<%BANNER%>

Real Options Framework for Acquisition of Real Estate Properties with Excessive Land

Permanent Link: http://ufdc.ufl.edu/UFE0021261/00001

Material Information

Title: Real Options Framework for Acquisition of Real Estate Properties with Excessive Land
Physical Description: 1 online resource (122 p.)
Language: english
Creator: Leung, Nga-Na
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: acquisitions, binomial, decisiontree, development, estate, land, lattice, montecarlo, options, real, simulations, valuation
Design, Construction, and Planning -- Dissertations, Academic -- UF
Genre: Design, Construction, and Planning thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Our study touches a field that few researchers explore: the valuation model for acquisition of a property with excessive land that can be potentially converted into a new development. Traditional valuation focuses mainly on the building improvement. With the drastic capitalization rate compression, however, it becomes critical to identify and explore any hidden value in an acquisition. One of such challenges is valuing a large partially vacant parcel that can be potentially converted into a new development. Valuation of these parcels is not straightforward. Traditional discounted cash flow approach (DCF) cannot take into account the uncertainty and development flexibility. Alternative approaches are real options analysis (ROA) and decision tree analysis (DTA). However, the 'twin asset' assumption required by the ROA methodology is often violated, especially for assets with private risk and rare events. The use of the same discount rate throughout valuation period in the DTA approach, regardless of changing risk characteristics upon the execution of decision making, allows for arbitrage opportunity. Our proposed real estate with real options (RERO) model is a framework that combines DCF, ROA and DTA analyses to specifically value real estate acquisition with excessive infill land. This methodology not only overcomes the shortcoming of current DCF method, but also is superior to the pure ROA or DTA analysis. Focusing on applicability in practice, this framework is developed intuitively with simple mathematics whenever possible. The study also explores a few unconventional real options cases, all of which could have been very complicated if modeled using the partial differential equations common in the academy, including (1) jump diffusion process that does not go back to normal diffusion, (2) risk drivers that do not follow the multiplicative stochastic movement, (3) private risk that has no market equivalent and hence violating the non-arbitrage option pricing assumption. All of these are implemented simply through binomial lattice with Monte Carlo simulation or DTA. The RERO framework is applied to a real case in Atlanta. Valuation has two parts: (1) the improvement is modeled using a combined approach with Monte Carlo simulation, and (2) the incremental value using a separated decision approach with binomial lattice technique. The valuation result is very close to the actual closing price. Three conclusions can be drawn from this study: (1) acquisition and development has different characteristics and deserve different kinds of attention; (2) consideration of managerial flexibility can change investment decisions; and (3) many unconventional real option valuation problems can be resolved by binomial lattice and Monte Carlo simulations. The novelty of this study is the research subject: property acquisition with excessive land. From the methodology standing point, the RERO framework is developed with ease of applicability in mind. It bridges the gap between research and practice for real options applications in the real estate industry.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nga-Na Leung.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Issa, R. Raymond.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021261:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021261/00001

Material Information

Title: Real Options Framework for Acquisition of Real Estate Properties with Excessive Land
Physical Description: 1 online resource (122 p.)
Language: english
Creator: Leung, Nga-Na
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: acquisitions, binomial, decisiontree, development, estate, land, lattice, montecarlo, options, real, simulations, valuation
Design, Construction, and Planning -- Dissertations, Academic -- UF
Genre: Design, Construction, and Planning thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Our study touches a field that few researchers explore: the valuation model for acquisition of a property with excessive land that can be potentially converted into a new development. Traditional valuation focuses mainly on the building improvement. With the drastic capitalization rate compression, however, it becomes critical to identify and explore any hidden value in an acquisition. One of such challenges is valuing a large partially vacant parcel that can be potentially converted into a new development. Valuation of these parcels is not straightforward. Traditional discounted cash flow approach (DCF) cannot take into account the uncertainty and development flexibility. Alternative approaches are real options analysis (ROA) and decision tree analysis (DTA). However, the 'twin asset' assumption required by the ROA methodology is often violated, especially for assets with private risk and rare events. The use of the same discount rate throughout valuation period in the DTA approach, regardless of changing risk characteristics upon the execution of decision making, allows for arbitrage opportunity. Our proposed real estate with real options (RERO) model is a framework that combines DCF, ROA and DTA analyses to specifically value real estate acquisition with excessive infill land. This methodology not only overcomes the shortcoming of current DCF method, but also is superior to the pure ROA or DTA analysis. Focusing on applicability in practice, this framework is developed intuitively with simple mathematics whenever possible. The study also explores a few unconventional real options cases, all of which could have been very complicated if modeled using the partial differential equations common in the academy, including (1) jump diffusion process that does not go back to normal diffusion, (2) risk drivers that do not follow the multiplicative stochastic movement, (3) private risk that has no market equivalent and hence violating the non-arbitrage option pricing assumption. All of these are implemented simply through binomial lattice with Monte Carlo simulation or DTA. The RERO framework is applied to a real case in Atlanta. Valuation has two parts: (1) the improvement is modeled using a combined approach with Monte Carlo simulation, and (2) the incremental value using a separated decision approach with binomial lattice technique. The valuation result is very close to the actual closing price. Three conclusions can be drawn from this study: (1) acquisition and development has different characteristics and deserve different kinds of attention; (2) consideration of managerial flexibility can change investment decisions; and (3) many unconventional real option valuation problems can be resolved by binomial lattice and Monte Carlo simulations. The novelty of this study is the research subject: property acquisition with excessive land. From the methodology standing point, the RERO framework is developed with ease of applicability in mind. It bridges the gap between research and practice for real options applications in the real estate industry.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nga-Na Leung.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Issa, R. Raymond.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021261:00001


This item has the following downloads:


Full Text
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 E20101206_AAAACO INGEST_TIME 2010-12-06T13:23:31Z PACKAGE UFE0021261_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 97345 DFID F20101206_AABDIK ORIGIN DEPOSITOR PATH leung_n_Page_028.jpg GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
664ca7cde3c6a9bf2fb22d42cd09a9a3
SHA-1
9c98ca0404f5bc554187685979b422ef2c0434c5
25489 F20101206_AABDHV leung_n_Page_008.jpg
8a60973e3cd1070c395cdcca50b6361e
6c99ed4774f3a6b1d2c9c08cbfcdf925c5ac4e02
107291 F20101206_AABDIL leung_n_Page_029.jpg
b1f6a51d80ca28f392559042aab0ad54
eae29037ce28dc7ce6070ad47e820b0f45f7f079
56475 F20101206_AABDHW leung_n_Page_009.jpg
e807725305d9a0c0fbdf55aa1535a74b
2a2e1b7ee26f9944dc50a2096a3de23895eba277
95707 F20101206_AABDJA leung_n_Page_045.jpg
a1dfd6c39a1e64e6d50768dc2c39de94
607be538d92b921d1c24e481626a6a8c3e5c32a6
106644 F20101206_AABDIM leung_n_Page_030.jpg
3f0ca8c6e9b5c3b113fc353d8819b284
125f9b185342563f34adf7c4e1cdeae5fc9720d3
106222 F20101206_AABDHX leung_n_Page_010.jpg
1fd38dc77865f44c33613969fef50102
9c152a516c900789183fadc1583d1901dc552bcf
104189 F20101206_AABDJB leung_n_Page_047.jpg
6af72a931aabf715efe863b303bcfa57
188fac5b32fd881ae2f501658e0f1e6510d12b7f
100045 F20101206_AABDIN leung_n_Page_031.jpg
8c84569d59a6baa98b8325a48da0a28d
41f71ba1f48094736ef33161ab40b8f4067c8489
40506 F20101206_AABDHY leung_n_Page_012.jpg
a5c6eb44e9c7acbc5f0ff9fcd886608f
eb4486a2b375f7e4a1d426af2ac5e8e0fabaf7dd
97501 F20101206_AABDJC leung_n_Page_048.jpg
590b4db41ccd575b73ac596d58166550
ecd007e6f518d7737230b87d78df418da85d6223
88338 F20101206_AABDIO leung_n_Page_032.jpg
4b86b01aac0f03ce24aceec56c5fe4d5
ebce341bee80c99b62286c395187c60d5c2692b7
93219 F20101206_AABDHZ leung_n_Page_013.jpg
5c077793144a3d551a570954c7aab285
e4f5cabd96da31c5b39e6820935eea13f37e331c
104607 F20101206_AABDJD leung_n_Page_049.jpg
92430ec4cc28a88626834d5293f36425
28f018fc5c4f5bf605e18446f51cfa0372011ee1
98200 F20101206_AABDIP leung_n_Page_033.jpg
c067c72d704199b018feb48d4bdff48b
8d290b7ab5202e0c2475b23fae196360269a2fbc
103548 F20101206_AABDJE leung_n_Page_050.jpg
e31b33d4fe04befa64f237a33816331e
92665254e1cb8f3e349174bf4851d7c765b785dd
95345 F20101206_AABDIQ leung_n_Page_035.jpg
ec83dae6ead523a8d6cd4d105fd0c44e
67ba036ba068551c4534e28cdf5cfe7edd3d00c1
72610 F20101206_AABDJF leung_n_Page_051.jpg
ba890feccf571b524054cec0f02cb629
9388a851dd29f4fef00da108ee401b7bf40976cf
81985 F20101206_AABDJG leung_n_Page_052.jpg
1f5670cc64832ec7bf9aac4578d15222
1996b5e08d30fd4e6b3821d5c1734564a4e286a8
108827 F20101206_AABDIR leung_n_Page_036.jpg
b5c6ea3f6977f8f8c2cfcc8305e2159d
64d595c72bd4ec26345e7987318632cd95fec12b
100557 F20101206_AABDJH leung_n_Page_053.jpg
ec8516a08464e1817ea44d4eab098fc4
daafd1d5070f7a538e3d5c25906fe0d1f934686f
57601 F20101206_AABDIS leung_n_Page_037.jpg
87155d9fbf1f41ddff1d91ac005d0524
864153d3cb5f9e30186cb8365cb228aa2edbfd0c
53332 F20101206_AABDJI leung_n_Page_054.jpg
445844cef04dcc931163e573ddcb3276
5f51aa836202a285d45e4e1c077a11e808cb320a
95702 F20101206_AABDIT leung_n_Page_038.jpg
0663a0c1e1c5ca495d704981727f67b3
bb4c78fc205a5b5e45d310e086bf46e6a4d4c5dd
86842 F20101206_AABDJJ leung_n_Page_055.jpg
e08a88c299c7cb56f18ac358fe6cc3ad
8a1528b7ad40f5624bb696b771b9842afb9e985b
66063 F20101206_AABDIU leung_n_Page_039.jpg
d50d51f4f316e84af24e769ff096f2ab
16af0ab789d9b46e76a221f013188ef241733a47
40738 F20101206_AABDJK leung_n_Page_056.jpg
801aa4e728665febc623399c1cf8182b
1bd341d1db2416d7b12256d77f0f93af56f1192e
89290 F20101206_AABDIV leung_n_Page_040.jpg
ff9ab4b51f3f32674b640521cb38184e
fa81a7703083f808977a4c5732b4f7f4f33619bc
90999 F20101206_AABDJL leung_n_Page_057.jpg
446938199644f02848664eecf9286755
3f9f058841ac68a50573d6ef047c5e2c0797d124
69605 F20101206_AABDIW leung_n_Page_041.jpg
70cf30b0cd1887b453db41f394c21f63
44a017c967d142f5beef73e72daf73b0abb3cf11
101282 F20101206_AABDJM leung_n_Page_058.jpg
eae109eed3ba9b9a4eda69008ba0e4f9
3c87837c5b87625bfc78063638d9dc92f4ac7367
78157 F20101206_AABDIX leung_n_Page_042.jpg
53605bdfbc55f0cef680673ebec32a89
6c774599b1768158308cbb9c55ea31eb388d2f21
95175 F20101206_AABDKA leung_n_Page_074.jpg
92f51be2f566ddaf8b689fd3b1024cb4
f4407ba9540cb1aadbf3f8bebfd30cd201f6567d
109421 F20101206_AABDJN leung_n_Page_060.jpg
393235a744c4370afc96af5d2d364e54
ba782a8e6c9b42478a9b747ba3fdb501aa47c44c
47186 F20101206_AABDIY leung_n_Page_043.jpg
5910ee59ecd7fb8b3ead7b34b00dbb65
a332ea13529522dcee418208d60f2b412bdbaef5
93869 F20101206_AABDKB leung_n_Page_075.jpg
a10879b1b4c55de29ce1ada5908704ef
fc3e8bb809b649112815f9b6e7d518e9f25ab7d1
112969 F20101206_AABDJO leung_n_Page_061.jpg
7c65dd542fd32a47807835ed1025bafc
96eed4a328954ba2e4f2975c1fe693b72d8b0e1d
48129 F20101206_AABDIZ leung_n_Page_044.jpg
6cd51602a5c1bbddf576d517341f7cfd
93fa20211101afa5fed487ffe09a7091ef8ca2ad
99167 F20101206_AABDKC leung_n_Page_076.jpg
3da2f93baf3d8a22aedff0a6ee8fd73e
91dd7fb8fd3327898c82a093cd0827e139b7db4d
111442 F20101206_AABDJP leung_n_Page_062.jpg
04b1e597ee02de2c76e964f37167b4f3
b021ef5b1739cd0a9ef12a3bbd2e8ff84988b680
84248 F20101206_AABDKD leung_n_Page_077.jpg
0abf49d758281d5508a044901066bf08
e8eeeb411be2787429c9db093454ce39831ee8af
95806 F20101206_AABDJQ leung_n_Page_063.jpg
cc5d2a8885b479cca1b037d64b377b12
1812667185581f8afaaf3233abe33660a332b161
93707 F20101206_AABDKE leung_n_Page_078.jpg
225a431a233d7bc68fe60e1c3edb0748
d574db4ec5ae41ca9ece2479b5d2e876bde5e9bf
90951 F20101206_AABDJR leung_n_Page_064.jpg
b4e7fa2341b492af5ac701866b55ee93
6e6cf78d11db8b6fa2739cb389622634c966ed1b
86947 F20101206_AABDKF leung_n_Page_079.jpg
a99ae047190deb194d8286e116d8d904
0e5cf5c431306202ab9cd1eec698563c32e57a91
96863 F20101206_AABDKG leung_n_Page_081.jpg
a42162b3757ba15bd9fe68cfa8975e1b
167704ba6066f61d6a0c8023d95027ae7bb2b4e5
60655 F20101206_AABDJS leung_n_Page_065.jpg
f873f06aeb9091ebad661652d55c4d17
2d37eda692cd7928957cd17f92d1874e528102d6
89635 F20101206_AABDKH leung_n_Page_083.jpg
b53177e6958df524d15c1e49b6c89f90
cd477ef31453feb3bf6a06de68fe071df3a86c60
75426 F20101206_AABDJT leung_n_Page_066.jpg
ec703ce24143fc26637d4c7046e49e65
ca4ff40d4af06e080044dac7baec9801cd3c3f56
54806 F20101206_AABDKI leung_n_Page_084.jpg
4087db12bce213a9ada5ac0361326532
bfe9fda83f47ecaa0a1872a04d24ef55efbe23cc
80916 F20101206_AABDJU leung_n_Page_067.jpg
8295489e7f2a7e7bf3c279f8b78fd888
b0e94ee876ae5bc5809632789528dfdc1febf4d6
89766 F20101206_AABDKJ leung_n_Page_085.jpg
07238c9a7cf710675e30df1385838c59
ee3d59a88fb0c79f471981200c422379211e93ff
75089 F20101206_AABDJV leung_n_Page_068.jpg
dda509921e1b5c2e46d976aaa29ec57c
f4e702911c799d1d0d8b60168ef5eefed50873bb
75418 F20101206_AABDKK leung_n_Page_086.jpg
7389b61490ac235b844a2227c380cc85
c9f698d07823994026e93febecd72c43bc7da2ed
90496 F20101206_AABDJW leung_n_Page_069.jpg
05fdb11e35b6a91b5c2381d36b691eaf
5d0c81dbc3e8ab9c8c9dceef32035625a46069b0
67976 F20101206_AABDKL leung_n_Page_087.jpg
1cb9f23a9942b8784355ad0a06f3074b
2b736ea4bbfe932358c1f84337a6ee203908e0d5
51185 F20101206_AABDJX leung_n_Page_070.jpg
86d96fd556f9d25388235de93d86f8e3
18708645ceb6885f71534a459b0194dd0cabc1bc
87205 F20101206_AABDLA leung_n_Page_103.jpg
f5b80fb7ee45608f657a4eb1e7c7c6be
7b4fe5ceb09aa972a3b9b9b7bb2cebd091a85201
85858 F20101206_AABDKM leung_n_Page_088.jpg
4a65651ba24558ff2eaab3f20cb1f1b8
400d625e61038adc70a9f1308407f66b1cd484e5
44305 F20101206_AABDJY leung_n_Page_071.jpg
6bf99785528447284e4cf29d7a142628
f9b603584bbea4cb1e30f00669add684e3555a02
66714 F20101206_AABDLB leung_n_Page_104.jpg
f4a7c0f7e4be290d494e2ad11c0adc3d
3677e99a2f094d964e100a97b4565ff0ad00ed3a
68721 F20101206_AABDKN leung_n_Page_089.jpg
03a2024fd475c90fe4211b024cf4966b
5497f0b45b697d931c0f6db143a3f0b4e9ecf55b
99595 F20101206_AABDJZ leung_n_Page_072.jpg
5974a632b21c6645e83f81134ee3931e
2175cfd13ecdade8673c1e71a72c8f74fc8e2618
80371 F20101206_AABDLC leung_n_Page_105.jpg
ff632e2359fcdc288e6dd4e405721220
499e832584028bcee6803901ac4c32197aac438d
64675 F20101206_AABDKO leung_n_Page_090.jpg
e22cc63d6cc12a93a2473300197057fb
d6f7ad79076c9d84183851e79431fa08f514b895
75121 F20101206_AABDLD leung_n_Page_107.jpg
5201801589ab564d97deb1ea277aada1
acd2865133a85fadad1a910600ddd405c9ec7eb0
78376 F20101206_AABDKP leung_n_Page_091.jpg
997056858c7281c71c19911cd3df3707
af71559ced1f90e00f13f3ff223e0d890339e543
84922 F20101206_AABDLE leung_n_Page_108.jpg
56937a4e2d2d8653360bd4737129ae5c
736f11859288348e40854326c90f41343196b623
65960 F20101206_AABDKQ leung_n_Page_092.jpg
66d9285ec00f8d2a090f96633f6aee87
83c72d7f484ba3b93d69ec83a44b857db9e7c030
88982 F20101206_AABDLF leung_n_Page_109.jpg
1a34751edf6913e907544e9b87cc7375
a8b318a7311c6b7016139bda4f34160d67527d38
59035 F20101206_AABDKR leung_n_Page_094.jpg
8a0aa3bc67ab9b2231cf34426f08d44d
d1c806cd6b14497e4219b14c69ccbe454e9b6c0c
64797 F20101206_AABDLG leung_n_Page_110.jpg
97fb98fb50ecdb885afb506812579d39
01b5288d08d71e2aecab7c109d66d54ae99a65bf
67640 F20101206_AABDKS leung_n_Page_095.jpg
966fd709282612d3b0840797e2ab692a
68bc938bf5c4f23e9224baaeb185550239cd1426
80230 F20101206_AABDLH leung_n_Page_111.jpg
6548dae0227289aa7d807bd797085915
1ae8eb629a37c759e29c96035ebb6ec7ffb61f29
63412 F20101206_AABDLI leung_n_Page_113.jpg
f15b4803f8593fc068327fe14a5307b8
5a0d2f99e95052c985697cb040472493ea9b8ca1
93858 F20101206_AABDKT leung_n_Page_096.jpg
fb066476f1d8231bcb9e53605a7be6d3
b5237bd1a310c8644317dcc0ae59d3df33231f0f
85079 F20101206_AABDLJ leung_n_Page_114.jpg
86a65ae0481f1f5167c721385a814c85
17cd3efbac38eed4aeb2ea5085fbb877a6bd42db
89792 F20101206_AABDKU leung_n_Page_097.jpg
61a299168ab74cf91c6d2b5a41513380
6285c3276ec2aedd49d341c5cff853d617727bf9
106939 F20101206_AABDLK leung_n_Page_115.jpg
3d43fa542a37fdbf0184ed8a6f766728
7e21f063b2886db28bee70bf47d5765683984247
100651 F20101206_AABDKV leung_n_Page_098.jpg
b5849e7d7ea4d5d49cd6cbd9ad8c3267
f9850a3e8ec813c18d95a8dead0f8a2ea5a278ec
115269 F20101206_AABDLL leung_n_Page_116.jpg
061b697270e86d7c869f43138fa69b64
03a4809dbc17442fc57bad83e304be2f035c225f
92747 F20101206_AABDKW leung_n_Page_099.jpg
72834d36f25e4c6d7764db9fe34b578d
ef9de44e677bf9c6a21d4d37ca61af8832c4f7b1
707262 F20101206_AABDMA leung_n_Page_012.jp2
5ebb2385441b57ac186509dcf4dd42e1
ce9d4380e1603ffce05b7a3dee84da6f4c953a2e
125786 F20101206_AABDLM leung_n_Page_118.jpg
e858bc265a0544ad2a3fc2d08d405f45
d0ca8561425b3655a34ae0f3c8bf136e840f4e58
86092 F20101206_AABDKX leung_n_Page_100.jpg
3a7235c52b217d94259d35d7a6e76bb3
160be75bed876ac56aaa107c93cb99657e7da073
97099 F20101206_AABDMB leung_n_Page_013.jp2
dbc7872ea408d53d6224054c83d632b0
f52506072b40cee86fdf4c8c12782cea86c9db29
126263 F20101206_AABDLN leung_n_Page_119.jpg
f3c4a8c3a22cd0428a7611b0c256b334
bd344497e04d3400dd1049d5d0534f09be4f673d
92118 F20101206_AABDKY leung_n_Page_101.jpg
6de4cc1c56e259146741256b416a7b85
5bd0713771d351b425d067ee7ac1039bbfecec3c
103102 F20101206_AABDMC leung_n_Page_014.jp2
2c1999ce67edfc81b89de6923d8cee46
ebde78939a196dc2dcdc7319e25249fd8d64892f
117702 F20101206_AABDLO leung_n_Page_120.jpg
f7a02884b8051f694b9cca5e93bcdf9b
8b3660b701b2be9200b11d34c96e7e04cae4f0a0
78840 F20101206_AABDKZ leung_n_Page_102.jpg
26ef8c02080174471502697cc7b238e2
8c28b0f691b7a8cc437fda30a080a2cc86303678
92985 F20101206_AABDMD leung_n_Page_015.jp2
35e73a7fdc44361d2f5e4f4b09c16ec2
375f836a17b2d9f9490ee137661305b46cd9948c
50278 F20101206_AABDLP leung_n_Page_121.jpg
29fb608eedb3cffcf549e1457fef5d64
216d37ed6095dd576797f71277f52ee6f254100d
115179 F20101206_AABDME leung_n_Page_016.jp2
87bea4aa14b5a6196562d42d30eab818
8dc069fc2a554170ab96c62e4a81261fb5022125
56455 F20101206_AABDLQ leung_n_Page_122.jpg
7af8f9724bfc67d2624d01a8e4a54dce
048d425d4e88972b0fd5684c4ae026468f6aeb14
114533 F20101206_AABDMF leung_n_Page_017.jp2
f3b7420ac0ae9e648bac27f6772e73b4
77753b2de323c37a1b1da8ad52f899b7d530fd0b
4959 F20101206_AABDLR leung_n_Page_002.jp2
2a985fdaea233da523372cc1e922afa5
0140c5737f5cac131673bc5b946754dca87d14db
111234 F20101206_AABDMG leung_n_Page_018.jp2
da45e88d0fb00518ac475f08a9e28670
1d2b209bc077fc4a3fe8718f254eafadd63f3b40
10439 F20101206_AABDLS leung_n_Page_003.jp2
4e91f71874f94e9872f1c8367b18b849
e579231702456cd1065208bdeed719c4c1eda144
100258 F20101206_AABDLT leung_n_Page_004.jp2
58ff1ac50ede61374257b04847b9506b
527fe435ad8729177485548e9e311044762dd369
99623 F20101206_AABDMH leung_n_Page_019.jp2
2b6175a5054dc4a262258ffbc333cc40
1f4d900d2b8931ca798e7b05c6b956e82672aec3
103858 F20101206_AABDMI leung_n_Page_020.jp2
a99eb16d28f890d5b04cb3ba0828871a
19d76414c790ae3c05978fcc54834efc716b5b91
1051975 F20101206_AABDLU leung_n_Page_006.jp2
67ee026e23713040f8cb4461f480b77f
f416ff782902c69ef6b95220b882a165bfbef94a
101890 F20101206_AABDMJ leung_n_Page_021.jp2
2ecd6a3a285dcd02b06ee35504cdf7bb
3d1942d75d88d25bed9eac61526739cd3be24fb0
1051956 F20101206_AABDLV leung_n_Page_007.jp2
2f2efd2a8c01629ddf1d0a8c4840dab2
8ce8827d1fe76c7f499f8b2e6ef8008f59ad2717
542480 F20101206_AABDMK leung_n_Page_022.jp2
c9d0c38a5b9cf29b18a5590755ebb818
a07eddb1dd6f125cbc63a60173e1c38735e77241
395856 F20101206_AABDLW leung_n_Page_008.jp2
eff2e3bb5cbb882d443892b99da61aa9
03723c75181a0abcbf5a2ff7d48adc72adb87da2
848842 F20101206_AABDML leung_n_Page_023.jp2
39b07c0b71ae65a8c18ae6fe66c30fed
e4bc53114d1a07af96f1bd2208a2bbba2829d9b2
1015939 F20101206_AABDLX leung_n_Page_009.jp2
a01780886d9e87cfb16845071c86c49e
c7304ac4e887fc0724dcf06f9dc485a5e7337423
91364 F20101206_AABDNA leung_n_Page_040.jp2
84b939fb98bd9b2379e1e69143aee650
d8fceef7d16252f4c8a7d7940ae0c0054f27551c
106058 F20101206_AABDMM leung_n_Page_025.jp2
0f4a04cf2e8d1606ccde8ee139c9f829
eb42680d128dc702c86aeaf7c857cb09a4334d53
1051986 F20101206_AABDLY leung_n_Page_010.jp2
37459f4a7daca4df30c852d4fca90403
11a72a827fd72a638e9a2453d050a9e2f7cd5bcc
727724 F20101206_AABDNB leung_n_Page_041.jp2
51d91b1cb10ff0a945ce9a79558e2241
4643ed9f7fc1bdb7761948a81f7f9875648517c2
117928 F20101206_AABDMN leung_n_Page_026.jp2
c10304f2d044b6bf369c245c62aba942
788d203704e6917d32005b0156bd304fab644261
1051982 F20101206_AABDLZ leung_n_Page_011.jp2
c5417a61a6ef53659a5c5ff94708a947
93e86b7859759459a42b684062af4639a4282b02
831790 F20101206_AABDNC leung_n_Page_042.jp2
ba8fcb7d7ae1faf093adaad690c972aa
bcd237c39bd911512e95bee55ac3e293723f66ce
588014 F20101206_AABDMO leung_n_Page_027.jp2
f3e09bb2a59ec8121db0c1878ba4ca31
474738f28e6c058acbe3a4ea7a533a8f464be67b
49919 F20101206_AABDND leung_n_Page_043.jp2
f2a35f003d06a0577e498de8561bcf7b
d10ea22b6a9c784ede4c45ed415c783a04412997
102063 F20101206_AABDMP leung_n_Page_028.jp2
cafe2632a1b7c1eaa5a7344d238394d6
9e1ce810e2b2a5cb5d0892cb3672c6988e1c17be
470864 F20101206_AABDNE leung_n_Page_044.jp2
c90ccaebfa5834660d402b799eb7ff9e
82ef5c9f7b587e00c8840e49dda393ff5c7e4255
114353 F20101206_AABDMQ leung_n_Page_029.jp2
b4f614e4a09efefa8b4303808476670c
6ada8e2b965757d1f58205e223edbd9beb1e9ce2
109799 F20101206_AABDNF leung_n_Page_047.jp2
a08a707a7a3cea7217a8bfd7c35167d3
d0b879e16405b6f7638d097a168f66b3327c1431
112209 F20101206_AABDMR leung_n_Page_030.jp2
ab9f4a8d584370eb2c05101c08511435
3f9af6b864db8d7ee79a70b597b53e819cc37de7
105013 F20101206_AABDNG leung_n_Page_048.jp2
2c474211aa99ee668cd9d87713301ff2
7f4ca7a93b80a9ef4ffbf88762d57bbad6809b5b
106122 F20101206_AABDMS leung_n_Page_031.jp2
a29cb1405a1cff384c1ec648b1c736f3
842a79016bd3f6929c49d886676f0f90a496e09e
112781 F20101206_AABDNH leung_n_Page_049.jp2
2c0378d48f15ac93613744b10d917110
76f1fece1d8c5744299e6673b1d49aa85f1cf538
94819 F20101206_AABDMT leung_n_Page_032.jp2
5417374551ba1c92794ce480a7cb1f99
39c32f82fb93ed9857c2e276faad199acbb08483
111510 F20101206_AABDNI leung_n_Page_050.jp2
9a7f8fa014a0739c9f2aa7860ae4b137
95ddfaf6245d6abdb5c9e7faa2f4d22e903433dc
89890 F20101206_AABDMU leung_n_Page_034.jp2
a81a8125b0a9fd8c5f4afdcc3611921a
790322a2548190f97ae3bdf252cd3c7ba20fdd4d
75776 F20101206_AABDNJ leung_n_Page_051.jp2
713cad8ecb8924463483115dc3543880
1b782318cbcbcd21a29da349790b3beafc02fc7f
86473 F20101206_AABDNK leung_n_Page_052.jp2
28c752eb03d56bb2e526c3a94d6c5a70
f2782ed7cd74efe5a582168dc2cae27a27a29c99
100847 F20101206_AABDMV leung_n_Page_035.jp2
1f1e179a7478dfc1193d814875abfa3b
436f881a87ff3341b65070c46c9f310c0316c6fc
57820 F20101206_AABDNL leung_n_Page_054.jp2
e68619180540076b04933160e9a2ca3e
fabb560d2e121e336eae4b4433c8bea664361256
114909 F20101206_AABDMW leung_n_Page_036.jp2
44f79c19c8ffd33eadca4252fa56a8c2
3ac2e767463d5cb458d6ed9042c4187e04955006
102142 F20101206_AABDOA leung_n_Page_075.jp2
ed23f72cef9317094d894c14d0d7ff7e
c34531004dbe17aeba93654228a3a536332fe66d
92927 F20101206_AABDNM leung_n_Page_055.jp2
ba0f54e0444fde95f953e0f768cd118f
b5ef7f0e037617f6788bcdbdde69f024f509303f
585856 F20101206_AABDMX leung_n_Page_037.jp2
ea263606192f37019a4f85ffc5dac6a3
df81ef31b20115498764f7097acb0abde6c5fa3e
945067 F20101206_AABDOB leung_n_Page_076.jp2
4e794295ae4e786e428a1b50d3fa5a5c
c4a75eb48d3bc71c5d0f0801a673c894e96e0acc
398279 F20101206_AABDNN leung_n_Page_056.jp2
e67a6bdefb1e4163105100c8e542a912
de974031403cdad5ab0448629c029a8361277fb2
102429 F20101206_AABDMY leung_n_Page_038.jp2
a49e2e7a1d31c3fcf228052302dfcb7c
55a20343c1ddb1d5a3ffb3c508f627afbf2273d3
98630 F20101206_AABDOC leung_n_Page_078.jp2
42327dd048f3eb7c722d1a62636f1181
838993b74881cb0e275cc5bff1db58a901cd11e0
98712 F20101206_AABDNO leung_n_Page_057.jp2
c8a07c4d1704e214de8f9aea21ca89d1
7ebb6f11b39b7b81f6f018ea58745a52f67826a0
70608 F20101206_AABDMZ leung_n_Page_039.jp2
ccfc913f9c275ccbefbd6e05dad39725
f97786a06f0fba42fe393227b8cce3e4db5a6a32
921022 F20101206_AABDOD leung_n_Page_079.jp2
864bee27f48d8228d7c8406ec59ae370
7dca6aaad0eeb726d22d4570a28cd9c28b32ea33
109171 F20101206_AABDNP leung_n_Page_058.jp2
a0bbeb45b8b1c169d3158fa7f95c6cf1
4abfbe52ef484d86f63ac1c1811df5dcd1a72062
574046 F20101206_AABDOE leung_n_Page_080.jp2
985abadb1aeb53bbe3f1d472d52a8b41
d0ee06b71cf9debef533fac2475c2c9a042a9960
115404 F20101206_AABDNQ leung_n_Page_059.jp2
2fe169f41c33e3557a08436b77840f05
9e985b089738c1f829c3807196fdc1d206bf1f20
103208 F20101206_AABDOF leung_n_Page_081.jp2
afe0e3ebc3b6cbb05ae15f6f0b3d2013
d6e7cd1302082667e0c230538a99e1e789997278
119451 F20101206_AABDNR leung_n_Page_062.jp2
64ffc1bc3f7b698f3dbaeea11d9e984f
677b32199b05283cb53eed8eb877826c55b724c7
997021 F20101206_AABDOG leung_n_Page_082.jp2
affb15facfbc87ef5833ccebae89436c
6fc42b7b5441b61cdad6cfd3c8af7b18c5770b92
99791 F20101206_AABDNS leung_n_Page_063.jp2
2ea5f1f96c8b14e510f44c771e3da44b
dbd07b82838f09dbaf0a4719d8bc12871bb8d8d0
966061 F20101206_AABDOH leung_n_Page_083.jp2
d1711a4c8737cb7d74ce40784f9a450e
8e941263843569f349f2be267439994cc9aadccd
96081 F20101206_AABDNT leung_n_Page_064.jp2
479ef6801f107769add07ac70f50987a
66d77044ab14476ff479390dd0ab848b2ac7f762
569141 F20101206_AABDOI leung_n_Page_084.jp2
9a36e44413b4f910239990336e3599a0
8d1ae147b31c62f2ea90056034b19701e533915a
83609 F20101206_AABDNU leung_n_Page_067.jp2
20959e1e04a974710535639a490c9e2f
3f38068ea5cda1b821630064df01bdc3c6b6cd40
792176 F20101206_AABDOJ leung_n_Page_086.jp2
5bc406fb54d20a31642c4001eaf90cff
6adeb711d58e8cb7bc5ba16de4cf2ec7cf4f4bad
784954 F20101206_AABDNV leung_n_Page_068.jp2
126583ac4cf52079528931b826a8eade
4d4522d658e04a81693a0e271b2c5cec5d2e8c32
751769 F20101206_AABDOK leung_n_Page_087.jp2
775645474c4e1445e00accd341ca4acc
9f6f3fe1b009eca0e12d984a0b908e4002ce3cf5
725041 F20101206_AABDOL leung_n_Page_089.jp2
1e773574f77ea2a42f2e792e51d1268b
6aab4a38bb2034091d54903a38a0861f0662db86
511645 F20101206_AABDNW leung_n_Page_070.jp2
2d632086cdd0b44e86a466be45cc270c
42812312e43db59aa2c71ee7bee606a67f61cb65
677939 F20101206_AABDOM leung_n_Page_090.jp2
be0dfa4a4eef8971ee2859bfcbfa6b55
66e812f28424550f14c99e6d8dc0d9412658d62e
46830 F20101206_AABDNX leung_n_Page_071.jp2
c66f3e1cba704bf96a765bb102ebb665
9275063ff6f271c050034839f1666eb6064b3073
808300 F20101206_AABDPA leung_n_Page_105.jp2
a2713afcb645030a9eebab31eeff0fc8
b6fb07bacb0525fdc58c5965cd5012238d96043c
85371 F20101206_AABDON leung_n_Page_091.jp2
8f83ef4501d2d8448cbc90da384c5083
ebdb78944e537883ac5b37d86365ec23a4841bfb
105118 F20101206_AABDNY leung_n_Page_072.jp2
cdc571d670ab7ef714aac784342d9540
bdc0b89089a248ba9a8661c0c9738a5771b2675e
1051984 F20101206_AABDPB leung_n_Page_106.jp2
24e25d2d75ac59034b4072af136b4feb
a2e2685741d5bd990957c4269b90ac3f8a556e9f
671256 F20101206_AABDOO leung_n_Page_092.jp2
e895c84698e4fa0ad46db9caac862ebe
4df3758adf28b31aea05ba957b57074e9e9a19d4
102201 F20101206_AABDNZ leung_n_Page_074.jp2
437833451b3a2c918a5d9a6b5432d283
7191edef35ce79316f60ea0d099f4430d4e76e62
88937 F20101206_AABDPC leung_n_Page_108.jp2
3be77ba7a88abf69b170537f7c2bc80b
365d9afed9242a030f64e9ee6394005aa1bcccf4
880425 F20101206_AABDOP leung_n_Page_093.jp2
de15256753ce93708b944877b35e3675
a5485ce1f68f6116a948a813ad0b4202d58ac1ee
959787 F20101206_AABDPD leung_n_Page_109.jp2
e057bbd116e7f0d0f309267583aeea52
6bc6e364e3fc7f10277310fbc6b047967b536663
650397 F20101206_AABDOQ leung_n_Page_094.jp2
501fe94a83d0e1ad9f114713cfb67587
06b18439f23df2f14b0b884845f2644a138e4570
745527 F20101206_AABDPE leung_n_Page_110.jp2
ce85e18c1e1093d06127fecf82d066da
ccd6ae12981e5469167d208b29e7d811e2758a41
878686 F20101206_AABDOR leung_n_Page_095.jp2
fa479613e6e28ce973eb40b535d65053
0431ded527a26c8c65f7c3405c7ff2065b14644e
920345 F20101206_AABDPF leung_n_Page_111.jp2
9d97a5a2faa0504af88df5dc9a412f7a
3284048ae3db8cfc29e015be545131984709cf66
99454 F20101206_AABDOS leung_n_Page_096.jp2
b06e90b50539c7a4bad332642396ce0a
51439a0dc7937ec3383407fe9e1c02d80e7d9a32
795809 F20101206_AABDPG leung_n_Page_112.jp2
d6f225f704688ad0892dc0c1540293c4
4aca3b828bb19513282ee62613275fc007eae997
94016 F20101206_AABDOT leung_n_Page_097.jp2
c8d514a291703c5661561b03342c2ba0
8b890d35bc873349dfaac91f44f8694e880b920e
834700 F20101206_AABDPH leung_n_Page_113.jp2
1b9b584a22eca6f204c5955e886035bd
79926ebb2f6badae6ca503c9d1572ebd6bc707aa
107970 F20101206_AABDOU leung_n_Page_098.jp2
fd93d8bd2405020b529771e859c97bd7
4b9b8e2bb6942b7221c9909e323d120a1eac8bc8
918865 F20101206_AABDPI leung_n_Page_114.jp2
1a4baa2027e60bcd87aa62ae90c79aff
f5472bf31f60ab97437626862468c546191e8bc2
1039344 F20101206_AABDOV leung_n_Page_099.jp2
9f67f8258dcfb1c1d26eac934b9f8bc4
bde210a4346865841cb7545e114bd04f9737f995
110678 F20101206_AABDPJ leung_n_Page_115.jp2
71ac4eb97fcbcc03ad1a81eb15ff8ef9
e1b246d7cbaeca4edc4322f55537d9f4a66ad1b3
1051965 F20101206_AABDOW leung_n_Page_100.jp2
bf21ed5d442a6c33f85918d62c0966b0
d03bf4d69d1d5699fba24abaf27a22966fe079fb
121649 F20101206_AABDPK leung_n_Page_116.jp2
423b3404ea16f279a4bf07d7a6712162
048941a215d2f6765f125a4e507726210787f9d4
40934 F20101206_AABDPL leung_n_Page_117.jp2
c6a6786fc74f2f059d34d470d0fbce13
5adff192ee077d8593753260f49284c6d08e158a
1051978 F20101206_AABDOX leung_n_Page_101.jp2
479c12e36f84532a3ebedefd9a52d400
2a3d6c26420b7123768f6381590fb0ab2bc9c957
25271604 F20101206_AABDQA leung_n_Page_012.tif
47d5783171a5ee2a60d550e6d3fb37c0
569ccdbc7ce978d224b1f95499aeca91ae328e8a
137419 F20101206_AABDPM leung_n_Page_118.jp2
7ed0a792b94a5cc9a888a3e2ddc9f1e6
ec1dc49a02a1d2553ede6f2a91f0dd130ec6bb49
817382 F20101206_AABDOY leung_n_Page_102.jp2
f29cac9511f2bc7612770d2bf3acd777
339fee447458f9c83965b50e24f7ba3201712f1d
1053954 F20101206_AABDQB leung_n_Page_013.tif
6aafb3392de3c42ad2aac0ca7fc43d2b
ca179a701d6017f7d1eef62421b0a4e80b6dcadc
137821 F20101206_AABDPN leung_n_Page_119.jp2
734abf3deffac13126739689d21cc781
ca2077b0f4a24440d0e12ea4251f4f130614288b
1051971 F20101206_AABDOZ leung_n_Page_104.jp2
b5d91275376ba3c39da369961cd6ffa8
9eca6c19a153baebee1bd8d3b20a3b2febb33070
F20101206_AABDQC leung_n_Page_015.tif
630b948cf5736d9cc6aadbc16993b11e
975db58214b71dad3865886ba8d8ab644bd2a0d5
132803 F20101206_AABDPO leung_n_Page_120.jp2
5a619cad0c84c8bc99e9c523b13753c1
260e290409a7812dd32ac02eaa67dc4b63b7c43b
F20101206_AABDQD leung_n_Page_016.tif
c107ea9a1382da87402d96902391cf43
88d4a94d9fbc52421c1c566ac252ae4f410cb082
59507 F20101206_AABDPP leung_n_Page_122.jp2
c6b46c0eb9b47241ed9d1c98e5237b83
07669aeea133a436a108f4b154f1a47fc2cf74f7
F20101206_AABDQE leung_n_Page_018.tif
17ea6ffdbd3e3fe4e8103a54707519ca
86e2b37735ad1fe4da3550a8cbf73dd7b28b0ca0
F20101206_AABDPQ leung_n_Page_002.tif
9ba94d883f722ffddef49287cb876bf1
a4b5ca21ec598aeeb0e94540a751d0bd455248de
F20101206_AABDQF leung_n_Page_020.tif
1f9fd86daa9ef8e420a1dc0cc8637233
5eb5fa051ced9d0d2ea4cf0f9873962e8d56351b
F20101206_AABDPR leung_n_Page_003.tif
351dee4a3d490b660e28b38bdfeaf161
5607fc2519fc6e719fabd0c8c38e70de4afc4862
F20101206_AABDQG leung_n_Page_021.tif
a2df5540cc6a3c825913f6d1b4447edc
d2e0bc1d8074fc40726c0d8fa60a9b89a9d7160b
F20101206_AABDPS leung_n_Page_004.tif
a2dede0dd4b40368f130ceb3036db71b
50bcf8cdd22970477fffb6572a95e21be3968963
8423998 F20101206_AABDQH leung_n_Page_022.tif
bc1a359ec41ef1d9e9fc8ece145df192
97474ae29ba4849fe732cccf0f0c4f574f91c64a
F20101206_AABDPT leung_n_Page_005.tif
a1b90923d668e31f33170c37bdd5377c
ada06ab6626e8bac76666e6734e1b422c24e179d
F20101206_AABDQI leung_n_Page_023.tif
e3e8e50d2bcf52a190ad451be22f70fc
a70eccf8562b32fb752e3098672ddf7c7b71ce64
F20101206_AABDPU leung_n_Page_006.tif
602901567ad2bafaa5155a5a2184163e
427dbf61296031dae595adf2548bb35ce7613c0e
F20101206_AABDQJ leung_n_Page_024.tif
b68c4f5a58c70215c341e878565a74e1
83aee39c977a30cb98fa8933faed0778af755879
F20101206_AABDPV leung_n_Page_007.tif
5c6678325a0497193ec4e6c347fe8e19
30b746635d725ad75a4d5ba8e8ac999c40572535
F20101206_AABDQK leung_n_Page_025.tif
941dec55020707d52d38dfbaaf7357b6
ddb8af8cb2a41d721b5746a68fb4f7f99cc28118
F20101206_AABDPW leung_n_Page_008.tif
b13627ec96bae2c13dffb3eae636a115
3faab1d45134dfff13ef07efb21a408bb82c40b0
F20101206_AABDQL leung_n_Page_026.tif
87a693792a271d54c6c475398c8e374c
e2b50d6ed4e19c3595ede842f402720886389968
F20101206_AABDPX leung_n_Page_009.tif
5a3f7b620a980a33903ce3ee84592a4c
31b99c6a807637582b55bc9e04cc87fd7c82d1b1
F20101206_AABDRA leung_n_Page_047.tif
75cbdadc3a73058178fe9f8e68d9f73b
25738d5225bc6c4dfafee7ab42a37bad392e44c5
F20101206_AABDQM leung_n_Page_027.tif
2875d242a86d654eab2eb6e3a1779379
a8f454635df46fde8b0943ea61be4b43d4cb4581
F20101206_AABDRB leung_n_Page_048.tif
bc461489aff8dd267b3e10b20c73555d
1057cf1a6ffd607aeea78b9dc977832422f0a8e6
F20101206_AABDQN leung_n_Page_028.tif
3b1d64780bf3fbfba9f0e93b8833aa25
ce305644ee6d2d370ac22c256eded5d1692d8ee7
F20101206_AABDPY leung_n_Page_010.tif
3a5fa4fb0461e49208d04d0e74d3dad7
c9caa3618cdd12e1b26bf676ae0433ececbf535b
F20101206_AABDRC leung_n_Page_049.tif
90250fb6901bac40fde5ff739b119ea2
1e7ede287cb45a525d37f5307a91339008baea38
F20101206_AABDQO leung_n_Page_030.tif
9c1fac55d6d8fc0d931471076defa9e0
545a5d076f6a049bacf7919b17a9fca7225c46ff
F20101206_AABDPZ leung_n_Page_011.tif
6bb590e5d2bac7ce82c3f103d9f0e4ba
350d74a722c1fc75ff279a4dc137dbc1328a84f7
F20101206_AABDRD leung_n_Page_050.tif
08fe47bb7a2ae1075b0a8f38a09718ed
37c9f01b0a2e03d931e9610f8df1743053759323
F20101206_AABDQP leung_n_Page_031.tif
847d290e9a7d815c070c788bd6905b06
d7227c89fe3555b7351442b5d0e9e8dee2d780f8
F20101206_AABDQQ leung_n_Page_032.tif
e3fa11669ec999ecded6f9a32f89fef5
127a7e7642b53246208d526b35764e9cec4a9ea8
F20101206_AABDRE leung_n_Page_051.tif
b66dca5ce40baf2fd45fa8ac4b75dcdd
f926714b6f32d0256e8228b6e9f401b456713b2c
F20101206_AABDQR leung_n_Page_035.tif
7855dfef2d8c4b1bf12fe3e70d3d5d25
373c2b52d2c5e35cd3a6432053843ac29825a71c
F20101206_AABDRF leung_n_Page_052.tif
4b4354cafb27468fe524f279eb787b52
51bcb9130400d1db58f234f24817c36ad00214d5
F20101206_AABDQS leung_n_Page_036.tif
0fbe9a4cd24cb3d520a9a95adf511783
3686c3f9bd187c30621f2a1760650fc49b0ffb65
F20101206_AABDRG leung_n_Page_053.tif
4fb1f971fcc91c5cfbec580e21c37603
44a553c929635414f096265761ddb81a3e5abec6
F20101206_AABDQT leung_n_Page_037.tif
c77abfb45e833298187890a09228ff10
f4031e6d485754aef3fe7333a04f635cf78e1286
F20101206_AABDRH leung_n_Page_054.tif
a51e4ab8bcda67082541d5196b186387
d7e2851a74db8f27c416904957da8a10dbebfe0c
F20101206_AABDQU leung_n_Page_038.tif
c8aef7bb371d0de6f5777c6d58387129
8a8d2c149ca10b716de83a1fd8f8072c13fcc819
F20101206_AABDRI leung_n_Page_057.tif
3d3ad5129e41278d894457f7c58f4220
bc4e6ec1b6359a2754af239c2cfb8ff2b5ea53c8
F20101206_AABDQV leung_n_Page_039.tif
cdabf6b6651dbb028b1f05b915a7a0fe
f921a443ee16ca9a99bb2a084c7cc5a8002b5fa7
F20101206_AABDRJ leung_n_Page_058.tif
60c6798529c8c9d5f0fa96f0e75880e5
cc17e7afaad53b292bcbb4b93ac7e9ae137823be
F20101206_AABDQW leung_n_Page_040.tif
01cf832801d9ebe6bdd5e3ee6407c4c8
0fb39418c1a029bbc456b83f7a8d2b3a093ada0b
F20101206_AABDRK leung_n_Page_060.tif
ca12bc265b0bbeaab3f4d423210f6398
a0385ed7a06f819e8b40ed482602aad4fd46a211
F20101206_AABDQX leung_n_Page_043.tif
2ad53a2f2f962e29b62593e59615163e
903ff98e24204ada4e7a95d3d9f07ad2b93ddca6
F20101206_AABDRL leung_n_Page_061.tif
79f8789de5f8d1c6a06191f88c0d6458
99370b2972227db516c9f0b078cc373022d6b238
F20101206_AABDQY leung_n_Page_044.tif
c0f0c9da533928e8df128077c9e1d00f
e0a37ae412e5ad8f2ad9bb4e47ff2e617bd6ff3e
F20101206_AABDSA leung_n_Page_078.tif
97d5154d39baaa9dfcac225045572c2b
812fb3fb1b9692899883fb199712d7461a9f306c
F20101206_AABDRM leung_n_Page_062.tif
754ee069b594714f00074790e0ed83fc
fdeb0af2be379317d2f2036de7d6040d1b2e3979
F20101206_AABDSB leung_n_Page_079.tif
eb05b89634ce8d120543f91b4c4f8e4d
f28f4b7cb4d34e6cfad18026c1fc8581275a0529
F20101206_AABDRN leung_n_Page_063.tif
1324b928d55f6649508e26dbb0e6a1ad
7421998ed931ca8114d154021a1a2b00794e30f9
F20101206_AABDQZ leung_n_Page_046.tif
533928d9bc2ed965b3a05ae16eb56107
ba69c2a5eca341f47fb138bda205293eab7d80c4
F20101206_AABDSC leung_n_Page_080.tif
a486422b0e1a80765388fec57d87c34b
699caca9b570d5b80e5172f5e3ff7f7218e365ac
F20101206_AABDRO leung_n_Page_064.tif
a211e53a34e9d0282cd926f9b4f59dff
a91abe97ceffbd8e30b64cafe19f3542cc09e609
F20101206_AABDSD leung_n_Page_081.tif
39f306bea15f24660c01dcd332952a04
5748a21173a610a924147e7a320a082fd2b077bc
F20101206_AABDRP leung_n_Page_066.tif
0d0c46b6a1096ed82c26caec56b6020f
bbe0a7d86039f7bfc07bf7dbebb3cbe250a2b9f0
F20101206_AABDSE leung_n_Page_082.tif
3da1a6e19572dab76cb5b4feffb3a779
c1aa79526f36d36c5d20a1104a00bda6998f4a12
F20101206_AABDRQ leung_n_Page_067.tif
07d9ae20d3159b6cf29c2db3ad748579
7da29207616778319e1ac33eff5475016227a4ee
F20101206_AABDSF leung_n_Page_084.tif
41eac96ffe3bf7472aafd391f36a75d8
92c39c96a5bc3bc904d160555f5d134ed3ed765e
F20101206_AABDRR leung_n_Page_068.tif
fecd1a6d633edd4e294d1b62766782b1
6a27f38b02110463f725655faa5d14cc5db9eea4
F20101206_AABDSG leung_n_Page_085.tif
cbc9d84b266ff4aaf232c510c45484aa
319c7bec13f8b2ada3298ab82c1ec91b27699e63
F20101206_AABDRS leung_n_Page_069.tif
01f3df2afc11f6519fc8c4c7c71ec4d8
9c9c4d886a4652be3c686f8cf73a0036a536d542
F20101206_AABDSH leung_n_Page_086.tif
b6169d25c8d9b15b7d5c1477bfbc54f7
a2d42f5281c8f4e97c347ee9c795a9052eab7b6f
F20101206_AABDRT leung_n_Page_070.tif
e11f39be9cffa89ea61187d44b7d92e8
74ec70726c0524385285d0ecf01373a38031f476
F20101206_AABDSI leung_n_Page_087.tif
6fe89ff68c3e2776e356a737017ba1ab
24763ecfd3cfdcbade87fb26283ab3ec80828013
F20101206_AABDRU leung_n_Page_071.tif
e937d8e35ce82bb854ea22df35ad136b
ee91a27d73e4cde1a24000aceeb6678d4eff71ef
F20101206_AABDSJ leung_n_Page_089.tif
59acded42e61b84cd0034e532aa58d82
9ca7212261813b71bd0e30d4cc34f80bb6b5e914
F20101206_AABDRV leung_n_Page_072.tif
5bfc8d43176a41ea7fd1e482dd392953
1236d7013cb439aba0803e3fa7d35fbf52128005
F20101206_AABDSK leung_n_Page_090.tif
ab46d3d26d298c85da8c85f56c577bb8
270eb84855a4b66c0ee327036f9b91550849e7fa
F20101206_AABDRW leung_n_Page_073.tif
37dba5d7fda9cae513d92932735cd174
329554b9f1679362b93ef3d702f3c09b868b97e5
F20101206_AABDSL leung_n_Page_091.tif
be0a333491008f89b9478f4367320572
7b438fe539a17769ba8d541e6abd9ad53a7b72fd
F20101206_AABDRX leung_n_Page_074.tif
297b04409606950ca2e1fc9f159a279c
b4e3df11b2fb6125e352d5d65c921828f3fc38b1
F20101206_AABDTA leung_n_Page_109.tif
59d8765c88060163e1522e8ceac70cde
6ef4024fd5789d84e5e18083a7cf96af438a596b
F20101206_AABDSM leung_n_Page_092.tif
28b43536ca4d43a49a4453e0a15b3679
c2e32a37487165b35526d01fdcba26a2d748c3c0
F20101206_AABDRY leung_n_Page_075.tif
5e5fbe17dbab762b895258e25c65363d
0927df2a6b16e04440dcb6220fee9178495bb9fa
F20101206_AABDTB leung_n_Page_110.tif
74ed34a4558529c4cebfa53902627e33
7afe92c7dde6d1ec8edaf1e93dc1f6c676b2c6dd
F20101206_AABDSN leung_n_Page_093.tif
a10153d8ae3aeffa05bfd4d084a271ab
8cb20f64b95f9769735d207bfdbecd81d2724730
F20101206_AABDRZ leung_n_Page_077.tif
49b11fdc29b24d6558a6cddc3d193ea0
828ad83b83ecb4103a9bd805481cd08bb701f42a
F20101206_AABDTC leung_n_Page_111.tif
38b11c72402323731e9d76d44ab4e9fc
1b758be779c797b3fc3f14ee7d2a888f85d6183b
F20101206_AABDSO leung_n_Page_094.tif
9f5862378fc9ef621fba1e168b7e3395
37057ed427a23e81b7c97efcdaeae914f1a36fa5
F20101206_AABDTD leung_n_Page_112.tif
14fa7ead04c79a5ac70f1f05df9d29a0
253b143d9424a858e79a451ff31badbf81b8ddc0
F20101206_AABDSP leung_n_Page_095.tif
6090c39bb694f4220317536f922eb36e
477e4815a2ef012b90a055111d784dc1df3f773f
F20101206_AABDTE leung_n_Page_113.tif
20ac2edb9787a47dee8eb292dc50c8c6
7584ee267a0b7a614e45cc73f8e4f37dde1f835e
F20101206_AABDSQ leung_n_Page_096.tif
f46078720fa4f2fd4a9f08e26a33552b
898655d52fb424dd05a18e6c1a728235d6747e16
F20101206_AABDTF leung_n_Page_114.tif
71c93fd7e7d95d17b0dc08e255fcd91f
4d07dd0a967abbc6cdd791b81bbfb2249dbad352
F20101206_AABDSR leung_n_Page_097.tif
55ba7979428c741f6392c34158d84554
1779cba083021bdb7214e4bd70da2b91d1a5beff
F20101206_AABDTG leung_n_Page_115.tif
79cbbce548abc1866e5498e7ab78296e
71d54a32b91a3f8d6ea4e1c0063427c77850a038
F20101206_AABDSS leung_n_Page_098.tif
ccb09542460844a040905c52cd0f449b
49ff0ff2dfed094e8ab89a08c1902539be576d60
F20101206_AABDTH leung_n_Page_117.tif
4056e292ed76901d0a5753fbfd31fb27
ba80bb0e70e2064c3df3c5959d45e9abf022adc4
F20101206_AABDST leung_n_Page_100.tif
3f57f94fdd3c8bb21a1f5b517301b447
abb2855fafb661e74707a144b932971525de5efa
F20101206_AABDTI leung_n_Page_118.tif
cb4b81a8d85f589c9fae4c1282cb2a51
0ff4d1f2a02b27bcdb5e6820f7fa1c0c134f0414
F20101206_AABDSU leung_n_Page_101.tif
6853b9932a97be31f2416d99d9fc4999
6b07ddc8a80584f7bfae25082887a93f36346346
F20101206_AABDTJ leung_n_Page_119.tif
1453d0cc81d1a516869c0369fffc2ab3
773b6417edb55cb0290913350707f04d4d37d513
F20101206_AABDSV leung_n_Page_102.tif
6fe8b12d618351c33edf5cb9b1687e59
4b9ac6736757925b8fb3954d908ca2b1b524f355
F20101206_AABDTK leung_n_Page_120.tif
0bb2bd1a2e7c7f2673c2942c15b6a9aa
8b7e37161a2853c53492ecfd5b8d903269a94cfb
F20101206_AABDSW leung_n_Page_103.tif
7bf8dc7cdd54632feddf9475b4aed306
6c00a10ac0e23b54e7a2a30e3e8ac3a898309454
F20101206_AABDTL leung_n_Page_121.tif
b187963bdb4f7e66c9f1dff8cd2cef41
9c529572b167e42a77fc73da3c8c703f35d818b4
F20101206_AABDSX leung_n_Page_104.tif
53f5a8f6873da9f7a407a6e88f5ca55b
0c0b43d9fcbd61b3d84b40db6cf92e7560f02644
F20101206_AABDTM leung_n_Page_122.tif
96faa50a36bbce24f1a838e5ac589d98
8a95ad7bcfd34d204894d9fd4dfb48eb6981155c
F20101206_AABDSY leung_n_Page_105.tif
16fa07624cd7450a878b0dd31bd6211d
e3b4cf144237aea46de9704a8f5bfb952490b59a
51901 F20101206_AABDUA leung_n_Page_018.pro
9fd476ff6db04e499899475eafff7770
e59c255af8c0f140891c8026b3d756d993c482c6
8071 F20101206_AABDTN leung_n_Page_001.pro
7ae7e06223faedfc53321c6c3be2e8d8
efe6009743da389227c89f3b78a6cdb94277c3d9
F20101206_AABDSZ leung_n_Page_106.tif
014ab8bf635c291de7d34e64f3df6a4a
00a500717958fce037c3620d0a1d5ed90004549a
44772 F20101206_AABDUB leung_n_Page_019.pro
6e1af36eb16ecb1fda412e957ca90c38
059c081cdf5d171581ce85c4684c9c5b98f8f700
3094 F20101206_AABDTO leung_n_Page_003.pro
e407c45ce02366bbaad540f4b5d3969e
8f23cf7577b5f6487d69b8e47f51533e2b75c6b5
48321 F20101206_AABDUC leung_n_Page_020.pro
6e729a261b067b385ac571c4f8af6292
c0e950cdcdf340ddf7a2bd3413f4000faa28d104
103312 F20101206_AABDTP leung_n_Page_006.pro
e5bb740c6476f4bcdf012b2cfe9a0553
5e1258db5ae7376aacd32630bc3c587205b516de
47732 F20101206_AABDUD leung_n_Page_021.pro
c41a6ab46886487d0b1c51b494186a98
18e9ec5b0d5ac3fefc619c1d3766770a71c0115c
115034 F20101206_AABDTQ leung_n_Page_007.pro
38f28024bfebf5dbe0555f5a021e983f
64ecdb4dd669a530655e8d5f11a9d0c368881e3f
38584 F20101206_AABDUE leung_n_Page_023.pro
6b1c9f0cedf848129d811789069fc538
ed0fa0262713bbf9774ec0fe70a6d9d3dcd5f7c3
16952 F20101206_AABDTR leung_n_Page_008.pro
fd31b9a43fdc0b139afa4cc24e96874e
a50cc2399b6b58ef0bc5680ce6f72f06bb6b2aa8
1875 F20101206_AABEAA leung_n_Page_085.txt
9be5fe7aecdd13c07ed852dce3b3fa94
09de3f03848dad3579cff592566ab1dda69d9219
52958 F20101206_AABDUF leung_n_Page_024.pro
ca5ce0780a7068c3cc1b166adcf327e2
2bf45440fbd44d3be603e46cb19da04e765c4d83
34893 F20101206_AABDTS leung_n_Page_009.pro
1f176ac21291aa73ebad724c3a15a761
62b3eaa503418d9343c10879449a50c8e6709dc0
2288 F20101206_AABEAB leung_n_Page_087.txt
03b059c4efaf525dfa3b65f51bc36db0
b77b4f2dfa2deaa2841a522098506de373cb4625
48489 F20101206_AABDUG leung_n_Page_025.pro
4a9cc73f0ab376938f186d3dbb16f07e
fdc4ff2a733c793d69d3e2bbebc0d1509b0e0ecb
71127 F20101206_AABDTT leung_n_Page_010.pro
fc5e4c95e29e4194b96879d498fb33cf
968c3c9ce1b6cdf289d90fecc1cbe69af7b769cb
1891 F20101206_AABEAC leung_n_Page_088.txt
cae7248fb8fbcf90f281c23839a4a49c
abff7640b4a6220052e4bbceefdf0c5b5eba3b4b
53481 F20101206_AABDUH leung_n_Page_026.pro
20a91d5fb362302ce789270a3e5fd442
0fee44edf822561d7284dd02f1854fb849afbd08
73867 F20101206_AABDTU leung_n_Page_011.pro
79032cdaf108462279b57246095c8577
c65703262f01f7cfb3afc922b4a67266131e03fc
1914 F20101206_AABEAD leung_n_Page_090.txt
214c69b4bccec887e2624981a7e4f8c0
6f7ec884eb4edbbca9239b179827c66306dfcba7
18837 F20101206_AABDUI leung_n_Page_027.pro
46548285fc309fc098fce22f5feae448
e3e05fc90378e861c426050f2873bf530038dd22
19940 F20101206_AABDTV leung_n_Page_012.pro
c6b71cda3b9028ee4d7eecd03339fac8
6e1205824893c308972294c01a6d43c497652650
2081 F20101206_AABEAE leung_n_Page_091.txt
b0a7692a973851a23593a4092b2c4589
d7d1f170ff220f2dab17aa2568f5e5a255f64cc5
50436 F20101206_AABDUJ leung_n_Page_028.pro
866af677b12aaf81be503b2341afb904
114655dc4446f4ddc479579a770ff9b23039ad9b
43941 F20101206_AABDTW leung_n_Page_013.pro
ab2bab120d01d39f21300d53a9eb1d3a
49f21145e0da1ae55b9fc111cc75bdd821894c36
1180 F20101206_AABEAF leung_n_Page_092.txt
3c5e82bd19f0714ebb01d77f018fb769
7d3fc324482de5605d617676fe8dce07d0c76d2e
55731 F20101206_AABDUK leung_n_Page_029.pro
97b1ec4ace95f843afd6654d809dee2e
2d2251c55b13bda2f0c8ddabe66abe59606cc482
47522 F20101206_AABDTX leung_n_Page_014.pro
78827659d0a244dc4c1724121ac43401
b51ec5175238fb790777cbfdd5c68ba08da37e7c
745 F20101206_AABEAG leung_n_Page_094.txt
fdbc0c88728983ef09e6ad670c143841
9b2f2c07ef02352f8330a074a62b5e0dce4584d6
F20101206_AABDUL leung_n_Page_030.pro
ee9e15307d50b24726d6e9ff2c5615be
ce53172a4ca834e712c146f8616043ad30f21aea
53463 F20101206_AABDTY leung_n_Page_016.pro
6ae045687ec89797b380ab8151c40f12
58dda80d9add6190a5ce7ac4764c8209a3f3004d
1110 F20101206_AABEAH leung_n_Page_095.txt
d6a41b8182c5fd9cdfbbc67944ec4cd4
7c344868dea9e984cd1397da28f96aba18b10f76
51486 F20101206_AABDVA leung_n_Page_050.pro
7b41362b1b13ced472dfa9eec6859c46
f58d68095972370df85f08e5a967d4f78aeaff8f
49548 F20101206_AABDUM leung_n_Page_031.pro
3a583938d6c220fd47dac81be4f65af1
15caa2256b6245f314af8db418758eb17f5e34cd
53899 F20101206_AABDTZ leung_n_Page_017.pro
67f0ecd42fc7f6e7b3d6f4da1615fab8
2a1a018ec18527b6e8e3ea0396dbbc952b4ecc11
36128 F20101206_AABDVB leung_n_Page_051.pro
2fca9ff98b44bb28dcc1da0d69635dfe
4b7995fd22f7391aa62bd109f570c895e19324ad
43194 F20101206_AABDUN leung_n_Page_032.pro
fdf99169638d7400d405360b0379bb12
da78a5f50d43ec4b0b168864b3005c0a3c1d71d7
1988 F20101206_AABEAI leung_n_Page_097.txt
dc6a09c828a038adfdf9e14e6ecaeced
fd2ef1c782edea7a799cac15878db5af24c94cb7
44456 F20101206_AABDVC leung_n_Page_052.pro
0386e5a592fdaf7f4a23e1fe03098cfc
2c8f2a6bfdf27b700e114dcf615b418f7cf9e8ec
55637 F20101206_AABDUO leung_n_Page_036.pro
392a193a2fa2425df71b4b71ccd29028
075897243f38e042f3fd6196fe10ac83e5206d62
1978 F20101206_AABEAJ leung_n_Page_098.txt
4dd6adc6b387eb0993f322264fe34b49
10c323110cebc22a752a1a07539f6c5920d9563d
50054 F20101206_AABDVD leung_n_Page_053.pro
e2753d76e2d47bcf51bc0696bafe0dbe
43e6f5a487ed052f820048eb39db41eda9b98cb4
27073 F20101206_AABDUP leung_n_Page_037.pro
5113778babf0578dc33e1eeaf707c827
dbe808cc838a6651fda73473757ea32ed96d9142
2141 F20101206_AABEAK leung_n_Page_099.txt
d83d5b60cb6a291c5905d9b77ad3bebd
59272fa7df4c54fb43bdaeaeeed1f95b7cc2777a
24996 F20101206_AABDVE leung_n_Page_054.pro
6f3fbbd28f2d073e8586e717832a8a6c
866f9467ec6615d8f01c8be83169b4e159e3a190
49278 F20101206_AABDUQ leung_n_Page_038.pro
ce8f6902356d190d72c53db8687caf71
23e741a2733b0e06087fc378354dcd7529dad865
2193 F20101206_AABEAL leung_n_Page_101.txt
681a9466159eefbee3c4b4575371aa3b
1f484723a11af701ef63cc0c945d124ec24b4489
41978 F20101206_AABDVF leung_n_Page_055.pro
4d8e3ced2366fa7d89184d33315d05b4
b6f7a18612dc10170d4af282eee6ca05aea1fe2d
27917 F20101206_AABDUR leung_n_Page_041.pro
b43164cdd7fbf793f2af35bd18366cb4
5a3ae132d6a0c56b2dc2e9d7d4767de7f65863d3
2531 F20101206_AABEBA leung_n_Page_119.txt
95ce0387b08216463938bc9ced115f01
78814caca7792e795dff0573f5561ed171e88e6b
1043 F20101206_AABEAM leung_n_Page_102.txt
b762c630dc7c441d619d92dfb9b4bba0
319f54b002ce204390e629058d8c8cf50821e8ff
12840 F20101206_AABDVG leung_n_Page_056.pro
ca38980dd326d71cb6aeaa30ed6f990b
7a2a7057e9f29960660e107c9f2094628ecc097e
36991 F20101206_AABDUS leung_n_Page_042.pro
c243f5ed55da05c91ee24d24e11af5d4
04668ce42a458aab752c03f3fb9897b196ed7cc2
2375 F20101206_AABEBB leung_n_Page_120.txt
9818a97bec86add2524eac1744d2416a
eba78b9d0c2ec623c3dce1ae5701eaeb8f3193f8
1837 F20101206_AABEAN leung_n_Page_103.txt
9c9ad33e0fb527d76b3c4d3a279822c3
d9cc5cf92fab33a7dc4d80f2632d6f3ef8f06436
45121 F20101206_AABDVH leung_n_Page_057.pro
41614ae5193d438d7ee16dd57b144b34
fda9ecc293709a90f868918684e1438fb6ea6f32
24490 F20101206_AABDUT leung_n_Page_043.pro
caaf08e3c1a9b211ce18b2759edfe52a
a2a946bc78f9e5362324337c40ca0a43103311d6
931 F20101206_AABEBC leung_n_Page_121.txt
3c24f3ab3d43d2a92944e647871e7fc5
873938e27b151e2ffc247f15a06049604e4e1786
1941 F20101206_AABEAO leung_n_Page_105.txt
7153d7f0ce0b7169db9d9d9e0a19c8de
c3d3bc2bc0d628c5f02b749880ea0fe677115fdb
54636 F20101206_AABDVI leung_n_Page_059.pro
b6f985e769c0faf03c4bb0a7e829926e
16bd9836c5eda59d6a0797177780f7a4d5615349
22278 F20101206_AABDUU leung_n_Page_044.pro
6fab89fb00048ff2a3cd6f3506ad0e2b
bb0771698ab41c6624b36806d0b76159689cdec4
1067 F20101206_AABEBD leung_n_Page_122.txt
b09b9c0ea58b899dce1f1bf214886ac7
e2919fb16a28e88b590eb18267f74b073fe8d498
1341 F20101206_AABEAP leung_n_Page_106.txt
3d1455a55f749f1c344a85204af0b9b8
925c26c68fddd49748513b72c63c1aa3acd982d4
55581 F20101206_AABDVJ leung_n_Page_060.pro
b8beffdc8f939150ca59b3bd06446aff
d611be6ec69d67c537f438cc11fa695d3533404a
33651 F20101206_AABDUV leung_n_Page_045.pro
c8eff05cd0cd7ac6face1e4cde295047
bdbbd964079a090cbe679cb1707a15a85da8d7a7
2001 F20101206_AABEBE leung_n_Page_001thm.jpg
856f25f1fe77afc9aab28954c4cfa9c8
e255ff6db957bb4f05bae8054f82c453f16c2b4d
1643 F20101206_AABEAQ leung_n_Page_107.txt
391428de3f65a9b41259156874689e3d
c05644c87cb46399d06d055dded5adc8d4e041ac
55735 F20101206_AABDVK leung_n_Page_061.pro
48b52dea69d63f3d284e6e992e331810
54946008dae079f4ae86601129bdf88ac168fdad
56470 F20101206_AABDUW leung_n_Page_046.pro
f6530d916fd97a7936ad03e9c9803b14
3b8e90ca686808403f05cc5f2f0472bfa9dadb52
2329087 F20101206_AABEBF leung_n.pdf
29b0ea8d50dbeb8a711f6d34b782caca
e7f00d30ae06a5f34090a0845843587e34e54dcd
1723 F20101206_AABEAR leung_n_Page_108.txt
454f0c90bba4ecc72f679c36723e1599
e0fd2b2b3f3122046b6d7ce4e6cd24dc56586e45
56093 F20101206_AABDVL leung_n_Page_062.pro
e20cf1a1ec6643ddae152e8379c90d78
eb451b7853680713a8e7adff5747d3fa5567eb18
53705 F20101206_AABDUX leung_n_Page_047.pro
7bfeebad1204d2823ba95b2e2c63590a
d06d43c55b668088d4b2403a913018212e0187ab
7911 F20101206_AABEBG leung_n_Page_033thm.jpg
34719ab33de6af93a8fadc5997d50b3d
5b2522129f2f0d9e005b784838ae7992ca7cb228
17354 F20101206_AABDWA leung_n_Page_080.pro
641348b510e70bc05972cc193106b2f1
4a33ed5ef89abb9febb252a3ef2167d5b541a58b
1711 F20101206_AABEAS leung_n_Page_109.txt
b2dc2942df71d748e06c6e0eb6e0f63a
6b176c95af800e725ff09e9075a6e9df1cc4cf71
45766 F20101206_AABDVM leung_n_Page_063.pro
dfa97dd911e842d976dd05766c556dbf
5ead1fa3d78d9c204254a0b999de64f4d9b9e6f0
48902 F20101206_AABDUY leung_n_Page_048.pro
164660dd6df0b5ee29444d502a6cafd7
ce632446ec7d152d9819bf928010e618abd3199f
8857 F20101206_AABEBH leung_n_Page_026thm.jpg
b01a31d759a2a827c0f6b66be43c7cf0
0453ad070989cc90c141c2a5f4d9c1cb175aedd3
812 F20101206_AABEAT leung_n_Page_110.txt
b9a9f0c800e074f281c2a5c9b977a43c
5509df4e2c155b0dcb5fb5336a4ef9d3b6e735eb
45886 F20101206_AABDVN leung_n_Page_064.pro
034dd0e7e834f1f55092f647d10175f6
70fa16b2acdd4904cb99f50fabf2e0675a6b7331
52600 F20101206_AABDUZ leung_n_Page_049.pro
0f5580225d9e61fb9117a115e668d918
bc912db5a84a3072f273d39faeb51993e07e8ae7
34225 F20101206_AABEBI leung_n_Page_024.QC.jpg
13d53ce1a115e46f8cc2182a54b44de9
4215bfb2f253c60645ebbaa66468ea35abf5fba8
49616 F20101206_AABDWB leung_n_Page_081.pro
8a718d2fecc5dbd9a95da187f99a6424
c8b9493b26748f3fe347fcc0d9a3e96cc46c6135
1866 F20101206_AABEAU leung_n_Page_111.txt
f8f4c15445f402e1fec07d3ddfd3e873
0aad6eab7a9e8176a4ed6d6443ccff2cb3d3be81
35868 F20101206_AABDVO leung_n_Page_065.pro
0a4c661c00a9b781bc66e8d3ea60fd76
4b90eae23d826f0a5fd0100c6db08794c7a96468
46183 F20101206_AABDWC leung_n_Page_082.pro
bbe6764348cd88e1f08aedaa97987f7d
b206f52fdb4f65c0a8e60aad4de0a0e900670978
1335 F20101206_AABEAV leung_n_Page_112.txt
402033d632db343c6cf5234ef8e3cdff
60959c0fd9d9432150036132c473e9d739639c88
37337 F20101206_AABDVP leung_n_Page_066.pro
53e83cf0037ea5ee6c3dd14ca1d671b2
b5e20dc10f2a0356d7c6a0e072cae36032ed0b59
23857 F20101206_AABEBJ leung_n_Page_041.QC.jpg
3910ce43cc795d9394d6a40527e06964
0c650cb487a7f496f91decaf32589afaa4eb6434
19733 F20101206_AABDWD leung_n_Page_084.pro
dfbb7df845246fa8614acedf11a601c8
987d8eb22487d03c6e3cff0d190c37d341e15258
683 F20101206_AABEAW leung_n_Page_113.txt
1f5ed175282b47b10c70da896bd493b1
c9dfa18cf2c0de74cf4abc9dc02df95d6a76d868
37994 F20101206_AABDVQ leung_n_Page_068.pro
6db6b0e27fe2e5ea1972f47886492c18
319976d08bc5114d50d985b8caec7ea91c4afb59
27346 F20101206_AABEBK leung_n_Page_015.QC.jpg
41d88c141b712eafc98d640f4b800181
921d6678724214c9bca722813965da09455cc58f
45898 F20101206_AABDWE leung_n_Page_085.pro
92397066f6217475e5124bbdf12199dc
e708df4d65d70f8bdf96c62084d9690204c52bf0
1513 F20101206_AABEAX leung_n_Page_114.txt
8ac0b98cb17e01eb06d35a79556e3f11
c78d9a6a9f638c44c137e9a33e8d310043e49a21
45709 F20101206_AABDVR leung_n_Page_069.pro
b13e680ee442761ad1c1ea48a2c1e3d9
5d5880aa3e279875fed9986bd3158c309a5875e7
25551 F20101206_AABECA leung_n_Page_093.QC.jpg
15fd08a7bd126e15d492c2476378c45a
a20b7ded3ae1fb5c46ffed0589b9aef32e189ea6
8003 F20101206_AABEBL leung_n_Page_048thm.jpg
7e21674d6cc923c0c4a188fd9c50d0e1
65ade215c8dabf7bbd3bc814879d0f2bcc346aa4
27131 F20101206_AABDWF leung_n_Page_086.pro
a36e6c15034c5320c162f55f866d4512
eeef6438b24480fef2fc99ea7c9fc41d11c2382f
2175 F20101206_AABEAY leung_n_Page_115.txt
94b5021b939780ecdce694da6ca6bf16
a2c037ba5093db680a73e49d615195a9498ae00b
17359 F20101206_AABDVS leung_n_Page_070.pro
d7f13de6eb3ede80683d908897e4e3ee
94707430588c79bb92398110592dce3261dd63d2
26576 F20101206_AABECB leung_n_Page_007.QC.jpg
ab8a358d6861447063b807c7fa056dbf
2134a56467e044df15a6186bd42b37b9a0af72ab
6351 F20101206_AABEBM leung_n_Page_073thm.jpg
53dac2113bf2b4671db2ec8ec2f752e2
04b98f8f6a2442e7739bc5d52e1c40a831ca7a94
41559 F20101206_AABDWG leung_n_Page_087.pro
f0e2f932429e4488c6494bed7076f9a2
d2cc7f716dc40b18c7fa63e33e97b7bb343f6781
2289 F20101206_AABEAZ leung_n_Page_116.txt
c5f509797487f49772f4468623e224f4
976bebb222f31d579249e39cf44c9c640b56e8c1
20416 F20101206_AABDVT leung_n_Page_071.pro
5065e5812289ddeffa2ade8b645089b2
4a7ccfc17b813168f18a1f1645e1cda77bf58abe
30133 F20101206_AABECC leung_n_Page_057.QC.jpg
3aadb0652d299a35ca3bfc47746da4fa
5b816d1c95699f2a58a9fd05df242b1141db8cfc
29075 F20101206_AABEBN leung_n_Page_064.QC.jpg
4940eda61cce2b3573896674714fb31a
c8c5c28da0e7f5f5d1f6fe19bb9a08eeaa2958ce
42077 F20101206_AABDWH leung_n_Page_088.pro
e357013164bcfc7077444485ecc8ccf1
49bf2288a870e7d0e2b6798d792c239ab5309e7f
48370 F20101206_AABDVU leung_n_Page_072.pro
f38a6dea68f949c5d42269117bbc7213
9910f28e170fe57bbc1df2d8eff7badb9b5c6de4
8395 F20101206_AABECD leung_n_Page_047thm.jpg
6dd48760cc2a09abf24eafffd21a5704
3f0b8681bee0d6925654858412c5ccd6ba3f15a8
31753 F20101206_AABEBO leung_n_Page_081.QC.jpg
70f40beb8c61ee7ca16241713e5cc27e
883931dcef6259515ec405884cbf7b8a02ef3161
31716 F20101206_AABDWI leung_n_Page_089.pro
70e8534290c2e42e2fff92f2156b0eaa
3854b5b43916d03e158bbb9e39f49c479d8c250e
19088 F20101206_AABDVV leung_n_Page_073.pro
779b5cfd239606d64eab7280c0781584
463728e7cc9f63810d9c83394085f5746a153386
7640 F20101206_AABECE leung_n_Page_100thm.jpg
d395c03065aae3146f2754989d57400d
09bd9cd9a0050dbcb58e9adcb399156ce9dbcf10
8964 F20101206_AABEBP leung_n_Page_059thm.jpg
7a3cd5e372104951f763a6a5485c875f
1f3361d2ba841e5a0b2a7c4eca71b8158b334223
29958 F20101206_AABDWJ leung_n_Page_090.pro
3ecbdd8e754a583cbc8318365d2b2640
d9e2d0fc495902a67d452691726ebec7c30b7d7a
46982 F20101206_AABDVW leung_n_Page_074.pro
22dcf9365ec85516558e3f1b9ce72382
0b2fbf035b9fc3a3bdc1f877f61ba2a1075a709e
6534 F20101206_AABECF leung_n_Page_041thm.jpg
8d43a857a84fd3cebf47ce829bef8b1f
514a7841fcf825a14455674d3c3c0be9a3097df8
8877 F20101206_AABEBQ leung_n_Page_049thm.jpg
993c15c15944b1b332ef49fe0d8313d1
0f44f242bf4c88141012e8d9e17c0afeaffd0deb
23539 F20101206_AABDWK leung_n_Page_092.pro
2d0b83a2fa5f82e6a6c2e8bfafba9245
71f8e250150296204e08e3a41780abdf42b7d88b
48006 F20101206_AABDVX leung_n_Page_075.pro
4ca70a0090b6a68bf7f89dca28445a71
d563dc19faf8d52dc344297ab83406254af0d3ed
8864 F20101206_AABECG leung_n_Page_118thm.jpg
c79f4ea389f377abcab26cf0da76ac99
810c4976cbada14294078099ca5cdc313dac0ec9
3657 F20101206_AABEBR leung_n_Page_071thm.jpg
a9656906d886b3a30d7d878dfee80d33
441faeaa849fda2b104df4c6fad7fb3fb0c52f5e
14864 F20101206_AABDWL leung_n_Page_094.pro
b0590526588762ac335f5d3567fd3e49
8fd153de7e646102e017d6843f0960dcf2c95dc4
50971 F20101206_AABDVY leung_n_Page_076.pro
632370c1c3717f9157b030244fec5cc6
8041d67aa91f2e8566860bf0d288a8a3b7b59b55
27054 F20101206_AABECH leung_n_Page_006.QC.jpg
1529bca2e8ddf3c13f97a7e4b97fe49b
0518ef971b380ddf7b8192bb44ccd1ac801e1b5d
33445 F20101206_AABDXA leung_n_Page_114.pro
7ae32fd7cd7ab39e56f22665e49942a0
f3bb66e83e7951964f7f2cb653fa828053424d2b
23271 F20101206_AABEBS leung_n_Page_106.QC.jpg
fae3fa039a5181b01175f4fdac4842e3
5cf8046b994d3a19bb6f18dd44db23df629541b5
20111 F20101206_AABDWM leung_n_Page_095.pro
1efd291cd5fdaf94f5d6206f6aa5920a
663aa0ab3c28492ca0cb06ebede99f326f14e5e5
48428 F20101206_AABDVZ leung_n_Page_078.pro
d19551353e5a2ee137a77d19acd5b80f
f0e2b9cc48848f2b86c3fb7bf4b3b7c059e1d01b
7283 F20101206_AABECI leung_n_Page_040thm.jpg
a6cc3c8e20ba28a49f029bee74b7e6e5
a54f611e06f0d62bdce96084cd68f446dc344744
57488 F20101206_AABDXB leung_n_Page_116.pro
719a1baf595895f0d43fa3737631e08c
6c8530be8cfbd9115fd1528540ccab86f4426060
8668 F20101206_AABEBT leung_n_Page_016thm.jpg
9d5e671c385a071b3e14ffad881d9b42
a1365f3ec89756532f53468d517ad336ba95353f
45295 F20101206_AABDWN leung_n_Page_096.pro
a2a7d0834867b5c55e5214d248b576e0
98cc6adcaf172ce74a8522ba4014d29cf7f49f00
24638 F20101206_AABECJ leung_n_Page_066.QC.jpg
