t < s) would be









v(s)es'"t'" and the present discounted value of all future compensation incomes would




PD'LV =P(t) =~ Iy(s)e- "(" 'ds -e"' my(s)e ""ds (4-3)

Differentiating P(t) with respect to t and ignoring depreciation we have


dP(t) -= Be' v(s)e-"d s -e" v(t)e -'= OP( t) -v(t) (4-4)


Therefore,

dP(t)
v(t) = OP(t) (4-5)


So, the required compensation income at any time is equal to the opportunity cost

on the current market value of the asset less the expected change in the market value of

the asset. The interpretation is that the 'fair' or competitive compensation for leasing an

asset consist of both the interest cost as well as the expected change in the value of the

asset. If the expected change in the value is positive the rental charges are decreased to

that extent since the value appreciation compensates the asset owner for a part of the

interest cost.

The net compensation v(t) is the opportunity cost for the asset value in its current

best use. It cannot be more than this cost as prospective renters cannot afford to pay more

as already argued. It cannot be less because a lower charge would transfer a surplus to the

renter attracting competition amongst renters.

Therefore, to find the amount to be appropriated as return to timberland it is

required that its value in current (best) use be determined and then the return would be

given by the opportunity cost of holding the land in its current (best) use.









The static Faustmann framework determines the timber land value or Land

Expectation Value (LEV) as the present value of net harvest revenues arising from

infinite identical rotations in timber farming use. In contrast, in the stochastic framework,

the ability to actively manage the investment adds an option value which must be

incorporated in the valuation method. As argued and shown by Plantinga (1998), Insley

(2002, 2005), and Hughes (2000) a price responsive harvest strategy adds a significant

option value to the investment.

In this study the land value was determined within the CC analysis assuming that

timber farming was the current best use. The parameters for the valuation are the current

values of timber price and plantation establishment cost as well as annual maintenance

costs. In the risk neutral analysis the current risk-free rate serves as the discount rate. The

infinite identical rotations methodology was used to capture the tradeoff with future

incomes meaning that the net expected surplus value over the first rotation was used as

the expected average value for future rotations. This may not effect the land value

significantly since, as observed by Bright and Price (2000), the present value of net

surplus in the first rotation forms most of (>80%) the estimated timberland value when

calculated in this way, for a sufficiently long rotation and high discount rate. Therefore,

the land value in current use can be estimated with information available to the decision

maker. And the land rent is the opportunity cost of this value. The mathematical

formulation of the land value estimation problem is given by Equation 4-6.



L V = max (4-6)
Ly =maxI E~[PIP,])(-e-rt C


Here,











L V = Present value of land
Eq = Risk neutral expectation operator
P, = Stochastic timber price at t period from present time 0
Q~t) = Deterministic merchantable timber yield function (of rotation age t)
at = Annual recurring plantation administration expenses treated as risk-free asset
Co = Value of plantation establishment expenses to be incurred today (at year 0)
r = Present risk-free interest rate assumed constant in future

Then, the present value of estimated land rent is rL V

There are some points to note about the above arguments and methodology

outlined for determining the land value in current best use. First, it is implied that the rent

value is calculated afresh by the decision maker every period. This is empirically true for

shorter duration uses like agriculture farming and there is no reason why it should not be

so for timber farming if decision makers are efficient information processors as normally

assumed and information is easily and freely accessible. If market information on

comparable land rents was available, it would be stochastic and the decision maker would

utilize the new information available every period for decision making.

It is also important that a stochastic rent value calculated as argued above captures

and transfers fresh information about the expected future to the decision making process.

That is, if the estimated land/rent value is high, it will increase the cost of rotation

extension and vice versa. For example, if the stand owner learns of a demonstrable

technological advance improving the financial returns to stand investments, in the midst

of the rotation, the stand owner will seek to apply the technology to the present rotation,

thereby adopting the 'best use'. However, if the improved technology cannot be applied

to the current rotation then there should be pressure on the decision maker to shorten the

present rotation so that the improved technology could be applied to the next rotation.









There is no empirical evidence known to support this result regarding timberland owner

behavior but it can be argued that timberland owners never have free and easy access to

the necessary information. It is also important to note that market prices of timberland

themselves provide no valuable input to the stand decision making process but rather it is

the value in current best use that is relevant. Thus, in periods of speculative inflation of

land prices one may not expect to observe any appreciable changes in stand decision

making behavior. It is the direction of changes in real input costs and output values which

result in changes in land rent.

Second, it is implied that the rent value is a function of the current timber pricess.

However, it need not be perfectly correlated with timber prices(s) since other parameters

of the valuation (the costs and discount rates) would be expected to follow (largely)

independent stochastic processes.

Third, the method outlined for estimation of land rent provides an estimate for a

single period i.e., for the present period only. Ideally, the rent value should be modeled as

a stochastic variable. But that would require information regarding the stochastic process

defining the plantation expenses (or non-timber sources of cash flow) and discount rate.

In the absence of data on the stochastic process for the other flows, in the following

analysis, land rent was assumed to behave like a risk-free asset.

On the Convenience Yield and the Timber Stand Investment

To solve the harvesting problem using the lattice approach the constant volatility of

the underlying variable is estimated from historical price data. The risk-free rate is

estimated from yields on treasury bills of matching maturity. However, the estimation of

the convenience yield poses a problem. The concept of convenience yield, as it is

popularly interpreted, was first proposed by Working (1948, 1949) in a study of









commodity futures markets. The phenomena of "prices of deferred futures....below that

of the near futures" (Working 1948, p. 1) was labeled an inverse carrying charge. The

carrying charge or storage cost is the cost of physically holding an asset over a period.

The concept can be illustrated as follows: ignoring physical storage costs, the arbitrage

free forward price F for future delivery of a commodity is determined by the relation

Poe't where P is the current unit price of the commodity, r is the borrowing/lending

rate while t is the period of the contract. Therefore, the forward price should be

proportional to the length of the contract. The inverse carrying charge or convenience

yield discussed by Working (1948, 1949) is said to accrue to the contract writer when the

no arbitrage relation does not hold for some contract lengths and F
an opportunity for arbitrage exists, arbitrageurs are unable to take advantage as nobody

that is holding the commodity in inventory is willing to lend the commodity for shorting.