c1419e132469b23bddbdaacfb828572c
daf3285273fdf30377b1c7357f029e612b22a0c3
17406 F20101206_AABDXC leung_n_Page_117.pro
95510d0fbd34c0735963ee7d7ae11619
4fd468a1b728e2340001f2f247a4c8735fde3b4a
32566 F20101206_AABEBU leung_n_Page_072.QC.jpg
2f2b4389742c36b04e6b5cbdf3b13324
dea3ce7c5e846308e81d46fb767ad60c016c8f07
45376 F20101206_AABDWO leung_n_Page_097.pro
108af0fb1eca0f1251120603ed180b06
36f8d2ce3be1f214a36aefafd35f138bcaf851ba
62819 F20101206_AABDXD leung_n_Page_118.pro
3fe8b141b04eee1ee52faa807da22065
c9e43dd1678f4fd028d24568d841794052c3c765
7062 F20101206_AABEBV leung_n_Page_091thm.jpg
a8d2351258aa7388db3f3600b275ce0d
8e08e814d866c6145d67da2138633fda5ef1deb5
49753 F20101206_AABDWP leung_n_Page_098.pro
2a24bdbc73be768632ba5800f17e5c1c
2fb3315def3d2aa7811625141eb03e23add2fd55
20837 F20101206_AABECK leung_n_Page_104.QC.jpg
f7e20b9afb1a119008ccb92d6f0b543c
f17e9fe2f38df818d1ea0146a74232dd2b50e360
62858 F20101206_AABDXE leung_n_Page_119.pro
7124d5e005cc0d833d2d25fccb47bae7
ce94bf08a162d7722a35873b6163d18b243bdc6d
22330 F20101206_AABEBW leung_n_Page_092.QC.jpg
8a3c31e2ccc45a51339c576433e93943
872562b53a45e178d8083430d6d88afd18aecd50
34909 F20101206_AABDWQ leung_n_Page_100.pro
e1dbff24e38c8bd6ba0144b63d15841a
a1b9dbee474789a63557ea4198025a475b0578a7
4565 F20101206_AABECL leung_n_Page_043thm.jpg
080bf5f69c1fcf45898bf5a9a06ad3f6
ebf2b9f091e584245d7e6bbba7439e883ea38eec
59000 F20101206_AABDXF leung_n_Page_120.pro
da35412261f96640a739596351a4fbd7
dd62895986840580b09ec6cb29d7e2183b39b1c3
31677 F20101206_AABEBX leung_n_Page_020.QC.jpg
71487e0baafd115e751d044051f162bb
9ca5166c82c23057eaa99d7de80584f0a53c24c1
41495 F20101206_AABDWR leung_n_Page_101.pro
772a7e8fa0f8ced6b7aab197928b5cae
85671cc85be19c927bd3ccc8f5c81238e8f5ecd5
8988 F20101206_AABEDA leung_n_Page_017thm.jpg
1a300625b363dddbd82d8eb3d5d64592
f5ed8824bc055614ed25cf4c019f2964b8ba556d
35105 F20101206_AABECM leung_n_Page_115.QC.jpg
c0d2fa183a4b4c95c1868cd58eedfee2
130b6eb79411e22bd37c1bb7142462d7e9189351
22749 F20101206_AABDXG leung_n_Page_121.pro
e04ca94afb9f4de140eec8b56e44cc9a
6b7371cdcf0a627093bd56c148e4eabb2cf8b1f6
5784 F20101206_AABEBY leung_n_Page_080thm.jpg
58e73fbfae1ff2674476cc6dad0fdb87
f8504c62d0fe9222f4735a47b0899fb67e050ceb
22959 F20101206_AABDWS leung_n_Page_102.pro
f4c9c4b9d9c91cf3b4409868202ea2be
439416a1f001b64d7fdc6b1bdfb9ed0d03917103
6162 F20101206_AABEDB leung_n_Page_039thm.jpg
a404b0621b04bd1712c31958e702dc36
c13788674fd7b09d68812d62ffd1e3085847082a
30320 F20101206_AABECN leung_n_Page_069.QC.jpg
fb6f6f1c133fafdb15948b5af2905de8
4cd7ceecc4ab0c4d09d611489ce522000a03a670
25609 F20101206_AABDXH leung_n_Page_122.pro
032ffc0e6656a6bbd3345bd52be2a6dc
b7b9e6d173035e58172577c99eff24b3a97b1ac5
9006 F20101206_AABEBZ leung_n_Page_120thm.jpg
ec27811355eddc69c7acb71794c29d87
c3e41a6fb0918efbe41331310d325b3fff6d1c01
42748 F20101206_AABDWT leung_n_Page_103.pro
531cca1322652a99d98b7900c8e65f36
cb23ca9f964aa61b2c67409ea44b84999aea153f
29653 F20101206_AABEDC leung_n_Page_082.QC.jpg
d15ecaa92f91691c8aec6effff7bdb65
80b5a8e5a8321025b49d43e6bc69dcf6fbb90629
34418 F20101206_AABECO leung_n_Page_050.QC.jpg
434c7950da43cebf0969141a60756937
d8a1af3e4178e9ebe877dd7cf251438d86e9fa37
465 F20101206_AABDXI leung_n_Page_001.txt
5f30403ea4c29b6a6a9906ce63989fe2
99022d7d9bc7458dbcafacce0654b77a3a0add73
41043 F20101206_AABDWU leung_n_Page_105.pro
a3e3750e36377d9fcbf871df013a0154
11f1b07564e7bd33a484c76203058a334cc88479
30888 F20101206_AABEDD leung_n_Page_048.QC.jpg
9907399985c2191d44fb802f4ac17f33
b1d2c8d1b5bf812bca7e3a655440ebe22e761e91
21689 F20101206_AABECP leung_n_Page_090.QC.jpg
349a4cee7c8ab05a8db4d7400e8a6042
9c8f8201ca76fffe98b3a67a56234dd382816779
88 F20101206_AABDXJ leung_n_Page_002.txt
c32e33bf3bb67b178976718081f79713
1b62ec721c0e54950f79bd3444664cb14a74864e
24055 F20101206_AABDWV leung_n_Page_106.pro
6ce8f07d4b91a08174b60892b62e294e
54974091f45c97359380210446510d8a69baef45
8104 F20101206_AABEDE leung_n_Page_011thm.jpg
e3c91d5cb81c654085ab4e67fd6050e2
eabfabbeb7b65a0748a99374182c3cf968ea8e48
7368 F20101206_AABECQ leung_n_Page_064thm.jpg
ff17158f301cec708043e8d3703cc409
8c7391d334dc61b4221d04750465a7cb41e44dc3
F20101206_AABDXK leung_n_Page_004.txt
e1ba6adac3765636a1455957ff8ce8bc
ac79be7041f573efff0f9c6065923927614a7c49
39555 F20101206_AABDWW leung_n_Page_109.pro
5b6f826024a4091a2e124919b57af712
b4fac0d57ceec340a3e5863dacbd29fb2539be0e
7080 F20101206_AABEDF leung_n_Page_108thm.jpg
033563be178574cdeefa7304fbe419d3
fd581d6dd8a92875a8bd454b7fff13a618465de6
F20101206_AABDYA leung_n_Page_021.txt
c862881e6fbfefaa3cc4b24ab1809c1c
816efb8681f90150b21c91f87e97c27d73665228
8120 F20101206_AABECR leung_n_Page_038thm.jpg
1a75dfa4d4eb7dc7bbc1a57d66985ddc
04badd7e937fc5a231c69173e53367671e0fb2c1
642 F20101206_AABDXL leung_n_Page_005.txt
a340ce50a583a8eee3a962931c57d5c4
2978429403f6fb6fdc1376fec6550669da727b32
30236 F20101206_AABDWX leung_n_Page_111.pro
b8843c2de6c9a0ef2b2445cb4dae4a3f
760869b7d4dccb86648e2f68853ed64e84b43ae9
20684 F20101206_AABEDG leung_n_Page_110.QC.jpg
03caa79b4479b2fa49f9d525d004fe14
1902a058c4f6e75b221adf97625b1d15ec674403
20233 F20101206_AABECS leung_n_Page_065.QC.jpg
10d27c3d1527472a4f4793582b95a5bf
6dc80642ae4b3abf29c334982bcef5445ea7eeee
4259 F20101206_AABDXM leung_n_Page_006.txt
3503c923ee06ad0bfa67b5b88c3d21da
0824d9ad2e0463fed8e4a22318626e91cf98875a
25350 F20101206_AABDWY leung_n_Page_112.pro
eafd45647510f3e4e7756bc3ac65a2f6
84473aca6a735e7a2a832eed0e3367512ed96e03
7208 F20101206_AABEDH leung_n_Page_093thm.jpg
f628348bd20f43936b43c675c619b0ef
9b77e12fe67a5a2a7408cccd4f242ae8172ead70
592 F20101206_AABDYB leung_n_Page_022.txt
f88382a56cf23cfb7ba5d4f9856ef8c4
81b4dcdc60ff8534ada3fe057ba6f57ccc84c65d
25207 F20101206_AABECT leung_n_Page_086.QC.jpg
4856463fa66a25f035e17dc58f3ddca3
979a467e428370329a0e0f31e06b432f86856713
806 F20101206_AABDXN leung_n_Page_008.txt
cdc9c7ea5a0f8d1a4ad418a1ffce506e
9697b1e45c5e989bc260a168618576ca667bcc29
13495 F20101206_AABDWZ leung_n_Page_113.pro
aafb9ba411fa181439e5f517de15c857
3547dd03ea5d2ada80a64df99d59ba569ea7f249
14096 F20101206_AABEDI leung_n_Page_071.QC.jpg
ed504d48fa13769e1c4351408c7f16b5
b5645478f0d32fc2bb143a0e4ef8b8afe032ba8f
1983 F20101206_AABDYC leung_n_Page_023.txt
8258248749da2d315f1c2c1f71c44f64
5ed2ceee476787f8cb8c9af08712ec54b3533fa0
35733 F20101206_AABECU leung_n_Page_060.QC.jpg
1e794a7c63e3b4d6f549f1bf803c2642
c51d40e833774648be078f5a824fe40de6a641d9
1454 F20101206_AABDXO leung_n_Page_009.txt
14da2f0b6d20c0bddfd7b27478d2f095
129911bd3eab4876528b75a65c8b1335d964cd40
4550 F20101206_AABEDJ leung_n_Page_054thm.jpg
c7b2ea46119a5737a16cd369f250ac37
31cfe4ab2688f71c640ca7fefc3322884fb1fa8c
2092 F20101206_AABDYD leung_n_Page_024.txt
e7aa37376c18a8ccd9d447da5df9264c
307852852b1f04c333e661647db17b892f1806af
6967 F20101206_AABECV leung_n_Page_079thm.jpg
9326646e27f6989f8f300f37fda27f2a
a0c4c78f6805ee684fc52c9cb4201b564b8556fd
2908 F20101206_AABDXP leung_n_Page_010.txt
34f36945b4ecd56d16507416830e1fdb
ecc54df158f29d36411b1b7879cbcc5598ba149c
7427 F20101206_AABEDK leung_n_Page_114thm.jpg
2863061fd17afbf8f2c4e8831e440dd5
23050319a367007ac27267b798a369ebffa52389
1969 F20101206_AABDYE leung_n_Page_025.txt
fb6adb624ffb8938d5ae79c69f5b593b
76e10eb5dad735720e00ca49e8e0530bf7b6accb
32754 F20101206_AABECW leung_n_Page_014.QC.jpg
f55b8479add45d7fbc7e0b7764ae8935
90648695c1c895bd7db03c1176f7da677c5900df
2895 F20101206_AABDXQ leung_n_Page_011.txt
f41f4b25bcc389f309dce335d16f4d84
6c47024ff6001b55eedbf67e72edbc32147c53c8
2098 F20101206_AABDYF leung_n_Page_026.txt
b2fc3f20e8ea55d1e1b86da2ccb2f64f
894f8ea87bdf97e2cbcbe90abcd6cab445b89e2e
7395 F20101206_AABECX leung_n_Page_102thm.jpg
2edece13f639d00cfda9c363990ed3f1
d6d23982b430f0f3e0328fa52dafa09c1f8a0206
796 F20101206_AABDXR leung_n_Page_012.txt
d1839467f486e99dc95056bb0e197ee1
781ed2ea92693faaf246188eea3eb5472c59a121
29891 F20101206_AABEEA leung_n_Page_085.QC.jpg
e22bdc9989c89b3354fb7e58d29bf7ef
c036cb377d61c0c02109819760cc9fd145e7a5ec
8008 F20101206_AABEDL leung_n_Page_035thm.jpg
ab8e863ab4746f52d9715ce3c7c79cd6
c66759480e48e7f4292536ebdd0367fb90c26973
788 F20101206_AABDYG leung_n_Page_027.txt
f00d85b73b5df39e0c52108953f96615
d05a744d5403a33520e8157ccf5d1c0495729cba
8480 F20101206_AABECY leung_n_Page_115thm.jpg
4e9529b3cf0555324cf54103836c5cc3
0243e2336e9cbf09f64932b036642eef0181ec2c
1998 F20101206_AABDXS leung_n_Page_013.txt
4efc75748481465d327b4365ed6d1aab
baeec024e4448e27e6192acfe7f8ec12be80e540
29987 F20101206_AABEEB leung_n_Page_075.QC.jpg
f967d5caa50f9abb9807cce4c034043f
6d394f34b7387ae0bb6b3eec33d0a8844dbd78ea
7211 F20101206_AABEDM leung_n_Page_015thm.jpg
79ef35864890114ee7f639d81e396185
c0059d182c972a89c0bd9c3bd4917a18afae509f
2295 F20101206_AABDYH leung_n_Page_028.txt
bd4e88bed98222ca20659bd5b9a2d83d
f4be6705841124bffbdbeda35496300da53f4344
7187 F20101206_AABECZ leung_n_Page_013thm.jpg
60a873b091037bc4b3d3b5a7b7977b44
dc1552f4da627995861fea824649eaab1511d57a
F20101206_AABDXT leung_n_Page_014.txt
341b3213dcf1c1acf54cb84b0ed6d8f4
1dc31dd43ede138290d2fdf67d05269d33f97052
18743 F20101206_AABEEC leung_n_Page_054.QC.jpg
3be3ad40e3887d29e3b63b19c172fdeb
ef72d26cb753107e2a349741b4a2404d4c67b126
5763 F20101206_AABEDN leung_n_Page_037thm.jpg
a80c747ccb3d4ad944db989ec3716fdb
f3a08abb4ab2e09cb98fe8f2f950f8c1ff602057
2500 F20101206_AABDYI leung_n_Page_029.txt
80bf293ac78bec3a6a51cdae100ff97b
8ac13f71c5d16bea70cf43531fc6f072d37baf40
1830 F20101206_AABDXU leung_n_Page_015.txt
705c53a9b96e25ce322515daebc561f3
e5a6179c0c9cd958125d80acaf79973706009b56
3138 F20101206_AABEED leung_n_Page_117thm.jpg
cf5ad3b02070394055e40dfdbda4f894
7faf67b5fa37fdff8eeb9e0f8cfeabb7ef380fa7
26282 F20101206_AABEDO leung_n_Page_112.QC.jpg
60dc91f7c1c999c6c05df28c222f4aea
3bd337b91f99c7bceabca729f948a296bdb6bcab
2002 F20101206_AABDYJ leung_n_Page_031.txt
443d1a9fb3a87b04e6b106310f4f9a1e
dee0ce71d44e1900a947d64c223d3c4eb87cdf84
2135 F20101206_AABDXV leung_n_Page_016.txt
ec590c065306f035e5d3ee07fdb47ac8
44c0a961a9f56e2c54a4058c722bf38af96b61f1
7045 F20101206_AABEEE leung_n_Page_076thm.jpg
098e5fc308f81e808f5ac6baf6029185
292b4fc58bcc7b381aebdd95eef449e69ffcacf2
12268 F20101206_AABEDP leung_n_Page_012.QC.jpg
bab5a39f8dd233b93149054f6fd01ad1
56f92467a809862c8791ddf50c4e4d3b76cd9798
1762 F20101206_AABDYK leung_n_Page_032.txt
5ec594d91f498a0ee155bd02bfd598f5
df90cdd65da347b45fe53d742fa20baceb3de1eb
2121 F20101206_AABDXW leung_n_Page_017.txt
c16d4ceab9ad9c1217031fa8a3ef83b1
04fdb2a21b1475f23f01ecfb31e92b376508cdc3
7568 F20101206_AABEEF leung_n_Page_085thm.jpg
2b418e24a2511aab79f4224afd16efa6
605d372d83f3c8f94dbe73de9480e4a858dbd64f
8370 F20101206_AABEDQ leung_n_Page_058thm.jpg
feaf3d32db988b94ec2bdee0fa4068fc
3890d345ba1f94b8f1378b1dbc81e1264bf37b7a
1994 F20101206_AABDYL leung_n_Page_033.txt
b3d12508d6cd15a7f68bdefee3efbca2
0f846e0288b47aa077a9073a446328e19a913dd1
2144 F20101206_AABDXX leung_n_Page_018.txt
270e474c446b3b99901081596373932a
e4fc70cceb35e251243751a6e805d0daca1e8a19
4596 F20101206_AABEEG leung_n_Page_122thm.jpg
181325495e61a32c1899449a07739824
752dd453e2204e1745c280d1947602faa1edea4a
1690 F20101206_AABDZA leung_n_Page_051.txt
5d0d940f67edc6421ef66585af8e3973
af22c494737e7df9eb21c91f7c34f22472664076
38345 F20101206_AABEDR leung_n_Page_116.QC.jpg
16ed23ec9bf6a465fba30da47d4c4b1e
83ca1fce0190d7ca34129c009caf9bf7112155c8
1812 F20101206_AABDYM leung_n_Page_034.txt
6dccb100ba54ff5f3182c7aae1abe9ce
cfffc5e784e911a4a4e02c64b7c2fd831e55adc5
1844 F20101206_AABDXY leung_n_Page_019.txt
27e540fe6f65f9c4fed925b1fee45fa5
7e145d3010e39f3a3a3810ee1d8034bc69db0fcb
26783 F20101206_AABEEH leung_n_Page_091.QC.jpg
0ce96fc5fa4948daa9c8c34feea66154
5d779c3273a2b968f250a7e95297e582d8e09807
2074 F20101206_AABDZB leung_n_Page_052.txt
cfdf10b8eba085d559f62cbe56fe0c0a
78eb6a1f376192bf90f03ac34512b17f8547f09a
7307 F20101206_AABEDS leung_n_Page_029thm.jpg
4aa2f372cc365450a4e5b619add16c25
7ad0a07cd611172fa54b4483915336438f0f5c62
2000 F20101206_AABDYN leung_n_Page_035.txt
2a894d481193490c07f0284a1dc1e345
1b4cb28ff83e4043b535d56351cd9480b55e210e
2007 F20101206_AABDXZ leung_n_Page_020.txt
352e1303fc6b38c443a2a37b15d8f385
4f06583242d435a40d9abe2bd208dadaff0ce457
23393 F20101206_AABEEI leung_n_Page_068.QC.jpg
8e515b790b1f54560378ea681ecf7055
a3ddb456f0437265bc5ef97c1f4de4f80b29053d
7646 F20101206_AABEDT leung_n_Page_086thm.jpg
9f8062e951114addef8d21016aaab0df
26189c0fa699625a47ba06113ae430fb037a1f1d
2151 F20101206_AABDYO leung_n_Page_038.txt
aa128c03ba7d781eb6a150f3e75e317b
012c6680e2fd823aa8a2dc9d0b37673e8cf174a1
6368 F20101206_AABEEJ leung_n_Page_007thm.jpg
ebf56d31727ba3f21a35d71318517e76
bd46873c16fdd34832d299ff5af8cab20fe3856a
1046 F20101206_AABDZC leung_n_Page_054.txt
8a67cc45ab88eba5a103c751ed869d91
0a16a5a3bb8dd389b7dcef65d60252460198d0d0
8240 F20101206_AABEDU leung_n_Page_025thm.jpg
88dfd6cff66f2dc611e9aa0827003be0
1a6d93524ebc910357407c723980614de40de1a6
1796 F20101206_AABDYP leung_n_Page_039.txt
fd2b62d51abaf7c0a2a1f70ecf3f2e87
64bb742bedd6033adf43852fecec2b64e4973b6c
8031 F20101206_AABEEK leung_n_Page_001.QC.jpg
003077ddf273aafd6c4ad69e2ba3f31e
1ef975ab9d9a48bf1f5bf65b16ec8649c30bff89
F20101206_AABDZD leung_n_Page_055.txt
6f42016dffe1edfc6d81dd770abf3316
6ab778c886e5873f23cee299919ebf380754f8d4
8431 F20101206_AABEDV leung_n_Page_018thm.jpg
65e8debb1623b4c34b55e532858ed48a
63740aa69aaab661e757a4d4f863db1702fcb05b
1926 F20101206_AABDYQ leung_n_Page_040.txt
3ff0e4c04dda9227da0c55b6565296ab
9197bc3f9c5d8077f57516745ade3a6e877f514c
8828 F20101206_AABEEL leung_n_Page_060thm.jpg
5e2eef24db2a18da19e9f474d407ec0f
8026d3651acd8ccc86eecfa83ada04188773631c
508 F20101206_AABDZE leung_n_Page_056.txt
357ac9cfdc7a8f3f3a3966c2cb088669
a67acb77f6ca77091b0180d2072411d4943057c4
8479 F20101206_AABEDW leung_n_Page_098thm.jpg
855f119d41adb7008b98432912540c50
080e9e349b5491c3e68db9f9307f3100a64fddf5
1164 F20101206_AABDYR leung_n_Page_041.txt
a0b8f00b50d692e436afa46301245c85
e8421769831db73449b0f90868238766d64cbfee
35625 F20101206_AABEFA leung_n_Page_026.QC.jpg
b3368f195d37b86fcac7049453d3f869
1f0e9520891ad47a20f8865369fd9608b7a76479
1809 F20101206_AABDZF leung_n_Page_057.txt
4e4187a0d7995072bc4e4877fde22ead
8d0f9fe4bb8859513b06e448661312a62f6da65f
9059 F20101206_AABEDX leung_n_Page_062thm.jpg
f4649185ef9d63436498d2af838e6bcc
68877304362e84702eb5d4a0e9e2a59210e8b7aa
1555 F20101206_AABDYS leung_n_Page_042.txt
831052f23991a268a37e0d3e1a7bb98a
6183d0c909880b184af3170fd9f924235a747f93
6587 F20101206_AABEFB leung_n_Page_066thm.jpg
ec52f7e9de421b731a4c40557e682255
4d18aa3b113b3f7d520045b93c5088c19443861c
5384 F20101206_AABEEM leung_n_Page_022thm.jpg
68c2a945bd119a95f4e19b46ac4da2f1
8a6c95903cf552e95d58b1c60868881c2527fe98
2033 F20101206_AABDZG leung_n_Page_058.txt
9dc7d704121ed42bd4b6ba86b8934da0
3d56ca6219ad681dbabda8a66c032e5b84c4b744
30750 F20101206_AABEDY leung_n_Page_083.QC.jpg
fabc40d1b1d41681217616db676dff10
b1cb60292b2d3304e238636d171e0a43edc58d9b
1230 F20101206_AABDYT leung_n_Page_044.txt
f4b2cbfae382a058df1b7ab6eecc0cb2
94e116b7971e6cfe9292115d30b1ee5cf4dde17d
36001 F20101206_AABEFC leung_n_Page_016.QC.jpg
fa6d67c967e008975682e44355808b33
57dafa0f5ce81ccfe8f5f3d8f40e3feaf4f0012a
21333 F20101206_AABEEN leung_n_Page_027.QC.jpg
2c1c80cdcfc3e5c8fdb8b7f04746e16e
a641c69622e49b216568cb17e509584e668c75ac
2145 F20101206_AABDZH leung_n_Page_059.txt
46393a8dace8720668902575b2eb7e6b
83a015d8f404f458739dee90c18bb30f8adf2319
8110 F20101206_AABEDZ leung_n_Page_075thm.jpg
55f3a04e16edeca2d1614eea78185154
72a5c79cd30184c1371432d3cd4e48d874d21212
1668 F20101206_AABDYU leung_n_Page_045.txt
ab424c9720412334439865ee5917b4f3
0c02c26625620b848987a42a457f75135f215447
7833 F20101206_AABEFD leung_n_Page_074thm.jpg
56ec7449f32fa52e37a1e6f14e0f3aae
e0fddd6395b0246d05028cee2bd12289d2911f3e
8092 F20101206_AABEEO leung_n_Page_101thm.jpg
55bdbecabd5cc48a6c4f8f44ada7131c
5465551df90636acd92d6f0ae92784010f476816
2196 F20101206_AABDZI leung_n_Page_060.txt
6954678a6b5d74479e79900283561da2
b4bdb50c8c2d99481261aa85bb0d4fed34167caa
2256 F20101206_AABDYV leung_n_Page_046.txt
a24975890c5f9686ae35908ff62d4246
b83d16cfbb602e58c3dc5474fa17b4eb6ede9616
12999 F20101206_AABEFE leung_n_Page_117.QC.jpg
74a05cff2fcdc528e9c3df74b85795dd
64a662f0a2e78ac523a0741a4f627f9b5f4f1b88
36077 F20101206_AABEEP leung_n_Page_062.QC.jpg
ba71044aa4a927fdc10b80a0b8681622
b7553c9ed328df3c0e8168560fb08ee4d38a46db
2201 F20101206_AABDZJ leung_n_Page_062.txt
d945443e4d89d86c77441521afc16862
862558b97d79f7ac0218fb6f3b1e0b204b700f87
2511 F20101206_AABDYW leung_n_Page_047.txt
4c7e39e829f28f10bffb469c5fc8ca5b
1db5b2906fbcf64eb7035a468e299ef08d2ab1f2
25172 F20101206_AABEFF leung_n_Page_105.QC.jpg
6c4eea1e5f82198906408ab533944b1a
1ca48e9a789b440a6b69bf0f3267d06308f5d9b1
26122 F20101206_AABEEQ leung_n_Page_067.QC.jpg
53ff634db79669212d9eb4211d10e712
69cc9d99639e09019b9a824682ac84236eca78c4
F20101206_AABDZK leung_n_Page_064.txt
3a9be7837dac063a983f353a385cec4a
3b192acb40e24ce2cbd452e3b3734ea170e6a96f
1953 F20101206_AABDYX leung_n_Page_048.txt
6d563390cac76f836239baaeb367bc2d
218f328b4ddf921d124a0b493f4c7f5d79e6c510
5689 F20101206_AABEFG leung_n_Page_110thm.jpg
214dfd97c00009974a79cf0f3733a941
a06d2cca2de7e9dd870aa1e497d4a5f15954403f
28601 F20101206_AABEER leung_n_Page_040.QC.jpg
a327ff14b9a00887ee5f53f19b06ae92
0cd68110aa0ecfd12fe9a5d9fafa6a963b9ca1e5
F20101206_AABDZL leung_n_Page_065.txt
399678cfa1eda19c0546a263e4d0544b
a39d63a260e6cd6de737c6bb99f6bc75fd04ca25
2080 F20101206_AABDYY leung_n_Page_049.txt
22f84f9f7e2039498c03fbe50a504cd3
efd8bfac4ae7063ff163e5a03326e757f3cc6aa3
21760 F20101206_AABEFH leung_n_Page_087.QC.jpg
1ead7a51a29253f1c71e0eee1a1bb31e
35a71c08fd51fe928e22abe9d1f60923e501d1b8
29260 F20101206_AABEES leung_n_Page_097.QC.jpg
f44b1187aad0fb5ca3c4aa336c4884fb
07641e41649c971331c04a7e6e0f208391f45552
2089 F20101206_AABDZM leung_n_Page_066.txt
7e37a7990ad47ad84a09bdc014c194a1
b49c1b079d67de55b69ff8c51ab4251df75cf096
2058 F20101206_AABDYZ leung_n_Page_050.txt
998b0042a5dbdaca8225177b00d19913
13731b650900585de537125bc31c76fae48dc940
1459 F20101206_AABDCG leung_n_Page_093.txt
00e9e97a94a9e3c172930261c3f0db21
535b26e1ba516867c6650a6d83ae26b7384c6343
31694 F20101206_AABEFI leung_n_Page_033.QC.jpg
8501c17870097fcf0bb24c65deec6083
6c690302ef5cc9dcf9d2c1767729c3d200a1b903
8117 F20101206_AABEET leung_n_Page_031thm.jpg
bbf6474202e2941966fa754e7ac43084
a6aff63753685e027e49394697012c8a86743ccc
1842 F20101206_AABDZN leung_n_Page_068.txt
8d34e0d138ff4f8fb17e4527edb7be74
0b8ac0163e197d2738bad9c17df39fc7a6f02b78
37778 F20101206_AABDCH leung_n_Page_117.jpg
d86bdd10e1f7a3af48f26a1ea48f8586
924421e389615af10a6898fc024a08a6a40dfee5
4033 F20101206_AABEFJ leung_n_Page_121thm.jpg
befda5e023b4c13bb8cfc0d8a20ebce4
5a979b0ba8243148f6f70faf4a6337933c35cffb
27826 F20101206_AABEEU leung_n_Page_088.QC.jpg
1f2bce4b9391d2c8227fdad49de7e80a
d59e62b6c9cdf3797b0f5a22a6b10b8a02d47019
1867 F20101206_AABDZO leung_n_Page_069.txt
807cf008e69a691b974b3abb41f41390
ab2075aaa4c44df66337d2e7e143a82dc5430f5a
45254 F20101206_AABDCI leung_n_Page_079.pro
1535c2b858b8d9c36eef394bccebda33
dd36b6f1d423af59b66d155994d23e08d5d77957
7597 F20101206_AABEFK leung_n_Page_103thm.jpg
9bb0d94261c61520434778b8b2a74234
f1d260a8e0fb1c0c4d2b89cf6ed87ba134bad48b
25303 F20101206_AABEEV leung_n_Page_042.QC.jpg
dd35c1b5976f5fdf07f9a611e9594bb7
26dc4219331349284801b9781671ee1fe207bfd8
753 F20101206_AABDZP leung_n_Page_070.txt
0e8be48f81bd58c172ef191e7738461c
6c0ab5e4c80d1789743ca46b0d64590f312ebb4f
80295 F20101206_AABDCJ leung_n_Page_093.jpg
084f837d2a709748a493e05465d395de
094dfa30599e1f8ede24091ce6349a4448ea6d97
6400 F20101206_AABEFL leung_n_Page_028thm.jpg
3e4208a8212e92cc130e995c1c98da0c
6270afa12a09d53d432219af36bfe575e2267e01
31240 F20101206_AABEEW leung_n_Page_078.QC.jpg
2beb5681bea370eaa3b1fe174dec3d22
f3a8b84a7ddba1d39a796a49ee469277a71b0124
2017 F20101206_AABDZQ leung_n_Page_072.txt
e5ea8545b795891572925e9efb946702
a46fa68d311f37f044457d37daa1f29832c40ec9
120625 F20101206_AABDCK leung_n_Page_046.jp2
cfd2c5b80dd25b132b13dd1973c53e86
9be17618bb3ddbe6c88c89845a237d2dc145c58f
6546 F20101206_AABEFM leung_n_Page_106thm.jpg
ace5971db5b6a1142336e719b514eb5e
89396cc92316192b5c01756f7e98a7ce803ecac3
29040 F20101206_AABEEX leung_n_Page_010.QC.jpg
8b81afacc1d330bdd3624e34d3c6deb9
6446005f1d795c469b06d4d1ceb64d9b1cfae7d0
878 F20101206_AABDZR leung_n_Page_073.txt
530063e8ac3e6452f2784093bad5a431
4ea42505592050e6cbe1fbe7fe77069410a5470f
29223 F20101206_AABEGA leung_n_Page_029.QC.jpg
6cf1a662a22dd1736d0a7404afd936fa
f3e4183efe7f23ed2143c09b2227234cbb96f060
19638 F20101206_AABEEY leung_n_Page_080.QC.jpg
bbb68aafde550f9473247c1d9614366c
3ffc8ece0fd8e4021af621bfaa73f84af52962ac
2015 F20101206_AABDZS leung_n_Page_075.txt
4131cb1a7d5c186a09bdc42e38b4c3a9
38fe95f02619778f583ef0390bd2d526a453e520
7185 F20101206_AABEGB leung_n_Page_010thm.jpg
92d8a7eb9d30ab4a43ca0639f60cc9b6
d1490c65337e52589f94dc3536b9032dcc46b5ae
779331 F20101206_AABDCL leung_n_Page_066.jp2
408efd04bcbd8982a157551d4c0f6715
042201de295b2b4538358af2d20aef68b78d6075
6624 F20101206_AABEFN leung_n_Page_006thm.jpg
1d7bcd2ddd2fb29a7a0a07eadfac82f2
973e3c7b0e135932b15accab64bd9d6f906e5145
31596 F20101206_AABEEZ leung_n_Page_047.QC.jpg
186aaff197862e839077e2ccadaa7539
8aba77f56386e4807b12e5ca1fa69ec6cdb7224a
1905 F20101206_AABDZT leung_n_Page_077.txt
a01476533781b0918897bd8f3d75bc6f
3acad96158750df524e94e664717a6412f3d01e2
44963 F20101206_AABDDA leung_n_Page_067.pro
a35dfd5acca20ad7858acad6643bc7dd
e162c57f02af5418fe6be5ecfd093aeef3e88630
6562 F20101206_AABEGC leung_n_Page_105thm.jpg
1c26735ed7a1cfff466edb4b347974db
d5f2c0292fb201f5a071d40678d605a2d6aa2200
36489 F20101206_AABEFO leung_n_Page_036.QC.jpg
3a47bb46183df6b67be1dfd6c06b790f
0438bd05867e66e93f7b712ed4567a05874df861
2039 F20101206_AABDZU leung_n_Page_078.txt
432ebbb8a446ce025246da0d5480f793
e8fb30c9e4ad2a7ed538077bd34ea1899c7e34fb
47445 F20101206_AABDDB leung_n_Page_033.pro
a6e3dc1fdc211a882c98f8baac712e6f
fe2c6d38b1c13aef15e4004c4f5efda45e0fb50e
8225 F20101206_AABEGD leung_n_Page_020thm.jpg
16a53e2ea24b403e20b9149d813b3744
626701d38da5ef59a7087472f3ed0793517a9a40
119791 F20101206_AABDCM leung_n_Page_061.jp2
1da3e5d165406791be53bb0cd627faf2
2df9f1bf1987e9088aeefa740bc5eaf8a520fe7b
6793 F20101206_AABEFP leung_n_Page_111thm.jpg
34e947ca9d7aba735bf8e2343f52cf8e
27f44bb3adc66f48e9d383af661310d933778970
2053 F20101206_AABDZV leung_n_Page_079.txt
251bc00e4320d8695b88687ca2c324bf
0c8edefc4d9f6851edc3ae6190a122d72d2d970d
33623 F20101206_AABDDC leung_n_Page_058.QC.jpg
5094ca85822d14874170c6a60ab7c7ed
1e113704efeb1d1b5f8959ae0736b576b0a69643
14023 F20101206_AABEGE leung_n_Page_056.QC.jpg
80696524e2775e614435e43f6c19fdb6
d5bc09df222802ee25fbde2cffdd37e27547238c
81095 F20101206_AABDCN leung_n_Page_023.jpg
b640f4d2979e3c7fb59ef797ff3390d4
2bd880d257a7bfe57a21fd4e7db1564ad84cbc1d
17607 F20101206_AABEFQ leung_n_Page_084.QC.jpg
c1a5e6170239f19466328fe0f8481e50
20d11a8613d1d0c680db16aa9fcba20cc51631d2
1007 F20101206_AABDZW leung_n_Page_080.txt
3e20e01a392fefccddcbfe83416e5fd9
8a9218be89e0761e6dd5679c61544069b6392658
66281 F20101206_AABDDD leung_n_Page_065.jp2
4763e3613ffdf76e2459977410801922
95c3e87405584223067ad6723f8ccdec5e0b64bf
6788 F20101206_AABEGF leung_n_Page_042thm.jpg
5984c1994fa03c93318edcd3fc46c9b0
ab239a89796aa7cf869b6e8c877d8cf7b61600a5
118112 F20101206_AABDCO leung_n_Page_060.jp2
6ee0cd6c996622603e2b2560e179de77
76f2028ea3b593ab7106f2676184047d9a374d4f
17438 F20101206_AABEFR leung_n_Page_022.QC.jpg
3f48af37f992d0384402c588cae344da
b2bc2196732666f18c7c61eeab541cfc1d34dae2
2014 F20101206_AABDZX leung_n_Page_081.txt
d8b6558a58946f084a6166d33d38135f
e66d3181f4d8e31368209d67b64a2da20ba1a185
35286 F20101206_AABDDE leung_n_Page_039.pro
1238b2b53a1f57e3c8ad4a991c21edee
eb7e79afea9bb6a807d08227cf6ae562087a7228
8021 F20101206_AABEGG leung_n_Page_021thm.jpg
b5d9b6a7c013d2f8c63daad20dd1ff24
56607b8be0a395ae0c1db9689fdb16de7dd7c24d
36772 F20101206_AABDCP leung_n_Page_046.QC.jpg
d310ccfa481c64fd5cde29949803363e
8780dfe21c7e955f168ac96cdce53be103b65312
8301 F20101206_AABEFS leung_n_Page_082thm.jpg
9655e5a87c03f9b0996a652e8cc91db8
1e678da5786f776b84e9c8b25a3156acfac5cf3d
1706 F20101206_AABDZY leung_n_Page_083.txt
8fc38f28f177f852cbcf44ff85aabfd5
4bd22e11b435aae1c44b9e17919fc85dd01fd116
F20101206_AABDDF leung_n_Page_001.tif
3e1183d299ae6613c34ae96eb0f5b451
3cd71425cd7dc169f957a34e9fb10afd44cf3e52
6702 F20101206_AABEGH leung_n_Page_107thm.jpg
15dfec14675cc9d57ca75819fe9d9655
b09835fdb93f07a06509f769dbab20906ec21d7d
30893 F20101206_AABDCQ leung_n_Page_004.QC.jpg
bfd7948c0c264173edf6a9c99c0ca20a
5ff077ff150b3fddf7772e512133f8b84f628f93
31264 F20101206_AABEFT leung_n_Page_101.QC.jpg
97cb88ecb36c3266517f276a23a0d48e
052585e71d97f43655773827a04c6516be7a1edc
1017 F20101206_AABDZZ leung_n_Page_084.txt
2496f0f22a99093645145dcf26b14f12
e3062eba0e8fe3f924d996a689a4508ec43fd51b
6269 F20101206_AABDDG leung_n_Page_087thm.jpg
551f240e2c233add8ac17b80d533eea2
e57c36427d468c5a232f2f0e55e433fc98858d71
7820 F20101206_AABEGI leung_n_Page_057thm.jpg
58a1a646614ab10e1e4a9a2f412635cd
b046cd218b100e09d7c81d28d3e5e0bf2d7aaeb2
F20101206_AABDCR leung_n_Page_116.tif
dc4d8e6bb258e2786f14ef77220c89ae
10e69bd2cdc0218f752bc872ee7b88916de5b176
8957 F20101206_AABEFU leung_n_Page_036thm.jpg
4f517233df468929118086b403df7abe
b7f93899b4d382be635e5f344e9fce3b70289e04
1146 F20101206_AABDDH leung_n_Page_002.QC.jpg
0557b4397d22973a53764edd1c24e3fb
fc93ec927d66bcd3a35c06dbec73409cd960eab7
182223 F20101206_AABEGJ UFE0021261_00001.xml FULL
c1e327a541a25818d7be8029774d00a0
192a7e5adcf5eb22520fd9f77f6f29edf99541a0
7396 F20101206_AABDCS leung_n_Page_030thm.jpg
5d52b3916d7a34713a95089c62d19758
0e15ccba91938342cfc0db618aa3610f365b0f09
1913 F20101206_AABEFV leung_n_Page_008thm.jpg
4d390c43e0fc408d339f187de0012cf2
a2a78ce5e29d0a0e78aac4433600e99a92483fd4
111419 F20101206_AABDDI leung_n_Page_024.jp2
ba99d7633eb3ddbef06c78e4d6592b26
b66613425b8dbe10f0b546276b56ae5596ecdd0b
520 F20101206_AABEGK leung_n_Page_002thm.jpg
a27d5b36befd0475839cedfa09b9a78c
e0a4af6e95868034945546c21eb9f58b0347b6e3
F20101206_AABDCT leung_n_Page_076.tif
81c9ae6b11e26f332f085cbd7bbe52d1
0d98ee1e43d9889d23d809811c3c41645d2b417a
30215 F20101206_AABEFW leung_n_Page_035.QC.jpg
b01ac9d06e7913bf5cd8416476692bba
ffe2ea31682df1f446d43245353bdd4ae730dd2c
107682 F20101206_AABDDJ leung_n_Page_059.jpg
9bb0714a9a81603f66e06be7e2651d9a
5ddd7629b2e4be62892d0ad71b473a806a3ed49a
3190 F20101206_AABEGL leung_n_Page_005thm.jpg
ac5fa6112ba2a5bfd327a943e56347eb
ec250726cdf57bd14f8a3319406f3a8f6e0ddbbb
91430 F20101206_AABDCU leung_n_Page_088.jp2
e521fbea3c00327da769100879db87ab
2ac448263d5774135854db472587bd50b41d67c5
29398 F20101206_AABEHA leung_n_Page_032.QC.jpg
aa517a94eb4841bdd094708b6a193666
ec8367f877555d4044e54835175394480f73c47e
12876 F20101206_AABEGM leung_n_Page_005.QC.jpg
909f3d99af0e9d233650d7853c562bcd
f14b36405582ca7bde6e933b5473cc7bad7122e7
843017 F20101206_AABDDK leung_n_Page_073.jp2
6ec0a5bf073cbc8f35d00730f820628e
efaf5f2e463f818e76a26bfef32be49a25b3351e
130448 F20101206_AABDCV leung_n_Page_007.jpg
439594dc2abab558dc97244b11d0a0a1
da43f885930421354cecaf81cf954fc93946bfc8
2439 F20101206_AABEFX leung_n_Page_003.QC.jpg
fdcc974806531e6291397feaa4085556
57ff9bd1a860f5801a5cdb9a3e908885d2cfa784
7302 F20101206_AABEHB leung_n_Page_034thm.jpg
3f72d9789932c1c86970a047039cca5c
09319f8136666e56b75b1fab2e272927f4ff3212
6843 F20101206_AABEGN leung_n_Page_008.QC.jpg
31a61a301315e25269d67d183bbcfb87
976fe308c44a19a4dfa4c42c69e4e80a662550d7
1868 F20101206_AABDDL leung_n_Page_074.txt
c04d604aafae43bf79dc2fef0692df49
4bc0e8666de6e02a08d446a26a85b17f82324e8f
6422 F20101206_AABDCW leung_n_Page_068thm.jpg
9b141044c19c6aa5269aaf94c3e94fbc
cf49a9230c9e1ff24d152c16d3c83fee7a2201f1
33476 F20101206_AABEFY leung_n_Page_031.QC.jpg
e531b5fd54ee70462b6cbc8252150249
eb2f5e2db46009d1bcaa98551a18603264641ee5
19880 F20101206_AABEHC leung_n_Page_037.QC.jpg
028bccb4c46c55cfde21467d4cb2c2a6
2f0e429998914b3595600a3177495fe3f9624279
2183 F20101206_AABDEA leung_n_Page_061.txt
15dcd71b40bebb119f2a855788294ab6
686d4f2669b5e8cf85f6c98d8113eafa5b28b37c
50613 F20101206_AABDCX leung_n_Page_058.pro
9aa8bc4b0133edc42569a7b71c6d221b
29f3e7d05fa13182d304c9aa7afc4415c144495b
1024 F20101206_AABEFZ leung_n_Page_003thm.jpg
6e54f79fec3d23c9c10a493ccbc1161c
1b7fb7eb573ea801abe831815b4376cb9011a27d
31444 F20101206_AABEHD leung_n_Page_038.QC.jpg
c58e83ad832484254a576e72bdd697bf
679123a8611f719db133478925cfb1a47a05590b
16141 F20101206_AABEGO leung_n_Page_009.QC.jpg
81e1e73a0a2f6b4eca6806033fb206c7
64663f30357ebddd40d0406246e3d635228f63a2
F20101206_AABDEB leung_n_Page_034.tif
1e5d1c2fbb419eeaa72876fb2f6cd887
d310942dbfb12954ddb9d32c3399c44dd2c2cf5a
F20101206_AABDDM leung_n_Page_059.tif
198b15cee411dc3d55f0bfcb3936ce90
26ebc0d6fbc6a72238feebefcc2483fb0cf9a4cb
122550 F20101206_AABDCY leung_n_Page_011.jpg
02149da954423839a534c3e29ba8c43f
6622399026cf1f2a0d7a36796628604938fb57fd
8453 F20101206_AABEHE leung_n_Page_045thm.jpg
4401e811e1685b62741103d1f7659b50
23afce435ce352030a53d1260eccbc35b91e6b5d
3063 F20101206_AABEGP leung_n_Page_012thm.jpg
cbc4e61258a53a83ff4792a667c3bca6
221c7a1a0566c3e8b1be2e3d5b706c0b33245a70
7657 F20101206_AABDEC leung_n_Page_004thm.jpg
9b6064ae0ad8584cca64b54c5609b668
cd06c9cf254deb68f4be87a29da677d661c6d9c3
163 F20101206_AABDDN leung_n_Page_003.txt
f2afe7d066f6798214880d932c828f04
1e2ad509653d3e76761535e201e4f97cedb7a20f
F20101206_AABDCZ leung_n_Page_107.jp2
272877c2efa6e271930781ce25eba212
f5353b17f5d48c697458056eb15b059630be2e4e
31881 F20101206_AABEHF leung_n_Page_045.QC.jpg
54205275d6d19fc4099abbd9e7a2d0d4
61015e035585245e6c2c28a084fa9553dc0afe29
29102 F20101206_AABEGQ leung_n_Page_013.QC.jpg
f88382127d1c8633937f4eff2f2fd930
1fddb1d8ba3fea2fa68ca609593c384179c9f131
101113 F20101206_AABDED leung_n_Page_025.jpg
d586813af22612afe4dd5b1d4b73642e
e146a7fa06b10f6466e4d48065b40f2ffb4c4271
5973 F20101206_AABDDO leung_n_Page_027thm.jpg
0eb66a1c662e15b4f1e71f8ae735d910
def98173b97eecceba76d436bf5c79b6f625ee68
9029 F20101206_AABEHG leung_n_Page_046thm.jpg
c2c17e264f4d80f50c41bc7a629eb4fb
00d669b1d1a08cea774bc254870f39deed76bfcd
7782 F20101206_AABEGR leung_n_Page_014thm.jpg
db1e68299af04b184ca59ebbab6c6f98
32c51bb04d5eec160810c2cd1bd633da6aa9d151
89991 F20101206_AABDEE leung_n_Page_077.jp2
f734bbb71a9570c8a641f8001c9fa6a7
242839566bf797e15e0338153ed56531ab77be83
F20101206_AABDDP leung_n_Page_029.tif
5ccf838ebcf74833a3942265fd273b7e
d89a2923095f36892109b0cd68dd65783a53d473
34450 F20101206_AABEHH leung_n_Page_049.QC.jpg
70e07a563819f289ff11d1bfabc188f1
5666713d5b80800dc38cde3eb9f95d729627df2a
34658 F20101206_AABEGS leung_n_Page_018.QC.jpg
a9f1ec9e1e6a3d62f3f431e40ac16d98
c50daba5ac7de13593ced8b4873020e50995cce0
F20101206_AABDEF leung_n_Page_107.tif
f9d9d72d903f142f6863f34abc8254c6
4464287c753a87ff9c845a0e792ce3fc76483350
F20101206_AABDDQ leung_n_Page_055.tif
a5ba80a6279c83483e530f1fec263715
cecf73080170e9655a57f4bd14194004a83d4b95
8570 F20101206_AABEHI leung_n_Page_050thm.jpg
4636c719927acccb62c1842421e469d3
09dbdaea478a9f059de87357d0eaebe7e68855b9
7511 F20101206_AABEGT leung_n_Page_019thm.jpg
df14c0f6967ad3733881a60090724db3
8bb450e03e7f3d3d4c2faac1147659d60075019f
109516 F20101206_AABDEG leung_n_Page_053.jp2
416ef2bf29a077afb8a370ce56ffaae2
414f113827fd266db70c2d9236a07994bfdfa246
15835 F20101206_AABDDR leung_n_Page_005.pro
1e51713569d61b4744dac9d77f756f55
186b478337d18aac7a20c4fa1c4d7044c8eeabb2
6504 F20101206_AABEHJ leung_n_Page_051thm.jpg
4a02aa9c2d1009a4dc98d36181d5944a
7330aa122580dff7d39a8413cd2ece1e3149dc92
30413 F20101206_AABEGU leung_n_Page_019.QC.jpg
ce44941fb166b31ab5e90a9632fa68b2
d710941940cb572090a823cf9653d549522f1559
1269 F20101206_AABDEH leung_n_Page_086.txt
a0d766ca2e99d841f3670218e592f729
f8ffc90b94409d0a49e6e637bbe0b432b795467d
28964 F20101206_AABDDS leung_n_Page_034.QC.jpg
1ef9e6b393f5609f95af3b9d911e67c0
7a844358b9044c41ef2518627d70461b85c120cb
22562 F20101206_AABEHK leung_n_Page_051.QC.jpg
9b51783d9274495ac054b4cde5bc9187
7ad2b6f54cf35ee9d9b3ee25bf0e5ed34ccda565
32316 F20101206_AABEGV leung_n_Page_021.QC.jpg
18ead2ad351a9be5e98cf32b939f74db
bc5c90dacae595d1f4b630bd5cb7d2a92828e34c
782 F20101206_AABDEI leung_n_Page_002.pro
aef77e001d80573957119c03b1ba78ac
a794f700e6563cb877758c6aa0dccc1ee452a5fe
112911 F20101206_AABDDT leung_n_Page_046.jpg
7d48a88d106786945018d2edfbd28d58
9f5e9bfa3bdde84afd115db1e8986e335518ebb5
32726 F20101206_AABEHL leung_n_Page_053.QC.jpg
956f06f2963963500069a400dce29607
f61f1be2e4139e82b48eff22bc76f3cba55065f7
27429 F20101206_AABEGW leung_n_Page_023.QC.jpg
b046913e62ee972d3f5c8538631e9371
237550aec1c60c586a8fcf2546adce2587185668
8773 F20101206_AABDEJ leung_n_Page_024thm.jpg
4ea53d968db9affe7b14ac907ed2a138
8c2d47233e8ebee67d24526bbd2e49a06280ee00
97768 F20101206_AABDDU leung_n_Page_014.jpg
0e7ea03e2474060d1daee16c39517fe7
c11de451b0da31c38e86432cbf777ea508a43b9b
26127 F20101206_AABEIA leung_n_Page_079.QC.jpg
91cf66eaa525231f894d2fed535d6351
ce8df1bafd7d2aec2eb6c8a4dbec9241e6a582ce
27590 F20101206_AABEHM leung_n_Page_055.QC.jpg
efa9c236d9508a9b5ae8e31c027071d9
7390dd053dd4866e48f2ff0cac0a03e06994c3fd
33063 F20101206_AABEGX leung_n_Page_025.QC.jpg
1da880126c51cc269dc4010807cf8ae9
7ee79ce1352747a4c253f88f7490bbe4b30f850f
40621 F20101206_AABDEK leung_n_Page_108.pro
9da2a42ba270ccc690f00e7006e4d28c
66ac0327d6e0429dfe0f9b2ffd0206a3556ca42a
4659 F20101206_AABDDV leung_n_Page_007.txt
1d2d50c5a990b3c6fb626377098d9509
06210d7c77d9e42549399c9e2ce3dfe3b8a1ec68
8112 F20101206_AABEIB leung_n_Page_083thm.jpg
27381d0cb3d866891ef4bef8a55c7844
81403123513f2cbece7f76748c61044c584de5a0
4005 F20101206_AABEHN leung_n_Page_056thm.jpg
6503ad75077d0185de6038b3832ffa0e
228dc64e79b584d32d53db85e822b71802cd722d
26181 F20101206_AABEGY leung_n_Page_028.QC.jpg
bb00191d77b08195e9c426c638acfc5f
39a225e740b315e304c844c031ae7b2c541c9915
2016 F20101206_AABDEL leung_n_Page_053.txt
b16d45b9cfbd06925ba31ef07c9c1eb5
89509ec0504d59a15a53e5ea0188b5f81142159f
2266 F20101206_AABDDW leung_n_Page_082.txt
09546d722f331fa3ea26b8cead588db4
8d769728ec8b261a12323816d9b4f1644247c7e8
5271 F20101206_AABEIC leung_n_Page_084thm.jpg
fc9314afd64fe3f50b132b8fc0a8dc79
0eaf8e996156256cdffcc2312d15f7444019566c
36564 F20101206_AABEHO leung_n_Page_059.QC.jpg
1df1d6a481869af6953e418188fc87da
c25a7d610a429865f19428f85a2a91f80a2f8432
6943 F20101206_AABEGZ leung_n_Page_032thm.jpg
0abfeceedda35c550a38fa307bda9c20
56c82b02b840f7ee81fe8b69e2a5f3db65b8f7f4
28955 F20101206_AABDEM leung_n_Page_030.QC.jpg
8cd64af2df3967d541ff2edfa5bd7d61
1313aa1bb9d9c0dda2e5c1052e58d9d4b6470e1d
F20101206_AABDDX leung_n_Page_056.tif
6686d2c1078ad08a071fc895b161721b
01e7b561965ac21674a6dfed4d82b823ea574e44
F20101206_AABDFA leung_n_Page_108.tif
7ec84c235b68a422519403349ce91fa2
b4707e83bcd84ae91fb48ed48c066dde15a90fd7
F20101206_AABEID leung_n_Page_088thm.jpg
cdc0499aff6093f816788aa9490ea1d9
c1122324efc6425520b4ed0c0270eb005a851bf2
102946 F20101206_AABDDY leung_n_Page_033.jp2
172b9b77dd1e7a4a0d537619177d6504
009cee6175694bc5db23f27d7971fde70d6165c2
F20101206_AABDFB leung_n_Page_069.jp2
824583f6daf7ff521267332424ca29dd
9841c47308e297357ee02b1973ee0b7481eb838b
6484 F20101206_AABEIE leung_n_Page_089thm.jpg
8b25a1ce1177601e81457fc946b10d2b
c6f2ceac48348dc62012708ef0ab4664710b1b8b
8983 F20101206_AABEHP leung_n_Page_061thm.jpg
dc5fdaccad4cf8cc57936c0525cbd10c
bd6ed572b4286b66a107f3c5ed625c1b4e315b41
39514 F20101206_AABDEN leung_n_Page_083.pro
a10bc01b21f81378a4fe44a3579df8cc
1021e6f46ccbf222759c784fde0af82f83d3bf02
7064 F20101206_AABDDZ leung_n_Page_052thm.jpg
4f513c050725901e06561867187a2a99
4df3b1e747324e2d3ca502d6a97b8a6fe4f57350
2528 F20101206_AABDFC leung_n_Page_118.txt
ce163c6ff45489f518e6135d734eb896
523f04a1cd605ffacffbeb9ecec393f47a75fb3c
23038 F20101206_AABEIF leung_n_Page_089.QC.jpg
2e76d877d37ba20496b1079d0da5a51f
bc2e20277642e014a8f96214a20b7c3f0e31e98d
7578 F20101206_AABEHQ leung_n_Page_063thm.jpg
0cfb8c801ef4cdf9861d2964bed34622
8aa7f68236b1acdb733c1240bb98cae32446afe0
40668 F20101206_AABDEO leung_n_Page_099.pro
1c1084a151be262322d7d1dc90b3a839
62558024a0b6ace1655fa8b0c4874c2e01737f95
21925 F20101206_AABDFD leung_n_Page_073.QC.jpg
e4bb3c11d266c0be96ea4c5c49bea3cc
818d9b5f818119dc144e82b58b6cd704a7ab1c30
5881 F20101206_AABEIG leung_n_Page_090thm.jpg
b9edf95ae1b76a86e0352642691e501c
7333b52014f7f9ee15b2fbd4421a0fdcf7ffe7fc
30835 F20101206_AABEHR leung_n_Page_063.QC.jpg
f5e9da204d5a38c39f2a0e0e635a866f
af9bb7ec99b19875a46385e3b0da82383968a206
34315 F20101206_AABDEP leung_n_Page_011.QC.jpg
1143c425ef902bd423c871b966487d8c
230cbc96bb6b63b7c117ff8791210f07d21f86e1
9020 F20101206_AABDFE leung_n_Page_116thm.jpg
deee6d1f19922e31481f770bf5e7dbcb
6fbd0aad90ceb7d5ed76e235bc375342ba1eeefb
5889 F20101206_AABEIH leung_n_Page_092thm.jpg
765e3db185824d565b8ff3dabe842504
f0b4e29eb207b00ae32e597d21ddb4411802256a
5625 F20101206_AABEHS leung_n_Page_065thm.jpg
6a4fdae6e6a8a64b4688ea2194af6383
7efb16d6f579d507dbf4ea595ac4ff27186f2ede
92852 F20101206_AABDEQ leung_n_Page_082.jpg
ab7c5adf8eb5cb0af70a3ade6fe93039
8404c5c65f4ee5501105ecd40dd0efbb03784096
26826 F20101206_AABDFF leung_n_Page_077.QC.jpg
b8046053e67da2b819b0bb1291d9276b
6cc01c670b99fa28f682f57b4a1daf1265ec87c8
5169 F20101206_AABEII leung_n_Page_094thm.jpg
65c8bc4fa3153d220bb378fb684167de
b6df56c24edc7da7130ca4ff190646e7f46d71c4
6885 F20101206_AABEHT leung_n_Page_067thm.jpg
2e57c501db1d42af04cabdf3da9efe5e
0a790a266376340e893cdf50afc6e0abadd3643b
59814 F20101206_AABDER leung_n_Page_027.jpg
2e441e423b3bca48d6e54b4196c034a0
02234bfc59a6800c325f41a636a9397852a60ae3
F20101206_AABDFG leung_n_Page_042.tif
840df7d26cde4e8470456857a96c166b
cc6c17ac67822543e9e0d2917666c9c264555fcf
20027 F20101206_AABEIJ leung_n_Page_094.QC.jpg
62a8f68ba5c9c4fbd8601225f4400eea
5367b8e3dd69eb38384c4059110efa1c11181f3a
5070 F20101206_AABEHU leung_n_Page_070thm.jpg
bee933b6bc66f1d8bdf3246c2c2ea795
0fce25dc7d0ea65c91258da9c1488c453af5c4b5
1634 F20101206_AABDES leung_n_Page_100.txt
fb53a0e49fbb09278cbcbed4c92f922b
c7ab6fd21d20a98593ba9aa046d0f8b16f5c856e
7140 F20101206_AABDFH leung_n_Page_023thm.jpg
9216a9a9b86d5e169a17311ef751b45e
b19520743f36854ceb20fd25d4375d923a342ec6
5734 F20101206_AABEIK leung_n_Page_095thm.jpg
9020f3d570325331c8229551a78824d3
a0909343cac3d2250babeb0ed5ea539e7ee7e217
8127 F20101206_AABEHV leung_n_Page_072thm.jpg
5b11d91c42aa65c8b442a819e83c619b
d5624bbf353158b6c3c29f7d70d5c43b56ab9633
42766 F20101206_AABDET leung_n_Page_015.pro
56a4691ebf683deec7054be0f8e79140
fb69443eb8396f957accf1ad7bb023e14482ccb2
30046 F20101206_AABDFI leung_n_Page_104.pro
07a42c03565e8a2ad4c20ac0dee6f1ba
4e9341819e98a9cb5f1c8acf8f4053840e32666c
7346 F20101206_AABEIL leung_n_Page_096thm.jpg
ed3003a1779a61e6c20defddfcd659e5
63023d26901cedb05962162e4f9f9599921537a5
30734 F20101206_AABEHW leung_n_Page_074.QC.jpg
f28c727ff07f7bad476a3550b2ea282c
ac9477f1154ad818cfbde98eebcf4976ea3ec870
1027910 F20101206_AABDEU leung_n_Page_103.jp2
ad36655ae010f2e1e87702393a759136
c86c7293370beeb5f3654f9ba8a896968d6393ac
18259 F20101206_AABDFJ leung_n_Page_122.QC.jpg
c856f3414654298e0a7e5e4eb972b04c
a4dade259a8403db2de381f208f030b93c1096eb
5937 F20101206_AABEJA leung_n_Page_113thm.jpg
9c15f002cb095f986acd1d369be178cc
95cc514c086011e74825af07b14d47a21f968fae
29922 F20101206_AABEIM leung_n_Page_096.QC.jpg
19e8f10a4aa190e821d98505b07da47c
c6058a811c15461d5dd1c34602e72730648fe5c5
29055 F20101206_AABEHX leung_n_Page_076.QC.jpg
1378746993879e093ac9cb084e1aec8f
9e0a488311626fbc57535a0e1d2b670b91b4e9b5
1852 F20101206_AABDEV leung_n_Page_089.txt
9dcfd23665ecee775c6118dd94f48420
3c0f2d5ccd13ff7e3dda7167a041667e3c40156f
F20101206_AABDFK leung_n_Page_063.txt
71a7bb21efce8b605723c2342ce6c44d
72ac96f8d5ae872e42c74403c5246cacfaf1cd3b
20859 F20101206_AABEJB leung_n_Page_113.QC.jpg
84dfaf875947e6ed4f7863f7e9afc26a
9d7319021b7099f867468809da1b70da3e1af7ba
7288 F20101206_AABEIN leung_n_Page_097thm.jpg
7f8fdabfae40afd637d2fb5a62a4d1d2
a8fe042ca0bff2f68e16a7274fa40c2c5bcaf68c
6648 F20101206_AABEHY leung_n_Page_077thm.jpg
f5b46c4d3495c71dce8f698ade75de6c
18f2e4b670bfcf9f1bd08fd6b6dfbbab0e304791
16573 F20101206_AABDEW leung_n_Page_070.QC.jpg
9b9ffe1e78c18a44b8dc93b472588d7a
656b21153bc365b9b08069f969cae612235a706c
F20101206_AABDFL leung_n_Page_014.tif
6f42622ed41391a907341068ac7de5d3
87b8cbaf87d5fb2430bac7b011a85bf505d3efa5
28105 F20101206_AABEJC leung_n_Page_114.QC.jpg
2da7046602f3b5ebf34e37f44544d9d9
5e43ca315ce4fb71bd736db6046f12723fe6e25c
32577 F20101206_AABEIO leung_n_Page_098.QC.jpg
e235ad319c76ef8a7f1dffb8cc6feb5c
990504de11d64416bbdc6d3a3f625075fa4352d2
8020 F20101206_AABEHZ leung_n_Page_078thm.jpg
025e8475b08e1a12a97cbf64e2fc57f0
3a1f998045427bb6114068a0af34946cd6758e67
40553 F20101206_AABDEX leung_n_Page_091.pro
a03179c7aed59bb3c69c2d140bb50402
9e65243e1a6c5191aaa87b9c6d9d6141bb3ecf9c
85096 F20101206_AABDGA leung_n_Page_034.jpg
ad75e39138ebd318c185dd7e71669a24
7c0a07caab24f1e250dc51720401831c54441e15
43409 F20101206_AABDFM leung_n_Page_077.pro
00c3c39c02a4312c4192606feb3f8db2
059a3bb61a90da8243c1675229e078b8dce2c0f9
35884 F20101206_AABEJD leung_n_Page_118.QC.jpg
6f7cae327b0461cbc531a5a62381a9c2
796a47ce020c3ae54807949d6682220f7d278c5b
7856 F20101206_AABEIP leung_n_Page_099thm.jpg
db05158c8c12f9c11cb1e414b2ec3989
1f4e4195d3cd3d1571121037a1907afadf0d265c
3067 F20101206_AABDEY leung_n_Page_104.txt
82b5ca7c70845d6bc6ceb9c54d467f15
7f2e9f421b157295dbba40eb85fdef471e24bf75
690 F20101206_AABDGB leung_n_Page_117.txt
d72d53f8a18d9eb5bab251841a4f7b0c
b9ffd491d3cbd4c787dbb18506049b83b0165195
1910 F20101206_AABDFN leung_n_Page_096.txt
2ec544a67033cf7d3a80a4f5fa737b91
972f2a0b339acb3356cd129ee0f0329af927c4fe
8967 F20101206_AABEJE leung_n_Page_119thm.jpg
f7bd51e0f665de488c4b7889226d0e6a
eefc92b1c9656a26e2fb23c39f53ddfa7d683f5d
53882 F20101206_AABDEZ leung_n_Page_121.jp2
2de4aafb5559825c12f0a67a61b5bb98
f1bf7bbe798957ea60a64b80ce71697212503e28
7791 F20101206_AABDGC leung_n_Page_081thm.jpg
83cb9eccf128b645e27e0a23b74a4768
8334f729bcb133fc1f3889dc738d77f59e0b4c59
35762 F20101206_AABEJF leung_n_Page_120.QC.jpg
a1c720820d7a0e5516e70c7293b20182
5da84aa785d3b22bcc1d4257c8faad949934c8de
30610 F20101206_AABEIQ leung_n_Page_099.QC.jpg
caa11c84217238ad7ad358b3313bb107
183366335594d626134e4d83881e1916dde6df1e
1051939 F20101206_AABDGD leung_n_Page_045.jp2
a60d3395e9088bf4a69a9bb06bdefa12
85070c7697da54b2b9dbd50fbab1c51071e2447c
2493 F20101206_AABDFO leung_n_Page_030.txt
fb6e03e83846fb89dc4138110640ca25
e44b7962b5cecc7196a0249fe090fc94fafe93a9
15357 F20101206_AABEJG leung_n_Page_121.QC.jpg
7b582af0a0a404198e4cba85197900f6
9b5c2cbc577de591bfd10ab1ec1582cb62d20e73
28190 F20101206_AABEIR leung_n_Page_100.QC.jpg
2bbcc4aedfabf1b1ea4629d76839699f
feabeba0b6689955c60b089e2eb7635b6731f65f
F20101206_AABDGE leung_n_Page_019.tif
b013ade945b3a2ae5406884a91972664
dfeb4906f9b5c0e8fb5cdd8c520a12605c668af3
7186 F20101206_AABDFP leung_n_Page_055thm.jpg
517a7f54404f5b07177265135352a910
8e76182e36a4208dc780acb1fca7c6f871271e33
26718 F20101206_AABEIS leung_n_Page_102.QC.jpg
f939565b84a7dcf3dcd216fbac57ccff
c4486fbc63bc7cf2c36e6ec7740e6f6a9a033c37
4373 F20101206_AABDGF leung_n_Page_009thm.jpg
0bd46dc88fc574eeaae01d7fcdc9a285
302edafd1fd3dc6e13cd9d0cd59cd723624290d6
74237 F20101206_AABDFQ leung_n_Page_106.jpg
c8650fb6d9ebdc8aab5bc51c61d439ed
ce53cf940b797c22539771982db1eac4ad5f77c5
6050 F20101206_AABEIT leung_n_Page_104thm.jpg
3bc79e96610aeb1146515461e11114c9
bed76aa5b9c9b8730ae923d4e3c5122df86cc5a0
44410 F20101206_AABDGG leung_n_Page_040.pro
4a59e63a7e306e8dd31b6240bda84399
a3ade60f9bd3c35b9ce45910ebbf3245ece4f783
9338 F20101206_AABDFR leung_n_Page_022.pro
7133cc60daac0c56b3a5ea9b3214d94c
09cbb06eeed26419a3f10512d8855294dde57aea
23785 F20101206_AABEIU leung_n_Page_107.QC.jpg
d85bdbd42fa9ef00d7e1474c14adc069
c21f31d840cd84ac068bcea532a8da57c32c4e2b
38229 F20101206_AABDGH leung_n_Page_005.jp2
e7f5e951d5517bcda55d8c8656d457be
63d3784b10506375e0a3bf5e76960f861b5d672c
F20101206_AABDFS leung_n_Page_033.tif
886364031d9d36de34a4b7cbb3defdce
5bf9dc37faa1382fd81284a562bfda214bea011e
26751 F20101206_AABEIV leung_n_Page_108.QC.jpg
06c372ef451312a066ba6a94ee2ab657
2e048a3af147ecdd876b98eb58f573c91c3c0dc3
F20101206_AABDGI leung_n_Page_045.tif
284605b0e027fb0b1108870fa0ee328f
e6b979d58612d02a61d4ff69d5832f6826a07a18
48524 F20101206_AABDFT leung_n_Page_035.pro
960108aeb18c47c2da8e01bdfc9b78c3
481eb0277f9e51c8ba09239069d376d3c86c88ec
7989 F20101206_AABEIW leung_n_Page_109thm.jpg
00d0978fdb8f6af0d15eb4363eab7e03
20e43c9c40eca8065c61deba0eb0260417d0e659
53902 F20101206_AABDGJ leung_n_Page_080.jpg
ee9a1b0fd9b4be9763d3810fda356e0d
105d8f5ec608e57241248c9373099688ec46a9b8
36604 F20101206_AABDFU leung_n_Page_119.QC.jpg
9b25392ea6fbbcf69b65f81a91287f4d
1ffc59ca8d223a97aa3f1eab4e60e66c2c14e1d5
30272 F20101206_AABEIX leung_n_Page_109.QC.jpg
b98fdfbe65d0558cb12b05fd58f98ae5
bab1e8c48432320e9af5ad33e30868548804c6df
74672 F20101206_AABDGK leung_n_Page_112.jpg
d68f966023cfc5d70539e355f3d9eb00
d1211c3ee57bb3bea4b544f847658d2ba92ebe5f
30463 F20101206_AABDFV leung_n_Page_103.QC.jpg
d9ab0dda5a930b387a1c9292cf382d19
01d11b4452b6ddc428b726c5dd8f9ca23899c4a9
26366 F20101206_AABEIY leung_n_Page_111.QC.jpg
16591d413d63c526345fe7d9eaf8d92e
d0baae166f80d04fef13be7f62df0e3f801a15c8
20815 F20101206_AABDGL leung_n_Page_095.QC.jpg
9ca136c6a4b0490acd7518370b10a291
d5a82b02eb0a65863e5a317a6c3aa817902783e9
52569 F20101206_AABDFW leung_n_Page_115.pro
da7c55ee6e45d43dae8a61e7f6cb8cbd
c1660954c8fc911f5a45f07a37f120d52bccaf48
6604 F20101206_AABEIZ leung_n_Page_112thm.jpg
e7d7be5bdcba61e197a0c36de9044027
951854bc573de677a8a6a042e815da6602243644
33171 F20101206_AABDHA leung_n_Page_093.pro
09c4d9674de961536d65ec7518b6c1c3
1d52dbeb2709d7babc7b19922a2232e1db520a1e
1275 F20101206_AABDGM leung_n_Page_037.txt
b08d49f22211565e5593291fdcd068d8
abb5f0d09afb065bae5d2f15591fe63addc33eec
F20101206_AABDFX leung_n_Page_083.tif
0791d505a964184e63595bd86b1b2bf8
7d1a161597d60e21c2741b32edc4974b044998d9
36541 F20101206_AABDHB leung_n_Page_061.QC.jpg
8870e9919108e7cf639087252f0df6f3
a6a64ed3c1b4f8ebfdfcbcfe3792c276ef74a391
17344 F20101206_AABDGN leung_n_Page_043.QC.jpg
ec026b147b4b23b82a3ddf1b09bd386d
302cbc50ff3df3dc3907a2966ffb736961cc5e81
F20101206_AABDFY leung_n_Page_017.tif
bdaad19969feee6e8a06cfe71d9e9cf4
e25046cdf5bf23412d96f6b86fa6f273212b0c63
42869 F20101206_AABDHC leung_n_Page_034.pro
15eae2c1f410c0a3274addeb9fa3189c
12a883378951edcc3f2b7d24065a636c6ce45c68
15557 F20101206_AABDGO leung_n_Page_044.QC.jpg
f4789e8b96d62a9797e410d0f0e93ffb
a66239c43ee32ec7237669e90baeb5bbf08e0ae8
F20101206_AABDFZ leung_n_Page_099.tif
4e3070ea219a3cbf1f502435571e5e07
6a0465c357f175cd16c1b101d7f40dd211623b74
8164 F20101206_AABDHD leung_n_Page_053thm.jpg
4faac099abff53a8d3e5ed7bb3328ead
82ee5e18e2f2a1545c86a9e39fe964c03032cd36
16446 F20101206_AABDHE leung_n_Page_110.pro
01005ee843f2a6a1188755885f600e19
9dfccdc1195f24029f4add70b28bd0311c778e69
35855 F20101206_AABDGP leung_n_Page_107.pro
2c095782108191d22a15e85948e8f32e
c5f9c7ec28e687e96c6996948fde0e39266a98f8
4810 F20101206_AABDHF leung_n_Page_044thm.jpg
1bb42bded6b43335e3e713ffb08dd031
c8f6f93f906302f00062a86abd355475e0bd599e
2072 F20101206_AABDGQ leung_n_Page_067.txt
624620acd4e3a5b50747b01e4935e7a9
83180d3f1c00a1bdc84b9125072ea0ed410aabb6
F20101206_AABDHG leung_n_Page_065.tif
624dcbb054418ba0a6fcf7ba923c3e29
d0668f649a41db2ecbdee05f76242950031c6c23
35119 F20101206_AABDGR leung_n_Page_017.QC.jpg
68bfa63716d04ff72406ced5e4ac50e6
5803ac2a2678df42afb66701077273d0d7e4ff5c
68136 F20101206_AABDHH leung_n_Page_073.jpg
44aac362998fbb7786eedb296dfb10fc
31ea7d0a2daf70ea17fadc7bbcc6173414897a9b
95609 F20101206_AABDGS leung_n_Page_085.jp2
c2e26d05d6f6fb12039109ece12c43da
2dff5ae8360a540ca6725b146341476887e6f5ac
45925 F20101206_AABDHI leung_n_Page_004.pro
13de5e8607c6487d1aa39376714f34b7
241db68ec4a2c3153ece4612173988475f383f7b
863 F20101206_AABDGT leung_n_Page_071.txt
7fcd635895c9c042e1cc982efd18a7db
bab8e540d8d9c54f40db96af3150c74f19e2668e
7457 F20101206_AABDHJ leung_n_Page_069thm.jpg
7d7ed8491a80eca950a978a432013014
f96f57bd66e92652644097d8e3bda2bdb9f58faa
2221 F20101206_AABDGU leung_n_Page_036.txt
d2f11022fd3ea45122763b0a50eb9eb5
d0bdedc49bcd000bf74ffa43ea92c48e6ff6c86e
26260 F20101206_AABDGV leung_n_Page_052.QC.jpg
15b78cf4c66b6e4cf649312805b3d2c7
45cd8e3ff0bb701b13fb20c1b7f3d95d555ceb3a
22560 F20101206_AABDHK leung_n_Page_039.QC.jpg
b9ca243f98822936ea38fe6cdc1b764c
044a7feb253a5e55850b386cd64a345eca88ed52
24279 F20101206_AABDGW leung_n_Page_001.jp2
01055123e3957e86215d5b113a911b6b
ab1e0305c62d39b89a156f795793a58e72fdd648
1243 F20101206_AABDHL leung_n_Page_043.txt
2635a2494ff5aa19203091f305b7c4f2
f9c6c176421c5a0f1a6d51fc528f3c27fd3d42c4
2236 F20101206_AABDGX leung_n_Page_076.txt
7396226a8175462fc4fec1e950a75df3
ecdbd006c553bb1cda77927be1b5881e68bbcb0c
86634 F20101206_AABDIA leung_n_Page_015.jpg
6fe83e5df9bdb02f339440608d3fcc80
2982e1d63c937c6594ac94fcf4b295119eace56b
140824 F20101206_AABDHM UFE0021261_00001.mets
a61a742ffb964433a7595aa8709ecb3f
200389cc93aa2495266097171c1255d6ce43d792
F20101206_AABDGY leung_n_Page_088.tif
201987d3a4a3a15abc5b356cea3d0fa6
ba6a30fee07439e73e8a2912d264b958d18ded37
108002 F20101206_AABDIB leung_n_Page_016.jpg
6c1d760d3b712aa9588009bdf24332ec
e0a538847e52dee033b2c38655f46f7857166102
F20101206_AABDGZ leung_n_Page_041.tif
9f8c72392419a2cb6e89126d884f5ff0
e8c1414448da18b48a1e0e1a21bf558791a74996
108398 F20101206_AABDIC leung_n_Page_017.jpg
b7c3ae1a12c4c6a94456418421179cb8
79540d37070d9db9cefbee95f6e938c82d2ccbea
F20101206_AABDID leung_n_Page_018.jpg
be7c41a38e4b219bb0f538a0e27c008e
c25b3565facde84edb8cf8abc94dcf774da7faad
26262 F20101206_AABDHP leung_n_Page_001.jpg
6189d83a878af7cd95fcb7c79a222907
3ada56c77e8a490566334ab93f4ea5c61123f721
92026 F20101206_AABDIE leung_n_Page_019.jpg
82f5956bd787088587b269bc471e3634
68130c328ab90fca88636cffe0bffcfe1f94bb39
96763 F20101206_AABDIF leung_n_Page_020.jpg
0c1f56a4bd9ed9402a58ae6bfbb1ae19
f522300cb298cf222dedc1e28e0ee7ce260bd1ca
3834 F20101206_AABDHQ leung_n_Page_002.jpg
7711da040c32c0b6958d5661dc78d1f4
410c7a5bb6db9063459624261cb2689a9cbccf5e
95841 F20101206_AABDIG leung_n_Page_021.jpg
29527bfc711d2253ffd9cc87d6396309
271fe17eefba16f36cdee73cfdaee60e16abf3d0
9623 F20101206_AABDHR leung_n_Page_003.jpg
0d2f7f25b79eccb3db0bdb712295ff77
93a2889a42ae4cb94adf646996dcf6a91b188961
58713 F20101206_AABDIH leung_n_Page_022.jpg
228248d9cdd30b0c78f0ef55b2f243e4
a519bd0eca801eac8e0bc90e539ffa436661c503
95457 F20101206_AABDHS leung_n_Page_004.jpg
a5aa2f732c4ddb67916d435438d952d0
de112922712ec1bf54bd665b9ae3997f67291b95
104409 F20101206_AABDII leung_n_Page_024.jpg
dbfe2b625d82f3c3927c61d6f82b74e0
e0686edd0fbe48ac56e1cc7fc947ec4ad4682083
35576 F20101206_AABDHT leung_n_Page_005.jpg
1bc45eaf126dc8682491ee91112e091e
c33d53f138aac973ce37c40f3a4b95b6e8bacedb
109411 F20101206_AABDIJ leung_n_Page_026.jpg
6ff9b722ca9709014b8f0532efbf62ee
c081b6873e10ca0db7a7bc2faf6707a5291b86ba
124904 F20101206_AABDHU leung_n_Page_006.jpg
83e6a89b068202b99689abd4071ebafa
82f1c7128e604ae7d793dca83077174397f97490