Inventory holder may be unwilling to lend the commodity when markets are tight

(Luenberger, 1998) i.e., supply shortage is anticipated. Brennan (1991) defines

convenience yield of a commodity as:

...the flow of services which accrue to the owner of a physical inventory but not to
the owner of a contract for future delivery. ....the owner of the physical commodity
is able to determine where it will be stored and when to liquidate the inventory.
Recognizing the time lost and the costs incurred in ordering and transporting a
commodity from one location to another, the marginal convenience yield includes
both the reduction in costs of acquiring inventory and the value of being able to
profit from temporary local shortages of the commodity through ownership of a
larger inventory. The profit may arise from either local price variations or from the
ability to maintain a production process despite local shortages of a raw material.
(Brennan 1991, p.33-34)

The convenience yield is not constant but would vary with the gross inventory of

the commodity in question, amongst other things.









If there exists a futures market for the commodity then the futures prices represent

the risk neutral expected values of the commodity. The risk neutral drift pu(t) which will

be a function of time since the convenience yield 3(t) and forward risk free rate r(t) are

empirically stochastic, can be calculated from the futures prices as (Hull 2003)

8[1n~t) F=+1
p~lt) = ]d =I In 1Ft (4-7)


Here, F(t) is the futures price at time t.

In the absence of a futures market, theoretically it should be possible to estimate the

convenience yield by comparing with equilibrium returns on an investment asset that

spans the commodity's risk (replicating portfolio).As discussed by McDonald and Siegel

(1985), the difference between the equilibrium rate of return on a financial asset that

shares the same covariance as the asset and expected rate of return on the asset will

yield 3 But, empirically, such an asset is difficult to locate or construct from existing

traded assets.

Similarly, we could estimate r 3 from the equivalent pu Alpo Usually, the

Capital Asset Pricing model (CAPM) for timber stands is estimated by regressing excess

returns on the historical timber price against the excess returns on the market portfolio.

Thus, this methodology suffers from the failure to incorporate the convenience yield in

total returns on timber stands. Using the estimated ilp by this method will only yield

pu Alpo = r i.e., a 3 value of zero. To the best of this authors' knowledge no method

for estimating convenience yield for timber is available in published literature. Therefore,

this study proceeds by assuming that the convenience yield 3 = 0 and pu Alpo = r The

results are tested for sensitivity to different levels of constant 6 .









Dynamics of the Price Process

Modeling the empirical price process is the key to the development and results of

the real options analysis. Beginning with Washburn and Binkley (1990a) there has been

debate over whether the empirical stumpage price returns process is stationary (mean-

reverting) or non-stationary (random walk). The debate has remained inconclusive due to

the conflicting evidence on the distorting effect of period averaging on prices. Working

(1960) was the first to show that the first differences of a period averaged random chain

would exhibit first order serial correlation of the magnitude of 0.25 (approximated as the

number of regularly spaced observations in the averaged period increased). Washburn

and Binkley (1990a) found consistent negative correlation at the first lag for several

quarterly and annual averaged stumpage price series though most were less than 0.25 and

statistically significant only for prices in one case.

On the other hand, Haight and Holmes (1991) have provided heuristic proof to the

effect that a stationary first order autoregressive process, when averaged over a period,

would behave like a random walk as the size of the averaging period was increased. They

used this proof to explain away the observed non-stationarity in the quarterly averaged

stumpage prices.

The stationarity of the price process has implications for the efficiency of stumpage

markets. "A market in which prices always "fully reflect" available information is called

"efficient"" (Fama 1970, p.3 83). Utilizing the expected rate of return format, market

efficiency is described as


E Pr ; .=,,i = +Ery : O $ (4-8)










Here, E is the expectation operator, P~, is the price of security j at time t, P,,r I its


random price at time t +1 with intermediate cash flows reinvested, r ,~t~l is the random


P, ri P
one-period percent rate of return .'' O, represents the information set assumed
P~,

to be fully reflected in the price at t .

The information set O, is further characterized according to the form of efficiency

implied i.e., weak form efficiency which is limited to the historical data set, semi-strong

form efficiency which includes other publicly available information and strong form

efficiency that also includes the privately available information. As Fama (1970)

discusses, the hypothesis that asset prices at any point fully reflect all available

information is extreme. It is more common to use historical data to test prices for weak

form efficiency in support of the random walk model of prices.

Washburn and Binkley (1990a) tested for the weak form efficiency using the

equilibrium model of expected returns with alternate forms of Sharpe' s (1963) single-

index market models. Ex-post returns to stumpage were regressed on a stock market

index and an inflation index. The residuals from the regressions were then tested for

serial correlation the presence of which would lead to rej section of the weak form

efficiency hypothesis. Since these tests required the assumption of a normal distribution

for the residuals, this was tested using the higher moments skewnesss and kurtosis). The

non-parametric turning points test was also conducted as an alternate test for serial

dependence. They found evidence of stationarity in returns generated from monthly

averaged data but returns generated from quarterly and annually averaged data displayed









non-stationarity. Significantly, they did not find evidence to support the normal

distribution assumption of the residuals.

Haight and Holmes (1991) used an Augmented Dickey-Fuller test and found

stationarity in instantaneous returns on monthly and quarterly spot stumpage prices and

non-stationarity in instantaneous returns on quarterly averaged stumpage prices.

Hultkrantz (1993) contended that the stationarity found in returns generated from

monthly averaged price series by Washburn and Binkley (1990a) could be consistent with

market efficiency when producers were risk averse. He used a panel data approach to

Dickey-Fuller tests and found that southern stumpage prices were stationary. Washburn

and Binkley (1993) in reply argued that the results of Hultkrantz' s analysis were by and

large similar to their analysis and point out that if Haight and Holmes (1991) proof of the

behavior of averaged prices is considered, then both (Hultkrantz 1993 and Washburn &

Binkley 1990) their analyses could be biased away from rej section of the weak form

market efficiency. Yin and Newman (1996) used the Augmented Dickey-Fuller and

arrived at conclusions similar to Hultkrantz' s (1993).

Gj olberg and Guttormsen (2002) applied the variance ratio test to timber prices to

check the null hypothesis of a random walk for the instantaneous returns. Their tests

could not rej ect the random walk hypothesis in the shorter periods (1 month and 1 year)

but over longer horizons, they found evidence of mean reversion.

Prestemon (2003) found that most southern pine stumpage price series returns were

non-stationary. He noted that tests of time series using alternate procedures may not agree

regarding stationarity or market informational efficiency as time series of commodity

asset prices may not be martingales.









McGough et al. (2004) argue that a first order autoregressive process for timber

prices is consistent with efficiency in the timber markets. They advocate the use of

complex models (VARMA) that include dynamics of the timber inventory while noting

that such models would be difficult to estimate and apply to harvesting problems.

In summary, in the absence of better data and models or stronger tests, it is difficult

to conclusively establish the efficiency or otherwise of stumpage markets and or choose

between the random walk or autoregressive models. This study considered both, the

stationary and non-stationary models, for the price process alternately.

Modeling the Price Process

Two alternate models for the stochastic price process were applied to the real

options model. The first model is the Geometric Brownian motion which a form of the

random walk process that incorporates a drift and conforms with the efficient market

hypothesis. Expressed mathematically it is

dP = puPdt + oPd: (4-9)

Here,

P =Price of the asset at time t
pu = Constant drift
a = Constant volatility
dz = Increment of a Weiner process

Geometric Brownian motion processes tend to wander far away from their

starting points. This may be realistic for some economic variables like investment asset

prices. It is argued that commodity prices (Schwartz 1997) must be related to their long-

run marginal cost of production. Such asset prices are modeled by Mean Reverting

processes, which is the second model used for the stochastic process in this analysis.

While in the short run the price of a commodity may fluctuate randomly, in the long run










they are drawn back to their marginal cost of production. The Ornstein-Uhlenbeck

process is a simple form of the MR process expressed as


dP= 9 P- Pdt+ rd (4-10)


Here,

r = Coefficient of reversion

P = Mean or normal level ofP

The r is interpreted as the speed of reversion. Higher values of r correspond to


faster mean reversion. P is the level to which P tends to revert. P may be the long run

marginal cost of production.. The expected change in P depends on the difference


between P and P. If P is greater (less) than P, it is more likely to fall (rise) over the next

short interval of time. Hence, although satisfying the Markov property, the process does

not have independent increments.

The Weiner process in discrete time is expressed as

z, q,= Z,+ e,~ (4-11)

Here,

E,= Realization of a Normal Random variable with mean 0 variance 1 and
Cov(e,,e,,)= 0 for jf0

In continuous time, the process is diz, = e,Jd A Weiner process z, is a random

walk in continuous time with the properties (Luenberger 1998)

i. For any s < t the quantity z(t) z(s) is a normal random variable with mean zero and
vaniancet -s .

ii. For any 0 < t, < t, < t, < t4 the random variables z(t,) z(t) land z(t4) 3~, r
uncorrelated.









iii. z(t,) = with probability 1.

The Geometric Brownian Motion Process

Applying Ito's lemma, the Geometric Brownian motion (GBM) process can be

expressed in logarithmic form as


dn =pi o1\dt +odz (4-12)

In discrete logarithmic form the equation becomes


IIn'~:.l g n t + odz (4-13)

Thus, the log-difference or the instantaneous rate of price change is normally

di stributed.

In order to model the GBM process an estimate of the volatility was required.

Following Tsay (2002), let r, = In P, In P Then, r, is normally distributed with mean


pY a At and vrianac a At, wher e Atii is inite timeinterval. If s denotes the

sample standard deviation i.e.,


i; r,- r
s t= g1 (4-14)


then


a = (4-15)

Here a denotes the estimated values of a from the data. For the nominal F.O.B. and

stumpage statewide pulpwood quarterly price data for Florida, using the above

methodology we obtain the estimates listed in Table 3-4.









However, as the TMS data is available in period average form while the GBM

process models the behavior of spot prices, it is necessary to account for any distortion to

the statistical properties of the data from averaging. Working (1960) has demonstrated

that to an approximation, the variance of rates of change calculated from arithmetic


averages of n consecutive regular spaced values of a random chain will be of the

variance of first difference of correspondingly positioned terms in the unaveraged chain,

as n increases. The prices reported by TMS are calculated as an arithmetic average of all

reported prices in a quarter. As discussed by Washburn and Binkley (1990b), the price

averages will be unbiased estimates of the arithmetic mean of prices at any n regular

intervals within the period so long as the likelihood of a timber sale occurring and the

expected transaction size are constant throughout each period.

Making the necessary correction to the estimated variance we obtain the revised

estimate of the variance listed in Table 4-4.

Table 4-4. Estimated GBM process parameter values for Florida statewide nominal
quarterly average pulpwood prices

Estimated Parameter FOB Stumpage

Uncorrected Values Standard Deviation 0.10 0.24
Corrected Values Standard Deviation 0.12 0.29


It may be noted that the calculated standard deviation for the F.O.B. price was

significantly lower than the standard deviation of the stumpage price. One possible

explanation is that pulp mills revise their mill delivered prices relatively infrequently,

whether they are gate purchase prices or supplier contracted prices. It is also possible that

while gate purchase prices are public knowledge, mill delivered price of pulpwood

purchased from other sources may be incompletely reported due to mill concerns with









strategic competitive disadvantage from revealing prices. On the other hand harvesting

and transportation costs change drastically from one stand to another, resulting in higher

volatility of reported stumpage prices. The stumpage prices reported are not the prices

experienced by a particular stand or a common price experienced by all stands but prices

experienced by different stands that reported selling timber in the period. The harvesting

and transportation costs are themselves volatile and likely imperfectly correlated with

FOB prices but it is possible that they do not account for the entire difference in the

reported standard deviations. Since stand owners experience the stumpage price and not

the FOB price, in the absence of data on volatility of harvesting and transportation costs,

this study uses the estimated standard deviation of reported stumpage prices to replace

the estimated volatility of F.O.B. prices while treating the harvesting and transportation

costs as non-stochastic. To account for the possibility of overestimation of timber price

variance the analysis was subj ected to tests of sensitivity to price volatility.