REAL OPTIONS FRAMEWORK
FOR ACQUISITION OF REAL ESTATE PROPERTIES
WITH EXCESSIVE LAND




















By

NGA-NA LEUNG


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

2007


































2007 Nga-Na Leung



























To my husband, Lezhou Zhan, and my family,


Lau Leung, Sau-Pik Fung, Shing-Pen Leung, and Shing-Chiu Leung









ACKNOWLEDGMENTS

I would never be able to adequately thank Dr. R. Raymond Issa, my chair, for making

room for me to develop my research question, as well as helping me to choose the direction of

my life. I want to thank him not only for his tremendous guidance, considerable patience and

encouragement throughout my study, but also for his endless trust, respect, and understanding,

which has forged me into a better person, not only with intelligence, but with responsibility.

I am especially grateful to Dr. Wayne Archer, Dr. Ian Flood, Dr. Kevin Grosskopf and Dr.

Robert Cox, for their discussions, suggestions, and encouragement during the development of

this dissertation. It is a great honor to have them serve on my committee. I am in debt to Dottie

Beaupied for her tremendous helps, especially during the dissertation submission process.

I would also like to acknowledge the generous financial support from the University of

Florida and the UF Alumni Association, from which I will carry the Gator spirit for the rest of

my life.

I am in debt to Andrew Weiss, who has been the best mentor in my real estate profession,

and has also provided generous help in data collection for this study. Besides him, I was working

with an amazing team in Parmenter Realty Partners, and especially thankful to Darryl Parmenter,

Ed Miller, and Mark Reese, for their insightful advice on career choices and their tremendous

helps at work.

Special thanks go to all my folks when I was in UF, whose love and friendship became

part of the happiest memory of my life. I am especially grateful to Yujiao Qiao, Yang Zhu,

Hongyan Du, Dongluo Chen, Jon Anderson, and Hazar Dib, whose encouragements have me to

complete this dissertation in time.









I want to extend a special word of thanks to all my mentors in the past, Dongshi Xu,

Fuchang Lai, Shensheng Xu, Shouqing Wang, and David Ling, whose wisdom and insight have

profound influence on my character and personality.

This work is dedicated to Lezhou Zhan, my husband and best friend, for his company

throughout my life in good days and in bad ones; and to my beloved family: Lau Leung, my

father; Sau Pik Fung, my mother; Shing-Chiu Leung, my little brother; and Shing-Pen Leung,

my deceased brother. The honor goes to them, for their thirty years of nurture with endless love

and care.









TABLE OF CONTENTS

page

A CK N O W LED G M EN T S ................................................................. ........... ............. .....

L IS T O F T A B L E S ................................................................................. 9

LIST OF FIGURES .................................. .. .... ..... ................. 10

ABSTRAC T ................................................... ............... 13

1 IN TR O D U C T IO N ................................................................................ 15

B a c k g ro u n d ....................................................................................................................... 1 5
Statement of Research Problem ...................................................................................................16
G oal and Objectives ............................................. 18
R research Scope ..................18................................................
Significance and Contributions................................................................ ...... 19
O organization of D issertation .............................................................................. ...............19

2 REVIEW OF REAL ESTATE VALUATION ...................................... ....................20

C u rren t P ra ctic e ..........................................................................................................2 0
Distinguishing Acquisition and Development ............... .....................................20
Typical A acquisition V aluation Process ........................................ ....................... 21
Current Real Option Approach and Limitations .................................. ...............24
D decision Tree Analysis and Lim stations ........................................ ...... ............... 25
R eal O options in R eal E state ................................................................................. .......... 25
Theoretical M odels ...................... ......... .. .......... ............... 25
E m pirical T testing ................................................................ 3 1
The RER O A approaches ................. .................................... .... ........ ...............3 1
Summary ......... ......... ......... .................................. ......... 32

3 L IT E R A TU R E R E V IE W .......................................... ......... .................. ............................33

Traditional Discounted Cash Flow Approaches..... .................... ...............33
C capital B u dgeting T heory ............................................................................. ....................34
M market R isk and P private R isk ............................................................... .....................34
C capital A sset Pricing M odel........................................ ..... .................... ............... 34
D iscou nt R ate ................................................................3 5
Option Pricing Theory .................. .. ... .............................. ........... 36
Definition and Type of Options ......... ...................... ................ 36
Black-Sholes Model and Stochastic Partial Differential Equations..............................38
L attic e s ................................................................4 2
M onte C arlo Sim ulation ......................................................................... ...................4 5
R eal O options A analysis A approaches ............................................... ............................. 46
Practical R eal Options M odel in Real Estate................................... .................................... 50


6









D decision T ree A naly sis........... ........................................................................ ...... ....... 53
S u m m ary ................... ...................5...................4..........

4 METHODOLOGY ................................. ......... ....................... 55

R E R O M modeling P procedures ......................................................................... ...................55
Problem Framing ............... ......... .......................55
Approach Selection ............................. ............. ........... .... .. .............. 57
Risk Drivers Identification and Estimation..... .................... ...............57
Base Case Modeling ....... ......... ....... ........ ................. ............... 57
O option M modeling ................... ...... ............................ .. ........ .. .............58
Sensitivity A analyses .................................... .. ......... .............. .. 58
RERO M modeling Approaches .................................................................... ............... 58
T he C om bined A approach ........................................................................ .................. 59
T he Separated A approach ........................................................................ ...................6 1
R E R O M odeling T echniques......................................................................... ...................63
Rational for Using Binomial Lattices.................. ............... .....................63
M onte C arlo Sim ulation ......................................................................... ................... 64
Replicating Portfolio ..................................... .. .. .. ...... .. ............64
Binom ial Lattice w ith Jum p Process ........................................ .......................... 66
Investm ent with Private Uncertainty .................................................... ...... ......... 68

5 THE COM BINED APPROACH................................................... ..................................... 72
5 THE COMBINED APPROACH.......... ... .. ........ ...... ........72

C a se D e sc rip tio n ............................................................................................................... 7 2
Building V valuation .............................................. 73
Problem Framing ............... ......... .......................73
A p p ro ach S election n ................................................................................................... 7 4
Base case NPV calculation ...................................................................................................74
R isk D rivers M modeling ..............................................................78
O option M modeling ....................................................... 85
Sen sitivity A naly ses ................................................................9 1
S u m m ary ................... ...................9...................5..........

6 TH E SEPA R A TED A PPR O A CH .................................................................................... 96

C a se D e sc rip tio n ............................................................................................................... 9 6
L a n d V a lu a tio n ................................................................................................................. 9 7
P ro b lem F ram in g ....................................................................................................9 7
Approach Selection ................................................ 98
Risk Drivers Identification and Estimation .......................................98
Base Case M modeling .................................................................... ......... 103
O option M modeling ...............................................................103
S en sitiv ity A n aly se s ................................................................................................ 10 8
S u m m ary ................... ...................1...................1.........4




7









7 CONCLUSIONS AND RECOMMENDATIONS.........................................................115

C o n c lu sio n s ............... ..................................................................................... .............. 1 1 5
Recom m endations for Future Research....................................................... ................... 116

L IST O F R E F E R E N C E S ..................................................................................... ...................118

B IO G R A PH IC A L SK E T C H .......................................................................... ....................... 122















































8









LIST OF TABLES

Table page

2-1 Comparison of Research Subjects, Model Variants, Contributions and Limitations. .......28

3-1 Type of Real Options. ............. .................................... ...................... 47

3-2 Financial Options versus Real Options.................. ........... .......................47

3-3 Correspondence between Financial and Real Options.................................................51

5-1 M major A ssum options for A rgus. ........................................ ............................................75

5-2 Correlation Between Random Variables. ........................................ ....... ............... 87

5-3 Statistical Summary of Monte Carlo Simulation Result.................................................87

5-4 Event Tree A ssum options. ......................................................................... .....................88

5-5 Sum m ary of Variable Effect on Option Value. .............................. ................................91

6-1 D evelopm ent A ssum options. ...................................................................... ...................97

6-2 Probabilities of Jump Diffusion and Binomial Processes..............................................107









LIST OF FIGURES

Figure page

2-1 Real estate phases and major factors to consider...........................................................22

2-2 Current acquisition valuation process ........................................ .......................... 23

2-3 Real Options approaches for land valuation. ........................................ ............... 27

3-1 Payoff of call option and put option. ............................................................................ 37

3-2 C all option payoff exam ple ............................................................................... .............37

3-3 C all prem ium vs. security price. ............................................................. .....................41

3-4 Stock and option price in a one-step binomial tree..........................................................42

3-5 Stock and option prices in general two-step tree. ................................... ............... 44

3-6 M onte Carlo sim ulation output. ............................................... ............................... 45

4-1 Critical steps in RER O analysis .............. .............................................. ............... 56

4-2 Two-step binomial lattice with different dividend yields ............................................66

4-3 Binomial lattice with jump process ........................... .......................... 68

4-4 Quadranom ial lattice ........... .............................................................. .. 70

4-5 Decision analysis. ...................................... .. ..... ..... .. ........... 70

5-1 211 Perim eter site plan ......................... ............ ... .. ........ ......... 73

5-2 B ase case N PV calculation. ...................................................................... ...................76

5-3 Spreadsheet model for Monte Carlo simulation. .................................... .................79

5-4 Historical market and subject property rental rates. ......................... .........................80

5-5 Returns correlation between market and subject property..............................................80

5-6 Normal distribution fit for historical returns on rental............... ..... .. ............... 82

5-7 Historical market and subject property occupancy rates. ...............................................83

5-8 Occupancy changes correlation between the local real estate market and the subject
p rop erty ............................................................... ................ 84




10









5-9 Normal distribution fit for historical occupancy rates. ................................................. 84

5-10 Snap shot of Monte Carlo simulation assumptions........................................................86

5-11 Monte Carlo Simulation Result of Forecasting Variable z. .............................................86

5-12 Normal distribution fit of forecasting variable z............................................87

5-13 Event tree present value without flexibility ..................................................................... 89

5-14 Present value w ith flexibility. ................................................ ................................ 90

5-15 Option value in relation with present value. ........................................... ............... 92

5-16 Option value in relation with replacement cost. ..................................... ............... 92

5-17 Option value in relation with present value and volatility..............................................93

5-18 Option value in relation with volatility and discount rate...................................... 94

5-19 Option value in relation with replacement cost and volatility. ........................................94

5-20 Option value in relation with present value and replacement cost. ..................................95

6-1 Historical market average rental rates and return volatility......................... ............99

6-2 Normal distribution fit for historical market rental returns. ............................................99

6-3 Gross rental rate movement and probabilities. ..................................... ............... 100

6-4 Building value movement and probabilities. ......................................... ............... 101

6-5 Historical construction cost for high-rise office building.........................................102

6-6 Construction cost change rate and inflation rate ............... ...... .... .....................102

6-7 D evelopm ent cost assume options ......... ................................................... ............... 103

6-8 Payoff and probabilities without flexibility. ...........................................104

6-9 Payoff matrices for project values without flexibility ............................... ...............105

6-10 Decision payoff and probabilities with flexibility. ................................ ............... 106

6-11 Payoff matrices of project value with flexibility. ............. ...................... ...............107

6-12 Present value in relation with rental rate and occupancy rate...................................109

6-13 Option value in relation with rental rate and occupancy rate. ............. ................110









6-14 Present value in relation with rental rate and development cost.................................. 110

6-15 Option value in relation with rental rate and development cost. ............. ................ 11

6-16 Present value in relation with rental rate and Cap rate. .............................112

6-17 Option value in relation with rental rate and Cap rate. ................. ...... .................112

6-18 Option value in relation with rental rate and Cap rate in 3D ................................... 113

6-19 Present value in relation with volatility and Cap rate............... ... .....................113

6-20 Option value in relation with volatility and Cap rate................... ................... ................114









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

REAL OPTIONS FRAMEWORK
FOR ACQUISITION OF REAL ESTATE PROPERTIES
WITH EXCESSIVE LAND

BY

Nga-Na Leung

August 2007

Chair: Raymond Issa
Major: Design, Construction, and Planning

Our study touches a field that few researchers explore: the valuation model for acquisition

of a property with excessive land that can be potentially converted into a new development.

Traditional valuation focuses mainly on the building improvement. With the drastic

capitalization rate compression, however, it becomes critical to identify and explore any hidden

value in an acquisition. One of such challenges is valuing a large partially vacant parcel that can

be potentially converted into a new development.

Valuation of these parcels is not straightforward. Traditional discounted cash flow

approach (DCF) cannot take into account the uncertainty and development flexibility.

Alternative approaches are real options analysis (ROA) and decision tree analysis (DTA).

However, the "twin asset" assumption required by the ROA methodology is often violated,

especially for assets with private risk and rare events. The use of the same discount rate

throughout valuation period in the DTA approach, regardless of changing risk characteristics

upon the execution of decision making, allows for arbitrage opportunity.

Our proposed real estate with real options (RERO) model is a framework that combines

DCF, ROA and DTA analyses to specifically value real estate acquisition with excessive infill









land. This methodology not only overcomes the shortcoming of current DCF method, but also is

superior to the pure ROA or DTA analysis. Focusing on applicability in practice, this framework

is developed intuitively with simple mathematics whenever possible. The study also explores a

few unconventional real options cases, all of which could have been very complicated if modeled

using the partial differential equations common in the academy, including (1)jump diffusion

process that does not go back to normal diffusion, (2) risk drivers that do not follow the

multiplicative stochastic movement, (3) private risk that has no market equivalent and hence

violating the non-arbitrage option pricing assumption. All of these are implemented simply

through binomial lattice with Monte Carlo simulation or DTA.

The RERO framework is applied to a real case in Atlanta. Valuation has two parts: (1) the

improvement is modeled using a combined approach with Monte Carlo simulation, and (2) the

incremental value using a separated decision approach with binomial lattice technique. The

valuation result is very close to the actual closing price.

Three conclusions can be drawn from this study: (1) acquisition and development has

different characteristics and deserve different kinds of attention; (2) consideration of managerial

flexibility can change investment decisions; and (3) many unconventional real option valuation

problems can be resolved by binomial lattice and Monte Carlo simulations.

The novelty of this study is the research subject: property acquisition with excessive land.

From the methodology standing point, the RERO framework is developed with ease of

applicability in mind. It bridges the gap between research and practice for real options

applications in the real estate industry.









CHAPTER 1
INTRODUCTION

Background

Our study touches a field that very few academicians have explored: the valuation model

for acquisition of a property with excessive land that can potentially be converted into a new

development.

The three major schemes in real estate property investment are acquisition, development,

and operation. Acquisition is the ownership transaction of land and improvement; development

is the process of adding improvement to the land; and operation is the daily management of the

property.

A majority of researchers focus on development, perhaps due to its high uncertainty.

Acquisition, on the other hand, has been ignored to a certain extent considering its volume and

size of transactions. Acquisition has been regarded as relatively low risk, since it is an

investment on a touchable real property, which has historical operating track records, and

numerous location attributes that last for decades and centuries.

In recent years, however, real estate capitalization rates (defined by dividing the

acquisition cost by annual net operating income) have compressed dramatically, meaning real

estate is far more expensive to acquire than ever before. It becomes critical to identify and

explore any hidden value in an acquisition target in order to be competitive.

The proposed acquisition model has two parts: firstly, valuation of the income producing

part of the property, mainly the improvement; secondly, the incremental value, mainly the

excessive land that, depending on the circumstance of where the property is located, may have

no value or substantial upside value.









The proposed real estate with real options (RERO) model is a framework that combines

real options and decision tree analyses. This methodology not only overcomes the shortcoming

of the current discounted cash flow method, but also is superior to the existing real options or

decision tree analysis. Focusing on applicability in practice, this framework is developed

intuitively using simple mathematics whenever possible. The improvement is modeled using a

consolidated approach with Monte Carlo simulation, and the incremental value using a separated

decision approach with binomial lattice technique.

Statement of Research Problem

The fundamental value of real estate is the income producing capability of the property,

which depends on many factors such as the amount of rental income to collect, the operating and

financing expenses, the level of risk of the cash flow, the appreciation or depreciation of property

value, and the performance of alternative investment instruments in the financial market.

Acquisition valuation is the projection of future earning capability of a property related to other

alternative investments. Traditional valuation mainly focuses on the building improvement.

With the drastic capitalization rate compression, however, it becomes critical to identify and

explore any hidden value in an acquisition. One such challenge is valuing a large partially

vacant parcel that can be potentially converted into a new development.

The attachment of excessive land to a property is not uncommon. Some developments

were initially planned in phases, but the later phases were never implemented due to economic

downturn or undesirable outcome of earlier phases. The land planned for later project phases

thus remains vacant for a long time. Some early developments were planned on large parcels to

insure sufficient space of surface parking. When the region becomes well developed and the

economy turns to be more favorable, the vacant land becomes valuable for dense urban infill.









Valuation of these parcels, however, is not as straightforward as applying the traditional

Discounted Cash Flow (DCF) approach, which discounts expected future cash flows at a certain

discount rate to get the Net Present Value (NPV). In the case of infill land, without new

development, all future cash flow will be 0; with certain assumptions of new development, it will

generate a value. Intuitively, in a hot real estate market where demand for developable land is

high, such as in the South Florida, those parcels are extremely valuable. But in a warm or cold

real estate market, the best use of such parcels may remain undeveloped until the market

matures. The uncertainty and development flexibility need to be taken into account. Whether or

not the land would be developed, when, what type, and what size all matters during the property

acquisition.

Alternative approaches are Real Options Analysis (ROA) and Decision Tree Analysis

(DTA). The ROA approach has evolved from the financial option pricing theory to value real

assets. Put simply, by acquiring a property, the owner has the right, but not the obligation, to

develop the excessive land to its full use at a certain point of time in the future. Therefore, the

value of a property with excess land should be higher than one without. The ROA methodology

has been used to evaluate vacant land and to explain factors that affect development decisions.

However, the ROA methodology requires one important assumption, that stochastic changes in

the underlying value of the real asset to be developed are spanned by existing tradable assets or a

dynamic portfolio of tradable assets, the price of which is perfectly correlated with the real asset

(Pindyck, 1991). This so called twin asset is hard to find, especially for assets with private risk

and rare events. Secondly, a lot of real options are compound options, which are options on

options, not simply on a single asset, and consequently more complicated to solve by the pure

option pricing methodology alone.









The DTA approach evolves from management science. It is a method to identify all

alternative actions with respect to the possible random events in a hierarchical tree structure.

The DTA approach is developed to handle interactions between random events and management

decisions. However, a major limitation of the DTA method is its use of the same discount rate

throughout the valuation period, regardless of changing risk characteristics upon the execution of

decision making, and thus allows for arbitrage opportunity (Copeland and Antikarov, 2005).

Recent studies have turned to the combination of option pricing methodology, decision

analysis, and game theory to solve real options problems. An ideal new approach should be able

to address the unique characteristics of acquisition valuation with infill land, to handle the

management flexibility, to take into account rare events such as new amenities driving up real

estate value. It also needs to be intuitively simple for practical implementation.

Goal and Objectives

To overcome the above mentioned disadvantages of the current DCF, ROA, and DTA

methodologies, this study has developed a framework, namely the Real Estate with Real Option

(RERO) framework, as a combination of all three methods to specifically value real estate

acquisition with excessive infill land. The objectives of this study are to:

* Develop a theoretical integrated framework to address real estate acquisition problems;

* Study factors affecting real estate acquisition and development, as well as their
characteristics and statistical distributions;

* Test and validate the model by applying it to real cases.

Research Scope

The research subject is real estate acquisition, which includes the value of the structural

improvement, and the incremental value represented by excess developable land. The definition

of excess land is that in addition to the portion necessarily attached to the existing structural









improvement; the excess portion that is large enough for new development and at the same time

meets local regulation requirements. Development factors are outside of our scope. Potential

users of the framework are real estate investors who need a tool to estimate the building value

and the land value during property acquisition. The proposed valuation model addresses mainly

the economic risk and uncertainty for acquisition and development.

Significance and Contributions

The novelty of our study is the research subject: property acquisition with excessive land.

To our knowledge, this is a field that few researchers have addressed. From the methodology

standing point, the RERO framework is developed with ease of applicability in mind. It bridges

the gap between research and practice for real options applications in the real estate industry.

Organization of Dissertation

In Chapter 2 we review the characteristics of real estate acquisition, existing valuation

approaches and their limitations, as well as what a new approach needs to achieve. In Chapter 3

we review the theory and technical details of the different approaches currently available, in

preparation for developing the proposed framework. We introduce the RERO framework in

Chapter 4, including valuation procedures, the combined and separated approaches, and some

new techniques developed to specifically apply to the case studies followed. Chapter 5 and 6 are

case studies of the combined approach and separated approach respectively. Collectively they

illustrate how the RERO framework can be applied to a broad spectrum of scenarios in practice.

In Chapter 7 we conclude the study and suggest future research directions.









CHAPTER 2
REVIEW OF REAL ESTATE VALUATION

This chapter discusses the current practice in acquisition valuation, alternative approaches

and their limitations, followed by a review of real options in real estate. It also analyzes how the

proposed RERO framework needs to resolve the practical problems unique to real estate

acquisitions.

Current Practice

Distinguishing Acquisition and Development

Analogous to the financial market, the three major schemes in the real estate investment

market are different and inter-related: acquisition, development, and operation. Acquisition is

similar to a lumpy investment in a well established company with, in many cases, 100%

ownership interest. Development is similar to the seeding of a start-up company and bringing it

to Initial Public Offering. Operation is the income producing process in the daily management of

the property.

This explains why research on development problems may not directly apply to acquisition

valuation problems. A real estate investment firm may have a different agenda for the infill land

than a real estate developer. The business of real estate development is to acquire and

accumulate a considerable land bank, wait for appropriate timing and market demand to build

new properties, and realize profit by selling the new properties to institutional investors. The

business of commercial real estate investment, on the other hand, is to acquire existing

properties, manage and improve the properties to receive the operating income from leasing. As

an investment vehicle, commercial real estates tend to be traded more frequently than vacant

land. As buildings get older and functionally obsolete, they usually change hands from passive

institutional investors to active value-added investors for cosmetic and functional upgrade and









tenant-mix adjustment. The developers, however, acquire land from different sources and wait

more patiently in a real estate cycle before putting up new products to capture the maximal gain.

Short holding periods and different business interest makes the infill land less valuable to an

investor than the vacant land to a developer.

The major factors to consider during acquisition are quite different from those in the

development and operation processes (Figure 2-1). During acquisition, the major factors are

location, market condition, market rent, pricing of the building and the land. Development

factors, such as impact fee and school zoning, are outside the scope. If the investor wins the bid,

he goes through the due diligence and financing process before actually plans for development of

the vacant land. Although our model consists of the building value and the land value assuming

possible development, it is by no means to substitute for a detailed financial planning before the

development breaks ground.

Typical Acquisition Valuation Process

A real estate investment company buys and manages properties to capture the cash flow

from operation. Many of these companies specialize in one or a few product types, such as

office, retail, industrial, or residential properties. To evaluate a property with infill land, the

management needs to answer the following questions:

* What is the building worth?

* What is the market demand for space?

* What is the likelihood that the company, after acquiring the property, will put up new
buildings?

* If the company does not intend to build new properties, what is the likelihood of the next
buyer to put up new buildings?

* What type and size of development can add value to the land, and thus add value to the
acquisition?













Acquisition
Location, Market,
Rents, Pricing of
Property and land



s No
Win Bid?

Yes
Acquisition I Due Dilience


Development


Feasibility Study
Zoning, Density,
Incentives, Impact Fee,
School zone


I


Operation


Operation
Rent, Expense, Tenant
Improvement; Leasing


Figure 2-1. Real estate phases and major factors to consider.










The typical decision process followed in current practice to acquire a property (an office

building for example) with infill land is shown in Figure 2-2. First, the building value and the

land value are segregated. Building value is derived from the standard DCF projection.

Depending on the investor's perspective towards the market, the land could have no value or

some value. In a weak demand region, the land probably does not generate any additional

income besides parking, thus it has little or no value to the investor. In a strong demand region

the investor conducts further investigation on the suitable product type to develop. If the best

product type to develop is one that the investor is familiar with, say an office tower, the investor

will further evaluate the project and land worth through a development model. If the best

product type is not one the investor is familiar with, say a residential condominium or an

industrial building, the investor probably hesitates to get involved in the development alone.




Potential Acquisition

Step 1: Segregating land value from building

Land Value Building Value

Step 2: Market demand analysis Strong Demand Weak Demand

Have Value No Value

Step 3: Product type analysis Other Type Office

Not to Build To Build
0
Step 4: Assigning land value Subjective Development
'.' Model v __
Land Value

Step 5: Summing total value
Offer Price



Figure 2-2. Current acquisition valuation process.









The investor might either find a development partner or consider selling off the land to such an

interested party. In either case, for the acquisition purpose the investor will simply assign a

subjective value to the land. The offer price consisting of the building and the land value is

derived and submitted to the broker.

Current Real Option Approach and Limitations

In the ROA approach, by acquiring the property the investor not only receives all cash

flows generated from leasing of the existing building, but also has the right, but not the

obligation, to develop the vacant land to its full use at a certain point of time in the future.

Therefore, the value of a property with infill land should be higher than one without.

However, the current ROA models are not without limitations. Firstly, valuation methods

for vacant land may not be suitable for infill land due to their different characteristics in the

following aspects: (1) the price of acquiring the land could be substantially lower; (2) the

building type to be developed may be restricted by zoning regulation on current property; (3) the

synergy effect could be substantial between the proposed building and the existing building; (4)

The surface parking is an inseparable part of the existing property.

Secondly, a real estate investment firm has a different agenda for the infill land than a real

estate developer. Short holding periods and different business interests make the infill land less

valuable to an investor than to a developer.

Thirdly, the current theoretical models are on a higher level to address real estate as a

whole, while investors need practical models to address individual cases. The current theoretical

models are on an aggregate level to explain real estate value in general. They have rigid

restrictions, and can only be applied to the simplest cases (Miller and Park, 2002). They also

lack flexibility to change variables to model realistic assumptions for practical use. Real assets









often possess unique location, physical and contractual characteristics, many of which are

subjective and unquantifiable. Using the real option method alone may be insufficient.

Last, the existing "omnipotent" real options models are mathematically correct but too

complicated to be used. Trigeorgis (2005) and others have advocated approximate methods to

simplify the calculation for practical applications.

In summary, although the ROA approaches can overcome some of the drawbacks of DCF

and provide better valuation for acquisition, the method itself is not fully developed to address

the specific needs of acquisition valuation in practice.

Decision Tree Analysis and Limitations

Another available approach is the Decision Tree Analysis approach (DTA). DTA is a

method to identify all alternative actions with respect to the possible random events in a

hierarchical tree structure. It is developed to handle the interaction between random events and

management decisions.

However, a major limitation of the DTA method is its use of the same discount rate

throughout the valuation period, regardless of changing risk characteristics upon the execution of

decision making, and thus allows for arbitrage opportunity (Copeland and Antikarov, 2005).

This means using DTA alone is not sufficient for the acquisition with infill land problem.

Real Options in Real Estate

Applications of ROA in the real estate industry can be classified into the following

categories: Vacant land for development, property redevelopment, and leasing (Ott, 2002). This

section summarizes some theoretical models as well as empirical studies.

Theoretical Models

Titman (1985) developed a simple binominal tree model to explain why a piece of land

could be more valuable remaining vacant today and when is optimal to develop. This seminal









work is frequently cited in later papers, which all use Partial Differential Equations (PDE) and

fall into two major categories by methodology: the optimal development timing problem, and the

game theoretical problem. The optimal timing problem is represented by Clarke and Reed

(1988, optimal timing and density for residential development), Capozza and Helsley (1990,

conversion from agricultural to urban land use), Williams (1991, optimal timing and density to

develop, optimal timing to abandon), and Geltner et al. (1996, two land use choice). The game

theoretical problem is represented by Williams (1993, competition on simultaneous

development), Grenadier (1996, competition on simultaneous or sequential development), and

Childs et al. (2001, inefficient market with noisy effect on value). Figure 2-3 shows the

genealogical relationship among these models. Table 2-1 itemizes the research subject, model

variant, contributions and limitations of each study.

Besides land valuation, there are two types of real estate applications of the ROA that are

closely related to our research: property redevelopment and operational research. Williams

(1997), Childs at al. (1996), Cederborg and Ekeroth (2004) have researched on the

redevelopment or renovation of real assets. They view existing buildings as assets that can be

repetitively invested and improved, sometimes by changing functional attributes, e.g., switching

from offices to apartments. Grenadier (1995, 2003), Adams, Booth and MacGregor (2001),

Bellalah (2002), Grenadier and Wang (2005), Capozza and Sick (1991), among others have

focused on options embedded in the commercial lease agreements, such as forward leases,

escalation clauses, leases with options to renew or cancel, adjustable rate leases, purchase

options, sale-leasebacks, ground leases, etc.

Acquisitions have not been thoroughly researched using the real options approach, though

common in practice. As discussed earlier, acquisitions with excessive land differ from ground









up development. They also differ from redevelopment, since they are not simple renovations of

the existing buildings. They might include valuation of the leases as a source of cash flow for

the potential development, but would require a much simpler valuation process on the leases. In

summary, although acquisition valuation is close to the three subjects mentioned above, the

approach is significantly different. A new approach needs to be able to address both the building

value and the land value, if any, for potential development.


1985



1987



1990



1991



1993



1996



2001


Clarke &
Reed


Development Timing


Competition / Game


Figure 2-3. Real Options approaches for land valuation.


I









Table 2-1. Comparison of research subjects, model variants, contributions and limitations.


Author / title Subject description
"Urban Land Explain why land is
Prices under more valuable
Uncertainty" remaining vacant for
(Titman, future development:
1985) increased uncertainty
leads to a decrease in
current development
activity.












"A Stochastic Examine the qualitative
Analysis of effects of the
Land different types of
Development uncertainty on the
Timing and timing and structural
Property density of land
Valuation" development on
(Clarke and residential projects.
Reed, 1987)


Model type & variant
One time period
binomial model
assuming rents have
two state values.

















PDE to solve for
optimal
development timing
and density
assuming rents and
development cost
follows stochastic
processes.


Contribution / limitation
Seminal work of ROA in
real estate. Simple. Two
policy implications: (1)
Government incentives to
stimulate construction
activities may actually
lead to a decrease if the
extent and duration of the
activity is uncertain. (2)
Initiation of height
restrictions may lead to an
increase in development
activity due to reduced
uncertainty regarding the
optimal height of the area.
One time period model.
Assume only two states,
and that construction costs
are certain.
Limited to residential
development. Two limited
assumptions: (1) new
construction is small so
that rents and
development costs are
uninfluenced by the newly
added construction.
However, in reality
development is lumpy and
will affect market rents
and vacancy rate. (2)
Efficient market in which
all agents have equal
information about the
future probability
distributions of rentals and
costs. However, in reality
real estate leasing and
sales information is not as
transparent as that in the
stocks market, but more
predictable, at least in a
short run.









Table 2-1. Continued.


Author / title
"The Stochastic
City"
(Capozza and
Helsley,
1990)














"Real Estate
Development
as an Option"
(Williams,
1991)












"Insights on the
Effect of
Aland Use
Choice"
(Geltner et
al. 1996)


Subject description
Examine the land
value of
conversion from
agricultural to
urban use based
on spatial
characteristic of
real estate such
as distance or
commuting time
to the CBD.







Optimal time to
develop, optimal
development
density, and
optimal time to
abandon a
project.










Examine whether
the multiple-use
zoning add value
to land by
analyzing the
land use choice
between two
different use
types.


Model type & variant
PDE model built on the
traditional mono-
centric urban theory to
study spatial
implication of land
conversion value,
assuming household
income, rents and land
prices follow
stochastic processes.








PDE model to solve for
optimal timing of
abandoning a project,
in addition to optimal
development timing
and density, assuming
carrying cost, rents
and development cost
follows GBM, also
assuming carrying cost
is significantly high so
that during some
circumstance it is
better to abandon the
project than bearing
the cost.
PDE to solve for optimal
choice between two
land use types,
assuming development
cost, value of first land
use, value of second
land use follow
stochastic processes.


Contribution / limitation
Uncertainty (1) delays
the conversion of land
from agricultural to
urban use, (2) imparts
an option value to
agricultural land, (3)
causes land at the
boundary to sell for
more than its
opportunity cost in
other uses, and (4)
reduces equilibrium
city size. Does not
explain very well land
value in the emerging
suburb economic
centers.
Looks at the downside of
a project: optimal time
to abandon. This is a
put option. Maximum
feasible density is
determined by zoning
restrictions. Assumes
perfectly competitive
market and perpetual
option.







Land use type choice is a
unique perspective in
real estate. Assume
construction unit cost
is the same regardless
of building type to be
developed.









Table 2-1. Continued.


Author / title

"Equilibrium and
Options on
Real Assets"
(Williams,
1993)









"The Strategic
Exercise of
Options:
Development
Cascades and
Overbuilding
in Real Estate
Markets"
(Grenadier,
1996)









"Noise, Real
Estate Markets,
and Options on
Real Assets:
Theory"
(Childs et al.
2001)


Subject description

Examine industry
equilibrium of
optimal exercise
policy under
competition: the
impact of
competition erodes
the value of the
option to wait and
leads to investment
at very near zero net
present value
thresholds.
Explain why building
booms in the face of
declining demand
and property values:
fearing preemption
by a competitor,
developers proceed
into a panic
equilibrium in which
all development
occurs during a
market downturn.







Optimal valuation of
noisy real asset in an
incomplete
information game


Model type and
variant
PDE to solve for
perfect Nash
equilibrium with
finite elasticity of
demand and finite
development
capacities in a less
than perfectly
competitive
environment.



Three-stage model to
explain real estate
boom-and-bust
cycle: valuation of
land, construction
lag, and "sticky
vacancy" in
operation











PDE, assume optimal
value include three
terms: forward
value estimate,
historical value
estimate, and the
term that corrects
for convexity
effects due to
incomplete
information


Contribution/ limitation

Among the first to
consider the effect of
competition.
Exercising options to
develop affects the
aggregate supply of
developed assets and
market price, which
preclude
simultaneous
exercise of the
option among all
developers.
Extend the Williams
model from
symmetric and
simultaneous
equilibrium to either
simultaneous or
sequential
development, and
allows for
preemptive
equilibria. Powerful
to explain boom-
and-bust markets
such as real estate.
Assume individual
firms are identical
and have all
information.
Extend to include the
price lagging effect
in real estate, where
estimate value is
different from
market value, i.e., in
a less than perfect
market.