Statistical Tests of the Geometric Brownian Motion Model

The GBM process in discrete logarithmic form is a discrete random walk with drift

i.e., it has the general form

y, = y,/ + a + E, where E, I N(0, a At) and Clov(e,E, ) = 0 for j f 0 (4-16)

The process is clearly non-stationary with a unit root. But if we take the first

difference we obtain a stationary process

Ay, = a + E, (4- 17)

The first difference process has mean a and variance o At Further, the

covariance Cov(Ay,, Ay,,) = 0 for s+ 0.









To see how well the empirical data fits the GBM model, the sample autocorrelation

function (ACF) at several lags was calculated and plotted for the difference logarithmic

form of the price data series. The sample ACF [p(h)] at lag h was calculated using the

formula




p(h)= n -n


tZ =1


For large n, the sample autocorrelations of an independent identically distributed


(iid) sequence with finite variance are approximately iid with distribution N(0, 1


(Brockwell and Davis 2003). Hence, for the iid sequence, about 95% of the sample

1.96
autocorrelations should fall between the bounds+ .


For the GBM process the instantaneous rate of price change r, = In P, In P, is





zero for all he 0 If the empirical price data is modeled by the GBM process, then the

sequence tr, J should be white noise i.e., it should be a sequence of uncorrelated random

variables. A plot of the sample autocorrelations for the instantaneous rate of price

changes of the reported nominal pulpwood statewide stumpage prices along with the 95%

confidence intervals are presented in Figure 4-1, plotted using the ITSM 2000 statistical

software (Brockwell and Davis 2003).










1 OO Sample ACF









80-

40- 2 5 O364








Figure 4-1. Sample autocorrelation function plot for nominal Florida statewide pulpwood
stumpage instantaneous rate of price changes

The dashed lines on either side of the centre plot the 95% confidence interval. If

the sequence is stationary, for the 40 lags plotted, 2 or less ACF's should fall beyond the

95% confidence bounds. For the stumpage price series, no more than 1 ACF beyond lag 0

fell outside the 95% confidence bounds. Significantly, as proved by Working (1960), the

ACF at lag 1 for stumpage price instantaneous rate of change sequence was approx. 0.25


( p(1) = -0.27 ). This could be the effect of the averaging process.


To check if the (r \ sequennncwa Gaussia i-e.,;~ if al of~1 its+E joint distributions are


normal the Jarque-Bera test was used. The Jarque-Bera test statistic is given by

(Brockwell and Davis 2003)



n +m distributed asymptotically as X (2) (4-19)












if (Yt>, } I ID N,,i~ cr)whr m


The results of the Jarque-Bera test applied to the stumpage prices, given in Table 4-

5, indicate that the normality hypothesis was weakly supported by the empirical data at

the 5% level of significance.

Table 4-5. Results of Jarque-Bera test applied to GBM model for Florida statewide
nominal quarterly average pulpwood stumpage prices

Test Value Stumpage

Jarque-Bera Test Statistic 6.0984
P-value 0.0474


The ACF test indicates that the GBM process can be used to model the empirical

data. However, this does not exclude the possibility of the true price process having a

non-constant drift and/or variance. Lutz (1999) tested stumpage price series for constant

variance. He found that the variance for stumpage price series examined was not constant

for the early parts of the series i.e., up to 1920. From 1920 onwards, the examined series

were found to display constant variance.

Even if stumpage price data is heteroskedastic, it was implicitly assumed that the

logarithmic transformation rendered the data homescedastic. The test results also did not

exclude the possibility of an alternate model providing a better fit. On the basis of the

ACF test it was only possible to conclude that there was insufficient evidence to rej ect

the GBM model.

The Mean Reverting Process

The simple MR process is given by













Hence, Pis normally distributed with E(P, | P, )= P+ -P e-t and


2r


Using the expected value and variance we can express P, as


1-e
2')9


41 ,= GP1P- + e, when (1-e") = 1 (4-20)


where E, IN 0,a2

The last equation provides a discrete time first order autoregressive equivalent of

the continuous time Ornstein-Uhlenbeck process. In order to estimate the parameters an

OLS regression of the form

p, 4F = a + bP + e, (4-21)

with a = yP and b = -r was run. Then, the estimated parameters are given by


P= -a = -b and a = o,


One problem with using this simple form of the MR process is that it allows

negative values for the stochastic variable. Plantinga (1998) justifies the choice of this

model for timber stumpage price by referring to the possibility of harvesting and

transporting costs exceeding the FOB timber price. In such a case the effective stumpage

price would be negative. However, it can be argued that the negative stumpage price









would still be bound by the harvesting and transportation costs i.e., if the FOB price were

zero, the negative stumpage price cannot be larger than the cost for harvesting and

removal. But the MR process described above is unbounded in the negative direction.

Hull (2003) describes an alternate log normal form of the MR process


dlni = 9 InP-Ing dtrcrd (4-22)

This model restricts the price process to positive values. Thus, In gF given InP, is



normally distributed with mean In P+~ In In Pu e-t and vanianceor 1 -e-2,) .The

deviations from the long-run mean are expected to decay following an exponential

decline. This analysis uses this form of the MR process to model the FOB prices. When

the harvesting and transportation costs are deducted from the stochastic values of the

FOB price the magnitude of resulting negative stumpage price is restricted to these costs.

However, adopting Equation 4-21 for estimation of P implies that the mean to


which the process reverts is constant over any period of time. Considering that P is

interpreted as the long run cost of production, over a short interval of a few days or

weeks, it may be feasible to assume that the value is constant. But when the analysis must

cover several years, this assumption is questionable. One common correction method

employed (Smith and McCardle 1999) is to regress the inflated values (present) of the

historical asset price, which yields an inflation adjusted estimate ofP It also implies that


for an analysis conducted in nominal terms, the future values of P must be inflated at an

estimated average inflation rate. The average rate of annual inflation computed from the

PPI (1921-2005) was approx.3.0%.










The possibility of a constant real or inflation adjusted nominal P for pulpwood

prices was corroborated by the historical performance of pulpwood prices over the 30

years or so of TMS reporting period as well as the RPA (2003) proj sections of future

performance. This phenomenon can be partly attributed to technological advances and in

some measure to adverse demand and supply movements. Considering that the other

parameter estimates are only marginally effected this analysis uses the inflation adjusted

parameter values.

To check for the effect of period averaging on the estimated parameter values,

simulation was carried out. The simulation revealed that regression of period averaged


data generated consistent estimates of P while cr was consistently underestimated by a

factor of approx. 0.67 or the Working' s correction. The result of regressing inflated past

values of the pulpwood prices using the Producers Price Index-All Commodities (PPI) on


estimated P and other parameters are listed in Table 4-6.

Table 4-6. Inflation adjusted regression and MR model parameter estimates


a b P r a*


Stumpage Price 0.2979 -0.1245 2.3922 0.1245 0.2230
Standard Error 0.3285 0.1278
FOB Price 0.5694 -0.1781 3.1963 0.1781 0.0945
Standrad Error 0.4338 0.1350

* Estimates corrected for period averaging effect.

Of particular importance are the reversion coefficient values. For both price series

the reversion coefficient values are low indicating that the annual price series exhibit low

or insignificant reversion behavior. The 'half life' of the MR process or the time it takes









10 0.5
to revert half way back to the long run mean, given by --, was approximately 2.6


years for stumpage price, illustrating the extremely slow reversion process. Regarding the

low values of mean reversion coefficients Dixit and Pindyck (1994) observe that this

seems to be the case for many economic variables and that it is usually difficult to rej ect

the random walk hypothesis using just 30 or 40 years data.

Secondly, the estimated variance for the FOB price process was sharply lower than

that for the stumpage price. Once again, this difference can be attributed to the stochastic

harvesting and transportation costs but may also partly be the result of the unsuitable

data. As in the GBM process case, the analysis was conducted by attributing the

stumpage price process variance to the FOB price process and using a non-stochastic

harvesting and transportation cost.

Finally, it must be noted that the lattice model for MR process used in this analysis

was based on the existence of futures markets for the commodity and hence knowledge of

futures prices, which represent the risk neutral expected future values. In the absence of


futures markets for timber, the value of the inflation adjusted estimated P was used. This

was justified for a long interval since mean reverting prices (and hence futures prices) are


expected to converge to P in the long run. However, in the short run this only serves as

an approximation.

Statistical Tests of the Mean Reverting Process Model

Examination of the stumpage price regression residuals shows first order serial

correlation (Figure 4-2) as shown by Working (1964).










Sample ACF












40- 2 5 0364


OO mpg Irc IR Ioe rersso I | 1a









Figre -2.Sampe atcrrlto fnto po o nominal Floridal statewie pulpwood tma pie

Tst ttsi tumpage priceMRmdlrgesorsius







Jarque-Bera Test Statistic 9.6299
P-value 0.0081



Instantaneous Correlation

In order to model the simultaneous stochastic evolution of two correlated stochastic


processes following the GBM, an estimate of the instantaneous correlation between the

two time series was required. The estimation of the instantaneous correlation of two


period averaged GBM processes is not effected by period averaging (Appendix). The

estimated instantaneous correlation for the TMS reported Florida statewide average


stumpage quarterly prices of pulpwood and chip-n-saw assuming GBM processes was

0.43.










The Data

Time series data on prices of the timber products was acquired from Timber Mart-

South (TMS). Price data for Florida extending from the last quarter of 1976 for pulpwood

and the first quarter of 1980 for chip-n-saw to the second quarter of 2005 are used for the

analysis. The stumpage price data are reported by Timber Mart-South as quarterly

average of final sale prices recorded in auctions for timber products in the reporting

region.

The data was used to represent spot timber prices in the analysis. However, due to

the nature of data generation, collection and reporting processes, the validity of the data

for this purpose is suspect. For example, the process starting from bidding for the timber

to removal of the timber from the stand is usually a few months long. This means that the

auction bid prices are a reflection of the bidder' s expectation regarding future prices

when the timber will actually reach the market, not the immediate price. Errors in

recording, approximations etc also undermine the data. Other shortcomings have been

discussed in various contexts above.

Harvesting and transportation cost was calculated using the difference between

reported F.O.B. and stumpage prices of timber. The appropriateness of this method is

questionable because of the time difference between auctions and actual movement of

timber from the stand to the market.

Growth and Yield Equations

Slash pine growth and yield equations developed by Pienaar and Rheney (1996) are

used. These equations for cutover forest land were developed using data from plantations

sites in Georgia. The average site index for the sites was 60 ft (at age 25). The equations

used in the analysis are







77


i. Expected Average dominant height (H in ft)

H = 1.3679S(1 e-C)7345dge 1 8()4 + (0.678Z, + 0.546Z2 + 1.395Z3 0.412Z Z )Age "e-C)(691Age

where


=Site Index
=1 if fertilized, zero otherwise
=1 if bedded, zero otherwise
=1 if herbicided, zero otherwise


N,e-)()(41(Age -Age
Age, and Age,


ii. Survival after the second growing season (in trees/acre) N,
where N, and N, are trees per acre surviving at
respectively (Age, > Age, ) .