Empirical Testing

A majority of the ROA empirical works in real estate has been in aggregate studies. Quigg

(1993), Holland et al. (2000), Sivitanidou and Sivitanides (2000), Bulan et al. (2004) all use a

large sample of real estate data to test the premium of land price over intrinsic value, whether

irreversibility is an important factor for real estate investment, whether uncertainty delays

construction, and whether competitions among developers decrease the option value of waiting.

As Bulan et al. (2004) point out, however, since real options models apply to individual

investment projects and predict that trigger prices are non-linear, aggregate investment studies

may obscure these relationships. Moreover, these empirical tests are limited to qualitative results,

such as whether each variable in the ROA model has positive or negative effect on the overall

option value. Few of the ROA empirical works has focused on individual case studies and its

implication in practice.


The RERO Approaches

The RERO framework attempts to move beyond the realm of academic interest to be used

quantitatively in practical problems of acquisition valuation, development decision making, and

land policy analysis. The approach should be able to address the unique characteristics of

acquisition valuation with infill land, to handle the management flexibility, to take into account

rare events such as new amenities driving up real estate value. This calls for the combination of

DCF, ROA and DTA methodologies. It also needs to be intuitively simple for practical

implementation.

To achieve this goal, the problem is divided into two sub-problems: (1) valuation of the

building structure and (2) valuation of the infill land. Valuation of the building structure

represents a normal case of acquisition. On the other hand, valuation of the infill land represents









the extra value stemmed from creative management, i.e., the ability to uncover the hidden value

in real estate and realize it through active development.

Real estate valuation is an art and science. The RERO framework is not built on rigid

reasoning and restricted assumptions to be precise, rather it is developed as a tool to solve a

broad spectrum of practical real options problems. Specifically, it explores a few unconventional

real option cases, including (1)jump diffusion process that does not go back to normal diffusion,

(2) risk drivers that do not follow the multiplicative stochastic movement, (3) private risk that

has no market equivalent and hence violating the non-arbitrage option pricing assumption. The

mathematical models for these kinds of unconventional problems could be very complicated, if

written in PDE equations. To facilitate practical implementation, the RERO framework applies

the binomial lattice with Monte Carlo simulations and decision analysis method. The RERO

framework is a simple yet powerful tool, intuitive to the practitioners, yet mathematically correct

and precise.

Summary

This chapter compares the difference between real estate acquisition and development,

reviews current practice of real estate acquisition valuation, discusses the three alternative

valuation approaches, DCF, ROA, DTA and their limitations. Built on the strengths of these

three approaches, the RERO framework needs to address practical problems of acquisition

valuation, development decision making, and land policy analysis. The next few chapters

explore modeling details of how this concept should be implemented.









CHAPTER 3
LITERATURE REVIEW

In Chapter 2 several different valuation methodologies were discussed conceptually: the

Discounted Cash Flow approaches (DCF), the Real Option Analysis approaches (ROA), the

Decision Tree Analysis approaches (DTA), and the proposed Real Estate with Real Option

approaches (RERO). In this chapter the technical modeling details of the first three approaches,

as well as the capital budgeting theory in finance will be discussed. The RERO approaches that

built on the existing three will be discussed in Chapter 4.

Traditional Discounted Cash Flow Approaches

The Discounted Cash Flow (DCF) approaches include payback period, Internal Rate of

Return (IRR), Net Present Value (NPV), and other forms such as Adjust Present Value. In this

study DCF refers to the NPV method alone. The principle of the NPV method is to discount all

projected free cash flow back to year 0, to get the net present value of the project (Equation 3-1).

The NPV must be greater than 0, or the IRR must be greater than the company's hurdle rate, in

order to justify the investment (Mun, 2002). If NPV is greater than 0, the project is regarded as

optimal to be executed immediately.


NPV= /p- (3-1)
=0 (1+ k)'

where
NPVis the net present value of the project at Year 0,
F, is the projected free cash flow (including income, cost and terminal value) in year i,
k is the project discount rate.

The DCF method is suitable to evaluate projects that are well structured, with predictable

future cash flows. For projects involve large uncertainty of timing, cost and cash flows, such as

a real estate development, using the DCF approaches are difficult in the following three aspects

(Miller and Park 2002; Feinstein and Lander 2002): firstly, selecting a fixed and appropriate









discount rate; secondly, taking into account new information and changing the plan accordingly;

thirdly, determining the optimal timing to carry out the project.

Capital Budgeting Theory

In the DCF approach and in all other approaches, one of the most influential factors is the

discount rate to be used. To better understand discount rate, a brief discussion of the capital

budgeting will follow.

Market Risk and Private Risk

Stocks are risky. For any individual stock, however, a large part of its risk can be

eliminated by holding it in a large well-diversified portfolio. A portfolio consisting of all stocks

is called a market portfolio. In reality, it can be approximated by a large amount of well-

diversified stocks. The part of the risk of a stock that can be eliminated is called private risk, or

diversifiable risk; while the part that cannot be eliminated is called market risk, or systematic risk

(Brigham et al. 1999, pl78). The Capital Asset Pricing Model (CAPM) indicates that the

relevant riskiness of any individual stock is its contribution to the riskiness of a well-diversified

portfolio, or the market risk portion only, which is measured by its /f coefficient.

Capital Asset Pricing Model

If the market portfolio m is efficient, the required return rOs of any stock i is the risk-free

interest rate r plus a risk premium, as shown in Equation 3-2.

= r + f (rm r) (3-2)

Where
r is the risk-free return,
rF is the expected market return,

= -", where am is the covariance between the stock and the market, and a o is the

variance of the market portfolio.









f, is an important variable to measure the risk characteristics of the stock i. If f, is greater

than 1, the stock is more volatile than the average stock market; and iffl, is less than 1, the stock

is less volatile than the average stock market. The more volatile a stock is, the more risky it is,

and consequently the higher the required return needs to be in order to justify the risk an investor

takes.

Discount Rate

A firm's hurdle rate is usually its Weighted Average Cost of Capital (WACC). A large real

estate investment firm is usually formed as a Real Estate Investment Trust (REIT), which does

not pay income taxes, so long as 95% of its income from operation is distributed to the investors

on an annual basis. The WACC k of a REIT is calculated by Equation 3-3.

S D
k = r +r D (3-3)
V V

where
r, and rd are the cost of equity and debt respectively,
S, D and V are the market values of equity, debt, and total asset respectively; S + D = V.

Equation 3-3 can also be used to value an investment project, as if every project was a

separate mini company. However, it is difficult to determine the cost of equity and debt for a

project, since the equity of a start-up project, for example, may not be publicly traded, and the

risk characteristics of a project are quite different than that of the company as a whole.

The capital budgeting theory indicates that finding the right discount rate is extremely

difficult, if not impossible. Since every company has different risk characteristics, the required

discount rate is different from company to company. Also every project within the same

company has different risk characteristics, and the correct discount rate required to value a

project may not be the same as the company's WACC. This makes both the DCF and the DTA









approached difficult to value infill land with development potential, although for an existing

building with operating history the DCF and DTA approaches may work fine.

Option pricing theory, on the other hand, does not rely on the risk characteristics of a

particular firm or project. Neither does it rely on the risk preference of an individual investor. It

is discounted at the risk-free interest rate r. The reason is that "private risk is alleviated through

portfolio diversification and market risk can be diminished through the option's replicating

portfolio" (Miller 2002). For development project that involves a lot of uncertainty, this is a

huge benefit over the traditional DCF method.

Option Pricing Theory

Definition and Type of Options

An option gives the holder the right but not the obligation to do something (Hull, 2006). In

the financial market, there are two basic types of options: call options and put options. A call

option gives the holder the right to buy the underlying asset by a certain date for a certain price.

A put option gives the holder the right to sell the underlying asset by a certain date for a certain

price (Figure 3-1). Based on exercise dates, options can be classified into two major types:

American options can be exercised at any time up to the expiration date. European options can

be exercised only on the expiration date. Most options are of the American type.

The value of a financial option is determined by the current price of the underlining asset

So, the strike price at maturity date K, the risk-free interest rate r, maturity date T, return

volatility of the underlining asset o, and sometimes the dividends expected during the life of the

option (Hull, 2006). Returns on options are asymmetric, i.e., options will only be exercised to

the benefit of the holders. For example, if a holder of a call option can buy the stock 3 months

later for $100 per share, and if the spot price at maturity becomes $120 per share, he will

exercise this option, then sell the stock immediately, and earn $20 per share. However, if the spot









price becomes $83 per share at maturity, he can let the option expire without exercised, thus

avoid losing $17 per share. He only losses the premium initially paid for the option (Figure 3-2).

His payoff is the difference between the spot price at maturity St and the exercise price K, or 0,

whichever is greater (Equation 3-4).

Max(S, -K,O) (3-4)


Payoff


01
Premium
K


Call Option


* Stock
Price


SPayoff


01
Premium


\ Stock
K Price


Put Option


Figure 3-1. Payoff of call option and put option.


SPayoff


K=$10
0 / Stock
S=$83 S=$120 Price

Call Option Example


120
20

100

83
0

Example Payoff


Figure 3-2. Call option payoff example.


Option pricing theory is to determine what premium, or option price, a holder should pay

for such flexibility. The types of option pricing methodology include continuous- and discrete-

time models (Miller and Park, 2002; Lander and Pinches, 1998). Continuous-time models









include closed-form equations and stochastic partial differential equations. Discrete-time models

are mostly lattice models and Monte Carlo simulation.

Black-Sholes Model and Stochastic Partial Differential Equations

The most famous closed-form equation is the Black-Scholes model, although it can only be

used to price European options. The Black-Scholes (1973) pricing formula is developed under

the following ideal assumptions: stock price change follows the Wiener process, distribution of

return is lognormal, efficient market, constant short-term interest rate, no dividend payment, no

transaction costs, and short selling is possible. A Wiener process, also called a Geometric

Brownian Motion (GBM), is a random process with a mean change of 0 and a variance rate of 1.

The values of dz for any two different short intervals of time dt, are independent (Equation 3-5).

dz = Esdt (3-5)

Where e has a standardized normal distribution 0(0,1), and (/,u, U) denotes a probability

distribution that is normally distributed with mean yu and standard deviation o. A generalized

Wiener process for a variable S can be defined by Equation 3-6.

dS = uSdt + cSdz (3-6)

where
S is the underlying asset whose value change follows the Wiener process;
dS is the change of value S during an infinitesimal time interval dt.

Ito's Lemma (Hull, 2006, p273) is a theorem of stochastic calculus that shows second order

differential terms of a Wiener Process can be considered to be deterministic when integrated over

a non-zero time period. Since the stock price S follows the Wiener process, an optionf(be it a

call option or a put option) contingent on S follows the Ito's Lemma (Equation 3-7).

Of Of 1 02f 2 +
df = (- + -+ a2S2_)dt+ Sdz (3-7)
d S +t 2 OS2 3S









The principle of option pricing methodology is to construct a riskless portfolio to prevent

arbitrage. This portfolio H is short one option and long 8f/8S shares of the underlying stock.

When the stock price S changes, the Of/8S shares must change accordingly. Later from

Equation 3-10 we will see this portfolio is riskless because it does not involves dz over the time

interval dt. The portfolio 7 is written as Equation 3-8.

S= -f + S (3-8)
as

During the time interval dt, the change in value of the portfolio is represented in Equation

3-9.

cd = -df + dS (3-9)
as
8S

Substitute dS from Equation 3-6 and dffrom Equation 3-7 into Equation 3-9,

Of 1 2f
dn = (- 2S2)dt (3-10)
at 2 S2

To prevent arbitrage, the portfolio earns risk-free interest r during the time interval dt.

cd = rHdt (3-11)

From Equation 3-8, Equation 3-10 and Equation 3-11, we have

af 1 a2f2 af
(- 1 2 CS2)dt = r(-f + S)dt
at 2 S2 as

Which simplifies to

+ S+ a2S2 = rf (3-12)
at as 2 S2

Equation (3-12) is the Black-Scholes partial differential equation. Subjected to the

following boundary conditions:

f = Max(S K,0), when t Tin the case of a call option, and









f = Max(K S,0), when t = Tin the case of a put option.

Integrating Equation 3-12, the Black-Scholes formula can be written as Equations 3-13 and

3-14 (Black and Scholes, 1973; Hull, 2006).

c= SN(d)- Ke rrN(d2) (3-13)

p = Ke rrN(-d2)- SoN(-d,) (3-14)

where
In(So/K)+(r +a2/2)T
d, =
UT
In(S/K) + (r 2 /2)T,
UJT
c is the value of a European call option;
p is the value of a European put option;
So is the current price of the underlying asset;
K is the strike price of the option at maturity;
r is the risk-free interest rate;
Tis the time to maturity;
N(*) is the cumulative standard normal distribution function.

The Black-Scholes model can be divided into two parts: The first part, SoN(dd), derives the

expected benefit from acquiring a stock right now. This is found by multiplying stock price So by

the change in the call premium with respect to a change in the underlying stock price N(d1). The

second part of the model, Ke-rrN(d2), gives the present value of paying the exercise price on the

expiration day. The fair market value of the call option is then calculated by taking the difference

between these two parts.

The boundary condition of a call option is best depicted in Figure 3-3. The solid black line

defines the call option value. The green line with square markers defines the maximum value of

the option. For non-arbitrage, the option should never be worth more than the stock price S,

otherwise an arbitrageur can easily make a risk-less profit by buying the stock and selling the call

option. The blue line with triangle markers defines the minimum value of the option. The call










option should be worth more than Max(So Ke r,0), otherwise an arbitrageur can buy an

option, short sell a share of stock, invest the surplus at risk-free interest rate and earn a profit.

The possible option values fall in the region defined by the green line and the blue line and vary

depending on the underlying stock volatility, option time to maturity, and risk-free interest rate.



Call Option vs. Stock Price


u -


30


0
0 30 60 90 120 15(
Stock Price

Lower Bound Option Value --- Upper Bound


Figure 3-3. Call premium vs. security price.


Though the Black-Scholes pricing model has a lot of restrictions and can only value

European options, there are a lot of stochastic partial differential equations with boundary

conditions that relax some restrictions to a certain extent and can be used to value more specific

questions. The benefits of these analytic continuous-time models are that they are flexible to

model different circumstances, and mathematically accurate (Miller and Park, 2002). The









drawback is that the modeling requires sophisticated mathematical knowledge, sometimes the

solution does not exist, and even if it does, the process itself could become as complicated as a

black-box for the practitioners to comprehend (Lander and Pinches, 1998).

In the case when analytical solutions to the stochastic differential equations do not exist,

they must be solved numerically by using finite-difference methods, or Monte Carlo simulations

(Miller and Park, 2002).

Lattices

Lattices are a type of discrete time model, which includes binomial tree, trinomial tree,

quadranomial tree, and other multinomial models. Lattices are the approximation of the

continuous models. The results of these two methods are very close when the time interval is

infinitely small.

The most commonly used binomial lattice was developed by Cox et al. (1979), in which

values of the underlying asset are assumed to follow a multiplicative binomial distribution. The

model assumes the up and down parameters u and d, the volatility of the underlying asset o, and

risk-neutral probabilities and 1 -p are constant (Figure 3-4).


SSoo




1-p
SSo'd
fd


Figure 3-4. Stock and option price in a one-step binomial tree.


An optionf(be it a call option or a put one) is valued by constructing a risk-less portfolio

H of a long position in 6 shares of stock and a short position in 1 option (Equation 3-15).









H = Sos -f


In an up movement of the stock price, the value of the portfolio is

= Su8 f,

In a down movement of the stock price, the value of the portfolio is

Hd = Sod fd

The two are equal when

Soud f, = Sod fd

or when

3= f fd (3-16)
So(u d)

The portfolio is risk-less and must earn the risk-free interest rate r. The present value of

the portfolio is represented by Equation 3-17.

H = (Sou- f,)e-r (3-17)

From Equation 3-15 and Equation 3-17, we have

So,- f = (Sou f)e-rT (3-18)

Substitute 6 from Equation 3-16 into Equation 3-18,

f =e rr[pf, + (1- p)fd] (3-19)

where
e -d
P=
u-d
u =e"

d=

Equation 3-19 is a one-step binomial model, which can be generalized to two-step and

multi-step models. Figure 3-5 shows a two-step binominal lattice. During each time step, the


(3-15)









stock value either moves up to u or down to d of its previous value. Option value is derived by

working backward fromf, and fd to calculated, fromfud andfdd to calculated, then from, and

fd to calculatef(Equations 3-20, 3-21 and 3-22).


So*u*u

So*u A




f fud



So'd
fd So*d*d
fdd

Figure 3-5. Stock and option prices in general two-step tree.

f, = e rt[pf, + (1 P)fd] (3-20)

fd = e t[pfd + (1- P)fdd] (3-21)

f =e t[pf + (1- p)fd ] (3-22)

Substituting from Equation 3-20 and Equation 3-21 into Equation 3-22, we get

f = e 2[p2 f, + 2p(l- p)fd + (1- )2 fdd] (3-23)

where
et -d
u-d
u =et

d=

In general, for a binomial lattice with n steps, the ith step (0 < i < n) option value is

calculated by Equation 3-24.









f = e t[pf,,, + (1- p)f +,d ] (3-24)

Lattice, though still complicated, is more intuitive to the practitioners than continuous time

models. It is especially useful to evaluate American options, since analytic solutions are almost

non-existing in the continuous models. The drawback is that using lattice by itself is hard to

model compound options. However, combined with DTA, lattice is capable to deal with a lot of

complicated situations, even more flexible than PDEs in many circumstances.

Monte Carlo Simulation

Originally named after the casinos in Monte Carlo, Monaco, Monte Carlo simulation is

about games of chance. It is now widely used to simulate stochastic processes by sampling large

quantity of random outcomes for the processes (Figure 3-6). Because of the repetition of

algorithms and the large number of calculations involved, Monte Carlo simulation is

computationally complex, yet easy to model and understand.



Histogram Statistic Preferences I Options


250 Rate of Value Change (2000 Trials) 1 .
---- 1.0

*OSr

D 0,5 IL


0.1


-0.2363 -0.1263 -0.0233 0.0737 0.1737 0.27=.f


Type ITwo-Tail -Infinity Certainty [(%)\ 1o0.0o


Figure 3-6. Monte Carlo simulation output.









In real options modeling, Monte Carlo simulation can be used where there are several

underlying variables. The drawback is that it is difficult to work backward to determine option

exercise strategy, since Monte Carlo simulation is forward looking. In the RERO model, it is

used as an intermediate step to estimate volatility of the project stems from multiple risk drivers.

Real Options Analysis Approaches

First coined by Myers (1977), the ROA approaches are to apply financial option pricing

theory and methodology to evaluate real assets (Miller and Park, 2002; Trigeorgis, 2005). In the

financial market, a derivative is a security whose value changes depend on the value changes of

some other underlying assets. In real asset valuation, the value of a project can be viewed as a

derivative contingent upon input costs, output yield, time and uncertainty (Miller and Park,

2002), and therefore can be evaluated by applying the financial option pricing principles.

By using ROA, investment decisions are viewed as real options or combinations of real

options, such as options to defer, expand, switch, contract, or abandon, as shown in Table 3-1

(Trigeorgis, 1996; Yao and Jaafari, 2003). Also included in the table are examples in the real

estate and construction industry. Contrary to DCF method, in the ROA context greater volatility

is not always worse, since losses are limited to the initial investment, or option premium, but the

option holder can capture greater upswings if things turn out to be favorable. ROA is applied

most commonly in the industries of natural resource, manufacturing, energy, research and

development, start-up companies, and others (Lander and Pinches, 1998; Trigeorgis, 1996).

Applications in the real estate and construction industries are still limited.

Although ROA borrows the option pricing theory, the distinguish characteristics of real

assets demand different valuation assumptions and methodologies from direct applications of the

option pricing theory without any modification. Table 3-2 lists the major differences between

financial options and real options (Mun, 2002).









Table 3-1. Types of real options.
Options Features Examples
Defer To postpone construction till optimal timing Time to develop

Stage To create a series of stages to allow for Phased development
abandonment or expansion in later stages
depending on outcomes of earlier stages

Contract To contract the project to a third party in order to Franchise stores
mitigate risk or to speed up market domination

Expand To expand the project scale in favorable market Airport expansion
conditions

Abandon To abandon the project and prevent severe lost in Bankruptcy of a
unfavorable market conditions project entity

Switch To change the output mix or input mix in response Coal-fired vs. gas-
input/output to changing market demand fired power plants

Compound Option on option, where the value of an earlier Case study in Chapter
option can be affected by the value of later 5 and 6
options. Most real world options are of this kind

Table 3-2. Comparison between Financial Options and Real Options.
Characteristics Financial options Real options
Maturity Short, usually in months Long, usually in years

Underlying asset Traded stocks, with comparable and Not traded project free cash flow,
pricing information proprietary in nature, with no
explicit market comparable

Management Value does not change due to Value has to do with individual
manipulation individual management assumptions management assumptions and
or actions actions

Competition and Irrelevant to pricing Direct drivers of value
market effect

One of the major differences between financial options and real options is how to handle

private risk. The underlying assets of financial options are traded market assets, and market risk

is the major source of risk among all financial options. Private risk can be treated simply as

errors. The underlying assets of real options, however, are usually non-traded assets that do not









have market equivalent. Private risks cannot be hedged. The other difference is the effect of

management and competition. Financial options on the same underlying asset and the same

maturity date are identical. They are widely held to be market efficient. A single transaction

usually does not affect the pricing of financial options, neither does management or competition.

Real options, on the other hand, are lumpy or one-of-the-kind in nature. Exercise of real options

by management can have profound impact on the underlying asset value.

Consequently, there are a lot of debates in the academic world about how real options

should be correctly priced. Borison (2005) classified existing real options approaches into 5

categories:

* The classic approach,
* The subjective approach,
* The Market Asset Disclaimer approach,
* The revised classic approach, and
* The integrated approach.

Borison also discussed the underlying assumptions of these approaches, the conditions that

are appropriate for their applications, and the mechanics in applying them.

The classic approach assumes that the capital market is complete, and an identical twin

asset or portfolio exits for every real asset under evaluation. It makes explicit use of no-arbitrage

argument, and applies directly the Black-Shores formula.

The subjective approach also assumes that the capital market is complete. However, it

relies on subjective judgment for input, as opposed to data from traded markets. This makes it an

inconsistent approach, and limits to qualitative result.

The Market Asset Disclaimer (MAD) approach assumes that the capital market is not

complete. It relies on the estimate value of the asset without flexibility as the "twin asset" for the

purpose of calculating the option value of the flexibility. Data is drawn from traded markets









when available, and subjective judgment when not. Proponents of this approach justified this

step explicitly: the same, weaker assumptions that are used to justify the applications of DCF can

be used to justify the applications of option pricing to flexible corporate investment (Copeland

and Antikarov, 2001).

The revised classic approach assumes that the capital market is partially complete. It

attempts to divide the world into black and white: For investments that have market equivalents,

it applies the classic approach using market data; for investments that do not have market

equivalents, it applies decision analysis using subjective judgment.

The integrated approach also assumes that the capital market is partially complete.

However, it uses capital market data for market risk and subjective judgment for private risk in

an integrated model.

The major difference among these approaches is how private risk is handled. The classic

approach ignores private risk completely and treats real options exactly like financial options that

all risks can be diversified away by constructing a hypothetical traded twin asset or portfolio.

The subjective approach handles private risk by substituting market data by subjective

assessment. The revised classic approach admits the limitations of direct applications of option

pricing theory to real options analyses and classifies investments into those either dominated by

market risk or by private risk. It applies the option pricing model only to investments dominated

by market risk, and applies decision analysis to those dominated by private risk. Although it is a

better approach than the previous two, the revised classic approach forces all investments into

black or white, and implements two totally different approaches.

The MAD approach, on the other hand, admits the difficulty of handling private risk, thus

does not rely on the existence of a traded replicating portfolio. Instead, it uses the project value









itself without flexibility as the twin security, as if it were traded in the financial market. After

all, the best correlation with the project is the project itself (Copeland and Antikarov, 2001).

Trigeorgis (1996) also argued that the assumptions underlying the DCF approach are traded

assets of comparable risk (same beta), and MAD assumptions are no stronger than those of DCF.

Contrary to Borison's understanding, Copeland and Antikarov (2005) clarified that the

MAD approach does not blindly use all subjective assumptions. Similar to the integrated

approach, MAD also uses traded market data whenever available, and uses subjective

assumptions only when market estimates are impossible. The MAD approach and the integrated

approach are considered to treat private risk in the same way, the difference remains only

technical: MAD relies on simulations to evaluate project volatility, and attempts to combine all

risks into one variable, whenever possible; while the integrated approach relies on utility

functions, and models market risks and private risks explicitly and separately. Neither is

superior to the other, and the selection of approaches depends on project characteristics on a

case-by-case basis. For this reason, the proposed RERO approaches are built on the MAD and

the integrated approaches.

Practical Real Options Model in Real Estate

Ghosh and Sirmans (1999) were among the first to address the applications of real options

to the corporate real estate practitioners, by developing a look-up table for the options value,

which is derived from an approximation of the Black-Scholes formula. They used the

correspondence in Table 3-3 between financial and real options in order to apply the Black-

Scholes formula directly to real options.

However, they did not explain whether the time value of money r is a risk-free rate or risk-

adjusted discount rate, nor how the risk of project cash flows o is determined.









Table 3-3. Correspondence between Financial and Real Options.
Variable Financial options Real options
So Stock price Present value of projects expected cash
flows

K Exercise/strike price Cost of investment

T Time to expiry Length of time the decision can be deferred

r Risk-free rate Time value of money

a Standard deviation of stock Risk of project cash flows
returns

They also developed a three-step approach to calculate the option value:

Step 1: Calculate NPVq from Equation 3-25.


NPVq = (3-25)
SK /(1 + r)

Step 2: Calculate oJT

Step 3: Read the value of the call option as a percentage of the value of the underlying

asset from the table.

For example, if the stock price S is $100, strike price K is $100, time to expiry Tis 1 year,

time value of money r is 5%, standard deviation of annual return a is 20%, then

NPV = S/[K/( + r)] = 100/[100/(1.05)] = 1.05

oT = 0.20 x 1 = 0.20

From the look-up table, C is 10.4% of the asset value, C = 0.104 x 100 = $10.40.

They did not specify how the look-up table is computed, but by comparing the Black-

Scholes formula and their three-step approach, it is not difficult to find that they did some

approximations in order to simplify the calculation.

From the Black-Scholes formula of Equation 3-13,









C Ke-rr
= N(dl) N(d2) (3-26)
So So

where
ln(S /K)+(r +a2 /2)T
oUJT
ln(S /K)+(r 02/2)T
d2 = = d, T .
UJT

K S S
K )T is an approximation of Ker and S can substitute S (r + 2 / 2)T
(1 + r) K /(1 + r)Y K

is ignored due to the low impact on the overall value. With the approximation and substituting

Equation 3-25 into Equation 3-26, we have

C 1 N[In(NPV)] (3-27)
= 1- N (3-27)
So NPV, aU

Equation 3-27 is the formula to develop the look-up table.

The Ghosh and Sirmans model falls into the subjective approach category of Borison's

classification (Borison, 2005). As discussed in the previous section, this approach uses

subjective assessment of variables without justification of its appropriateness. At a first glance,

this approach is intuitive, especially for practitioners who are comfortable with NPV but

unfamiliar with ROA. However, this direct application of the Black-Scholes model is not without

its limitations. Firstly, it is restricted to European options, where timing of execution of the

option is perfectly known in advance. Secondly, it assumes future cash flow is as deterministic

as in the traditional NPV method, and allows for only one scenario analysis. It does not allow

for stochastic and dynamic changes of the underlying variables, such as development cost and

rental rate, does not solve for optimal development timing. Lastly, while there is a trade-off

between simplicity and accuracy, the value derived from the look-up table has 10% variance









from that calculated from the Black-Scholes model, which is deemed inaccurate in many

circumstance. In summary, the model developed by Ghosh and Sirmans is a good attempt to

build the understanding of management flexibility value of corporate real estate in practice,

however, it lacks accuracy and depth of applicability in the real estate industry, which is what

this study plans to overcome.

Decision Tree Analysis

First coined by Howard (1964, in Ng and Bjornsson, 2004), decision analysis is the

discipline comprising the philosophy, theory, methodology, and practice necessary to address

important decisions. Graphical representation of decision analysis problems commonly use

influence diagrams and decision trees. DTA is a method to identify all alternative actions with

respect to the possible random events in a hierarchical tree structure. It is developed to handle

the interaction between random events and management decisions. Uncertainties are represented

through probabilities and distributions. The attitude of a decision maker to risk is represented by

utility functions.

Unlike the DCF approaches, there are no objectively correct DTA models. An appropriate

model depends on the preferences and beliefs of the decision maker and hence is subjective. A

decision analysis includes the following typical steps: first, defining the scope of the analysis;

second, setting up a decision basis, including generating alternatives, collecting information, and

estimating risk preference; third, constructing a decision tree with decision and uncertainty

nodes; and forth, analyzing sensitivity of factors that have the largest effects (Ng and Bjornsson,

2004).

Decision analytic methods are used in a wide variety of fields, including business,

environmental remediation, health care research and management, energy exploration, litigation

and dispute resolution, etc.









DTA relies on subjective assessment of probabilities and distributions. This method alone

cannot prevent arbitrage opportunity. However, the combination of ROA and DTA can

eliminate the short-coming of both, and creates a much better approach.

Summary

In this chapter we reviews modeling details of the DCF, ROA, DTA approaches, as well as

capital budgeting theory, ROA applications in real estate. Treatment of private risk differentiates

these approaches from one another. In ROA methodologies alone, there are various approaches

advocated and debated in the academic community. Due to the characteristics of real options, it

is inappropriate and inaccurate to directly apply the option pricing formula without any

modification. The correct real option methods must be able to handle private risk as well as

market risk in a consistent way. Only the MAD and the integrated approaches are considered

appropriate and are subject to further use.










CHAPTER 4
METHODOLOGY

The RERO framework consists of two approaches to value real estate acquisitions: the

combined approach and the separated approach. This chapter introduces the key elements and

steps of the RERO approaches. The next two chapters present case studies that implement the

principles introduced in this chapter.

As mentioned in the previous chapter, the Market Asset Disclaimer (MAD) and the

integrated approaches in ROA were adopted for this study.

RERO Modeling Procedures

The RERO framework adopts real options and decision analysis methodologies. It consists

of a series of processes to solve a decision tree backward. The event tree starts by laying out all

possible events and corresponding cash flows. Starting at the end of the analysis, we work

backward through the tree at each decision node to calculate the payoff of all possible actions,

using replicating portfolio or risk neutral discounting, choosing the optimal action that generates

the highest payoff at each node. Eventually the possible cash flows generated by these future

events and actions are folded back to a present value. The following 6 steps are critical in

performing the RERO analysis (Figure 4-1):

* Problem framing;
* Approach selection;
* Risk drivers identification and estimation;
* Base case modeling;
* Option modeling; and
* Sensitivity analyses.

Problem Framing

For real estate acquisition, the first task is to review the case qualitatively, and to determine

whether the asset itself is a sound investment. An investment that seems good by the numbers









may not necessarily turn out to be a good investment in the end. Location, neighborhood

development, economy growth, property visibility, accessibility, physical conditions, ownership

and occupancy history, management capability, all these are unique characteristics of real estate

that are non-quantifiable. Comprehensive local business knowledge and experience is needed to

determine whether a piece of land is worth acquiring.


Figure 4-1. Critical steps in RERO analysis.









After this critical screening, if a property is good enough to go through the hassle of

quantitative analysis, the problem is framed into a model and the story is told in a mathematical

way. The goal becomes how much it is worth. Management flexibility and strategic options, if

any, should be identified to determine which approach to use.

Approach Selection

DCF can solve most simple and conventional acquisition problems. It is only when a case

has strategic options that cannot be valued by DCF should the RERO approaches be used.

Depending on the characteristics of a project, the first step is to determine whether to use the

combined approach or the separated approach. The differences between the two approaches are

discussed in later sections.

Risk Drivers Identification and Estimation

The next step is to identify the risk drivers. Uncertainties of real estate acquisitions and

development include rental income, operating costs, capital expenditure, discount rate, cap rate,

development cost, etc. These variables flow through the model to affect the project value. Risk

drivers are those key variables that have the most profound impact on project value change.

To estimate the volatility of each risk driver, objective methods such as time series forecast

or regression analysis should be used, if historical or comparable data exists. Alternatively,

subjective methods may be used, such as subjective guesses, growth rate assumptions, expert

opinions, etc (Mun, 2002).

Base Case Modeling

The expected project value without flexibility is the base case for the subsequent option

value analysis. The base case value acts as the "twin asset" that the real option approach is based

on.









Option Modeling

From the problem framing step, some strategic options have been identified; from the

approach selection step, the combined approach or the separated approach has been selected;

from the risk driver identification and estimation approach, the key uncertainties have been

identified and their volatilities quantified. Now in the option modeling step, a Monte Carlo

simulation is run, an event tree is constructed, with managerial flexibilities incorporated in each

node, option values are calculated, optimal decisions are made at each node, and the value are

tracked from the end of the analysis back to the starting time of the analysis. This process may

be run back and forth for several times to ensure all option values are calculated correctly and the

corresponding rational decisions are made.

Sensitivity Analyses

Setting the project value with flexibility and/or option value as the dependent variables,

each risk variable can be changed, and the trend of value changes in the dependent variables can

be observed. This sensitivity analysis helps the user to see the whole picture and determine how

each risk variable should be managed. It also helps in understanding how uncertainty could have

otherwise altered decision making.

RERO Modeling Approaches

For different treatments of risk drivers, there are two types of RERO modeling approaches:

the combined approach and the separated approach. The combined approach is used for

valuation of an existing building with a historical operating track record. For uncertainties of

infill land development, the separated approach is more suitable.

MAD has two key assumptions: firstly, the present value of the underlying risky asset

without flexibility is the best estimate of the project value with flexibility. Secondly, properly

anticipated cash flows fluctuate randomly. The second theorem allows the user to combine any









number of uncertainties into a spreadsheet, and to produce an estimate of the project NPV

conditional on the set of random variables drawn from their underlying distributions by using

Monte Carlo simulation techniques (Copeland and Antikarov, 2001, p219). This is the

theoretical foundation of the combined approach.

By using the combined approach, uncertainties are assumed to be able to be resolved

continuously over time. This assumption generally holds for stabilized assets. However, many

projects in real estate, such as infill land development, have major uncertainties that do not get

resolved smoothly over time. Many rare events, e.g., permit approval, development activities in

the neighborhood, a new mall, a new subway station, can significantly change the real estate

value. For projects with any risk of such jumping effect, the actual event tree is asymmetric with

changes in value occurring when a significant part of the uncertainty is resolved. The separated

approach is used to isolate the risks with jump diffusion effect from those resolved continuously,

and to model their interaction explicitly. In other words, the separated approach also assumes

that the underlying project value without flexibility is the best estimate of the project value with

flexibility, but it does not assume that the cash flows fluctuate randomly. Rather, it separates the

risk drivers with jump effect from the others without, and models the jump effect explicitly.

The Combined Approach

The combined approach is most suitable for valuation with risks resolved continuously.

This approach can be best applied to acquisition valuation of stabilized real estate assets. The

process is to model the parameters of different uncertainties and to estimate their effect on the

volatility of the project value using Monte Carlo simulation techniques. The effects of individual

risk drivers are thus combined into the project volatility, which is used to generate a binomial

event tree. Actions of managerial flexibility are added to solve for option value.









The following variables are typical in a property acquisition model: rental rate, occupancy

rate, rentable square footage, expense recovery, operating expenses, capital expenditure, tenant

improvement, leasing commission, going-out cap rate, discount rate, etc. Among these variables,

the most influential ones are rental rate, stabilized occupancy rate, going-out cap rate, and

discount rate. Rentable square footage is usually fixed; expense recovery and operating expenses

vary but in a controllable small range related to the rental rate change; capital expenditure, tenant

improvement, and leasing commission are tricky in reality, but could be assumed to be fixed on

an annual basis for a high-end office building.

Rental rate and stabilized occupancy rate will be used as the two major variables in the

case analyses. Rental rate is set by the market, and directly impacts the property value. For

value-added type of investors, who intend to upgrade amenities and enhance occupancy, the

stabilized occupancy rate is an important factor for revenue estimation. The discount rate,

however, is subjective to each investor. In finance theory, the discount rate should reflect the

level of risk of a project. In practice, however, for an individual investor, the discount rate is

usually his weighted average cost of capital. Risk is mainly adjusted through the Cap rate rather

than discount rate (Wheaton et al., 2001). The discount rate can therefore be regarded as fixed.

The change of rental rate depends on many factors, such as macro economics, employment

growth, market occupancy rate, new construction pipeline, net absorption rate, etc. The change

of rental rate is assumed to follow the multiplicative stochastic process. Historical data of rental

rates will be examined in the next chapter.

Another factor that affects rental revenue is stabilized occupancy rate. For a building that

is not fully leased, there might be upside potential to lease up the vacant space, depending on

market demand. In a market with strong job growth, demand for office space is also strong. It is









relatively easy to lease up the vacant space. Assuming that vacant space can be leased up, the

incremental Net Operating Income (NOI) is substantial compared to the incremental revenue,

since the incremental operating expense is minimal. In other words, whether a building is 50%

occupied or 100% occupied, a majority of the operating expenses is fixed, the 50% lease-up can

potentially triple the NOI. Note that a multi-tenant office building is seldom fully occupied,

therefore stabilized occupancy rate usually is close to but never reaches 100%. A general

vacancy factor is deducted from the fully leased revenue. The change of occupancy rate is

assumed to follow the additive stochastic process. This process is similar to the multiplicative

stochastic process with the only difference being that the up and down movements in the lattice

are assumed to be additive rather than multiplicative (Copeland and Antikarov, 2001, p123).

The Separated Approach

The separated approach is more complicated than the combined approach and should be

used only when needed. It is best used for projects with major private risks that do not get

resolved continuously. The infill land valuation is an example in this study that can be better

modeled using the separated approach.

The following variables are typical in an infill land development model: rental rate,

development cost, development timing, development scale, operating expenses, expense

recovery, cap rate, discount rate, etc. Among these variables, the most uncertain ones are rental

rate, development cost, and development timing. Development scale is regarded as a major

economic factor, but not a major uncertainty in the context of our case study, due to approved

permit of the development scale. Since the goal of most commercial developments is to

maximize the investor's wealth, developments are usually built to the largest size allowed by

zoning and legal restrictions. Unless the development involves zoning changes, development

scale is predictable, and thus is not modeled as a risk driver. As discussed in the combined









approach, operating expenses and expense recovery are in a controllable range, and the discount

rate for a particular project is fixed to a specific investor. Cap rate is assumed to be fixed in the

integrated approach for simplicity.

Development costs include hard costs and soft costs, and can be subdivided into costs

associated with land, structure, tenant improvement, leasing commission, legal, finance, taxes,

insurance, marketing, etc. Hard costs are construction costs that include demolition, foundation,

structure, mechanical and engineering systems, general conditions, bonds and insurance of

construction, design and management fees, tenant improvement, etc. Soft costs are intangible

costs that go to legal, survey, marketing, financing, taxes, leasing commissions, etc. Since every

project is unique, development costs represent the major private risk that does not correlate with

the traded financial market, and thus cannot be replicated by the so called traded twin asset.

Rental rate is discussed in the combined approach during normal circumstance. What

needs to be pointed out in addition is the jump diffusion process. A jump diffusion process is

defined as a type of stochastic process that has large discrete movements (jumps, or shocks),

rather than small continuous movements (Amin, 1993). As Wheaton et al. (2001) noted: "In

reaction to positive shocks, returns initially increase, but eventually diminish with the arrival of

new supply. Similarly, negative shocks lead to building conversions, loss of stock and an

eventual recovery of returns." One of the distinguishing characteristics of real estate, compared

to traded securities, is its inelasticity, or slow reaction to shocks. The jump diffusion can be

ignored in the acquisition of a nearly fully occupied property, since rental rates cannot be

changed until lease expirations, which could be years from the emergence of the shock. But

jump diffusion could be a major uncertainty in development, since all rental square footage is

newly available. Developers can ask for higher rental rates in markets with rising demand.









Development timing is also important. Development timing is different from development

duration. Given the size of a development project, the duration of construction is usually fixed,

but when to start the project could have profound impact on the value, given the real estate cycle.

One of the major disadvantages of DCF valuation is its inability to determine the optimal

development timing. The RERO framework, on the other hand, can analyze all possible

scenarios and indicate the best action at each point in time. It is extremely valuable for the

investor to hold the option of when to start the development.

Another important factor is development scale, or the size of development. In the case

study, the permit for around 1 million square feet of mix-used development has been approved.

Consequently no assumption needs to be made for changing development scale. But in many

cases, when rezoning is required in order to develop more density, development scale is an

important factor and should be modeled in the decision tree as whether or not the rezoning

requirement will be approved.

RERO Modeling Techniques

Rational for Using Binomial Lattices

Copeland and Antikarov (2001, p222) made the assumption that change in asset prices

follow Geometric Brownian Motion, based on Samuelson's proof that "properly anticipated

prices fluctuate randomly." In other words, change in asset value follows a random walk even if

the risk drivers do not. This means multiple risk drivers, so long as they evolve continuously,

can be combined and reduced to a single uncertainty, namely the expected underlying asset value

change over time. This provides the rationale for using a binomial lattice to calculate real option

value.









Monte Carlo Simulation

Monte Carlo simulation randomly generates values for uncertain variables to simulate a

real-life model. In the combined approach, Monte Carlo simulation can be used as an

intermediate step to estimate volatility of the project, the value of which is depended on multiple

risk drivers. For this study Risk Simulator is used. Other simulation software available are

Crystal Ball and @ Risk.

The steps followed in the combined approach are to:

1. Identify risk drivers;

2. Estimate the probability distribution of each risk driver using historical data or subjective
estimates;

3. Build present value model;

4. Define input variables with the possible range of value and a probability distribution in an
MS Excel spreadsheet equipped with Monte Carlo simulation tools;

5. Define correlations among the risk variables;

6. Define forecast variables., e.g., rate of return for the project;

7. Run the simulation a thousand times;

8. Read the outputs of the forecast variables and their volatility distributions; and

9. Use the outputs as input variables to build the event tree.


Replicating Portfolio

In most cases the project cash flows are discounted at the risk-adjusted rate to get to the

project NPV. The risk-adjusted discount rate is higher than the risk-free discount rate, since it is

adjusted up to accommodate higher risk of the project than that of the treasury bonds. In order to

apply a binomial lattice that is developed based on risk-neutral probabilities and risk-free

discount rates, risk-adjusted probabilities should be used together with risk-adjusted discount

rates. To calculate the value of the option, the replicating portfolio method is used, but not the









discounting method, since the risk characteristics of the project change over time depending on

the decision made, and consequently the risk-adjusted discount rates also change over time

(Copeland and Antikarov, 2001). The risk-adjusted up movement factor u and down movement

factor d are the same as those in the risk-neutral binomial lattice (Equations 4-1 and 4-2).

u = e- (4-1)


d = (4-2)


where a is the project volatility, and t is the time in years of each step in the binomial tree.

The replicating portfolio formula can be derived by the same method as the option price is

derived from binomial lattice. Construct a portfolio that consists of n shares of stock S and b

amount of value in risk-free bonds. After a period of time t, the value of the portfolio can go up

or down. Let the value be equal to the option value at that time.

nuS +bert = C, (4-3)

ndS +bert = Cd (4-4)

From Equations 4-3 and 4-4, derive Equations 4-5 and 4-6.

C, -C,
n = d (4-5)
S(u d)


b = ud d (4-6)
er (u d)

Consequently, the value of the option is calculated by Equation 4-7.

C nSb Cd uCd dC
C = nS +b = C d (4-7)
u-d e' (u d)









Binomial Lattice with Dividend

Chapter 3 covers binomial lattice without dividend. In real estate, the net cash flows from

operation are collected from the property and distributed to the investor, which is similar to the

dividend distribution of a stock. The stock dividend is usually assumed to be distributed at a

constant yield, since corporations plan and manage the distribution process. The net cash flows

at the property level, on the other hand, are the actually amounts collected from the property, and

hence vary from period to period. Denote 6, to the dividend yield at Step i for 0 < i < n, and

using all other notions in Chapter 3, the asset value changes are depicted in Figure 4-2 for a two-

period lattice.


O So*u*u
SOououo(1-2)
so So u-(]461)
So*u
Soouod -)

So So (- d (-)2)

Soo-d(J-61)SO
Sood-d

SoS*d*(1 -62)
So* d* d* (1-32)


Figure 4-2. Two-step binomial lattice with different dividend yields.


At Step 2, the three possible values are calculated using Equations 4-8, 4-9, and 4-10.

C, = Max[Suu(1- ,2) K,0] (4-8)

Cud = Max[Sud(1 ,) K,O] (4-9)

Cdd = Max[Sdd(1 ,2) K,0] (4-10)

To calculate the option value at Step 1, the dividend yield 62 needs to be added back to the

option value, before discounting at the risk-free rate, which is shown in Equations 4-11 and 4-12.









SpC. + (1- p)C. (4-11)
(1- 32 )e

pCud + (1 p)Cdd
Cd = (4-12)
(1 2 )ert

The same method is followed to calculate the option value at Step 0, as shown in Equation

4-13.

S= pC + (1- p)Cd (4-13)
C = (4-13)
(1- 31)er"

In general, for a binomial lattice with n steps, the ith step (0 < i < n) call option value with

dividend is calculated by Equation 4-14.

C, = pC,+,u + (1- p)C,+,d (4-14)
C( e (4-14)
(1- +, z)e"

Binomial Lattice with Jump Process

Chapter 3 covers binomial lattice during normal circumstance that the underlying asset

strictly follows the GBM movement. However, in reality, the asset movement could be a jump.

For example, the zoning change from agricultural land to urban land, the establishment of new

amenities in the neighborhood, the construction of new freeway exits, all can have a sudden and

profound influence on the estate value in an area. These events seldom happen. But once occur,

they will completely change the project payoff pattern. Hence, these jump diffusion effects

cannot be priced using the binomial lattice developed by Cox et al. (1979). Amin (1993)

developed a discrete time model to value options when the underlying process follows a jump

diffusion process. Unlike the financial jump diffusion process that reverses back to normal value

quickly, a jump diffusion process in real estate usually is irreversible, at lease not in a short

period of time. That is, if a large scale development occurs that drives up the rental rate in a









neighborhood, that rental rate is likely to remain at the same level for several years until a new

event happens. In this study the Amin model was modified to accommodate this change. Based

on the assumption that the jump risk is diversifiable, a one-period call option is priced in the

Equation 4-15 (Figure 4-3).



yS Cy

x/ x

-) uS 1-X Cu
S C
dS CC
(1-X)(1-p) dS (1-X)(1-p) Cd


Figure 4-3. Binomial lattice with jump process.

C =e t{AC, +(1- )[pC + (1- p)Cd]} (4-15)

where
A is the probability of the jump event according to the Poisson distribution, and defined by
e "n
x! (where n is the expected number of successes, and x is the number of
successes per unit);
y is the capital gain return on the underlying asset when the jump event occurs;
Cy is the option value at the time the jump event occurs;
p is the adjusted probability of an up movement, and defined by
e"' -A d
p-
P 1- A
u-d

Investment with Private Uncertainty

As discussed in Chapter 3, many investments include private and market uncertainties.

Market uncertainty can be replicated with market participation and therefore diversifiable.

Private uncertainty cannot. For example, the development project value depends on both the

market uncertainty of rental rate and the private uncertainty of development cost.









The principle of pricing in such investment, if no correlation between the market risk and

private risk exists, is to use risk-neutral probability for the market uncertainty and actual

probability for the private uncertainty, both discounted at risk-free rate (Luenberger, 1998;

Copeland and Antikarov, 2001; Smith and McCardle, 1999). Although formulas for pricing

uncertainties with correlation exist, the no correlation assumption usually holds.

To implement this principle, there are two alternative methods: the quadranomial lattice

and the decision analysis method.

The first method is to implement a quadranomial lattice. Figure 4-3 shows a one-step

quadranomial lattice. If an option C is contingent upon the value of two underlying assets S1 and

S2, assuming no correlation between S1 and S2, then the value of C is priced as Equation 4-16.


C= e (p,,Cl +p12C12 +p21C21 +p22C22) (4-16)

where

P11 = PP2
P12 = P(1- p2)
P21 = (1- p )p2
P22 = (1-p1)(1- p2)

p, is the risk-neutral probability if S, is market uncertainty, or the actual probability if S, is

private uncertainty. For each uncertainty, it can have more than two bifurcations. For example,

if S is a market risk with jump diffusion (three bifurcations), and S2 is a private risk with three

bifurcations, then C could be priced with nine nodes with corresponding probabilities and

discount at the risk-free rate. In theory, an option can be contingent upon more than two

separated assets, but in practice, the complexity of implementation will soon become

intimidating. This study thus focuses on a few key risk drivers and combine them into two kinds

of separated uncertainties: market uncertainty and private uncertainty.












Pi
Si p
dSS


U2S2


d2S2


Figure 4-4. Quadranomial lattice.


Another way is to implement decision analysis methodology (Smith and Nau, 1995). For

example, if the two underlying risks for a development are cost and rental rate, it can be modeled

as shown in Figure 4-5. The expected value at each node is calculated and discounted at the risk-

free rate. Equation 4-17 shows how the expected value E(PVo) can be calculated.


E(PVo)= ip, [E(PV)]
J-1

where
j is a scenario labeled from 1 to m, 1 < j < m;
E(PVj) is the expected present value of scenario for all the years i, 1 < i < n.