iii. Basal area (B in ft2 /ce

B =e3 394-35 668 4e 1 336+6 2)5.4g () 366+3 155.4g

(0.557Z, + 0.436Z, + 2. 134Z3 0.3 54Z,Z )ag eOe- 09.4ge
where

Z, = 1 if burned, zero otherwise


iv. Stem Volume outside bark( V in ft3/ce

~~~r-( ) O82 17- 1 (1eg )16+"""~;S


v. Merchantable volume prediction (T in ft3ice
T38 15"


where


V 9, =per acre volume of trees with dbh>d inches to a merchantable diameter t inches
outside bark

D = quadratic mean dbh in inches =
0.005454N\/
tr = pl










The merchantable yield output from the growth and yield models is in units of ft3

outside bark/acre. To convert the yield to tons/acre conversion factors of 90 ft3/COrd and

2.68 tons/cord (Timber-Mart South) were used.

These equations were developed from experimental plantations reaching an age of

16 growing seasons. For this reason, their use for extrapolating growth and yield to

higher rotation ages is questionable (Yin et al.1998) and may not represent the true stand

growth. Nevertheless, for the purpose of this analysis, these equations are the best source

for modeling the growth and yield of slash pine.

Plantation Establishment Expenses

Average plantation establishment expenses for cutover land in the US South

reported by Dubois et al. (2003) were used. The relevant reported costs are listed in Table

4-8.

Table 4-8. Average per acre plantation establishment expenses for with a 800
seedlings/acre planting density

Expense Head 2002 2005

$/acre $/seedling $/acre $/seedling

Mechanical Site preparation* 166.50 195.82

Burning** 15.02 17.66

Planting cost* 49.99*** 58.79

Seedling cost 0.04 0.05


Total Cost for 800 seedlings/acre 280.00 329.21

* All Types ** Others *** Planting cost for average 602 seedlings/acre

The Producers Price Index-All Commodities was obtained from the Federal

Reserve Economic data and used to extrapolate the nominal plantation expense data










reported for 2002 to 2005. The index stood at 132.9 in December 2002 and rose to 156.3

by July 2005. For an acre planted with 800 seedlings the total planting cost under the

above listed expense heads in July 2005 was estimated at $329.21 or approx. $330/acre.

Risk-Free Rate of Return

The yield on Treasury bills with 1 year maturity (Federal Reserve Statistical

Release) was used as the estimated risk-free rate of return. The reported risk-free rate for

July 2005 was 3.64%.

The Model Summarized

The value of options available to the decision maker were analyzed using a CC

valuation procedure. The analysis also highlighted the form of the optimal strategy. The

following are the important points of the model

1. The model considers an even-aged mature (20 year age) slash pine pulpwood
plantation in 2005. Only revenues from sale of timber are considered significant for
the analysis. Since the analysis focuses on the pulpwood crop, the plantation was
assumed to have been planted dense (800 trees/acre initial planting density) with no
thinnings up to the present age. The plantation was assumed to be cutover with site
index 60 ft (rotation age 25). Site preparation activities assumed are mechanical site
preparation (shear/rake/pile) and burning only. A clear-cut harvest was considered for
the final harvest. When the thinning option was the subj ect of analysis only a single
thinning in the form of a row thinning that removes every third row of trees was
considered.

2. For a stand with the chosen initial planting density and site index on a cutover site,
the growth and yield equations produce a single product yield curve that peaks
approximately at age 43. Rotation age 43 was selected as the terminal age for the
options on the stand in this study. This terminal age was applied uniformly to all
models for comparability of results. Even though later stand products would have
later yield peaks, current empirical practices and unreliability of the yield curve for
higher rotation ages were arguments in favor of the lower terminal age.

3. Only the timber price (prices for multiple product analysis) was modeled as a
stochastic variable. It was assumed that the stand growth and yield models provide a
reliable forecast of the future merchantable timber yields.

4. The present values of other parameters of the valuation model like the risk-free
interest rate, the land rent and the intermediate expenditure/cash flows on plantation










were assumed known to the decision maker. Some intermediate cash flows could be
positive in the form of regular realizations of amenity values or sale of some
minor/non-timber products while others could be negative in the form of annual taxes
and overhead expenditures associated with maintenance activities. The basic analysis
assumes that the net result from a combination of both positive and negative cash
flows was a negative cash flow of $10/acre/year. For the purpose of consistency, all
intermediate cash flows are treated as occurring at the beginning of a period. This
arrangement does not effect the analysis since the intermediate cash flows are
assumed non-stochastic. Non-stochastic variables are unaffected by the expectation
operator but are effected by discounting. So, regardless of where they occur in the
period their value at the beginning of the period can be considered as the
appropriately discounted value. These known values were extrapolated like risk-free
variables i.e., with close to zero variance (and no correlation with the stochastic
variables). Harvesting and transportation costs per unit merchantable timber were
assumed constant i.e., the effect of economies of scale observed for older or larger
stands was ignored for want of data.

5. The unit FOB price of the timber product was modeled as the stochastic variable and
the unit harvesting and transportation costs deduced from empirical data served as the
strike price for the option on the stand. The estimated empirical values of variance for
the timber stumpage price were used to model the variance of the FOB price.

6. The GBM and MR models applied were assumed to have constant parameters i.e., the
drift and variance for the GBM model and the reversion coefficient and variance
parameters for the MR models were assumed constant.

7. Land rent was estimated for the stochastic price process using the CC valuation as
detailed earlier.

8. Taxes are not specifically treated in the analysis.

9. Ideally the term structure of interest rates should be used to model the risk-free rate.
For simplicity, a single constant risk-free interest rate was used instead.

10. An assumption was made that the pulpwood stand was located so as to experience
low/moderate relative timber product prices.

11. For the basic model the convenience yield was assumed to be zero. Sensitivity
analysis to consider the effect of positive values of the convenience yield was
conducted.

















CHAPTER 5
RESULTS AND DISCUSSION

A Single Product Stand and the Geometric Brownian Motion Price Process

In the following section the entire merchantable output of the stand at any rotation

age was treated as a single undifferentiated product, in this case pulpwood. As argued

earlier, this would be the case for a stand experiencing low relative timber product prices.

Figure 5-1 plots the per acre merchantable timber yield curve for a cutover slash pine

stand in Florida with the following site description and management history


140.00-


120.00


2 100.00


t 80.00

-*-Total Merchantable Wood

60.00


T 40.00


20.00


0.00

Rotation age (Years)



Figure 5-1. Total per acre merchantable yield curve for slash pine stand











* Site Index -60 (age 25)
* Site Preparation- Burning only
* Initial planting density- 800 Trees per acre
* Thinnings None

Parameter values used for the analysis are listed in Table 5-1.

Table 5-1. Parameter values used in analysis of harvest decision for single product stand
with GBM price process


Parameter Effective Date/ Unit Value
Period


FOB price II Qtr 2005 $/Ton 21.96
Stumpage price II Qtr 2005 $/Ton 7.42
Harvesting and transportation cost II Qtr 2005 $/Ton 14.54

Initial plantation expenses II Qtr 2005 $/acre 330.00
Estimated land rent II Qtr 2005 $/acre/year 34.00
Other annual expenses II Qtr 2005 $/acre/year 10.00

Estimated standard deviation 07-01-2005 Annual 0.29
of GBM price process
Risk free rate 07-01-2005 %//annum 3.64
Constant convenience yield Annual 0.00
Present age of stand 07-01-2005 Years 20.00


In order to value the option to postpone the clear-cut harvest the FOB price for

pulpwood was modeled as a stochastic variable following a GBM process with a constant

standard deviation of 0.29. A binomial lattice was constructed using Equations 3-28, 3-29

and 3-37 for this stochastic variable with a one year period. The backward recursive

option pricing procedure was then implemented to determine the option value. The

GAUSS Light version 5.0 (Aptech Systems, Inc.) software was used for finding

solutions.

The per acre pre-tax value of an immediate harvest and sale as pulpwood of the

entire merchantable yield at rotation age 20 at current stumpage price of $7.42/ton was











$567. The maximum or terminal rotation age considered was 43 years. At $966/acre or


$12.64/ton the calculated option value was higher than the value of immediate harvest.


Figure 5-2 plots the upper bounds of the stumpage prices for the harvest region or

the crossover price line. Since a discrete time approximation with large period values


(annual) was used continuity was sacrificed i.e., the reported values of crossover prices


display large jumps. The crossover line has also been smoothened to remove the

incongruities in the data recovered fr~om the discrete lattice structure.


200.00-

180.00

160.00

1 40.00

S120.00

S100.00 -m--Optimal cross-o\Rr prices

a. 80.00

S60.00

40.00

20.00

0.00
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
Rotation Age (Years)



Figure 5-2. Crossover price line for single product stand with GBM price process

The region to the RHS of the line is the harvesting region and to its LHS is the


continuity region. The form of the crossover line suggests that the optimal strategy will


comprise of harvesting only if the rotation age approaches the terminal age and the


stumpage prices decrease to zero. As the rotation age approaches the terminal age

harvesting at higher stumpage prices becomes feasible. These results conform to the









findings of Thomson (1992a) and the discussion in Plantinga (1998) on the results of a

Geometric Brownian motion price process. The form of the optimal harvesting strategy

implies that harvesting was only feasible to avoid uneconomic outcomes or when there

was a low probability of improving returns by waiting any further in the time left to the

terminal date.

This result for the GBM price process is also confirmed from the results for plain

financial (American) options on non-dividend bearing stocks that are always optimally

held to the maturity/terminal date. The crossover line for stand harvesting is observed

because of the presence of the intermediate expenses.

Sensitivity Analysis

Sensitivity of the results to changes in values of various parameters was considered

next. The land rent was re-estimated to reflect the change in value of the parameter under

consideration. First, the response of the results to changes in intermediate expenses was

considered. The option value corresponding to an increase in intermediate expenses by

$10/annum/acre was $859/acre, a decrease of more than $100/acre. On the other hand the

option value for an increase in intermediate expenses by $40/annum/acre decreased the

option value to $617/acre a drop of about $3 50/acre.

If the higher intermediate expenses are considered to arise from payments for

purchase of insurance against non-marketed undesirable risks, it is possible to see the

effect that catastrophic risks have on the harvesting strategy and option values. Thus, the

observed empirical rotations of less than 30 years could be partly explained by the

presence of non-marketed undesirable risks.

On the other hand, lowering intermediate expenses by $10/annum/acre increased

the option value to $1,088/acre, an increase of more than $100/acre. Thus, positive and









































20 2122 23 2425 2627 2829 30 3132 33 3435 3637 3839 4041 42
Rotation age (Years)


previsible cash flows in the form of, say, non-timber incomes or aesthetic values would

lead to longer optimal rotations.


400-


350

300


S250


S200

E 150

100

50


0


-oUnchanged Intermediate Expenses
-m- Less $5
-a Less $10
-x- Less $20


Figure 5-3. Crossover price lines for different levels of intermediate expenses

Figure 5-3 illustrates the effect of changing the magnitude of intermediate cash

flows. As the intermediate cash flows in the form of expenses or negative cash flows


increase the crossover line shifts to the left towards lower rotation ages


From the option pricing theory it is known that option value is directly related to


the magnitude of the variance of the underlying stochastic asset value. The variance for


stumpage prices estimated from the TMS data may be higher than the variance


experienced by individual pulpwood stand owners for reasons discussed earlier. Higher

variances mean the possibility of higher positive payoffs even while the effect of the


higher negative values is limited to zero.











The results of the sensitivity analysis for different levels of variances confirmed the

known behavior of option values. The option value for a standard deviation value of 0.20

was $765/acre as compared to $966/acre for the base standard deviation of 0.29. The

option value dropped further to $658/acre for a standard deviation of 0. 10.

Figure 5-4 shows that when the variance level is lower the crossover lines lie to the

left of higher variance models so that optimal harvesting at lower rotation ages as well as

lower stumpage prices becomes feasible. This implies that in a situation of large expected

variances arising, say, from an unpredictable regulatory environment, harvesting should


be optimally postponed.


200-

180

160

1 40

S120- Unchanged Standard Deviation 0.29
100 -A- Standard Deviation 0.2











Rotation age (Years)



Figure 5-4. Crossover price line for different levels of standard deviation

Instead of using a convenience yield value of zero, the use of a positive constant

convenience yield will alter the risk-neutral expected drift of the process (Equation 3 -3 8).

For a constant convenience yield of 0.005 the option value dropped to $874/acre,

dropping further to $803/acre for convenience yield value 0.01 and to $755/acre for











convenience yield value 0.015. Since higher levels of convenience yield are associated

with low levels of inventory and associated higher market prices, it suggests that optimal


rotations should be shorter when the markets are tight.