Cost


(4-17)


Rent


Figure 4-5. Decision analysis.










Summary

This chapter discusses the 6-steps RERO framework: problem framing; approach

selection; risk drivers identification and estimation; base case modeling; option modeling; and

sensitivity analysis. Two modeling approaches are introduced to deal with different risk

characteristics: the combined approach for projects with risk drivers that get resolved

continuously, and the separated approach for project either with risk drivers that follow the jump

diffusion process or involving private risk. The modeling techniques that will be applied in the

case studies are also introduced, including the rationale of using the binomial lattice, Monte

Carlo simulation, replicating portfolio, binomial lattice with jump diffusion process, and

investment with private risk.










CHAPTER 5
THE COMBINED APPROACH

Chapter 5 and 6 present case studies that implement the principles of RERO described in

Chapter 4. The two chapters describe the valuation of two parts of one case: valuation of the

building using the combined approach, and valuation of the infill land using the separated

approach. Together, these two case studies demonstrate how the RERO framework can be

applied to different scenarios in the real estate acquisition and development analysis.

Case Description

The case identified is 211 Perimeter in Atlanta. This property is located in the Central

Perimeter submarket of Atlanta. Adjacent to the Perimeter Mall and a subway station, 211

Perimeter is located in one of the largest suburban office markets in Atlanta. The property has an

office building of 226,000sf rentable area, and 13 acres total land. The current owner has got

approvals for over 1 million square feet of mixed-use development on the 9.5 acres developable

site, and has built a 6-storey parking garage with the intention to get as much value as the

regulations allow from development of the excessive land (Figure 5-1). Furthermore, the

property is strategically located within a larger neighborhood redevelopment planning of 38

acres and nearly 3 million square feet mixed-use development, although the timing of the

neighborhood development is unknown.

The land obviously has some value, but development might not break ground immediately.

The real estate market in Atlanta is a commodity market, which means developments are spread

out with few restrictions. As 2005, the Central Perimeter office submarket was over built, with

several old office buildings torn down for new residential developments. It would be interesting

to know how current bidders should price the land in addition to the building.






























.. .......



Figure 5-1. 211 Perimeter site plan.


Building Valuation

In this chapter only the building is evaluated using the combined approach with Monte

Carlo simulation. The land valuation will be investigated in the next chapter using the separated

approach. The following are the 6 steps used to perform the RERO valuation:

* Problem framing;
* Approach selection;
* Base case modeling;
* Risk drivers identification and estimation;
* Option modeling; and
* Sensitivity analyses.

Problem Framing

The property is located in a premium office market, with superior quality and tenant mix.

Its strategic location within a larger neighborhood redevelopment plan makes real estate price









appreciation in the future extremely promising, although the timing is still unknown. In short,

the 211 Perimeter project is a sound investment that deserves further valuation.

After the preliminary qualitative analysis, this project appears acceptable for quantitative

analyses. The 11-floor office building consists of 226,000sf rentable area. Current occupancy

rate is 85%, with 15% upside potential to lease up the space. Major tenants collectively occupy

68% of the rentable square footage, which is deemed to be a sign of solid cash flow over the

future.

One of the major decisions to make is about the chiller system upgrade. The existing

chillers are still in working condition but are at their maximum capacity, and consume far more

energy than new ones. Preliminary research shows that replacement of the existing chillers will

cost $950,000, and will increase the net cash flow by 5% per year. If both rental rates and

occupancy rates are good, replacement of the chillers can justify its cost, and add value to the

property. Otherwise, the capital improvement may not break even, and keeping the existing

chillers is more economical.

Approach Selection

The combined approach is selected since both the rental rate and occupancy rate are market

driven, and can be combined into the Monte Carlo simulation.

Base case NPV calculation

The following variables are typical in the NPV valuation model: rental rate, occupancy

rate, rentable square footage, expense recovery, operating expenses, capital expenditure, tenant

improvement, leasing commission, going-out cap rate, discount rate. Table 5-1 shows the

assumptions used in the base case NPV calculation. Figure 5-2 shows the cash flow output from

Argus, a software package for real estate valuation.









Table 5-1. Major assumptions for Argus.
Average rental rate $17/sf Capital expenditure $75,000

Occupancy rate 85% Tenant improvement $18/sf

Rentable sf 225,924 sf Leasing commission 6.0%

Expense recovery $0 Going-out Cap rate 7.0%

Operation expenses $7.75/sf Discount rate 9.0%


From the Argus cash flow output, modifications are made so that the model can be used for

Monte Carlo simulation using Risk Simulator. Rental rate and occupancy rate have been

identified as the two major risk variables that need to be simulated. Annual average rental rate

and annual average occupancy rate are calculated from the Argus output, which are used to

derive annual net cash flow. Purchase price is assumed to be fixed, so that we can compare the

project value with and without flexibility. Operating expenses and expense recoveries are

controllable variables. Capital items, such as capital expenditure, tenant improvement, and

leasing commission, are also controllable. Cap rate and discount rate are also assumed to be

fixed.

Ignoring the option of chiller replacement, the project NPV has two components: (1) Total

acquisition cost, including purchase price and closing cost; (2) Present value of annual net cash

flow from operation and present value of net residual value (gross sale proceeds net out selling

cost). These two parts are also called cost and benefit. The option of chiller replacement will be

modeled later.

In real estate fundamental analysis, property value consists of residual value and net cash

flow from operation. The residual value, or value when the project is sold, is the major part. It is

determined by Net Operating Income (NOI) and Capitalization rate (Cap rate). NOI is the gross










Schedule Of Prospective Cash Flow
In Inflated Dollars for the Fiscal Year Beginning 10/1/2005


Year 1


Year 2


Year 3


For the Years Ending
Potential Gross Revenue
Base Rental Revenue
Absorption & Turnover Vacancy
Base Rent Abatements
Scheduled Base Rental Revenue
Expense Reimbursement Revenue
Miscellaneous
Conference Room
Antenna Revenue
Total Potential Gross Revenue
General Vacancy
Effective Gross Revenue
Operating Expenses
Cleaning
Repairs and Maint.
Utilities
Grounds
Security
Parking/Fitness Center
Management
Administrative
RE Taxes for Building
Insurance
Non-Recoverable
Total Operating Expenses
Net Operating Income
Leasing & Capital Costs
Tenant Improvements
Leasing Commissions
Reserves
8F Corridor & Common Area
Total Leasing & Capital Costs
Cash Flow Before Debt Service


Sep-2006 Sep-2007 Sep-2008 Sep-2009


$3,865,560 $3,933,779 $4,055,362 $4,187,044


(536,603) (120,821)


(557,764)
2,771,193

2,400
6,000
44,874
2,824,467


(335,242)
3,477,716

2,472
6,180
46,220
3,532,588


2,824,467 3,532,588


181,060


(6,223) (17,347)


(193,496)
3,855,643
26,417
2,546
6,365
47,607
3,938,578
(137,519)
3,801,059


4,169,697
52,555
2,623
6,556
49,035
4,280,466
(149,114)
4,131,352


184,366 216,739 222,801


243,591 250,899 258,426 266,178


318,091 326,111


42,095
128,504
8,182
116,706
193,246


43,358


355,126 365,464


44,659


45,998


132,359 136,330 140,420


8,427
106,141


8,680
133,037


8,941
144,597


199,043 205,015 211,165


418,558 431,115 444,048 457,370


62,129
45,185
1,757,347
1,067,120


64,277
46,747
1,792,843
1,739,745


119,610 1,818,406
33,160 396,647


33,889
75,000
261,659
805,461


35,060


2,250,113
(510,368)


66,233
48,169
1,916,462
1,884,597


11,118
9,094
36,127


56,339
1,828,258


68,197
49,598
1,980,729
2,150,623


Figure 5-2. Base case NPV calculation.


Year 4









income from all sources (rental, storage, tenant reimbursement, antenna lease, etc) minus all

operating expenses (common area maintenance, management fee, security, landscaping,

insurance, real estate taxes, etc). For this reason, NOI is also regarded as the net income of the

property. This is different from what the investor actually gets, which is called the Net Cash

Flow. Net cash flow is calculated by taking out capital items from NOI. These capital items,

such as capital improvement, tenant improvement, and leasing commission, are one-time-off in

nature. All these analyses are on an unleveraged before-tax basis, meaning debt financing and

taxation are not considered.

Figure 5-3 shows the modified Argus cash flow output for NPV calculation. For

simulation simplicity, modifications of the Argus output are made so that the net operating

income and net cash flow are calculated by Equation 5-1 and Equation 5-2.

NOI Q SF Occ+ER OE (5-1)

NCF = NOI- TI LC CapX (5-2)
where
NOI is the net operating income;
Q is the average rental rate;
SF is the rentable square footage;
Occ is the actual occupancy rate;
ER is the expense recovery and other income;
OE is the operating expenses;
NCF is the net cash flow;
TI is the tenant improvement;
LC is the leasing commission;
CapXis the capital expenditure.

The residual value at sales is calculated by Equation 5-3.


V = NOI SC (5-3)
Cap

where
Vn is the net residual value at year n, and n is the holding period of the project;
Cap is the going-out Cap rate;
SC is the selling cost.









The total benefit of the project PV,, which includes the present value of net cash flow NCF,

and residual value Vn, can be calculated by Equation 5-4.

NCF, V
PV = (- + 1 (5-4)
S(1+ k)'- (1+ k)"

where
PVj is the project present value at Yearj, and 0 < j < n, where n is the holding period.
When = 0, it is the present value at time 0, or PVo.
NCF, is the net cash flow at Year i,
k is the discount rate of the project.

The NPV of the project is the present value of total cost PPo and total benefit PVo at time

0, as calculated by Equation 5-5.

NPVo = PVo -PPo (5-5)

Risk Drivers Modeling

Among the variables, those that have the most profound impact on the project NPV

changes are rental rate and stabilized occupancy rate, both are market driven. Rental rates differ

lease-by-lease, but for simplicity we take the average rental rate over the entire building.

Stabilized occupancy rate is subjective based on management's estimates In this case the 15%

vacant space is assumed to be leased up within 2 years, after which a general vacancy factor of

3% is taken out.

Figure 5-4 shows the historical rental rates of the Central Perimeter Class A office market

and the subject property in 15 years. The quarterly data is from CoStar. The change of rental

rate is assumed to follow GBM. This means the logarithm of the rental rate Qi is normally

distributed; and the return (also called the change of rental rate) qi follows a random walk.

Using Equation 5-6, a rental return analysis was performed and the scatter chart was plotted as

shown in Figure 5-5, with market return variables on X-axis and corresponding subject property

return variables on Y-axis. It shows negative correlation (-0.1445), which indicates that the rental










Rental Square Footage
Base Rent psf
Rental Adjustment Multiple
Return Random Variable
Occupancy Rate
Occupancy Adjustment Variable
Occupancy Random Variable



For the Years Ending
Potential Gross Revenue
Base Rental Revenue
Vacancy
Abatements
Scheduled Base Rental Revenue
Other Reimbursement Revenue
Total Potential Gross Revenue
General Vacancy
Effective Gross Revenue
Operating Expenses
Total Operating Expenses
Net Operating Income
Leasing & Capital Costs
Total Leasing & Capital Costs
Cash Flow Before Debt Service


Net Sales Proceeds (Cap at 7%, 2% selling cost)


Total Net Cash Flow

Discount Rate
PVo of Cash Flow
PVI of Cash Flow
PVo of Cash Flow Static


805,359



738,862
805,359
738,862


(510,762) 31,927,568


(429,898)
(468,589)


24,653,941
26,872,795


(429,898) 24,653,941


Forecasting Variable

Purchase and Closing Cost (3%)

NPV of Project


Figure 5-3. Spreadsheet model for Monte Carlo simulation.


225,924


$17.11
16.9121
1.0117
85.68%
0 8542
0 0026

Year 1
Sep-2006


Year 0
Sep-2005


$17.41
17.2087
1.0117
89.15%
0 8889
0 0026

Year 2
Sep-2007


$3,933,337
(426,767)
(29,248)
3,477,322
54,872
3,532,194


3,532,194


1,792,843
1,739,351


2,250,113
(510,762)


$18.53
18.3157
1.0117
99.72%
0 9946
0 0026

Year 4
Sep-2009


$4,186,372
(11,722)
(5,623)
4,169,027
110,769
4,279,796
(149,114)
4,130,682


1,980,729
2,149,953


$17.95
17.7424
1.0117
99.91%
0 9965
0 0026

Year 3
Sep-2008


$4,055,336
(3,650)
(196,069)
3,855,617
82,935
3,938,552
(137,519)
3,801,033


1,916,462
1,884,571


56,339
1,828,232


30,099,336


$3,865,560
(553,548)
(540,920)
2,771,091
53,274
2,824,365


2,824,365


1,757,347
1,067,018


261,659
805,359


1.0900

(24,205,000)

757,904









rate change of the subject property, 211 Perimeter, has very weak, if not negligible, correlation


with the market.


$26.00

$23.00

$20.00

$17.00

$14.00


/ .


\1 -/ r* ,


1990 1992 1994 1996 1998 2000 2002


2004


3Q 3Q 3Q 3Q 3Q 3Q 3Q 3Q

Market Subject Property


Figure 5-4. Historical market and subject property rental rates.





y6830.00%--

20.00%
y = -0.3276x 8E-05


Subject Property


R = 0.0209


0.0 *

YA-


-7.00% -5.00% -3.00% -1.00% 1.00% 3.00%


5.00% 7.00%


-10.00% *
*

-20.00%

Market


Figure 5-5. Returns correlation between market and subject property.










q, = ln( ) (5-6)



The seemingly controversial result of weak or no correlation between the rental return of

the subject property and that of the market can be explained as due to two reasons:

(1) Data reliability. CoStar started as a service portal mainly for commercial brokerage

firms. In its early years data is derived from broker volunteer contributions. This would

inevitably have led to data accuracy and timeliness issues. For example, from the first quarter of

1998 to the third quarter of 1999, the rental rates data of the subject property are missing, which

are assumed to be $18.90/sf by the author for the purpose of data completeness.

(2) The inelastic nature of real estate market. Compared to the financial market, the real

estate market is lumpy and the performance is somewhat predictable, at least for the near term.

Commercial lease terms are usually 3 to 7 years for office leases, 5 to 20 years for anchor retail

leases, and even 100 years for ground leases. In most cases, the rental payment is set and

documented in the contract throughout the terms. Market rental rate changes can only slowly

affect individual property ask rates, since the landlord can change rental rate only when a lease

negotiation happens, usually before the lease expires. However, market rates can directly affect

the rates for new construction, since all spaces are newly available.

Nevertheless, the data set from CoStar is the most comprehensive and consistent data

available in the real estate industry. The characteristics of real estate require a different method

than the one used to estimate stock volatility in the financial industry. Thus the correlation

between the market and the subject property was ignored on purpose, and only the subject

property rental rate data was used to estimate its volatility for acquisition.









Risk Simulator is used to influence the distribution of the population from the available

sample data. A lognormal distribution was chosen since the rental rates will never be negative.

Due to the limitation of available data, the statistical significance of this distribution is low (P-

Value of 0.1625). Nevertheless, this is the most reasonable fit for the data. By fitting the sample

data into a lognormal distribution (Figure 5-6), the following variables are determined: / is

0.0056 and a is 0.0548. Annualizing the quarterly o, and using Equation 5-7 and 5-8, mean of

18.0189 and standard deviation of 2.0218 for the return distribution are derived. To get the

annual auto-correlation of the rental return, the quarterly return data is annualized by taking the

average of the 4 quarters of each year, which turns out to be -0.0916. This auto-correlation of

the samples is assumed to be the same as that of the population.

X= e + 2 /2) (5-7)


SD = e2(p ) -e 2 (5-8)

Statistical Summary
Normal Distribution
eoetical vs. Empirical Disribution Mu = 0.0056
1 ~Sigma = 0.0548


Kolmogorov-Smirnov Test Statistic
Test Statistic: 0.3406
i:ii I P-Value: 0.0000
Actual Theoretical
IC0.0 Mean 0.0007 0.0056
Stdev 0.0548 0.0548
I -I C0.I- Skewness 0.7670 0.0000
Kurtosis 11.3812 0.0000


Figure 5-6. Normal distribution fit for historical returns on rental.


CoStar also provides historical occupancy rates data for the market and subject property

(Figure 5-7). Occupancy rate is assumed to follow the additive stochastic process. This means









the change of occupancy rate o, between any two quarters is simply the difference of the

occupancy rate 0, and O,_1 (Equation 5-9). From the scatter plot of the change of occupancy data

shown in Figure 5-8, it can be concluded that the occupancy rate of the property also has very

weak correlation with the market (0.1263). Thus, this correlation is also ignored on purpose and

only the historical occupancy rates of the subject property will be relied on for forecasting.

o, = 0, ,01 (5-9)


Using RiskSimulator, the population u and a, the respective population mean and

standard deviation of the normal distribution, are determined to be 0.0039 and 0.0471

respectively (Figure 5-9). Due to the limitation of available data, the statistical significance of

this distribution is low (P-Value of 0.00004). However, this low P-value might be a limitation of

the software itself, i.e., its estimation of data in a small range is inaccurate. Nevertheless, this is

the most reasonable fit for the data. To preserve accuracy, it was decided to keep the sample

mean as the population mean (0.0026), and annualize the sample standard deviation as the


100.0%

80.0% -----------

60.0%

40.0% -
40.0% -----------------------------------------------
20.0%
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
4Q 4Q 4Q 4Q 4Q 4Q 4Q 4Q 4Q 4Q

Market Subject Property


Figure 5-7. Historical market and subject property occupancy rates.












20.0%


1-0.0%


y = 0.4502x + 0.0018
R2 = 0.016


P -10.0% -5.0% 0.( 5.0% 10.0%


| 10.0%



-20.0%-----------------

-------------- -2-a0.0% ------------------------------

-30. 0%

Market



Figure 5-8. Occupancy changes correlation between the local real estate market and the subject
property.


Figure 5-9. Normal distribution fit for historical occupancy rates.


vs. Empirical Distrilbution


-Statistical Summary


Normal Distribution
Mu= 0.0039
Sigma = 0.0471


Kolmogorov-Smirnov Test Statistic
Test Statistic: 0.2799
P-Value: 0.0000

Actual Theoretical
Mean 0.0026 0.0039
Stdev 0.0705 0.0471
Skewness -1.2849 0.0000
Kurtosis 15.0876 0.0000


==NMI










population volatility (0.1409). To calculate the auto correlation, the change of occupancy rate

data is annualized by taking the average of the 4 quarters of each year, which turns out to be

0.1185.

The correlation between rental return and change of occupancy rate is similar to the auto-

correlation of the two, which comes out to be -0.1575.

For Monte Carlo simulation, the project volatility is the volatility of percentage changes in

the value of the project from one time period to the next, defined by the forecasting variable z

(Equation 5-10). This value is computed using the simulated present value of the project in Year

1 divided by the expected present value of the project in Year 0. In other words, PV1 is dynamic,

while PVo is static.


z = (5-10)
PVo

Option Modeling

In the previous step the rental rate, occupancy rate, their respective volatilities, auto-

correlations, and the correlation between the two have been identified and quantified. With these

variables, rental rates and occupancy rates for each year can be set as risk variables for the

project value simulation. A total of 8 risk variables are defined and highlighted as shown in

Figures 5-43, 5-10, and Table 5-2. The cash flows go through Equations 5-1 to 5-5 to generate

annual net cash flow for the first 3 years. PVo and PVi are calculated based on the annual net

cash flow. The forecasting variable z is defined in Equation 5-10. Setting PVo to be static and

PV1 to be dynamic, and running the simulation for a 1000 times, the simulation result ofz is

obtained as shown in Figure 5-11. Table 5-3 also shows the statistical summary of z, with a

mean of 1.079 and standard a deviation of 0.3283.










Name
Enabled
Cell
Dynamic Simulation

Range
Minimum
Maximum

Distribudin
Mean
Standard Deviation


Yr 4 Rertrn
Yes
$F$7
No



-infinity
+Infinity

Lognormal
0.0056
0.10968


Name
Enabled
Cell
Dynamic Simulation

Range
Minimum
Maximum

Disribution
Mean
Standard Deviation


Figure 5-10. Snap shot of Monte Carlo simulation assumptions.


Figure 5-11. Monte Carlo Simulation Result of Forecasting Variable z.

The statistical distribution fit for Variable z is then performed. By plotting the 1000 z

values from the simulation output, as shown in Figure 5-12, it is determined that they are

normally distributed with P-Value of 0.8737. This result fits quite well with the theory


Yr 1 Occ
Yes
$C$O1
No



-Infinity
+ infinity

Normal
0.0026
0. 409


4.00

3.S0



3.00

F, R7 '7 F' 17 q7 1 11 1 'R


- .00

-.50



1O. ''

5'0 ; -1 31 -ni 1 1i 17 3


SI,',. .. -- 1 ,3,',

I I I


IIrI I II
S" '
...., -,,


______7_










Table 5-2. Correlation between random variables.
Yr 1 Yr 2 Yr 3 Yr 4 Yr 1 Yr 2 Yr 3 Yr 4
return return return return Occ Occ Occ Occ
Yr 1 return 1.00
Yr 2 return -0.09 1.00
Yr 3 return 0.00 -0.09 1.00
Yr 4 return 0.00 0.00 -0.09 1.00
Yr 1 occ -0.16 0.00 0.00 0.00 1.00
Yr 20cc 0.00 -0.16 0.00 0.00 0.12 1.00
Yr 3 Occ 0.00 0.00 -0.16 0.00 0.00 0.12 1.00
Yr4 Occ 0.00 0.00 0.00 -0.16 0.00 0.00 0.12 1.00

Table 5-3. Statistical summary of Monte Carlo simulation result.
Description Value
Number of data points 1000
Mean 1.0797
Median 1.0569
Standard deviation 0.3283
Variance 0.1078
Average deviation 0.2561
Maximum 2.4431
Minimum 0.0977
Range 2.3454
Skewness 0.3787
Kurtosis 0.7041
25% percentile 0.8722
75% percentile 1.2831
Error precision at 95% 0.0188

Statistical Summary
Normal Distribution
Teorellcal vs. Elliirial Disirlliilon Mu = 1.0738
Sigma = 0.3246

/ \ Kolmogorov-Smirnov Test Statistic
-Test Statistic: 0.0275
P-Value: 0.4326
S |\ Actual Theoretical
Mean 1.0797 1 0738
Stdev 0.3283 0 3246
'Skewness 0.3787 0.0000
Kurtosis 0.7041 0.0000


Figure 5-12. Normal distribution fit of forecasting variable z.









developed by Samuelson and adopted by Copeland and Antikarov (2001), as discussed in

Chapter 4, that changes in correctly expected asset prices follow Geometric Brownian Motion.


From the Monte Carlo simulation, the mean u and the volatility a of forecasting variable z

are calculated as 1.0797 and 0.3283 respectively. This means the expected average project

return is 7.97% (1.0797 minus 1), and the volatility of the project is 30.4% (0.3283 divided by

1.0797).

Using the assumptions in Table 5-4, with 30.4% volatility, and $24,963,000 PV derived

from the base case analysis, a value tree is constructed as shown in Figure 5-13. Net cash flows

are modeled as dynamic dividend yield times PV in the base case (Refer to Chapter 4 for details

of binomial lattice with dividend). For example, in Year 1, the PV can go up to $34,664,000

with an up factor of 1.3886, the post dividend cash flow is therefore $33,638,000 (after taking

out 2.96% yield from the $34,664,000 before dividend cash flow).


Table 5-4. Event tree assumptions (Dollars in $1,00(

Assumptions
PV of asset value $24,963
Implementation cost $24,205
Maturity (years) 3.00
Risk-free discount rate (%) 5.00%
Volatility (%) 32.83%
Lattice steps 3
Option type Call

NCF as percentage of PV
Year 1
NCFi $805
PVi $27,210
Percentage 2.96%


Intermediate computations
Stepping time (dt)
Up step size (up)
Down step size (down)








2
($511)
$28,781
-1.78%


1.0000
1.3886
0.7201


3
$1,828
$31,928
5.73%











46,7166,014

34,664 7,50 62,234


24,963 33,638
24,224 34,235

17,977 32,275

17,445 24,655

17,755
12,563 16,738
16,738
12,786


9,208

8,681


Figure 5-13. Event tree present value without flexibility (Number in $1,000).

With the event tree of PV without flexibility, the chiller replacement option can now be

modeled. An event tree of PV with flexibility is constructed (Figure 5-14). At the end nodes, the

decision is whether to keep the existing chillers or replace them with new ones. For example, the

value of Node A' is calculated as follow.

Max (Replace, Keep) = Max (Present Value 1.05 Cost, Present Value)
= (62234 1.05 950, 62234)
= 64396 (Replace)

At the intermediate nodes, the decision is about whether to leave the option open or to

execute it immediately. To calculate the value of leaving the option open, the replicating

portfolio method developed in Chapter 4 must be used, but not the discounting method, since

risk-adjusted probability and risk-adjusted discount rate are used to construct the spread sheet

and event tree. Equation 4-7 is the replication portfolio formula to be applied.












48,137 C A 68,175
35,486 8 A' 64,396
S34,4 ReplReplace
25,421
Open
pen Opn 4,537 B 34,899

18,1 B' 32,939
173 26 Replace

Open 1Open
17,755
12,563 16,738
16,738
12,786 Keep
Open

9,208

8,681
Keep


Figure 5-14. Present value with flexibility (Numbers in $1,000).


For example, the value of keeping the option open at Node C' is

68175- 34899 1.3886 x34889- 0.7201 x68175 4
C = + = 48877
1.3886 0.7201 e0051 (1.3886 0.7201)

Therefore, the value of node C' is

Max (Replace, Open) = Max (47540*1.05-950, 48877)= 48967 (Replace)

The decision is to replace the chiller system immediately. Using Equation 4-14 to add

back the implied net cash flow of negative $830,000, the before dividend present value is

$48,137,000. Working backward the value at each node can be similarly calculated and the

optimal action can be selected to maximize the present value, and eventually the maximum

present value can be derived at time 0. The present value increases from $24,963,000 (without









flexibility) to $25,421,000 (with flexibility), or an increase by $458,000. The NPV of the project

is now $1,216,000. In other words, the option to replace the chillers system creates $458,000

value. If the building could be purchased at $24,205,000, the NPV increases to $1,216,000.

Sensitivity Analyses

Sensitivity analyses are conducted using option value as dependent variable, and present

value, replacement cost, discount rate and volatility as independent variables. Table 5-5

summarizes the effect of each independent variable as well as their combined effects on the

option value.

Present value has positive effect on the option value (Figure 5-15). Replacement of the

chiller system increases the annual net cash flow by 5%. And present value is positively related

to net cash flow. Therefore, the higher the present value is, the higher the additional net cash

flow would be when exercising the replacement option, and hence the higher the option value

would be.


Table 5-5. Summary of variable effect on option value.
Present Replacement Discount rate Volatility
value cost
Present value Positive Uncertain Positive, most Positive, most
Sensitive when in- Sensitive when at-
the-money the-money

Replacement Negative Uncertain, most Uncertain, most
cost Sensitive when at- Sensitive when at-
the-money the-money

Discount rate Positive Positive, most
Sensitive when at-
the-money

Volatility Positive










1,000
3 800
> 600
S 400
o 200


10,000 20,000 30,000
Present Value


Figure 5-15. Option value in relation with present value.


As shown in Figure 5-16, the replacement cost has negative effect on the option value.

The higher the replacement cost is, the less likely the replacement is breakeven, and hence the

less likely the option would be exercised.



1,200
S 1,000
800
S 600
S 400
0 200

500 1,000 1,500 2,000

Replacement Cost

Figure 5-16. Option value in relation with replacement cost.


Volatility also has positive effect on the option value (Figure 5-17). The higher the

volatility, the wider the present value spread becomes in later years, but the replacement option

is only exercised in those scenarios with positive net cash flows. Therefore, the more uncertain

the future cash flow is, the more valuable the option becomes.












1,000

800

600

6 400

200


10,000 20,000 30,000
Present Value

20% Volatility 33% Volatility 45% Volatility

Figure 5-17. Option value in relation with present value and volatility.

Risk-free interest rate has positive effect on the option value. But the effect is not

significant.

After examining the effect of each independent variable on the option value, combinations

of each two independent variables can be looked at. The combination of present value and Risk-

free interest rate has positive effect on the option value.

The two pairs of (1) present value and volatility (Figure 5-17), (2) volatility and risk-free

rate (Figure 5-18) both exercise positive effect on option value, and are most sensitive when the

option is at-the-money.

The three pairs of (1) replacement cost and volatility (Figure 5-19), (2) replacement cost

and risk-free rate, (3) present value and replacement cost (Figure 5-20) all display uncertain

effect on the option value. This conclusion is best illustrated in Figure 5-20. The 3-dimensional

curve indicates that the higher the present value and the lower the replacement cost, the higher

the option value. However, this effect is non-linear. With higher present value and higher









replacement cost, the option value may be higher or lower, depending on whether the option


value is in-the-money.




600 --


550
500
450
400
350
300


10% 20% 30% 40%


Volatility

3% Risk-Free 5% Risk-Free --- 7% Risk-Free



Figure 5-18. Option value in relation with volatility and discount rate.


1,200
1,000
800
600
400


200


50%


500 1,000 1,500


2,000


Replacement Cost

20% Volatility 33% Volatility -- 45% Volatility


Figure 5-19. Option value in relation with replacement cost and volatility.











2,500

2,000

1,500

1,000

500







Cost


Option Value


ralue


Figure 5-20. Option value in relation with present value and replacement cost.

Summary

This chapter applies the combined approach to determine the building value of the 211

Perimeter property in Atlanta. Rental rate and stabilized occupancy rate are identified as the two

major risk drivers and their volatilities are estimated using historical data. The risk variables are

combined in a spread sheet. Monte Carlo simulation is performed to estimate the project

volatility. Event tree is constructed, in which the option to replace the chiller system is

incorporated. The RERO approach indicates that the building is worth $25,421,000, and the

value of managerial flexibility is worth $458,000.









CHAPTER 6
THE SEPARATED APPROACH

This chapter is the second part of the case study described in Chapter 5. In the previous

chapter the RERO framework is applied to analyze the building structure and a managerial

decision of chiller replacement. The combined approach with Monte Carlo simulation is used as

the major methodology. This chapter, however, is about valuation of the infill land using the

separated approach, with jump diffusion process and decision tree analysis techniques.

Together, these two parts demonstrate how the RERO framework can be applied to different

scenarios in the analysis of real estate acquisition and development.

Case Description

The previous chapter has full description of the case 211 Perimeter in Atlanta. This

chapter only repeats the infill land portion. Besides the existing office building and the 6-story

garage, the current owner has got approvals for over 1 million square feet of mixed-use

development on the 9.5 acres developable site. Furthermore, the property is strategically located

within a larger neighborhood redevelopment planning of 38 acres and nearly 3 million square

feet mixed-use development, although the timing of neighborhood development is unknown.

The land obviously has some value, but development might not break ground immediately.

The real estate market in Atlanta is a commodity market, which means, with little control of

urban sprawl, developments are spread out easily as far as market demand exists. The Perimeter

office submarket is currently overbuilt, with several old office buildings torn down for new

residential developments. It would be interesting to know how current bidders should price the

land in addition to the building.









Land Valuation

The value of the infill land (9.5 acres out of the 13 acres total) depends on the value and

cost of the improvement should it be developed. The value of the improvement is determined by

a function of its annual rental income and operating cost, just like the existing building. The cost

of development includes hard costs and soft costs. Since every project is unique, development

cost is assumed to be a private risk that does not correlate with the traded financial market.

Problem Framing

The addition of a 6-story garage has freed the infill land from its original function as

surface parking. With the 1 million square feet mix-used development approval, the land can be

sold for $4.75 million at anytime during the holding period. Its best value for the investor is

being either developed or spin-off for $4.75 million.

Table 6-1 shows the development assumptions. Assume the land allows for 1 million

square feet to be built, gross rent is $24.5/sf, stabilized occupancy rate is 85%, operating expense

is $8.5/sf, required cap rate is 8%, risk-free interest rate is 5%. Expected development cost is

$227.5/sf Land carrying cost is assumed to be negligibly small compared to the development

value. The land can be sold for $4.75 million at anytime. This can be viewed as the exercise

price of a put option to the investor.


Table 6-1. Development assumptions.
Rentable sf 1,000,000 Site acres 9.50
Gross rent psf $24.50 Land $4.75
Occupancy rate 85.0% Value $154.06
Operating expenses psf $8.50 Cost $177.50
Net rent psf $12.33
Riskfree rate 5.0% Cap rate 8.0%









In addition, management believes that the groundbreaking for the larger neighborhood

redevelopment will have significant impact on the demand for new office space, and hence drive

up rental rate of this development by 20%. This is a one-time event, but once the rental rate

rises, it will remain at that level during the entire analysis period.

Approach Selection

The separated approach is selected because the impact when the rental rate jumps up by

20% is significant, and the chance is uncertain, depending on the timing of the neighborhood

redevelopment. This is an example where one risk driver (the rental rate) does not get resolved

smoothly, and must be modeled separately from the other risks.

Risk Drivers Identification and Estimation

The risk drivers are rental rates and development cost. Unlike the existing office building,

the new building does not have a historical track record. For income, the building rental rate is

assumed to have some premium over the average market rental rate. Changes in rental rate are

assumed to follow the GBM movement, with a jump-diffusion process corresponding to the

groundbreaking of the neighborhood project. Figure 6-1 shows the historical market average

rental returns for Class A office properties in the Central Perimeter submarket. Using the Risk

Simulators, the quarterly lognormal returns are plotted into a normal fit as shown in Figure 6-2.

Converted into annual data, the market rental rate volatility is 4.84%. As explained in Chapter 5,

individual property is far more volatile than the market average. The management estimate

doubles and becomes 9.68% per year for the infill land development project.

The current gross rental rate is $21/sf for the average Class A building in the Central

Perimeter submarket. According to management experience, a $3.50/sf premium for a brand

new building can be secured.










$30.00 6.00%


$20.00 2 \ ,, Ii I 2.00%
S$15.00 V / -2.00%
$10.00 l -4.00%
$5.00 ------ --- -------- 6.00%
$0.00 -8.00%
1990 3Q 1992 3Q 1994 3Q 1996 3Q 1998 3Q 2000 3Q 2002 3Q 2004 3Q

-- Rental Return


Figure 6-1. Historical market average rental rates and return volatility.

Statistical Summary
Normal Distribution
Soretical vs. Empirical Distribrtion Mu = -0.0019
Sigma = 0.0242


-20. Kolmogorov-Smirnov Test Statistic
Test Statistic: 0.0691
1' P-Value: 0.9282
1 i Actual Theoretical

.-. Mean -0.0024 -0.0019
I ., Stdev 0.0242 0.0242
-I -5 0.'5 1 Skewness -0.4240 0.0000
S Kurtosis -0.0318 0.0000


Figure 6-2. Normal distribution fit for historical market rental returns.

Rental rate changes are assumed to follow the GBM movement. A Poisson distribution

jump-diffusion process corresponds to the groundbreaking of the neighborhood residential

project, with 10% annual probability. The option value is calculated using Equation 4-15

developed in Chapter 4, where A is 10% and y is 1.2 (1 plus 20%).

Figure 6-3 shows how to get rental rate changes from one period to the next period. At

Year 0, gross rental rate is $24.50/sf. It could have three values in the next year: $29.40/sf (1.2









times $24.50/sf) if the neighborhood development breaks ground, $26.99/sf (up movement) or

$22.24/sf (down movement) if the neighborhood development does not break ground, with

probabilities of 0.10, 0.5895, and 0.3105 respectively. In year 2, it could have five values. If the

neighborhood development breaks ground in Year 1, the rental rate $29.40/sf will follow the

GBM movement with possible value of $32.39/sf or $26.69/sf, with probabilities of 0.7402 and

0.2598 respectively. If no development breaks ground in Year 1, the rental rates of $26.99/sf and

$22.24/sf each follows the GBM with jump diffusion process and has three values, which

combine into 5 possible values. In Year 3 the rental rates follow the same process and can have

seven values. Notice, however, the probabilities to get to these values are different with and

without the jump diffusion process.


Sigma 9.68% a 1.1016 1 1( 'I':J
t 1 d 0.9077 y 1.20
rf 5.:1: o p 0.7402 p 0.6550
1-p 0.2598 (1-p 0.5895
(1-1Xx1-p) 0.3105


0.7402


S24.50


0.3105


0.3105


$32.39

$26.69





$29.73

S24.50

S20: 19


Year 0 Year Year 2

Figure 6-3. Gross rental rate movement and probabilities.


$35.68

$29.a4

$24.23


S32 76

$26.99

$22.24

$18.33

yea 3









Taking out revenue lost from the 15% vacant space, $8.5/sf operating expense, and

capping the net cash flow at 8% Cap rate, we can get the corresponding per square foot building

value contingent upon the gross rental rate, stabilized occupancy, operating expenses, cap rate,

and the likelihood of the neighborhood residential development (Figure 6-4).


$272.85
0.7402 $7.87
$206.13 S2 06.13
0.25i9 5 $177.30
0.1 / 51.14


0.1 05895 $211.78
0.5895 20967
$180.52 Y .3105 18052
$154.06 O. > $154.06
035 $130.05 05895 / 30.05
0$108.24
0.3105 5


Year 0 Year 1 Year 2 Year 3

Figure 6-4. Building value movement and probabilities.


There is no direct comparable data on development cost. Development cost includes hard

and soft costs. For hard cost, the RS Means Building Cost Data manual (RS Means, 1998-2006)

can be used. The cost per square foot data for high-rise office buildings from Year 1998 to Year

2006 is shown in Figure 6-5. The historical data shows an upward trend, at a pace generally

consistent with the inflation rate from inflatiodata.com (Figure 6-6). RS Means compiles market

average data nation wide, which does not reflect the volatility of local markets. More over, there

are no data about the soft cost. Each project is unique in some soft cost items, such as land

acquisition cost, permit application cost, unexpected cost, etc. The best estimate would be from










experienced managers. The development cost is assumed not to change with the financial

market. It is a private risk that depends on the geological condition of the site, material and labor

condition of the local market, etc. Management has estimated that with 50% probability the

development cost would be $175/sf, with 20% to be $150/sf, and with 30% to be $200/sf, or


170.00

150.00

130.00

110.00

90.00

70.00
199


-.



_- - ---_-_ - -_


1999 2000 2001 2002 2003 2004

-*- Low Mid --- High


2005 2006


Figure 6-5. Historical construction cost for high-rise office building.


14.00%
12.00%
10.00%
8.00%
6.00%
4.00%
2.00%
0.00%
1999


0 m f


2000 2001


2002 2003

- Cost Inflation


Figure 6-6. Construction cost change rate and inflation rate.


2004


2005


2006


98


w r









expected cost of $177.50/sf (Figure 6-7). Cost increases by 3% annually, consistent with the

average inflation rate over the past 7 years. For simplicity, the buildable square footage is

assumed to be the same as the rentable square footage.


0 150.00 $154.50 $159.14 $163.91

S177.50 175.00 $180.25 $185.66 $191.23

0.3 2.0 $S206.600 $212.18 $218.55


YeO 0 Year 1 Yea 2 Ye 3

Figure 6-7. Development cost assumptions.


Base Case Modeling

The expected PV without any flexibility is calculated as shown in Figure 6-8. It is better

represented in matrices. Each table in Figure 6-9 is a matrix of possible PVs for a given year.

Starting from Year 3, the possible outcomes of building values are listed in the first row, and the

possible outcomes of development costs are listed in the first column. The values inside the

rectangle are all possible combinations of costs and values. The same applies to the values for

Year 2, Year 1 and Year 0. In Year 0, the expected value is calculated as the sum of the three

values times the respective probabilities of their development cost.

Option Modeling

There are three possible kinds of decisions at each node: (1) to develop the land, (2) to

keep the land as-is, and (3) to sell it for $4.75 million. Figure 6-10 depicts the decisions and

payoffs corresponding to the matrices in Figure 6-11. In this lattice, the notation below the value

represents the optimal decision to be made: D for developing the land; K for keeping the option

alive; and S for selling the land.










$108.94
0.7402 $7874
$51.63 :-2 22
0.1 0.2598 $18.17
($12 77)

0.1 5895 /$77.87
0.5895 50.53
$26.02 03105 $16.61
4_06 0t 1 ($5_ ->
0.3105 (24.45) 0.5895 (S33. 6'I
03105 "($50.89)
0.3105
(3105 75.45)


$81.62
0.7402 $52.22
S 25.88 $14.90
0.2 0.1 0.2598 ($8.35)
(4-I i OS"

.1 0 5895 $50.55
0.5895 // 24.01
0.5 0.27 03105 ($10.71)
2 .;44) I.2l': 94);' 0.1 ($31.60)
0.3105 "$5 i 05895/ (S61-18)
0.3105 ($77.41)
($102271)


0.3 7 54-31
0.7402 $25.69
f 12 ($12.42)
0.1 0.25987 ($34-88)
($671.4

0 .1 895 $2323
0.5895 (S2.51)
($25 48) 03105 ( ..
45.94) 01 ($58 12.I
0 5895
0.31, ($75.95) 5895 ($88.50)
0.3105 ($10394)
($130.09)


Year 0 Year 1 Ye 2 Year 3

Figure 6-8. Payoff and probabilities without flexibility (Dollars in $1,000,000).













Development 163.91
Cost 191.23
218.55





Development 159.14
Cost 185.66
212.18





Development 154.50
Cost 180.25
206.00


T=3
Building Value
272.85 206.13 151.14 241.78 180.52 130.05 88.45
108.94 42.22 (12.77) 77.87 1661 (33.86) (75.45)
81.62 14.90 (40.08) 50.55 (10.71) (61.18) (102.77)
54.31 (12.42) (67.40) 23.23 (38 02) (88.50) (130.09)

T=2
Building Value
237.87 177.30 209.67 154.06 108.24
78.74 18.17 50.53 (5.07) (50.89)
52.22 (8.35) 24.01 (31.60) (77.41)
25.69 (34.88) (2.51) (58.12) (103.94)


206.13
51.63
25.88
0.12


T=1
Building Value
180.52 130.05
26.02 (24.45)
0.27 (50.20)
(25.48) (75.95)


T=0
Building Value
154.06
Development 150.00 4.06
Cost 175.00 (20.94) (23.44)
200.00 (45.94)

Figure 6-9. Payoff matrices for project values without flexibility (Numbers in $1,000,000).

In Year 3, the decision will be either to develop the land or to sell it for $4.75 million,

whichever generates the higher payoff. For example, the PV of Node A is calculated as follows:

Max (Develop, Sell) = Max (Building Value Cost, Salvage Value)
=(206.13- 163.61, 4.75)
= 42.22 (Develop)

Working backward, in Year 2, the payoff is the greatest of the three: (1) the payoff of

developing the land, which is the building value minus development cost; (2) the payoff of

keeping the option open, i.e., the corresponding payoff in Year 3 discounted at risk-free interest

rate using the binomial or jump diffusion probabilities calculated in Table 6-2; (3) the payoff of











0.7402
$68-99 < _
0.1 (K) 02598 B



01 .5895
0 5895
-5 69 03105
(K) 01/ C
$12.60 A 0.5895
0_3105 12 5
(K) 0.3105


0.7402
S4- 94
(K) 0.2598



0.1 58E95
52S 47 0 3105
(K) 0.1
S5.59 4g05895
(K)
0.3105




0.7402
2?S 93
(K) 0.2598g


S16.
(K)
0.3105 U
(s)


$87.14
(K)
$30_90
(K)


$58.93
(K)
$14.73
(K)

(S)


S61.16
(K)
$11.66
(K)


S.; .51
(K)
$5.48
(K)
5-175
(S)


0.3105


(K) for keepIt jg die :op:i .i'.e (D) for developing the land


Year 0


Year 1


(S) for selling the land


Year 2


Year 3


Figure 6-10. Decision payoff and probabilities with flexibility (Dollars in $1,000,000).


$22.14
(K-)


C I'S 94
(D)
A 42 22
(D)
'-175
(S)
$77.87
(D)
$16.61
(D)
-4.75

$4.75
(S)

$81 62
(D)
$14.90
(D)
-14.75
(s)
$50.55
(D)

(S)
54-75

-4'75
(S)

$54.31

'-1.75
(D)

$4.75
(S)
$23.23
(D)
-1475
(S)
4-175
(S)
.4 -75
(S)










T=3
B-uildig Value
272.85 206.13 151.14


108.94
81.62
54.31


42.22
14.90
4.75


4.75
4.75
4.75


T=2
Buiking Value
237.87 177.30 209.67


87.14
61.16
39.41


30.90
11.66
4.75


58.93
37.51
19.60


241.78 180.52 130.05


77.87
50.55
23.23


16.61
4.75
4.75


4.75
4.75
4.75


154.06 108.24


14.73
5.48
4.75


4.75
4.75
4.75


Buildig Value
206_13 180-52 130_05


Development
Cost


154 50
180.25
206.00


150.00
175.00
200-00


154.06
35.91
21.99 2 22.14
13-21


Figure 6-11. Payoff matrices of project value with flexibility (Numbers in $1,000,000).

Table 6-2. Probabilities of jump diffusion and binomial processes.
Jump diffusion No jump
Jump Up Down Up Down
X (l1-X) (1-X)(1-p) p 1-p
0.1000 0.5895 0.3105 0.7402 0.2598

the put option, which is to sell the land for $4.75 million. For the normal stochastic process, the

payoff of keeping the option open at Node B, for example, is calculated using Equation 3-19 as

follows:

C = e [pC,, + (1 p)Cd =e e05 1 [0.7402 x 42.22 + 0.2598 x 4.75] =30.90


Development
Cost


163.91
191.23
218.55


88.45
4.75
4.75
4.75


Developet
Cost


159.14
185.66
212.18


68 99
45.94
28.93


45 69
28.47
16.14


1260
5.59
4.75


T=0


Deelopment
Cost


I I









Consequently, the PV of Node B is calculated as follow.

Max (Develop, Keep, Sell)
= Max (Building Value Cost, Payoff of Keeping Option Open, Salvage Value)
= (177.30 159.14, 30.90, 4.75)
= 30.90 (Keep)

For the jump diffusion, the payoff of keeping the option open at Node C, for example, is

calculated using Equation 4-15 as follows:

C = e rt{C, + (1 )[pC + (1 p)Cd]}
= e 005" {0.1 x 42.22 + 0.5895 x 16.61+ 0.3105 x 4.75} = 14.73

Consequently, the PV of Node C is calculated as follows:

Max (Develop, Keep, Sell)
= Max (Building Value Cost, Payoff of Keeping Option Open, Salvage Value)
= (154.06 159.14, 14.73, 4.75)
= 14.73 (Keep)

Working backward to Year 0, the PV of the project is expected PV of each cost scenario

times its corresponding probability. The PV of Node D is calculated using Equation 4-17 as

follows:


E(PV) = p [E(PV)] = 0.2 x35.91+ 0.5 x 21.99 + 0.3 x13.21= 22.14
J1

The PV of the project increases from negative $23.44 million without flexibility to positive

$22.14 million with the development and sell-off flexibility. The option value is

$22.14 (-$23.44) = $45.57 million.

Sensitivity Analyses

Sensitivity analyses are conducted using gross rental rates, occupancy rates, volatility, Cap

rates, and development cost as independent variables, and on two dependent variables: project

value and option value. Project value is the PV of the project with the flexibility of deferred

development, spin-off the land, and immediate development. Option value is the difference









between PV with flexibility and PV without flexibility. Since the PV without flexibility also

changes with variables, the project value and option value analyses have quite different results

and implications.

As shown in Figure 6-12 the rental rate has a positive effect on project value. Rental rate

is directly linked to revenue. The higher the rental rate is, the higher the income the project will

generate, and hence the higher the project value is. However, as shown in Figure 6-13 it has a

negative effect on option value. This is because the higher the rental rate is, the more likely the

project will be developed immediately, hence the option to wait or abandon the development by

selling off the land is less worthy. In other words, higher rental rate not only increases the

project value with flexibility, it also increases the value without flexibility at even higher pace.

These two values cancel out each other, resulting in minimal option value.

The combination of rental rate and occupancy rate has the same result: positive effect on

the project value (Figure 6-12), and negative effect on the option value (Figure 6-13). Note that

the option value is sensitive to stabilized occupancy rate when the option is at-the-money.


250
Z 200 ----------------------------------------
S200

I 150
100
> 50


3 6 9 12 15 18 21 24 27 30 33 36

Gross Rent

-- 60% Occ 85% Occ -- 100% Occ


Figure 6-12. Present value in relation with rental rate and occupancy rate.













300
250
200
150
100
50


3 6 9 12 15 18 21 24 27 30 33 36

Gross Rent


-- 60% Occ 85% Occ -- 100% Occ


Figure 6-13. Option value in relation with rental rate and occupancy rate.



Just opposite to the effect of rental rate, as shown in Figure 6-14, development cost has a

negative effect on project value, but positive effect on option value (Figure 6-15), for the same

reason as explained above.


PV with Flexibility


200
180
160
140
120
100
80
60
40
20


Gross Rent


0

Development
Cost


0
0"
C'


Figure 6-14. Present value in relation with rental rate and development cost.











400
350
300
250
200 Option Value
150
100
50


33
27
21
300 15 Gross Rent
Development 200 9
tCost 1o0


Figure 6-15. Option value in relation with rental rate and development cost.

As shown in Figure 6-16, cap rate has negative effect on project value. This is because cap

rate is inversely related to property value. (Property value is determined by dividing net

operating income by cap rate.) However, the effect of cap rate on option value is more profound.

Figure 6-17 shows that at normal rental rate range ($11/sf to $3 1/sf), cap rate has a positive

impact on the option value; however, in the low rental rate range ($0/sfto $11/sf), its impact is

the opposite. Figure 6-18 illustrates how the combination of rental rate and cap rate results in

different option value. Unlike most situations where a variable has monotonic impact on the

option value, the shape of cap rate on option value is convex. For example, at $20/sf gross rent,

the option value at 2% cap rate is $71 million, at 4% cap rate the option value drops to $47

million, and at 8% cap rate the option value comes back to $77 million.










250 r------------------------------------------------------------
250
200
150
1 00 -------------------------------------------- --------- _
100
50 --


3 6 9 12 15 18 21 24 27 30 33 36

Gross Rent

-- 6% Cap 8% Cap 10% Cap


Figure 6-16. Present value in relation with rental rate and Cap rate.


300
250
S200
S150
100
50


3 6 9 12 15 18 21 24 27 30 33 36

Gross Rent

6% Cap- 8% Cap 10/o Cap


Figure 6-17. Option value in relation with rental rate and Cap rate.


As shown in Figures 6-19 and 6-20 volatility has positive impact on both project value and

option value. This finding is consistent with many observations in real options research (Titman,

1985; Williams, 1991; Quigg, 1993) that greater volatility increases option value, which is also

the reason why the real options methodology should be applied to projects with high uncertainty.











900

800 -- ----
700 -- "- -----------------
700

600 -


Option Value 500
400


300 1


200

100


104
1p 3% 7% 9%
Cap Rate


Figure 6-18. Option value in relation with rental rate and Cap rate in 3D.



150

100
100 ------------------------------------5---
5 0


3% 6% 9%


12% 15% 18% 21% 24% 27% 30% 33% 36%


Volatility

- 6% Cap 8% Cap 10% Cap


Figure 6-19. Present value in relation with volatility and Cap rate.










100
80-
> 60
S40
0 20


3% 6% 9% 12% 15% 18% 21% 24% 27% 30% 33% 36%
Volatility

6% Cap 8% Cap -- 10% Cap


Figure 6-20. Option value in relation with volatility and Cap rate.


Summary

This chapter applies the separated approach to value the infill land of the 211 Perimeter

property in Atlanta. Rental rate and development cost are identified as the two major risk

drivers. Rental rate is assumed to have jump diffusion effect due to the uncertainty of the larger

neighborhood redevelopment project. Development cost is assumed to be a private risk with no

corresponding traded twin asset and it is estimated subjectively based on management's

experience. DTA methodology is applied and an event tree is constructed, in which three options

are incorporated: the option to develop immediately, the option to delay development, and the

option to sell the land. The RERO approach indicates that the land is worth $22,140,000 and the

value of managerial flexibility is worth $45,570,000.

In Chapter 5, the building is estimated to be worth $25 million; in this chapter, the land is

estimated to be worth $22 million, totaling $47 million. This is very close to reality, because the

property was actually sold for $43.5 million in 2005.









CHAPTER 7
CONCLUSIONS AND RECOMMENDATIONS

Conclusions

Three main conclusions are drawn from this research: (1) acquisition and development has

different characteristics and deserve different kinds of attention; (2) consideration of managerial

flexibility can change investment decisions; and (3) many unconventional real option valuation

problems can be realized by using binomial lattice and Monte Carlo simulations.

Acquisition and development have different characteristics and thus deserve different kinds

of valuation. The option value of acquisition is usually on a much lower scale than that of

development, but by no means is it less significant. In the case studies, the option in the existing

building is replacement of the chiller system. Its value is $496,000, or 52% of the replacement

cost of $950,000. On the other hand, the option on the infill land is development timing and

abandonment. The option value is as high as $45.65 million, but only 26% of the development

cost of $177.5 million. Due to the scale of the valuations, it is better to have the option in the

building and the options in the land valued separately. But the impact of management flexibility

on acquisition and operation is as significant as, if not more than, that on development.

The consideration of operating flexibility in acquisition is important. It adds competitive

value to the bid for a property. In the case studies, the building is worth $25 million, and the

land is worth $22 million, totaling $47 million. In other words, the infill land is worth almost as

much as the building. This is very close to reality, because the property was actually sold for

$43.5 million. Note that the present value of the development project without any flexibility is

negative $23 million. With negative NPV, the project will not break ground. This means if

management does not incorporate the flexibilities into the land valuation, the development is

deemed worthless, and so is the land.









The RERO framework explores a few unconventional real option cases, including (1)jump

diffusion process that does not go back to normal diffusion, (2) risk drivers that do not follow the

multiplicative stochastic movement, (3) private risk that has no market equivalent and hence

violating the no-arbitrage option pricing assumption. All of these can be implemented through a

binomial lattice with Monte Carlo simulations or the DTA approach. The RERO framework is a

simple yet powerful tool, intuitive to the practitioners, yet mathematically correct and precise.

Recommendations for Future Research

There are at least three directions that future research can go in: model perfection, game

theory and phase investment. Model perfection is to improve the preciseness of outcome from

the RERO models. Lattice is a discrete-time method for option pricing. The smaller the time

step, the closer the result will be to that calculated by continuous-time methods. At the same

time, the development cost is assumed to have three values in our case study: the optimistic

value, the most likely value, and the pessimistic value. More branches can be added to produce a

more precise result. By dividing the lattice into more time steps, and breaking the development

cost into more branches, a more precise result will be generated.

A significant factor not considered in this study is competition. Without the consideration

of competition, in most cases it is optimal to defer exercising an option until the end of the

holding period. However, competition erodes the value of waiting, affects the value of option as

competitors enter or exit the market place and changes the market dynamics (Williams 1993;

Myerson, 1991). Should game theory be incorporated into the RERO framework, we predict the

option value would be slightly lower, and hence even closer to the closing price.

The other direction is stage investment and phased investment. Real estate development is

a lengthy process, and it usually takes 2 to 3 years, if not longer. During this period, a lot of

uncertainties can change the managerial strategies. Stage investment refers to dividing a real









estate development project into different stages: planning, design, construction, sales, etc. This

process can be valued similar to pharmaceutical research and development. Phased investment

refers to dividing a large real estate development project into different phases, for example,

Phase I retail corridor, Phase II residential condominium, Phase III office and hotel towers, etc.

Decisions at later phases are contingent upon the outcome of earlier phases. However, there can

be timing overlaps between two phases. While this problem is best solved by decision tree

analysis, the combination of real options and decision analysis could be beneficial.











LIST OF REFERENCES


Adams, Andrew, Philip Booth, and Bryan MacGregor. (2001). "Lease Terms, Option Pricing and
the Financial Characteristics of Property," City University Business School London.
Retrieved September 2005, from
http://www.cass.city.ac.uk/refig/papers/LeaseTermsOptionPricing.pdf

Amin, Kaushik. (1993). "Jump Diffusion Option Valuation in Discrete Time," The Journal of
Finance 48(5), 1833-1863.

Arnold, Tom, and Timoth Falcon Crack. (2003). "Option Pricing in the Real World: A
Generalized Binomial Model with Applications to Real Options," Seventh Annual
International Conference on Real Options: Theory Meets Practice, Washington, DC, 10-
12 July. Retrieved March 05, 2007, from http://www.realoptions.org/abstracts/
abstracts03.html

Black, F. and M. Scholes. (1973). "The Pricing of Options and Corporate Liabilities," Journal of
Political Economy 81 (May-June), 637-654.

Bellalah, Mondher. (2002). "Valuing Lease Contracts Under Incomplete Information: A Real-
Options Approach," The Engineering Economist 47(2), 194-212.

Borison, Adam. (2005). "Real Options Analysis: Where Are the Emperor's Clothes?" Journal of
Applied Corporate Finance 17 (2) (Spring), 17-31.

Brigham, Eugene F., Louis C. Gapenski, Michael C. Ehrhardt. (1999). Financial Management:
Theory and Practice. 9th Edition. Dryden Press, Fort Worth, TX.

Bulan, Laarni, Christopher Mayer, and C. Tsuriel Somerville. (2004). "Irreversible Investment,
Real Options, and Competition: Evidence from Real Estate Development," unpublished
manuscript, Faculty of Commerce, University of British Columbia, Vancouver, CA.
Retrieved March 05,2007, from http://people.brandeis.edu/~lbulan/Vanc.pdf

Capozza, Dennis, and Robert W. Helsley. (1990). "The Stochastic City," Journal of Urban
Economics 28, 187-203.

Capozza, Dennis, and Gordon Sick. (1991). "Valuing Long Term Leases: The Option to
Redevelop," Journal of Real Estate Finance and Economics 4, 209-223.

Cederborg, Andreas, and Stefan Ekeroth. (2004). Real Options and Real Estate: A Master Thesis
About The Option To Convert Offices To Flats, Goteborg University, Sweden. Retrieved
December 2005, from http://www.hgu.gu.se/files/cff/uppsats%20cffo/20-%20se%20ac.pdf

Childs, Paul D., Timothy J. Riddiough, and Alexander J. Triantis. (1996). "Mixed Uses and the
Redevelopment Option," Real Estate Economics 24 (3), 317-339.









Clarke, Harry R., and William J. Reed. (1988). "A Stochastic Analysis of Land Development
Timing and Property Valuation," Regional Science and Urban Economics 18, 357-381.

Copeland, Thomas E., and Vladimir Antikarov. (2001). Real Options: A Practitioner's Guide.
Texere, New York.

Copeland, Thomas E., and Vladimir Antikarov. (2005). "Real Options: Meeting the Georgetown
Challenge," Journal of Applied Corporate Finance 17 (Spring), 32-51.

Cox, J., S. Ross, and M. Ribinstein. (1979). "Option Pricing: A simplified Approach," Journal of
Financial Economics 7, 229-263.

Childs, Paul S., Steven H. Ott and Timothy J. Riddiough. (2001). "Noise, Real Estate Markets,
and Options on Real Assets: Theory". Unpublished Manuscript, MIT, 2001. Retrieved
03/15/2007, from http://www.bus.wisc.edu/realestate/pdf/pdf/
NoisyAssets_%20Theory_3_01.pdf

Feinstein, Steven, and Diane M. Lander. (2002). "A Better Understanding of Why NPV
Undervalues Managerial Flexibility," The Engineering Economist 47 (4), 418-435.

Geltner, David, Timothy Riddiough, and Srdjan Stojanovic. (1996). "Insights on the Effect of
Land Use Choice: The perpetual Option on the Best of Two underlying Assets," Journal of
Urban economics 39, 20-50.

Ghosh, C, and CF Sirmans. (1999). An Introduction to Real-Options Analysis for Corporate Real
Estate. The IDRC Foundation, Research Bulletin No. 24.

Grenadier, Steven R. (1995). "Valuing Lease Contracts: A Real-Options Approach," Journal of
Financial Economics 38, 297-331.

Grenadier, Steven R. (1996). "The Strategic Exercise of Options: Development Cascades and
Overbuilding in Real Estate Markets," The Journal ofFinance 11(5), 1653-1679.

Grenadier, Steven R. (2003). "An Equilibrium Analysis of Real Estate Leases," Working Paper,
Stanford University. Retrieved September 2005, from
https://www.gsb.stanford.edu/news/pdf/grenadier leasing.pdf

Grenadier, Steven R., and Neng Wang. (2005). "Investment under Uncertainty and Time-
Inconsistent Preferences," Working Paper #1899, Stanford University.

Holland, A. Steven, Steven H. Ott, and Timothy J. Riddiough. (2000). "The Role of Uncertainty
in Investment: an Examination of Competing Investment Models Using Commercial Real
Estate Data," Real Estate Economics 28 (1), 33-64.

Hull, John C., (2006). Options, Futures, and Other Derivatives. 6th Edition. Prentice-Hall,
Upper Saddle River, New Jersey.









Lander, Diane M., and George E. Pinches. (1998). "Challenges to the Practical Implementation
of Modeling and Valuing Real Options," Quarterly Review of Economics and Finance 38
Special Issue, 537-567.

Luenberger, David G., (1998). Investment Science. Oxford University Press, New York.

Miller, Luke T., Chan S. Park (2002). "Decision Making Under Uncertainty Real Options to
the Rescue?" The Engineering Economist 47 (2), 105-150.

Myers, S. (1977). "Determinants of Capital Borrowing," Journal ofFinancial Economics 5 (2),
147-175.

Mun, J. (2002). Real Options Analysis: Tools and Techniques for Valuing Strategic Investments
andDecisions. John Wiley & Sons, New York.

Myerson, R.B. (1991). Game Theory: Analysis of Conflict. Harvard University Press,
Cambridge, Massachusetts.

Ng, Frances P., and Hans C. Bjornsson. (2004) "Using real option and decision analysis to
evaluate investments in the architecture, construction and engineering industry,"
Construction Management and Economics 22, 471-482.

Ott, Steven H. (2002). "Real Options and Real Estate: A Review and Valuation Illustration,"
Real Estate Valuation Theory, an American Real Estate Society Monograph 8, 411-423.

Pindyck, Robert S. (1991). "Irreversibility, Uncertainty, and Investment," Journal of Economic
Literature 29, 1110-1148.

Quigg, Laura. (1993). "Empirical Testing of Real Option-Pricing Models," The Journal of
Finance 48 (2), 621-640.

RS Means. (1998-2006). Building Construction Cost Data. Kingston, Mass.

Sivitanidou, R., and P. Sivitanides, (1999). "Office Capitalization Rates: Real Estate and Capital
Market influences," Journal of Real Estate Finance and Economics 18, 297-323.

Smith, James E., and Robert F. Nau. (1995). "Valuing Risky Projects: Option Pricing Theory and
Decision Analysis," Management Science 41(5), 795-816.

Smith, James E., and Kevin F. McCardle. (1999). "Options in the Real World: Lessons Learned
in Evaluating Oil and Gas Investments," Operations Research 47(1), 1-15.

Titman, Sheridan (1985). "Urban Land Prices Under Uncertainty," American Economic Review
75, 505-514.

Trigeorgis, Lenos. (1996). Real Options: Managerial Flexibility and Strategy in Resource
Allocation. MIT Press, Cambridge, Massachusetts.









Trigeorgis, Lenos. (2005). "Making Use of Real Options Simple: an Overview and Applications
in Flexible / Modular decision Making," The Engineering Economist 50, 25-53.

Wheaton, William C., Raymond G Torto, Petros S Sivitanides, Jon A Southard, Robert E.
Hopkins, James M. Costello. (2001). "Real Estate Risk: a Forward-Looking Approach,"
Real Estate Finance 18(3), 20-28.

Williams, Joseph T. (1991). "Real Estate Development as an Option," Journal of Real Estate
Finance andEconomics 4, 191-208.

Williams, Joseph T. (1993). "Equilibrium and Options on Real Assets," The Review ofFinancial
Studies 6 (4), 825-850.

Williams, Joseph T. (1997). "Redevelopment of Real Assets," Real Estate Economics 25 (3),
387-407.

Yao, Junkui, and Ali Jaafari. (2003). "Combining Real Options and Decision Tree," The Journal
of Structured and Project Finance 9 (Fall), 53-70.









BIOGRAPHICAL SKETCH

Nga-Na Leung earned her PhD degree in building construction from the University of

Florida, Gainesville, FL. While earning this degree, she worked as an acquisition analyst for

Parmenter Realty Partners in Miami, FL later for Acadia Realty Trust in White Plains, NY, and

now for Antares Investment Partners in Greenwich, CT.

She also holds a master of science degree in real estate from the University of Florida, a

master's degree in building from the National University of Singapore, Singapore, and a bachelor's

degree in architecture from Tongji University, Shanghai, China.

Nga-Na worked as an assistant project manager in the Environetics Design Group in

Shanghai, China prior to coming to the US. At UF, she was supported by the Alumni

Fellowship, the highest merit-based award for graduate students. After graduation Nga-Na will

continue her career in commercial real estate investment, including acquisitions, development,

and management.





PAGE 1

1 REAL OPTIONS FRAMEWORK FOR ACQUISITION OF REAL ESTATE PROPERTIES WITH EXCESSIVE LAND By NGA-NA LEUNG 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 2007

PAGE 2

2 2007 Nga-Na Leung

PAGE 3

3 To my husband, Lezhou Zhan, and my family, Lau Leung, Sau-Pik Fung, Shing-Pen Leung, and Shing-Chiu Leung

PAGE 4

4 ACKNOWLEDGMENTS I would never be able to adequately tha nk Dr. R. Raymond Issa, my chair, for making room for me to develop my res earch question, as well as helping me to choose the direction of my life. I want to thank him not only for hi s tremendous guidance, considerable patience and encouragement throughout my study, but also for his endless trust, respect, and understanding, which has forged me into a better person, not only with intelligence, but with responsibility. I am especially grateful to Dr. Wayne Arch er, Dr. Ian Flood, Dr. Kevin Grosskopf and Dr. Robert Cox, for their discussions, suggestions, and encouragement duri ng the development of this dissertation. It is a great honor to have them serve on my committee. I am in debt to Dottie Beaupied for her tremendous helps, especially during the dissertati on submission process. I would also like to acknowledge the generous financial support from the University of Florida and the UF Alumni Associ ation, from which I will carry the Gator spirit for the rest of my life. I am in debt to Andrew Weiss, who has been the best mentor in my real estate profession, and has also provided generous he lp in data collection for this study. Besides him, I was working with an amazing team in Parmenter Realty Partners and especially thankful to Darryl Parmenter, Ed Miller, and Mark Reese, for their insightfu l advice on career choices and their tremendous helps at work. Special thanks go to all my folks when I wa s in UF, whose love and friendship became part of the happiest memory of my life. I am especially grateful to Yujiao Qiao, Yang Zhu, Hongyan Du, Dongluo Chen, Jon Anderson, and Hazar Dib, whose encouragements have me to complete this dissertation in time.

PAGE 5

5 I want to extend a special word of thanks to all my mentors in the past, Dongshi Xu, Fuchang Lai, Shensheng Xu, Shouqing Wang, and Da vid Ling, whose wisdom and insight have profound influence on my character and personality. This work is dedicated to Lezhou Zhan, my husband and best friend, for his company throughout my life in good days and in bad ones; and to my beloved family: Lau Leung, my father; Sau Pik Fung, my mother; Shing-Chiu Leung, my little brother; and Shing-Pen Leung, my deceased brother. The honor goes to them, for their thirty years of nurture with endless love and care.

PAGE 6

6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES................................................................................................................ .......10 ABSTRACT....................................................................................................................... ............13 1 INTRODUCTION..................................................................................................................15 Background..................................................................................................................... ........15 Statement of Research Problem..............................................................................................16 Goal and Objectives............................................................................................................ ....18 Research Scope................................................................................................................. ......18 Significance and Contributions...............................................................................................19 Organization of Dissertation...................................................................................................19 2 REVIEW OF REAL ESTATE VALUATION.......................................................................20 Current Practice............................................................................................................... .......20 Distinguishing Acquisition and Development.................................................................20 Typical Acquisition Valuation Process...........................................................................21 Current Real Option Approach and Limitations.............................................................24 Decision Tree Analysis and Limitations.........................................................................25 Real Options in Real Estate....................................................................................................25 Theoretical Models..........................................................................................................25 Empirical Testing............................................................................................................31 The RERO Approaches..........................................................................................................31 Summary........................................................................................................................ .........32 3 LITERATURE REVIEW.......................................................................................................33 Traditional Discounted Ca sh Flow Approaches.....................................................................33 Capital Budgeting Theory.......................................................................................................34 Market Risk and Private Risk..........................................................................................34 Capital Asset Pricing Model............................................................................................34 Discount Rate..................................................................................................................35 Option Pricing Theory.......................................................................................................... ..36 Definition and Type of Options.......................................................................................36 Black-Sholes Model and Stochastic Partial Differential Equations................................38 Lattices....................................................................................................................... .....42 Monte Carlo Simulation..................................................................................................45 Real Options Analysis Approaches........................................................................................46 Practical Real Options Model in Real Estate..........................................................................50

PAGE 7

7 Decision Tree Analysis......................................................................................................... ..53 Summary........................................................................................................................ .........54 4 METHODOLOGY.................................................................................................................55 RERO Modeling Procedures..................................................................................................55 Problem Framing.............................................................................................................55 Approach Selection.........................................................................................................57 Risk Drivers Identification and Estimation.....................................................................57 Base Case Modeling........................................................................................................57 Option Modeling.............................................................................................................58 Sensitivity Analyses........................................................................................................58 RERO Modeling Approaches.................................................................................................58 The Combined Approach................................................................................................59 The Separated Approach.................................................................................................61 RERO Modeling Techniques..................................................................................................63 Rational for Using Binomial Lattices..............................................................................63 Monte Carlo Simulation..................................................................................................64 Replicating Portfolio.......................................................................................................64 Binomial Lattice with Jump Process...............................................................................66 Investment with Private Uncertainty...............................................................................68 Summary........................................................................................................................ .........71 5 THE COMBINED APPROACH............................................................................................72 Case Description............................................................................................................... ......72 Building Valuation............................................................................................................. .....73 Problem Framing.............................................................................................................73 Approach Selection.........................................................................................................74 Base case NPV calculation..............................................................................................74 Risk Drivers Modeling....................................................................................................78 Option Modeling.............................................................................................................85 Sensitivity Analyses........................................................................................................91 Summary........................................................................................................................ .........95 6 THE SEPARATED APPROACH..........................................................................................96 Case Description............................................................................................................... ......96 Land Valuation................................................................................................................. ......97 Problem Framing.............................................................................................................97 Approach Selection.........................................................................................................98 Risk Drivers Identification and Estimation.....................................................................98 Base Case Modeling......................................................................................................103 Option Modeling...........................................................................................................103 Sensitivity Analyses......................................................................................................108 Summary........................................................................................................................ .......114

PAGE 8

8 7 CONCLUSIONS AND RECOMMENDATIONS...............................................................115 Conclusions.................................................................................................................... .......115 Recommendations for Future Research................................................................................116 LIST OF REFERENCES.............................................................................................................118 BIOGRAPHICAL SKETCH.......................................................................................................122

PAGE 9

9 LIST OF TABLES Table page 2-1 Comparison of Research Subjects, Model Variants, Contributions and Limitations........28 3-1 Type of Real Options....................................................................................................... ..47 3-2 Financial Options versus Real Options..............................................................................47 3-3 Correspondence between Fina ncial and Real Options.......................................................51 5-1 Major Assumptions for Argus...........................................................................................75 5-2 Correlation Between Random Variables...........................................................................87 5-3 Statistical Summary of M onte Carlo Simulation Result....................................................87 5-4 Event Tree Assumptions....................................................................................................88 5-5 Summary of Variable Effect on Option Value..................................................................91 6-1 Development Assumptions................................................................................................97 6-2 Probabilities of Jump Diff usion and Binomial Processes................................................107

PAGE 10

10 LIST OF FIGURES Figure page 2-1 Real estate phases and major factors to consider...............................................................22 2-2 Current acquisition valuation process................................................................................23 2-3 Real Options approaches for land valuation......................................................................27 3-1 Payoff of call option and put option..................................................................................37 3-2 Call option payoff example................................................................................................37 3-3 Call premium vs. security price.........................................................................................41 3-4 Stock and option price in a one-step binomial tree............................................................42 3-5 Stock and option prices in general two-step tree...............................................................44 3-6 Monte Carlo si mulation output..........................................................................................45 4-1 Critical steps in RERO analysis.........................................................................................56 4-2 Two-step binomial lattice w ith different dividend yields..................................................66 4-3 Binomial lattice with jump process....................................................................................68 4-4 Quadranomial lattice....................................................................................................... ...70 4-5 Decision analysis.......................................................................................................... .....70 5-1 211 Perimeter site plan.................................................................................................... ...73 5-2 Base case NPV calculation................................................................................................76 5-3 Spreadsheet model for Monte Carlo simulation................................................................79 5-4 Historical market and su bject property rental rates...........................................................80 5-5 Returns correlation between market and subject property.................................................80 5-6 Normal distribution fit for historical retu rns on rental.......................................................82 5-7 Historical market and subj ect property occupancy rates...................................................83 5-8 Occupancy changes correlat ion between the local real es tate market and the subject property....................................................................................................................... .......84

PAGE 11

11 5-9 Normal distribution fit for historical occupancy rates.......................................................84 5-10 Snap shot of Monte Ca rlo simulation assumptions............................................................86 5-11 Monte Carlo Simulation Result of Forecasting Variable z ................................................86 5-12 Normal distribution fi t of forecasting variable z ................................................................87 5-13 Event tree present value without flexibility.......................................................................89 5-14 Present value with flexibility............................................................................................ .90 5-15 Option value in relati on with present value.......................................................................92 5-16 Option value in relation with replacement cost.................................................................92 5-17 Option value in relation with present value and volatility.................................................93 5-18 Option value in relation with volatility and discount rate..................................................94 5-19 Option value in relation with replacement cost and volatility...........................................94 5-20 Option value in relation with pr esent value and replacement cost....................................95 6-1 Historical market average rent al rates and return volatility...............................................99 6-2 Normal distribution fit for hist orical market rental returns...............................................99 6-3 Gross rental rate move ment and probabilities.................................................................100 6-4 Building value movement and probabilities....................................................................101 6-5 Historical construction cost for high-rise office building................................................102 6-6 Construction cost change rate and inflation rate..............................................................102 6-7 Development cost assumptions........................................................................................103 6-8 Payoff and probabilitie s without flexibility.....................................................................104 6-9 Payoff matrices for project values without flexibility.....................................................105 6-10 Decision payoff and probabilities with flexibility...........................................................106 6-11 Payoff matrices of projec t value with flexibility.............................................................107 6-12 Present value in re lation with rental rate and occupancy rate..........................................109 6-13 Option value in relation with re ntal rate and occupancy rate..........................................110

PAGE 12

12 6-14 Present value in rela tion with rental rate and development cost......................................110 6-15 Option value in relation with re ntal rate and development cost......................................111 6-16 Present value in relation with rental rate and Cap rate....................................................112 6-17 Option value in relation with rental rate and Cap rate.....................................................112 6-18 Option value in relation with re ntal rate and Cap rate in 3D...........................................113 6-19 Present value in relation w ith volatility and Cap rate......................................................113 6-20 Option value in relation w ith volatility and Cap rate.......................................................114

PAGE 13

13 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 REAL OPTIONS FRAMEWORK FOR ACQUISITION OF REAL ESTATE PROPERTIES WITH EXCESSIVE LAND BY Nga-Na Leung August 2007 Chair: Raymond Issa Major: Design, Construction, and Planning Our study touches a field that few researchers explore: the valuation model for acquisition of a property with excessive land that can be po tentially converted into a new development. Traditional valuation focuses mainly on th e building improvement. With the drastic capitalization rate compression, however, it beco mes critical to identify and explore any hidden value in an acquisition. One of such challenges is valuing a large partially vacant parcel that can be potentially converted into a new development. Valuation of these parcels is not straight forward. Traditional discounted cash flow approach (DCF) cannot take into account the uncertainty and development flexibility. Alternative approaches are real options analysis (ROA) and d ecision tree analysis (DTA). However, the twin asset assumption require d by the ROA methodology is often violated, especially for assets w ith private risk and rare events. The use of the same discount rate throughout valuation period in the DTA approach, regardless of changing risk characteristics upon the execution of decision making, allows for arbitrage opportunity. Our proposed real estate with real options (RERO) model is a framework that combines DCF, ROA and DTA analyses to sp ecifically value real estate acquisition with excessive infill

PAGE 14

14 land. This methodology not only overcomes the shor tcoming of current DCF method, but also is superior to the pure ROA or DTA analysis. Focusing on applicability in practice, this framework is developed intuitively with simple mathematic s whenever possible. The study also explores a few unconventional real options cases, all of whic h could have been very complicated if modeled using the partial differential equations common in the academy, including (1) jump diffusion process that does not go back to normal diffus ion, (2) risk drivers that do not follow the multiplicative stochastic movement, (3) private ri sk that has no market equivalent and hence violating the non-arbitrage option pricing assu mption. All of these are implemented simply through binomial lattice with M onte Carlo simulation or DTA. The RERO framework is applied to a real case in Atlanta. Valuation has two parts: (1) the improvement is modeled using a combined appr oach with Monte Carlo simulation, and (2) the incremental value using a separated decision ap proach with binomial lattice technique. The valuation result is very close to the actual closing price. Three conclusions can be drawn from this study: (1) acquisition and development has different characteristics and deserv e different kinds of attention; (2) consideration of managerial flexibility can change investment decisions; a nd (3) many unconventional real option valuation problems can be resolved by binomial lattice and Monte Carlo simulations. The novelty of this study is th e research subject: property acq uisition with excessive land. From the methodology standing point, the RERO framework is developed with ease of applicability in mind. It bri dges the gap between research and practice for real options applications in the real estate industry.

PAGE 15

15 CHAPTER 1 INTRODUCTION Background Our study touches a field that very few academicians have explored: the valuation model for acquisition of a property with excessive land that can potentia lly be converted into a new development. The three major schemes in real estate prope rty investment are acquisition, development, and operation. Acquisition is the ownership tran saction of land and improvement; development is the process of adding improvement to the land; and operation is the da ily management of the property. A majority of researchers focus on developm ent, perhaps due to its high uncertainty. Acquisition, on the other hand, has been ignored to a certain exte nt considering its volume and size of transactions. Acquisition has been rega rded as relatively low risk, since it is an investment on a touchable real property, whic h has historical operati ng track records, and numerous location attributes that last for decades and centuries. In recent years, however, r eal estate capitalization ra tes (defined by dividing the acquisition cost by annual net ope rating income) have compressed dramatically, meaning real estate is far more expensive to acquire than ev er before. It becomes critical to identify and explore any hidden value in an acquisiti on target in order to be competitive. The proposed acquisition model has two parts: firstly, valuation of the income producing part of the property, mainly the improvement; secondly, the incremental value, mainly the excessive land that, depending on the circumstance of where the property is located, may have no value or substantial upside value.

PAGE 16

16 The proposed real estate with real options (RERO) model is a framework that combines real options and decision tree analyses. This methodology not only overcomes the shortcoming of the current discounted cash flow method, but also is superior to the existing real options or decision tree analysis. Focusi ng on applicability in practice, this framework is developed intuitively using simple mathematics whenever possible. The improvement is modeled using a consolidated approach with Monte Carlo simula tion, and the incremental value using a separated decision approach with binomial lattice technique. Statement of Research Problem The fundamental value of real estate is th e income producing capability of the property, which depends on many factors such as the amount of rental income to collect, the operating and financing expenses, the level of ri sk of the cash flow, the apprecia tion or depreciation of property value, and the performance of alternative investment instruments in the financial market. Acquisition valuation is the project ion of future earning capability of a property related to other alternative investments. Trad itional valuation mainly focuses on the building improvement. With the drastic capitalization rate compression, however, it beco mes critical to identify and explore any hidden value in an acquisition. One such challenge is valuing a large partially vacant parcel that can be potentially converted into a new development. The attachment of excessive land to a prope rty is not uncommon. Some developments were initially planned in phases, but the later phases were ne ver implemented due to economic downturn or undesirable outcome of earlier phases. The land pl anned for later project phases thus remains vacant for a long time. Some early developments were planned on large parcels to insure sufficient space of surface parking. When the region becomes well developed and the economy turns to be more favorable, the vacant land becomes valuable for dense urban infill.

PAGE 17

17 Valuation of these parcels, however, is not as straightforward as a pplying the traditional Discounted Cash Flow (DCF) approach, which disc ounts expected future cas h flows at a certain discount rate to get the Net Present Value (N PV). In the case of infill land, without new development, all future cash flow will be 0; wi th certain assumptions of new development, it will generate a value. Intuitively, in a hot real es tate market where demand for developable land is high, such as in the South Florida, those parcels are extremely valuable. But in a warm or cold real estate market, the best use of such parcels may remain undeveloped until the market matures. The uncertainty and de velopment flexibility n eed to be taken into account. Whether or not the land would be developed, when, what type, and what size all matters during the property acquisition. Alternative approaches are Real Options Analysis (ROA) and Decision Tree Analysis (DTA). The ROA approach has evolved from the financial option pricing theory to value real assets. Put simply, by acquiring a property, the owner has the right, but not the obligation, to develop the excessive land to its fu ll use at a certain point of time in the future. Therefore, the value of a property with excess land should be higher than one without. The ROA methodology has been used to evaluate vacant land and to expl ain factors that affect development decisions. However, the ROA methodology requires one importa nt assumption, that st ochastic changes in the underlying value of the real asset to be devel oped are spanned by existing tradable assets or a dynamic portfolio of tradable assets the price of which is perfectly correlated with the real asset (Pindyck, 1991). This so called twin asset is hard to fi nd, especially for assets with private risk and rare events. Secondly, a lot of real opti ons are compound options, which are options on options, not simply on a single a sset, and consequently more co mplicated to solve by the pure option pricing methodology alone.

PAGE 18

18 The DTA approach evolves from management science. It is a method to identify all alternative actions with respect to the possible random events in a hierarchical tree structure. The DTA approach is developed to handle intera ctions between random events and management decisions. However, a major limitation of the DT A method is its use of the same discount rate throughout the valuation period, regardless of cha nging risk characteristics upon the execution of decision making, and thus allows for arbitrag e opportunity (Copeland and Antikarov, 2005). Recent studies have turned to the combination of option pricing methodology, decision analysis, and game theory to solv e real options problems. An ideal new approach should be able to address the unique characteristics of acquisi tion valuation with in fill land, to handle the management flexibility, to take into account rare events such as new amenities driving up real estate value. It also need s to be intuitively simple for practical implementation. Goal and Objectives To overcome the above mentioned disadvantag es of the current DCF, ROA, and DTA methodologies, this study has developed a framewor k, namely the Real Estate with Real Option (RERO) framework, as a combination of all thr ee methods to specifically value real estate acquisition with excessive infill land. The objectives of this study are to: Develop a theoretical integrated framework to address real estate acquisition problems; Study factors affecting real estate acquisition and devel opment, as well as their characteristics and statistical distributions; Test and validate the model by applying it to real cases. Research Scope The research subject is real estate acquisition, which includes the value of the structural improvement, and the incremental value represen ted by excess developable land. The definition of excess land is that in addition to the portion necessarily attached to the existing structural

PAGE 19

19 improvement; the excess portion that is large eno ugh for new development and at the same time meets local regulation requirements. Developmen t factors are outside of our scope. Potential users of the framework are real estate investors who need a tool to estimate the building value and the land value during propert y acquisition. The proposed valu ation model addresses mainly the economic risk and uncertainty for acquisition and development. Significance and Contributions The novelty of our study is the research subj ect: property acquisition with excessive land. To our knowledge, this is a fiel d that few researchers have addressed. From the methodology standing point, the RERO framework is developed with ease of applicability in mind. It bridges the gap between research and practice for real opti ons applications in the real estate industry. Organization of Dissertation In Chapter 2 we review the characteristics of real estate acquis ition, existing valuation approaches and their limitations, as well as what a new approach needs to achieve. In Chapter 3 we review the theory and technical details of th e different approaches currently available, in preparation for developing the proposed framew ork. We introduce the RERO framework in Chapter 4, including valuation procedures, the co mbined and separated approaches, and some new techniques developed to specifically apply to the case studies followed. Chapter 5 and 6 are case studies of the combined approach and sepa rated approach respectively. Collectively they illustrate how the RERO framework can be applied to a broad spectrum of scenarios in practice. In Chapter 7 we conclude the study and s uggest future research directions.

PAGE 20

20 CHAPTER 2 REVIEW OF REAL ESTATE VALUATION This chapter discusses the curr ent practice in acquisition valu ation, alternative approaches and their limitations, followed by a review of real options in real estate. It also analyzes how the proposed RERO framework needs to resolve th e practical problems unique to real estate acquisitions. Current Practice Distinguishing Acquisition and Development Analogous to the financial market, the three ma jor schemes in the real estate investment market are different and inter-related: acquisi tion, development, and operation. Acquisition is similar to a lumpy investment in a well es tablished company with, in many cases, 100% ownership interest. Development is similar to the seeding of a startup company and bringing it to Initial Public Offering. Oper ation is the income producing pro cess in the daily management of the property. This explains why research on development pr oblems may not directly apply to acquisition valuation problems. A real estate investment fi rm may have a different agenda for the infill land than a real estate developer. The business of real estate development is to acquire and accumulate a considerable land bank, wait for appropriate timing and market demand to build new properties, and realize profit by selling the ne w properties to institutional investors. The business of commercial real estate investment on the other hand, is to acquire existing properties, manage and improve th e properties to receiv e the operating income from leasing. As an investment vehicle, commercial real estates tend to be traded more frequently than vacant land. As buildings get older and functionally obsolete, they usua lly change hands from passive institutional investors to activ e value-added investors for cosm etic and functional upgrade and

PAGE 21

21 tenant-mix adjustment. The developers, however acquire land from different sources and wait more patiently in a real estate cycle before put ting up new products to ca pture the maximal gain. Short holding periods and different business inte rest makes the infill land less valuable to an investor than the vacant land to a developer. The major factors to consider during acquis ition are quite different from those in the development and operation processes (Figure 21). During acquisition, the major factors are location, market condition, mark et rent, pricing of the building and the land. Development factors, such as impact fee and school zoning, are outside the scope. If th e investor wins the bid, he goes through the due diligence and financing pro cess before actually plans for development of the vacant land. Although our model consists of the building value and the land value assuming possible development, it is by no means to substitu te for a detailed financial planning before the development breaks ground. Typical Acquisition Valuation Process A real estate investment company buys and manages properties to capture the cash flow from operation. Many of these companies specia lize in one or a few product types, such as office, retail, industrial, or re sidential properties. To evaluate a property with infill land, the management needs to answer the following questions: What is the building worth? What is the market demand for space? What is the likelihood that the company, after acquiring the pr operty, will put up new buildings? If the company does not intend to build new pr operties, what is the likelihood of the next buyer to put up new buildings? What type and size of development can add va lue to the land, and thus add value to the acquisition?

PAGE 22

22 Figure 2-1. Real estate phases and major factors to consider. Acquisition Feasibility Study Due Diligence End Public Relationship Design Construction Regulatory Schedule, Cost, Quality Control Permits, Approvals Equity, Loan, Title, Physical condition Zoning, Density, Incentives, Impact Fee, School zone Appearance, Plans, Structure, Building system Location, Market, Rents, Pricing of Property and land Community, Environmental Operation Rent, Expense, Tenant Improvement; Leasing Finance? Develop? Win Bid? N o Yes Yes Yes N o N o Disposition Sale price, Taxes, Loan repayment, Equity distribution Operate? Yes N o Acquisition Development Operation

PAGE 23

23 The typical decision process followed in curren t practice to acquire a property (an office building for example) with infill land is show n in Figure 2-2. First, th e building value and the land value are segregated. Build ing value is derived from the standard DCF projection. Depending on the investors perspective towards the market, the land could have no value or some value. In a weak demand region, the land probably does not generate any additional income besides parking, thus it has little or no value to the investor. In a strong demand region the investor conducts further inve stigation on the suitabl e product type to develop. If the best product type to develop is one that the investor is familiar with, say an office tower, the investor will further evaluate the projec t and land worth through a development model. If the best product type is not one the investor is familia r with, say a residential condominium or an industrial building, the in vestor probably hesitates to get i nvolved in the development alone. Figure 2-2. Current acquisit ion valuation process. Step 1: Segregating land value from building Step 2: Market demand analysis Step 3: Product type analysis Step 4: Assigning land value Step 5: Summing total value Potential Acquisition Building Value Land Value No Value Have Value To Build Not to Build Strong Demand Weak Demand Office Other Type Offer Price Land Value 0 Subjective Development Model

PAGE 24

24 The investor might either find a development partner or consider selling off the land to such an interested party. In either cas e, for the acquisition purpose the investor will simply assign a subjective value to the land. The offer price c onsisting of the building and the land value is derived and submitted to the broker. Current Real Option Approach and Limitations In the ROA approach, by acquiring the propert y the investor not onl y receives all cash flows generated from leasing of the existing building, but also has the right, but not the obligation, to develop the vacant land to its full use at a certain point of time in the future. Therefore, the value of a property with infi ll land should be higher than one without. However, the current ROA models are not with out limitations. Firstly, valuation methods for vacant land may not be suitable for infill land due to their different characteristics in the following aspects: (1) the price of acquiring the land could be substantially lower; (2) the building type to be developed may be restricted by zoning regulation on cu rrent property; (3) the synergy effect could be substantial between th e proposed building and the existing building; (4) The surface parking is an inseparable part of the existing property. Secondly, a real estate investment firm has a different agenda for the infill land than a real estate developer. Short holding periods and diffe rent business interests make the infill land less valuable to an investor than to a developer. Thirdly, the current theoretical models are on a higher level to addre ss real estate as a whole, while investors need practic al models to address individual cases. The current theoretical models are on an aggregate level to explain real estate value in genera l. They have rigid restrictions, and can only be applied to the simp lest cases (Miller and Park, 2002). They also lack flexibility to change variables to model rea listic assumptions for practical use. Real assets

PAGE 25

25 often possess unique location, physical and cont ractual characteristics, many of which are subjective and unquantifiable. Using the real option method alone may be insufficient. Last, the existing omnipotent real options models are mathematically correct but too complicated to be used. Trigeorgis (2005) and others have advocated approximate methods to simplify the calculation for practical applications. In summary, although the ROA approaches can overcome some of the drawbacks of DCF and provide better valuation for acquisition, the method itself is not fully developed to address the specific needs of acquisi tion valuation in practice. Decision Tree Analysis and Limitations Another available approach is the Decision Tr ee Analysis approach (DTA). DTA is a method to identify all alternativ e actions with respect to the possible random events in a hierarchical tree structure. It is developed to handle the inte raction between random events and management decisions. However, a major limitation of the DTA met hod is its use of the same discount rate throughout the valuation period, regardless of cha nging risk characteristics upon the execution of decision making, and thus allows for arbitrag e opportunity (Copeland and Antikarov, 2005). This means using DTA alone is not sufficient for the acquisition with infill land problem. Real Options in Real Estate Applications of ROA in the real estate i ndustry can be classified into the following categories: Vacant land for development, property redevelopment, and leasing (Ott, 2002). This section summarizes some theoretical mode ls as well as empirical studies. Theoretical Models Titman (1985) developed a simple binominal tree model to explain why a piece of land could be more valuable remaining vacant today and when is optimal to develop. This seminal

PAGE 26

26 work is frequently cited in later papers, whic h all use Partial Differen tial Equations (PDE) and fall into two major categories by methodology: th e optimal development timing problem, and the game theoretical problem. The optimal timing problem is represented by Clarke and Reed (1988, optimal timing and density for resident ial development), Capozza and Helsley (1990, conversion from agricultural to urban land us e), Williams (1991, optimal timing and density to develop, optimal timing to abandon), and Geltner et al. (1996, two land use choice). The game theoretical problem is represented by Williams (1993, competition on simultaneous development), Grenadier (1996, competition on si multaneous or sequential development), and Childs et al. (2001, inefficient market with noi sy effect on value). Figure 2-3 shows the genealogical relationship among these models. Ta ble 2-1 itemizes the research subject, model variant, contributions and limitations of each study. Besides land valuation, there are two types of re al estate applications of the ROA that are closely related to our research: property rede velopment and operational research. Williams (1997), Childs at al. (1996), Cederborg a nd Ekeroth (2004) have researched on the redevelopment or renovation of real assets. They view existing bu ildings as assets that can be repetitively invested and improved, sometimes by changing functional attributes, e.g., switching from offices to apartments. Grenadier ( 1995, 2003), Adams, Booth and MacGregor (2001), Bellalah (2002), Grenadier and Wang (2005), Capozza and Sick (1991), among others have focused on options embedded in the commercial lease agreements, such as forward leases, escalation clauses, leases with options to renew or cancel, adjustable rate leases, purchase options, sale-leasebacks, ground leases, etc. Acquisitions have not been thoroughly research ed using the real opt ions approach, though common in practice. As discussed earlier, ac quisitions with excessive land differ from ground

PAGE 27

27 up development. They also differ from redevelopm ent, since they are not simple renovations of the existing buildings. They might include valuat ion of the leases as a source of cash flow for the potential development, but would require a much simpler valuation process on the leases. In summary, although acquisition valua tion is close to the three s ubjects mentioned above, the approach is significantly different. A new approach needs to be ab le to address both the building value and the land valu e, if any, for potential development. Figure 2-3. Real Options approaches for land valuation. Titman Clarke & Reed Cappozza & Helsley Williams Geltner et al. Williams Grenadier Child et al. 1985 1987 1990 1991 1993 1996 2001 Competition / Game Development Timing

PAGE 28

28 Table 2-1. Comparison of research subjects, m odel variants, contributions and limitations. Author / title Subject description Model type & variant Contribution / limitation "Urban Land Prices under Uncertainty" (Titman, 1985) Explain why land is more valuable remaining vacant for future development: increased uncertainty leads to a decrease in current development activity. One time period binomial model assuming rents have two state values. Seminal work of ROA in real estate. Simple. Two policy implications: (1) Government incentives to stimulate construction activities may actually lead to a decrease if the extent and duration of the activity is uncertain. (2) Initiation of height restrictions may lead to an increase in development activity due to reduced uncertainty regarding the optimal height of the area. One time period model. Assume only two states, and that construction costs are certain. "A Stochastic Analysis of Land Development Timing and Property Valuation" (Clarke and Reed, 1987) Examine the qualitative effects of the different types of uncertainty on the timing and structural density of land development on residential projects. PDE to solve for optimal development timing and density assuming rents and development cost follows stochastic processes. Limited to residential development. Two limited assumptions: (1) new construction is small so that rents and development costs are uninfluenced by the newly added construction. However, in reality development is lumpy and will affect market rents and vacancy rate. (2) Efficient market in which all agents have equal information about the future probability distributions of rentals and costs. However, in reality real estate leasing and sales information is not as transparent as that in the stocks market, but more predictable, at least in a short run.

PAGE 29

29 Table 2-1. Continued. Author / title Subject description Model type & variant Contribution / limitation "The Stochastic City" (Capozza and Helsley, 1990) Examine the land value of conversion from agricultural to urban use based on spatial characteristic of real estate such as distance or commuting time to the CBD. PDE model built on the traditional monocentric urban theory to study spatial implication of land conversion value, assuming household income, rents and land prices follow stochastic processes. Uncertainty (1) delays the conversion of land from agricultural to urban use, (2) imparts an option value to agricultural land, (3) causes land at the boundary to sell for more than its opportunity cost in other uses, and (4) reduces equilibrium city size. Does not explain very well land value in the emerging suburb economic centers. "Real Estate Development as an Option" (Williams, 1991) Optimal time to develop, optimal development density, and optimal time to abandon a project. PDE model to solve for optimal timing of abandoning a project, in addition to optimal development timing and density, assuming carrying cost, rents and development cost follows GBM, also assuming carrying cost is significantly high so that during some circumstance it is better to abandon the project than bearing the cost. Looks at the downside of a project: optimal time to abandon. This is a put option. Maximum feasible density is determined by zoning restrictions. Assumes perfectly competitive market and perpetual option. "Insights on the Effect of Aland Use Choice" (Geltner et al. 1996) Examine whether the multiple-use zoning add value to land by analyzing the land use choice between two different use types. PDE to solve for optimal choice between two land use types, assuming development cost, value of first land use, value of second land use follow stochastic processes. Land use type choice is a unique perspective in real estate. Assume construction unit cost is the same regardless of building type to be developed.

PAGE 30

30 Table 2-1. Continued. Author / title Subject de scription Model type and variant Contribution/ limitation "Equilibrium and Options on Real Assets" (Williams, 1993) Examine industry equilibrium of optimal exercise policy under competition: the impact of competition erodes the value of the option to wait and leads to investment at very near zero net present value thresholds. PDE to solve for perfect Nash equilibrium with finite elasticity of demand and finite development capacities in a less than perfectly competitive environment. Among the first to consider the effect of competition. Exercising options to develop affects the aggregate supply of developed assets and market price, which preclude simultaneous exercise of the option among all developers. "The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets" (Grenadier, 1996) Explain why building booms in the face of declining demand and property values: fearing preemption by a competitor, developers proceed into a panic equilibrium in which all development occurs during a market downturn. Three-stage model to explain real estate boom-and-bust cycle: valuation of land, construction lag, and "sticky vacancy" in operation Extend the Williams model from symmetric and simultaneous equilibrium to either simultaneous or sequential development, and allows for preemptive equilibria. Powerful to explain boomand-bust markets such as real estate. Assume individual firms are identical and have all information. "Noise, Real Estate Markets, and Options on Real Assets: Theory" (Childs et al. 2001) Optimal valuation of noisy real asset in an incomplete information game PDE, assume optimal value include three terms: forward value estimate, historical value estimate, and the term that corrects for convexity effects due to incomplete information Extend to include the price lagging effect in real estate, where estimate value is different from market value, i.e., in a less than perfect market.