Figure 5-5 plots the effect of different levels of constant convenience yield on the

crossover price lines. It shows the leftward shift of the crossover lines in response to


higher levels of constant positive convenience yields.


200-

180

160

1 40

~ 120 ~Convenience Yield =0
8 'Convenience Yield = 0.005
S100
-A- Convenience Yield = 0.01
80t Convenience Yield = 0.015









20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
Rotation age (Years)



Figure 5-5. Crossover price lines for varying levels of positive constant convenience
yield

It iz also of interest to know if the optimal decision changes for a different current


price i.e., does a higher or lower current stumpage price induce earlier harvesting. The


per acre option value corresponding to a present stumpage price of $1/ton ($76/acre) was

$7/ton ($548/acre). On the other hand the per acre option value for a present stumpage


price of $20/ton ($1,529/acre) was $25/ton ($1,933/acre). The possibility of higher










payoffs as a result of higher current prices inflates the land rent reducing the relative

option values.

Figure 5-6 plots the results of considering different levels of current stumpage

prices. The plots show that the cross-over price lines shift to the left for a price increase

and vice versa. This results partly from the effect of a direct relation between land rent

and current prices. All other things being constant, a higher current timber price increases

the present land value which increases the cost of waiting through the land rent. At the

same time higher present stumpage price also means lower possibility of unfavorable

outcomes but this effect is overwhelmed by the increase in land values.


200-

180

160

140

12 -o- ~Unchanged Stumpage Price
= $7.42/Ton
100 -x-Stumpage Price = $1.00/Ton

-Stumpage Price = $20/Ton
0.. 8 0

S60

40

20


0L L L`rb~~~0 C~O~'b~9 ~ r

Rotation Age (Years)


Figure 5-6.


Crossover price lines for different levels of current stumpage price









Next, by changing the present rotation age of the stand from 20 to 25 and 30 we

can observe the drop in option values commonly associated with financial options as the

time remaining till the terminal date is reduced. This is due to the lower probability of

higher payoffs in the remaining time. For the timber stand, for a present rotation age of

25 the associated option value was $9.97/ton ($999/acre). Similarly, for a present rotation

age of 30 the option value was $8.88/ton ($1,027/acre).

Finally, the effect of a change in the initial planting density was studied. The

current plantation establishment expenses were adjusted to reflect the cost of planting less

plants which effects the estimated land rent, though only marginally. The important

observation is that lower initial planting densities did not change option values which

were $12.62/ton ($909/acre) for 700 tpa and $12.64/ton ($781/acre) for 500 tpa. The

option value calculated earlier for a 800 tpa initial planting density was $12.64/ton.

Comparison with the Dynamic Programming Approach

This section applies the DP approach to the single product slash pine pulpwood

stand with timber prices following a GBM process. The binomial lattice was set up using

Equations 3-28 and 3-29 with the subjective probability given by Equation 3-27 instead

of the risk-neutral probability given by Equation 3-37. The estimated value of the drift pu


for pulpwood stumpage prices was 0.05 (with a standard error of =0.053 or >100%).

A variety of discount rates have been used in published forestry literature using the DP

approach, the most common being a real rate of 5%. Since this analysis was conducted in

nominal terms and the average inflation estimated from the PPI series was 3%, a nominal

discount rate of 8% was used in this DP analysis. Further, some of the published

literature assumes the intermediate costs are constant in real terms. Therefore, for










comparability, future values of intermediate expenses including the estimated land rent

and harvesting and transportation cost were inflated at the average inflation rate of 3%

computed from the PPI series. The land rent was estimated using the DP procedure. All

other parameter values used were unchanged from Table 5-1.

The option value derived from the DP approach, parameterized as above, was

$2,393/acre. This value was more than twice the option value derived using the CC

approach i.e., $966/acre. The use of a discount rate of approximately 12.5% brought

down the estimated option value using the DP approach close to the option value

estimated using the CC approach. As noted and illustrated in Hull (2003) the appropriate

discount rate for options is much higher than the discount rate applicable to the

underlying asset.

First, it should be noted that at 12.5% the discount rate is much higher than typical

rates considered in forestry literature on options analysis. Second, this discount rate is not

a constant but would vary according to the parameter values of the problem. This is

evident from the sensitivity of the option values to parameters exhibited above.

This illustration serves to highlight the problems associated with using the DP

approach in the absence of a method for determining the appropriate discount rate.

A Single Product Stand and the Mean Reverting Price Process

In this section the optimal harvesting strategy for the single product pulpwoodd)

stand is analyzed with a mean reverting FOB price process. The stand description and

management history were identical to those considered for the GBM price process

analysis. The parameters used in the basic analysis are listed in Table5-2.










The problem was modeled by considering only the FOB price for pulpwood as

stochastic following a MR process of the form given by Equation 4-22 with a constant

standard deviation of 0.22 and constant reversion coefficient with value 0. 18.

Table 5-2. Parameter values used in analysis of harvest decision for single product stand
with MR price process


Parameter Effective Date/ Unit Value
Period


FOB price II Qtr 2005 $/ton 21.96
Stumpage price II Qtr 2005 $/ton 7.42
Harvesting and transportation cost II Qtr 2005 $/ton 14.54
Mean FOB price level II Qtr 2005 $/ton 24.44

Initial plantation expenses II Qtr 2005 $/acre 330.00
Estimated land rent II Qtr 2005 $/acre/year 24.00
Other annual expenses II Qtr 2005 $/acre/year 10.00

Estimated standard deviation 07-01-2005 Annual 0.22
of MR price process
Estimated constant reversion 07-01-2005 Annual 0.18
coefficient
Risk free rate 07-01-2005 %//annum 3.64
Constant convenience yield Annual 0.00
Present age of stand 07-01-2005 Years 20.00
Estimated average inflation rate %//annum 3.00


The option value at $1,290 was higher than present stumpage value of $567.

From the form of the crossover price line (drawn after smoothing) for the mean

reverting FOB prices (Figure 5-7) it is evident that the strategy for the optimal harvest is

significantly different than that for the GBM prices. The form of the crossover line

suggests that the optimal strategy would be to harvest if a sufficiently high stumpage was

received at each rotation age, the crossover price declining with the rotation age. These

results are consistent with those reported for the reservation prices obtained using search

algorithms and for other studies with first order autoregressive or mean reverting prices.