PAGE 31

31 Empirical Testing A majority of the ROA empirical works in real estate has been in aggregate studies. Quigg (1993), Holland et al. (2000), Sivitanidou and Siv itanides (2000), Bulan et al. (2004) all use a large sample of real estate data to test the premium of land price over intrinsic value, whether irreversibility is an important factor for real estate investment, whether uncertainty delays construction, and whether competitions among deve lopers decrease the option value of waiting. As Bulan et al. (2004) point out, however, sin ce real options models apply to individual investment projects and predict that trigger prices are non-linear, aggregate investment studies may obscure these relationships. Mo reover, these empirical tests are limited to qualitative results, such as whether each variable in the ROA model has positive or negative effect on the overall option value. Few of the ROA empirical works has focused on individual case studies and its implication in practice. The RERO Approaches The RERO framework attempts to move beyond th e realm of academic interest to be used quantitatively in practical problems of acquisi tion valuation, development decision making, and land policy analysis. The approach should be able to address the unique characteristics of acquisition valuation with infill land, to handle the management fl exibility, to take into account rare events such as new amenities driving up real es tate value. This calls for the combination of DCF, ROA and DTA methodologies. It also needs to be intuitively simple for practical implementation. To achieve this goal, the problem is divided into two sub-problems: (1) valuation of the building structure and (2) valuation of the in fill land. Valuation of the building structure represents a normal case of acquisition. On the other hand, valuation of th e infill land represents

PAGE 32

32 the extra value stemmed from creative management i.e., the ability to uncover the hidden value in real estate and realize it through active development. Real estate valuation is an art and scien ce. The RERO framework is not built on rigid reasoning and restricted assumptions to be precise, rather it is developed as a tool to solve a broad spectrum of practical r eal options problems. Specificall y, it explores a few unconventional real option cases, including (1) jump diffusion pr ocess that does not go back to normal diffusion, (2) risk drivers that do not follow the multiplicati ve stochastic movement, (3) private risk that has no market equivalent and hence violating the non-arbitrag e option pricing assumption. The mathematical models for these kinds of unconven tional problems could be very complicated, if written in PDE equations. To facilitate pract ical implementation, the RERO framework applies the binomial lattice with Monte Carlo simulati ons and decision analysis method. The RERO framework is a simple yet powerful tool, intuitive to the practitioners, yet mathematically correct and precise. Summary This chapter compares the difference between real estate acquis ition and development, reviews current practice of real estate acquis ition valuation, discusses the three alternative valuation approaches, DCF, ROA, DTA and their limitations. Built on the strengths of these three approaches, the RERO framework needs to address practical problems of acquisition valuation, development decision making, and land policy analysis. The next few chapters explore modeling details of how this concept should be implemented.

PAGE 33

33 CHAPTER 3 LITERATURE REVIEW In Chapter 2 several different valuation me thodologies were discussed conceptually: the Discounted Cash Flow approaches (DCF), the Real Option Analysis approaches (ROA), the Decision Tree Analysis approaches (DTA), and the proposed Real Estate with Real Option approaches (RERO). In this chapter the technical modeling details of the first three approaches, as well as the capital budgeting theory in finan ce will be discussed. The RERO approaches that built on the existing three will be discussed in Chapter 4. Traditional Discounted Cash Flow Approaches The Discounted Cash Flow (DCF) approaches include payback period, Internal Rate of Return (IRR), Net Present Value (NPV), and other fo rms such as Adjust Present Value. In this study DCF refers to the NPV method alone. The principle of the NPV me thod is to discount all projected free cash flow back to year 0, to get th e net present value of the project (Equation 3-1). The NPV must be greater than 0, or the IRR must be greater than the companys hurdle rate, in order to justify the investment (Mun, 2002). If NPV is greater than 0, the pr oject is regarded as optimal to be executed immediately. n i i ik F NPV0) 1 ( (3-1) where NPV is the net present value of the project at Year 0, Fi is the projected free cash flow (including income, cost and terminal value) in year i k is the project discount rate. The DCF method is suitable to evaluate projec ts that are well structured, with predictable future cash flows. For projects involve large uncertainty of timing, cost and cash flows, such as a real estate development, usi ng the DCF approaches are difficult in the following three aspects (Miller and Park 2002; Feinstei n and Lander 2002): firstly, sele cting a fixed and appropriate

PAGE 34

34 discount rate; secondly, taking into account new information and ch anging the plan accordingly; thirdly, determining the optimal timing to carry out the project. Capital Budgeting Theory In the DCF approach and in all other approaches one of the most influential factors is the discount rate to be used. To better understand discount rate, a brief di scussion of the capital budgeting will follow. Market Risk and Private Risk Stocks are risky. For any i ndividual stock, however, a larg e part of its risk can be eliminated by holding it in a large well-diversified portfolio. A portfolio consisting of all stocks is called a market portfolio. In reality, it can be approxi mated by a large amount of welldiversified stocks. The part of th e risk of a stock that can be elim inated is called private risk, or diversifiable risk; while the part th at cannot be eliminated is called market risk, or systematic risk (Brigham et al. 1999, p178). The Capital Asset Pricing Model (CAPM) indicates that the relevant riskiness of any individu al stock is its contri bution to the riskiness of a well-diversified portfolio, or the market risk porti on only, which is measured by its coefficient. Capital Asset Pricing Model If the market portfolio m is efficient, the required return rs of any stock i is the risk-free interest rate r plus a risk premium, as shown in Equation 3-2. ) ( r r r rm i s (3-2) Where r is the risk-free return, mr is the expected market return, 2m im i where im is the covariance between the stock and the market, and 2 m is the variance of the market portfolio.

PAGE 35

35 i is an important variable to measure the risk characteristics of the stock i If i is greater than 1, the stock is more volatile th an the average stock market; and if i is less than 1, the stock is less volatile than the average stock market. The more volatile a stock is, the more risky it is, and consequently the higher the requi red return needs to be in order to justify the risk an investor takes. Discount Rate A firms hurdle rate is usually its Weighted Average Cost of Capital (WACC). A large real estate investment firm is usually formed as a Real Estate Investment Trust (REIT), which does not pay income taxes, so long as 95% of its income from operation is distributed to the investors on an annual basis. The WACC k of a REIT is calculated by Equation 3-3. V D r V S r kd s (3-3) where rs and rd are the cost of equity and debt respectively, S, D and V are the market values of equity, debt, and total asset respectively; S + D = V. Equation 3-3 can also be used to value an i nvestment project, as if every project was a separate mini company. However, it is difficult to determine the cost of equity and debt for a project, since the equity of a start-up project, for example, ma y not be publicly traded, and the risk characteristics of a projec t are quite different than that of the company as a whole. The capital budgeting theory indicates that fi nding the right discount rate is extremely difficult, if not impossible. Since every company has different risk charac teristics, the required discount rate is different from company to co mpany. Also every project within the same company has different risk characteristics, a nd the correct discount ra te required to value a project may not be the same as the company s WACC. This makes both the DCF and the DTA

PAGE 36

36 approached difficult to value infill land with development potential, although for an existing building with operating history the DCF and DTA approaches may work fine. Option pricing theory, on the other hand, does not rely on the risk characteristics of a particular firm or project. Neith er does it rely on the risk preferen ce of an individual investor. It is discounted at the risk-free interest rate r. The reason is that private risk is alleviated through portfolio diversification and market risk can be diminished through the options replicating portfolio (Miller 2002). For deve lopment project that involves a lot of uncertainty, this is a huge benefit over the traditional DCF method. Option Pricing Theory Definition and Type of Options An option gives the holder the right but not the obligation to do something (Hull, 2006). In the financial market, there are two basic types of options: call options and put options. A call option gives the holder the right to buy the underlying asset by a certain date for a certain price. A put option gives the holder the right to sell the underl ying asset by a certain date for a certain price (Figure 3-1). Based on exer cise dates, options can be cla ssified into two major types: American options can be exercised at any time up to the expiration date. European options can be exercised only on the expiration date. Mo st options are of the American type. The value of a financial option is determined by the current price of the underlining asset S0, the strike price at maturity date K, the risk-free interest rate r, maturity date T, return volatility of the underlining asset and sometimes the dividends e xpected during the life of the option (Hull, 2006). Returns on options are asymme tric, i.e., options will only be exercised to the benefit of the holders. For example, if a holder of a call option can buy the stock 3 months later for $100 per share, and if the spot pri ce at maturity becomes $120 per share, he will exercise this option, then sell the stock immediately, and earn $20 per share. However, if the spot

PAGE 37

37 price becomes $83 per share at maturity, he can let the option expire without exercised, thus avoid losing $17 per share. He only losses the pr emium initially paid for the option (Figure 3-2). His payoff is the difference between the spot price at maturity St and the exercise price K, or 0, whichever is greater (Equation 3-4). ) 0 (K S Maxt (3-4) Figure 3-1. Payoff of call option and put option. Figure 3-2. Call option payoff example. Option pricing theory is to determine what pr emium, or option price, a holder should pay for such flexibility. The types of option pric ing methodology include co ntinuousand discretetime models (Miller and Park, 2002; Lander a nd Pinches, 1998). Continuous-time models 0 Payoff Stock Price K Call Option Premium 0 Payoff Stock Price K Put Option Premium 0 Payoff Stock Price K=$100 Call Option Example S=$120 S=$83 100 120 20 83 0 Example Payoff

PAGE 38

38 include closed-form equations and stochastic partial differential e quations. Discrete-time models are mostly lattice models and Monte Carlo simulation. Black-Sholes Model and Stochastic Partial Differential Equations The most famous closed-form equation is the Black-Scholes model, although it can only be used to price European options. The Black-Sc holes (1973) pricing formula is developed under the following ideal assumptions: stock price change follows the Wiener process, distribution of return is lognormal, efficient market, constant short-term interest rate no dividend payment, no transaction costs, and short se lling is possible. A Wiener pr ocess, also called a Geometric Brownian Motion (GBM), is a rando m process with a mean change of 0 and a variance rate of 1. The values of dz for any two different short intervals of time dt, are independent (Equation 3-5). dt dz (3-5) Where has a standardized normal distribution ) 1 0 ( and ) ( denotes a probability distribution that is normally distributed with mean and standard deviation A generalized Wiener process for a variable S can be defined by Equation 3-6. Sdz Sdt dS (3-6) where S is the underlying asset whose value change follows the Wiener process; dS is the change of value S during an infinitesimal time interval dt Ito's Lemma (Hull, 2006, p273) is a theorem of stochastic calculus th at shows second order differential terms of a Wiener Process can be consid ered to be deterministic when integrated over a non-zero time period. Since the stock price S follows the Wiener process, an option f (be it a call option or a put option) contingent on S follows the Itos Lemma (Equation 3-7). Sdz S f dt S S f t f S S f df ) 2 1 (2 2 2 2 (3-7)

PAGE 39

39 The principle of option pricing methodology is to construct a riskless portfolio to prevent arbitrage. This portfolio is short one option and long S f shares of the underlying stock. When the stock price S changes, the S f shares must change accordingly. Later from Equation 3-10 we will see this portfolio is riskless because it does not involves dz over the time interval dt The portfolio is written as Equation 3-8. S S f f (3-8) During the time interval dt, the change in value of the portfolio is represented in Equation 3-9. dS S f df d (3-9) Substitute dS from Equation 3-6 and df from Equation 3-7 into Equation 3-9, dt S S f t f d) 2 1 (2 2 2 2 (3-10) To prevent arbitrage, the portf olio earns risk-free interest r during the time interval dt. dt r d (3-11) From Equation 3-8, Equation 310 and Equation 3-11, we have dt S S f f r dt S S f t f) ( ) 2 1 (2 2 2 2 Which simplifies to rf S S f S S f t f 2 2 2 22 1 (3-12) Equation (3-12) is the Black-S choles partial differential e quation. Subjected to the following boundary conditions: ) 0 (K S Max f when t = T in the case of a call option, and

PAGE 40

40 ) 0 (S K Max f when t = T in the case of a put option. Integrating Equation 3-12, the Black-Scholes fo rmula can be written as Equations 3-13 and 3-14 (Black and Schol es, 1973; Hull, 2006). ) ( ) (2 1 0d N Ke d N S crT (3-13) ) ( ) (1 0 2d N S d N Ke prT (3-14) where T T r K S d ) 2 / ( ) / ln(2 0 1 ; T d T T r K S d 1 2 0 2) 2 / ( ) / ln( ; c is the value of a European call option; p is the value of a European put option; S0 is the current price of the underlying asset; K is the strike price of the option at maturity; r is the risk-free interest rate; T is the time to maturity; N() is the cumulative standard normal distribution function. The Black-Scholes model can be divide d into two parts: The first part, S0N(d1) derives the expected benefit from acquiring a stock right now. This is found by multiplying stock price S0 by the change in the call premiu m with respect to a change in the underlying stock price N(d1) The second part of the model, Ke-rTN(d2) gives the present va lue of paying the exercise price on the expiration day. The fair market value of the cal l option is then calculate d by taking the difference between these two parts. The boundary condition of a call option is best depi cted in Figure 3-3. The solid black line defines the call option value. The green line with square markers defines the maximum value of the option. For non-arbitrage, the option should never be wort h more than the stock price S otherwise an arbitrageu r can easily make a risk-less profit by buying the stock and selling the call option. The blue line with tr iangle markers defines the minimum value of the option. The call

PAGE 41

41 option should be worth more than ) 0 (0rTKe S Max otherwise an arbi trageur can buy an option, short sell a share of stock, invest the surplus at risk-free interest rate and earn a profit. The possible option values fall in the region defi ned by the green line and the blue line and vary depending on the underlying stock volatility, option time to maturity, and risk-free interest rate. Call Option vs. Stock Price 0 30 60 90 120 150 0306090120150 Stock PriceCall Optio n Lower Bound Option Value Upper Bound Figure 3-3. Call premium vs. security price. Though the Black-Scholes prici ng model has a lot of restri ctions and can only value European options, there are a lot of stochastic partial differential equations with boundary conditions that relax some restrict ions to a certain extent and can be used to value more specific questions. The benefits of these analytic contin uous-time models are that they are flexible to model different circumstances, and mathemati cally accurate (Mille r and Park, 2002). The

PAGE 42

42 drawback is that the modeli ng requires sophisticated mathem atical knowledge, sometimes the solution does not exist, and even if it does, the process itself could become as complicated as a black-box for the practitioners to co mprehend (Lander and Pinches, 1998). In the case when analytical solutions to the stochastic differential equations do not exist, they must be solved numerically by using finite -difference methods, or Monte Carlo simulations (Miller and Park, 2002). Lattices Lattices are a type of discrete time model, which includes binomial tree, trinomial tree, quadranomial tree, and other multinomial models. Lattices are the approximation of the continuous models. The results of these two methods are very close when the time interval is infinitely small. The most commonly used binomial lattice wa s developed by Cox et al. (1979), in which values of the underlying asset are assumed to fo llow a multiplicative binomial distribution. The model assumes the up and down parameters u and d the volatility of the underlying asset and risk-neutral probabilities p and 1 p are constant (Figure 3-4). Figure 3-4. Stock and option pri ce in a one-step binomial tree. An option f (be it a call option or a put one) is va lued by constructing a risk-less portfolio of a long position in shares of stock and a short pos ition in 1 option (Equation 3-15). S0 f S0d fd S0u fu p 1 p

PAGE 43

43 f S 0 (3-15) In an up movement of the stock pric e, the value of the portfolio is u uf u S 0 In a down movement of the stock pric e, the value of the portfolio is d df d S 0 The two are equal when d uf d S f u S 0 0 or when ) (0d u S f fd u (3-16) The portfolio is risk-less and must earn the risk-free interest rate r The present value of the portfolio is repres ented by Equation 3-17. rT ue f u S ) (0 (3-17) From Equation 3-15 and Equation 3-17, we have rT ue f u S f S ) (0 0 (3-18) Substitute from Equation 3-16 into Equation 3-18, ] ) 1 ( [d u rTf p pf e f (3-19) where d u d e prT Te u u d1 Equation 3-19 is a one-step binomial model, wh ich can be generalized to two-step and multi-step models. Figure 3-5 shows a two-step binominal lattice. During each time step, the

PAGE 44

44 stock value either moves up to u or down to d of its previous value. Option value is derived by working backward from fuu and fud to calculate fu, from fud and fdd to calculate fd, then from fu and fd to calculate f (Equations 3-20, 3-21 and 3-22). Figure 3-5. Stock and option pri ces in general two-step tree. ] ) 1 ( [ud uu rt uf p pf e f (3-20) ] ) 1 ( [dd ud rt df p pf e f (3-21) ] ) 1 ( [d u rtf p pf e f (3-22) Substituting from Equation 3-20 and Equation 3-21 into Equation 3-22, we get ] ) 1 ( ) 1 ( 2 [2 2 2 dd ud uu rtf p f p p f p e f (3-23) where d u d e prt te u u d1 In general, for a binomial lattice with n steps, the ith step (n i 0) option value is calculated by Equation 3-24. S0 f S0d fd S0u fu S0ud fud S0uu fuu S0dd fdd

PAGE 45

45 ] ) 1 ( [, 1 1 d i u i rt if p pf e f (3-24) Lattice, though still complicated, is more intuit ive to the practitioners than continuous time models. It is especially useful to evaluate American options, si nce analytic solutions are almost non-existing in the continuous models. The drawback is that using lattice by itself is hard to model compound options. However, combined with DT A, lattice is capable to deal with a lot of complicated situations, even more flex ible than PDEs in many circumstances. Monte Carlo Simulation Originally named after the casinos in Mont e Carlo, Monaco, Mont e Carlo simulation is about games of chance. It is now widely used to simulate stochastic processes by sampling large quantity of random outcomes for the processes (F igure 3-6). Because of the repetition of algorithms and the large number of calcula tions involved, Monte Carlo simulation is computationally complex, yet easy to model and understand. Figure 3-6. Monte Ca rlo simulation output.

PAGE 46

46 In real options modeling, Monte Carlo simu lation can be used where there are several underlying variables. The drawback is that it is difficult to work backward to determine option exercise strategy, since Monte Ca rlo simulation is forward looking. In the RERO model, it is used as an intermediate step to estimate volatilit y of the project stems from multiple risk drivers. Real Options Analysis Approaches First coined by Myers (1977), the ROA approach es are to apply financial option pricing theory and methodology to evaluate real assets (Miller and Park, 2002; Trigeorgis, 2005). In the financial market, a derivative is a security whos e value changes depend on the value changes of some other underlying assets. In real asset valua tion, the value of a project can be viewed as a derivative contingent upon input costs, output yield, time and uncertainty (Miller and Park, 2002), and therefore can be evaluated by applyi ng the financial option pricing principles. By using ROA, investment deci sions are viewed as real options or combinations of real options, such as options to defer, expand, switc h, contract, or abandon, as shown in Table 3-1 (Trigeorgis, 1996; Yao and Jaafari, 2003). Also included in the ta ble are examples in the real estate and construction industry. Contrary to DCF method, in th e ROA context greater volatility is not always worse, since losses are limited to the initial investment, or option premium, but the option holder can capture greater ups wings if things turn out to be favorable. ROA is applied most commonly in the industries of natural re source, manufacturing, energy, research and development, start-up companies, and others (Lander and Pinches, 1998; Trigeorgis, 1996). Applications in the real estate and cons truction industries are still limited. Although ROA borrows the option pricing theory, the distinguish charac teristics of real assets demand different valuation assumptions and methodologies from direct applications of the option pricing theory without any modification. Table 3-2 lists the major differences between financial options and real options (Mun, 2002).

PAGE 47

47 Table 3-1. Types of real options. Options Features Examples Defer To postpone constructio n till optimal timing Time to develop Stage To create a series of stages to allow for abandonment or expansion in later stages depending on outcomes of earlier stages Phased development Contract To contract the project to a third party in order to mitigate risk or to speed up market domination Franchise stores Expand To expand the project scale in favorable market conditions Airport expansion Abandon To abandon the project and prevent severe lost in unfavorable market conditions Bankruptcy of a project entity Switch input/output To change the output mix or input mix in response to changing market demand Coal-fired vs. gasfired power plants Compound Option on option, where the value of an earlier option can be affected by the value of later options. Most real world options are of this kind Case study in Chapter 5 and 6 Table 3-2. Comparison between Fi nancial Options and Real Options. Characteristics Financial options Real options Maturity Short, usually in months Long, usually in years Underlying asset Traded stocks, with comparables and pricing information Not traded project free cash flow, proprietary in nature, with no explicit market comparables Management manipulation Value does not change due to individual management assumptions or actions Value has to do with individual management assumptions and actions Competition and market effect Irrelevant to pricing Direct drivers of value One of the major differences between financia l options and real opti ons is how to handle private risk. The underlying assets of financial options are traded market assets, and market risk is the major source of risk among all financial op tions. Private risk can be treated simply as errors. The underlying assets of real options, however, are usually non-traded assets that do not

PAGE 48

48 have market equivalent. Private risks cannot be hedged. The other difference is the effect of management and competition. Financial opti ons on the same underlying asset and the same maturity date are identical. They are widely he ld to be market efficient. A single transaction usually does not affect the pricing of financial options, neithe r does management or competition. Real options, on the other hand, are lumpy or one-ofthe-kind in nature. Exer cise of real options by management can have profound imp act on the underlying asset value. Consequently, there are a lot of debates in the academic world about how real options should be correctly priced. Borison (2005) classi fied existing real opti ons approaches into 5 categories: The classic approach, The subjective approach, The Market Asset Disclaimer approach, The revised classic approach, and The integrated approach. Borison also discussed the underl ying assumptions of these ap proaches, the conditions that are appropriate for their applications, and the mechanics in applying them. The classic approach assumes that the capital market is complete, and an identical twin asset or portfolio exits for every real asset under evaluation. It ma kes explicit use of no-arbitrage argument, and applies directly the Black-Shores formula. The subjective approach also assumes that th e capital market is complete. However, it relies on subjective judgment for input, as opposed to data from traded markets. This makes it an inconsistent approach, and limits to qualitative result. The Market Asset Disclaimer (MAD) approach assumes that the capital market is not complete. It relies on the estimate value of the a sset without flexibility as the twin asset for the purpose of calculating the option va lue of the flexibility. Data is drawn from traded markets

PAGE 49

49 when available, and subjective judgment when not. Proponents of this approach justified this step explicitly: the same, weaker assumptions that are used to justify the applications of DCF can be used to justify the applica tions of option pricing to flexib le corporate investment (Copeland and Antikarov, 2001). The revised classic approach assumes that the capital market is partially complete. It attempts to divide the world into black and white: For investments that have market equivalents, it applies the classic approach using market da ta; for investments that do not have market equivalents, it applies decision anal ysis using subjective judgment. The integrated approach also assumes that the capital market is partially complete. However, it uses capital market data for market risk and subjec tive judgment for private risk in an integrated model. The major difference among these approaches is how private risk is handled. The classic approach ignores private risk completely and treats real options exactly like financial options that all risks can be diversif ied away by constructing a hypothetical traded twin asset or portfolio. The subjective approach handles private ri sk by substituting market data by subjective assessment. The revised classic approach admits th e limitations of direct applications of option pricing theory to real options analyses and classifies invest ments into those either dominated by market risk or by private risk. It applies the option pricing mo del only to investments dominated by market risk, and applies decision analysis to those dominated by privat e risk. Although it is a better approach than the previous two, the revised classic appro ach forces all investments into black or white, and implements tw o totally different approaches. The MAD approach, on the other hand, admits th e difficulty of handli ng private risk, thus does not rely on the existence of a traded replica ting portfolio. Instead, it uses the project value

PAGE 50

50 itself without flexibility as the twin security, as if it were traded in the financial market. After all, the best correlation with the project is the project itsel f (Copeland and Antikarov, 2001). Trigeorgis (1996) also argued that the assump tions underlying the DCF approach are traded assets of comparable risk (same beta), and MAD assumptions are no stronger than those of DCF. Contrary to Borisons unders tanding, Copeland and Antikar ov (2005) clarified that the MAD approach does not blindly use all subjectiv e assumptions. Similar to the integrated approach, MAD also uses traded market data whenever available, and uses subjective assumptions only when market estimates are impo ssible. The MAD approach and the integrated approach are considered to treat private risk in the same way, the difference remains only technical: MAD relies on simulations to evaluate project volatility, and attempts to combine all risks into one variable, whenever possible; wh ile the integrated approach relies on utility functions, and models market risks and private risks explicitly and separately. Neither is superior to the other, and the selection of approaches depend s on project characteristics on a case-by-case basis. For this reason, the pr oposed RERO approaches are built on the MAD and the integrated approaches. Practical Real Options Model in Real Estate Ghosh and Sirmans (1999) were among the first to address the applicatio ns of real options to the corporate real estate pr actitioners, by developing a lookup table for the options value, which is derived from an approximation of the Black-Scholes formula. They used the correspondence in Table 3-3 between financial a nd real options in orde r to apply the BlackScholes formula directly to real options. However, they did not explain whether the time value of money r is a risk-free rate or riskadjusted discount rate, nor how the risk of project cash flows is determined.

PAGE 51

51 Table 3-3. Correspondence between Financial and Real Options. Variable Financial options Real options S0 Stock price Present value of proj ects expected cash flows K Exercise/strike price Cost of investment T Time to expiry Length of time the decision can be deferred r Risk-free rate Time value of money Standard deviation of stock returns Risk of project cash flows They also developed a three-step appr oach to calculate the option value: Step 1: Calculate NPVq from Equation 3-25. T qr K S NPV ) 1 /(0 (3-25) Step 2: Calculate T Step 3: Read the value of th e call option as a percentage of the value of the underlying asset from the table. For example, if the stock price S is $100, strike price K is $100, time to expiry T is 1 year, time value of money r is 5%, standard deviation of annual return is 20%, then 05 1 ] ) 05 1 /( 100 /[ 100 ] ) 1 /( /[1 T qr K S NPV 20 0 1 20 0 T From the look-up table, C is 10.4% of the asset value, 40 10 $ 100 104 0 C. They did not specify how the look-up table is computed, but by comparing the BlackScholes formula and their three-step approach, it is not difficult to find that they did some approximations in order to simplify the calculation. From the Black-Scholes fo rmula of Equation 3-13,

PAGE 52

52 ) ( ) (2 0 1 0d N S Ke d N S CrT (3-26) where T T r K S d ) 2 / ( ) / ln(2 0 1 ; T d T T r K S d 1 2 0 2) 2 / ( ) / ln( Tr K ) 1 ( is an approximation of rTKe, and Tr K S) 1 /(0 can substitute K S0, T r ) 2 / (2 is ignored due to the low impact on the overall value. With the approximation and substituting Equation 3-25 into Equation 3-26, we have T NPV N NPV S Cq q) ln( 1 10 (3-27) Equation 3-27 is the formula to develop the look-up table. The Ghosh and Sirmans model falls into the subjective approach cat egory of Borisons classification (Borison, 2005). As discussed in the previous s ection, this approach uses subjective assessment of variables without justification of its appropriateness. At a first glance, this approach is intuitive, especially for practitioners who are co mfortable with NPV but unfamiliar with ROA. However, this direct application of the Black-Scholes model is not without its limitations. Firstly, it is restricted to European options, where timing of execution of the option is perfectly known in advance. Secondly, it assumes future cash flow is as deterministic as in the traditional NPV method, and allows for only one scenario analysis. It does not allow for stochastic and dynamic changes of the underlyi ng variables, such as development cost and rental rate, does not solve for optimal developm ent timing. Lastly, while there is a trade-off between simplicity and accuracy the value derived from the look-up table has 10% variance

PAGE 53

53 from that calculated from the Black-Scholes model, which is deemed inaccurate in many circumstance. In summary, the model developed by Ghosh and Sirmans is a good attempt to build the understanding of management flexibility value of corporate real estate in practice, however, it lacks accuracy and depth of applicability in the real es tate industry, which is what this study plans to overcome. Decision Tree Analysis First coined by Howard (1964, in Ng and Bjornsson, 2004), decision analysis is the discipline comprising the philosophy, theory, me thodology, and practice necessary to address important decisions. Graphical representation of decision an alysis problems commonly use influence diagrams and decision trees. DTA is a method to identify all a lternative actions with respect to the possibl e random events in a hierarchical tree structure. It is developed to handle the interaction between random events and manage ment decisions. Uncertainties are represented through probabilities and distributio ns. The attitude of a decision maker to risk is represented by utility functions. Unlike the DCF approaches, there are no objecti vely correct DTA models. An appropriate model depends on the preferences a nd beliefs of the decision maker and hence is subjective. A decision analysis includes the following typical step s: first, defining the scope of the analysis; second, setting up a decision basis, including gene rating alternatives, collecting information, and estimating risk preference; third, constructing a decision tree with decision and uncertainty nodes; and forth, analyzing sensitivity of factors that have the largest effects (Ng and Bjornsson, 2004). Decision analytic methods are used in a wi de variety of fields, including business, environmental remediation, health care research and management, energy exploration, litigation and dispute resolution, etc.

PAGE 54

54 DTA relies on subjective assessment of probabil ities and distributions. This method alone cannot prevent arbitrage opportunity. Howeve r, the combination of ROA and DTA can eliminate the short-coming of both, and creates a much better approach. Summary In this chapter we reviews modeling details of the DCF, ROA, DTA approaches, as well as capital budgeting theory, ROA applica tions in real estate. Treatmen t of private risk differentiates these approaches from one another. In ROA methodologies alone, there are various approaches advocated and debated in the academ ic community. Due to the char acteristics of real options, it is inappropriate and inaccurate to directly apply the option pricing formula without any modification. The correct real option methods must be able to handle private risk as well as market risk in a consistent way. Only the M AD and the integrated approaches are considered appropriate and are subject to further use.

PAGE 55

55 CHAPTER 4 METHODOLOGY The RERO framework consists of two approach es to value real estate acquisitions: the combined approach and the separated approach. This chapter introduces the key elements and steps of the RERO approaches. The next two ch apters present case studies that implement the principles introduced in this chapter. As mentioned in the previous chapter, the Market Asset Disclaimer (MAD) and the integrated approaches in ROA we re adopted for this study. RERO Modeling Procedures The RERO framework adopts real options and d ecision analysis methodologies. It consists of a series of processes to solve a decision tree backward. The event tree starts by laying out all possible events and corresponding cash flows. St arting at the end of the analysis, we work backward through the tree at ea ch decision node to calculate th e payoff of all possible actions, using replicating portfolio or ri sk neutral discounting, choosing the optimal action that generates the highest payoff at each node. Eventually the possible cash flows generated by these future events and actions are folded back to a presen t value. The following 6 steps are critical in performing the RERO analysis (Figure 4-1): Problem framing; Approach selection; Risk drivers identification and estimation; Base case modeling; Option modeling; and Sensitivity analyses. Problem Framing For real estate acquisition, the first task is to review the case qualitatively, and to determine whether the asset itself is a sound investment. An investme nt that seems good by the numbers

PAGE 56

56 may not necessarily turn out to be a good i nvestment in the end. Location, neighborhood development, economy growth, property visibili ty, accessibility, physical conditions, ownership and occupancy history, management capability, all these are unique characteristics of real estate that are non-quantifiable. Comprehensive local bu siness knowledge and experience is needed to determine whether a piece of land is worth acquiring. Figure 4-1. Critical steps in RERO analysis. Problem Framing Approach Selection Risk Drivers Identification Base Case Modeling Sensitivity Analysis Option Modeling

PAGE 57

57 After this critical screening, if a prope rty is good enough to go through the hassle of quantitative analysis, the problem is framed into a model and the story is told in a mathematical way. The goal becomes how much it is worth. Management flexibility a nd strategic options, if any, should be identified to de termine which approach to use. Approach Selection DCF can solve most simple and conventional acqui sition problems. It is only when a case has strategic options that cannot be valued by DCF should the RERO approaches be used. Depending on the characteristics of a project, the first step is to determine whether to use the combined approach or the separated approach. The differences between the two approaches are discussed in later sections. Risk Drivers Identification and Estimation The next step is to identify the risk drivers. Uncertainties of real estate acquisitions and development include rental income, operating cost s, capital expend iture, discount rate, cap rate, development cost, etc. These vari ables flow through the model to affect the project value. Risk drivers are those key variables that have th e most profound impact on project value change. To estimate the volatility of each risk driver, objective methods such as time series forecast or regression analysis should be used, if historical or comparable data exists. Alternatively, subjective methods may be used, such as subjec tive guesses, growth rate assumptions, expert opinions, etc (Mun, 2002). Base Case Modeling The expected project value without flexibility is the base case for the subsequent option value analysis. The base case value acts as the t win asset that the real option approach is based on.

PAGE 58

58 Option Modeling From the problem framing step, some strategi c options have been identified; from the approach selection step, the combined approach or the separated approach has been selected; from the risk driver identification and estimation approach, the key uncertainties have been identified and their volatilities quantified. Now in the option modeling step, a Monte Carlo simulation is run, an event tree is constructed, w ith managerial flexibilities incorporated in each node, option values are calculated, optimal decisi ons are made at each node, and the value are tracked from the end of the analysis back to th e starting time of the analysis. This process may be run back and forth for several times to ensure all option values are cal culated correctly and the corresponding rational d ecisions are made. Sensitivity Analyses Setting the project value with flexibility and/ or option value as the dependent variables, each risk variable can be changed, and the trend of value changes in the dependent variables can be observed. This sensitivity analysis helps th e user to see the whole picture and determine how each risk variable should be mana ged. It also helps in understa nding how uncertainty could have otherwise altered decision making. RERO Modeling Approaches For different treatments of risk drivers, th ere are two types of RERO modeling approaches: the combined approach and the separated approach. The combined approach is used for valuation of an existing building with a historic al operating track record. For uncertainties of infill land development, the separated approach is more suitable. MAD has two key assumptions: firstly, the pr esent value of the underlying risky asset without flexibility is the best estimate of the project value with flexibility. Secondly, properly anticipated cash flows fluctuate randomly. The second theorem a llows the user to combine any

PAGE 59

59 number of uncertainties into a spreadsheet, and to produce an estimate of the project NPV conditional on the set of random variables drawn from their underlying distributions by using Monte Carlo simulation techniques (Copeland and Antikarov, 2001, p219). This is the theoretical foundation of the combined approach. By using the combined approach, uncertainties are assumed to be able to be resolved continuously over time. This assumption generally holds for stabilized assets. However, many projects in real estate, such as infill land deve lopment, have major uncertainties that do not get resolved smoothly over time. Many rare events, e. g., permit approval, development activities in the neighborhood, a new mall, a new subway stati on, can significantly ch ange the real estate value. For projects with any risk of such jumpi ng effect, the actual event tree is asymmetric with changes in value occurring when a significant part of the uncertainty is resolved. The separated approach is used to isolate the risks with jump diffusion effect from t hose resolved continuously, and to model their interaction explicitly. In other words, the separated approach also assumes that the underlying project value without flexibility is the best estimate of the project value with flexibility, but it does not assume that the cash flows fluctuate randomly. Rather, it separates the risk drivers with jump effect from the others without, and models the jump effect explicitly. The Combined Approach The combined approach is most suitable for valuation with risks re solved continuously. This approach can be best applie d to acquisition valuation of stabilized real estate assets. The process is to model the parameters of different uncertainties and to estimate their effect on the volatility of the project value us ing Monte Carlo simulation technique s. The effects of individual risk drivers are thus combined into the project volatility, which is used to generate a binomial event tree. Actions of managerial flexibili ty are added to solve for option value.

PAGE 60

60 The following variables are typical in a prope rty acquisition model: re ntal rate, occupancy rate, rentable square footage, expense recovery operating expenses, capit al expenditure, tenant improvement, leasing commission, going-out cap rate, discount rate etc. Among these variables, the most influential ones are rental rate, stab ilized occupancy rate, goi ng-out cap rate, and discount rate. Rentable square footage is usually fixed; expens e recovery and operating expenses vary but in a controllable small range related to th e rental rate change; capital expenditure, tenant improvement, and leasing commission are tricky in reality, but could be assumed to be fixed on an annual basis for a high-end office building. Rental rate and stabilized occupancy rate will be used as the two major variables in the case analyses. Rental rate is set by the market, and directly impacts the property value. For value-added type of investors, who intend to upgrade amenities and enhance occupancy, the stabilized occupancy rate is an important f actor for revenue estimation. The discount rate, however, is subjective to each inve stor. In finance theory, the discount rate should reflect the level of risk of a project. In practice, however, for an individual investor, the discount rate is usually his weighted average cost of capital. Risk is mainly adju sted through the Cap rate rather than discount rate (Wheaton et al., 2001). The discount rate can therefore be regarded as fixed. The change of rental rate depends on many factors, such as macro economics, employment growth, market occupancy rate, new construction pi peline, net absorption ra te, etc. The change of rental rate is assumed to follow the multiplicative stochastic process. Historical data of rental rates will be examined in the next chapter. Another factor that affects rental revenue is stabilized occupancy rate For a building that is not fully leased, there might be upside poten tial to lease up the vacant space, depending on market demand. In a market with strong job growth demand for office space is also strong. It is

PAGE 61

61 relatively easy to lease up the vacant space. Assuming that vacant space can be leased up, the incremental Net Operating Income (NOI) is subs tantial compared to the incremental revenue, since the incremental operating expense is minimal. In other words, whether a building is 50% occupied or 100% occupied, a majority of the ope rating expenses is fixe d, the 50% lease-up can potentially triple the NOI. Note that a multi-te nant office building is seldom fully occupied, therefore stabilized occupancy ra te usually is close to but never reaches 100%. A general vacancy factor is deducted from the fully leased revenue. The change of occupancy rate is assumed to follow the additive stochastic process. This process is similar to the multiplicative stochastic process with the only difference bei ng that the up and down mo vements in the lattice are assumed to be additive rather than multip licative (Copeland and Antikarov, 2001, p123). The Separated Approach The separated approach is more complicated than the combined approach and should be used only when needed. It is best used for pr ojects with major private risks that do not get resolved continuously. The infill land valuation is an example in this study that can be better modeled using the separated approach. The following variables are typical in an infill land development model: rental rate, development cost, development timing, development scale, operating expenses, expense recovery, cap rate, discount rate etc. Among these variables, the most uncertain ones are rental rate, development cost, and development timing. Development scale is regarded as a major economic factor, but not a major uncertainty in the context of our case study, due to approved permit of the development scale. Since the goa l of most commercial developments is to maximize the investors wealth, developments are usually built to the largest size allowed by zoning and legal restrictions. Unless the deve lopment involves zoning changes, development scale is predictable, and thus is not modeled as a risk driver. As discussed in the combined

PAGE 62

62 approach, operating expenses and expense recove ry are in a controllabl e range, and the discount rate for a particular project is fixed to a specific investor. Cap rate is as sumed to be fixed in the integrated approach for simplicity. Development costs include hard costs and soft costs, and can be subdivided into costs associated with land, structure, tenant improveme nt, leasing commission, le gal, finance, taxes, insurance, marketing, etc. Hard costs are cons truction costs that include demolition, foundation, structure, mechanical and engineering system s, general conditions, bonds and insurance of construction, design and management fees, tenant improvement, etc. Soft costs are intangible costs that go to legal, survey, marketing, financ ing, taxes, leasing commissions, etc. Since every project is unique, develo pment costs represent the major privat e risk that does not correlate with the traded financial market, and thus cannot be re plicated by the so called traded twin asset. Rental rate is discussed in the combined approach during normal circumstance. What needs to be pointed out in addition is the jump diffusion process. A jump diffusion process is defined as a type of stochastic process that has large discrete movements (jumps, or shocks), rather than small continuous movements (Ami n, 1993). As Wheaton et al. (2001) noted: In reaction to positive shocks, returns initially increa se, but eventually diminish with the arrival of new supply. Similarly, negative shocks lead to building conversions, lo ss of stock and an eventual recovery of returns. One of the distinguishing characteris tics of real estate, compared to traded securities, is its inelasticity, or sl ow reaction to shocks. The jump diffusion can be ignored in the acquisition of a nearly fully o ccupied property, since rental rates cannot be changed until lease expirations, which could be y ears from the emergence of the shock. But jump diffusion could be a major uncertainty in de velopment, since all rental square footage is newly available. Developers can ask for highe r rental rates in markets with rising demand.

PAGE 63

63 Development timing is also important. Devel opment timing is different from development duration. Given the size of a development project the duration of construc tion is usually fixed, but when to start the project could have profound imp act on the value, given the real estate cycle. One of the major disadvantages of DCF valuati on is its inability to determine the optimal development timing. The RERO framework, on the other hand, can analyze all possible scenarios and indicate the best action at each point in time. It is extremely valuable for the investor to hold the option of when to start the development. Another important factor is development scale, or the size of development. In the case study, the permit for around 1 million square feet of mix-used development has been approved. Consequently no assumption needs to be made for changing development scale. But in many cases, when rezoning is required in order to de velop more density, development scale is an important factor and should be modeled in th e decision tree as whet her or not the rezoning requirement will be approved. RERO Modeling Techniques Rational for Using Binomial Lattices Copeland and Antikarov (2001, p222) made the a ssumption that change in asset prices follow Geometric Brownian Motion, based on Sa muelsons proof that properly anticipated prices fluctuate randomly. In other words, chan ge in asset value follows a random walk even if the risk drivers do not. This means multiple risk drivers, so long as they evolve continuously, can be combined and reduced to a single uncerta inty, namely the expected underlying asset value change over time. This provides the rationale for using a binomial lattice to calculate real option value.

PAGE 64

64 Monte Carlo Simulation Monte Carlo simulation randomly generates valu es for uncertain variables to simulate a real-life model. In the combined approach Monte Carlo simulation can be used as an intermediate step to estimate volatility of the project, the value of which is depended on multiple risk drivers. For this study Risk Simulator is used. Other simulation software available are Crystal Ball and @ Risk. The steps followed in the combined approach are to: 1. Identify risk drivers; 2. Estimate the probability distribution of each risk driver using historical data or subjective estimates; 3. Build present value model; 4. Define input variables with the possible range of value and a probability distribution in an MS Excel spreadsheet equipped with Monte Carlo simulation tools; 5. Define correlations among the risk variables; 6. Define forecast variables., e.g., rate of return for the project; 7. Run the simulation a thousand times; 8. Read the outputs of the forecast variable s and their volatility distributions; and 9. Use the outputs as input variables to build the event tree. Replicating Portfolio In most cases the project cash flows are discount ed at the risk-adjusted rate to get to the project NPV. The risk-adjusted discount rate is higher than the risk-free discount rate, since it is adjusted up to accommodate higher risk of the project than that of the trea sury bonds. In order to apply a binomial lattice that is developed base d on risk-neutral proba bilities and risk-free discount rates, risk-adjusted proba bilities should be used togeth er with risk-adjusted discount rates. To calculate the value of the option, the replicating portf olio method is used, but not the

PAGE 65

65 discounting method, since the risk characterist ics of the project change over time depending on the decision made, and consequently the risk-a djusted discount rates al so change over time (Copeland and Antikarov, 2001). The risk-adjusted up movement factor u and down movement factor d are the same as those in the risk-neutr al binomial lattice (Equations 4-1 and 4-2). te u (41) u d 1 (4-2) where is the project volatility, and t is the time in years of each step in the binomial tree. The replicating portfolio formula can be derive d by the same method as the option price is derived from binomial lattice. Construct a po rtfolio that consists of n shares of stock S and b amount of value in risk-free bonds. After a period of time t the value of the portfolio can go up or down. Let the value be equal to the option value at that time. u rtC be nuS (4-3) d rtC be ndS (4-4) From Equations 4-3 and 4-4, de rive Equations 4-5 and 4-6. ) ( d u S C C nd u (4-5) ) (d u e dC uC brt u d (4-6) Consequently, the value of the optio n is calculated by Equation 4-7. ) (d u e dC uC d u C C b nS Crt u d d u (4-7)

PAGE 66

66 Binomial Lattice with Dividend Chapter 3 covers binomial lattice without divide nd. In real estate, the net cash flows from operation are collected from the property and distri buted to the investor, which is similar to the dividend distribution of a stock. The stock dividend is usuall y assumed to be distributed at a constant yield, since corporations plan and mana ge the distribution process. The net cash flows at the property level, on the other hand, are the actually amounts collected from the property, and hence vary from period to period. Denote i to the dividend yield at Step i for n i 0, and using all other notions in Chapter 3, the asset va lue changes are depicted in Figure 4-2 for a twoperiod lattice. Figure 4-2. Two-step binomial lattic e with different dividend yields. At Step 2, the three possible values are cal culated using Equations 4-8, 4-9, and 4-10. ] 0 ) 1 ( [2 0K uu S Max Cuu (4-8) ] 0 ) 1 ( [2 0K ud S Max Cud (4-9) ] 0 ) 1 ( [2 0K dd S Max Cdd (4-10) To calculate the option value at Step 1, the dividend yield 2 needs to be added back to the option value, before discounting at the risk-free rate, which is s hown in Equations 4-11 and 4-12. S0 S0u S0u(11) S0d S0d(11) S0uu S0uu(12) S0ud S0ud(12) S0dd S0dd(12)

PAGE 67

67 rt ud uu ue C p pC C) 1 ( ) 1 (2 (4-11) rt dd ud de C p pC C) 1 ( ) 1 (2 (4-12) The same method is followed to calculate the opt ion value at Step 0, as shown in Equation 4-13. rt d ue C p pC C) 1 ( ) 1 (1 (4-13) In general, for a binomial lattice with n steps, the i th step (n i 0) call option value with dividend is calculated by Equation 4-14. rt i d i u i ie C p pC C) 1 ( ) 1 (1 1 1 (4-14) Binomial Lattice with Jump Process Chapter 3 covers binomial lattice during nor mal circumstance that the underlying asset strictly follows the GBM movement. However, in reality, the asset movement could be a jump. For example, the zoning change from agricultura l land to urban land, the establishment of new amenities in the neighborhood, the construction of new freeway exits, all can have a sudden and profound influence on the esta te value in an area. These events seldom happen. But once occur, they will completely change the project payoff pattern. Hence, these jump diffusion effects cannot be priced using the binomial lattice developed by Cox et al. (1979). Amin (1993) developed a discrete time model to value opti ons when the underlying process follows a jump diffusion process. Unlike the financial jump diffusi on process that reverses back to normal value quickly, a jump diffusion process in real estate usually is irreversible, at lease not in a short period of time. That is, if a la rge scale development occurs that drives up the rental rate in a

PAGE 68

68 neighborhood, that rental rate is likely to remain at the same le vel for several years until a new event happens. In this study the Amin model was modified to accommodate this change. Based on the assumption that the jump risk is diversifiable, a one-period call option is priced in the Equation 4-15 (Figure 4-3). Figure 4-3. Binomial lat tice with jump process. ]} ) ~ 1 ( ~ )[ 1 ( {d u y rtC p C p C e C (4-15) where is the probability of the jump event according to the Poisson distribution, and defined by ) ( x n e xx n (where n is the expected number of successes, and x is the number of successes per unit); y is the capital gain return on the underlying asset when the jump event occurs; Cy is the option value at the time the jump event occurs; p is the adjusted probability of an up movement, and defined by d u d y e prt 1 ~. Investment with Private Uncertainty As discussed in Chapter 3, many investments include private and market uncertainties. Market uncertainty can be replicated with mark et participation and therefore diversifiable. Private uncertainty cannot. For example, th e development project va lue depends on both the market uncertainty of rental rate and th e private uncertainty of development cost. C Cd Cu Cy (1)p (1)(1-p ) S dS uS yS (1)p (1)(1-p )

PAGE 69

69 The principle of pricing in such investment, if no correlation between the market risk and private risk exists, is to use risk-neutral pr obability for the market uncertainty and actual probability for the private uncertainty, both di scounted at risk-free rate (Luenberger, 1998; Copeland and Antikarov, 2001; Smith and McCa rdle, 1999). Although formulas for pricing uncertainties with correlation exist, the no correlation assumption usually holds. To implement this principle, there are tw o alternative methods: the quadranomial lattice and the decision analysis method. The first method is to implement a quadranom ial lattice. Figure 4-3 shows a one-step quadranomial lattice. If an option C is contingent upon the value of two underlying assets S1 and S2, assuming no correlation between S1 and S2, then the value of C is priced as Equation 4-16. ) (22 22 21 21 12 12 11 11C p C p C p C p e Crt (4-16) where ) 1 )( 1 ( ) 1 ( ) 1 (2 1 22 2 1 21 2 1 12 2 1 11p p p p p p p p p p p p pi is the risk-neutral probability if Si is market uncertainty, or the actual probability if Si is private uncertainty. For each uncertainty, it can have more than two bifurcations. For example, if S1 is a market risk with jump di ffusion (three bifurcations), and S2 is a private risk with three bifurcations, then C could be priced with nine node s with corresponding probabilities and discount at the risk-free rate. In theory, an option can be contingent upon more than two separated assets, but in practice, the comp lexity of implementation will soon become intimidating. This study thus focuses on a few key risk drivers and combine them into two kinds of separated uncertainties: market uncertainty and private uncertainty.

PAGE 70

70 Figure 4-4. Quadranomial lattice. Another way is to implement decision an alysis methodology (Smith and Nau, 1995). For example, if the two underlying risks for a developmen t are cost and rental rate, it can be modeled as shown in Figure 4-5. The exp ected value at each node is calcul ated and discounted at the riskfree rate. Equation 4-17 shows how the expected value E(PV0) can be calculated. m j j jPV E p PV E1 0)] ( [ ) ( (4-17) where j is a scenario labeled from 1 to m m j 1; E(PVj) is the expected present value of scenario j for all the years i n i 1. Figure 4-5. Decision analysis. Jump Up Down Jump Up Down Jump Up Down Low Middle High Cost Rent C C22 C21 C12 C11 P21 p12 P22 p1 u1S1 d1S1 S1 p1 1-p1 u2S2d2S2S2 p2 1-p2

PAGE 71

71 Summary This chapter discusses the 6-steps RERO framework: problem framing; approach selection; risk drivers identification and estima tion; base case modeli ng; option modeling; and sensitivity analysis. Two modeling approaches are introduced to deal with different risk characteristics: the combined approach for pr ojects with risk drivers that get resolved continuously, and the separated approach for project either with risk drivers that follow the jump diffusion process or involving private risk. The modeling techniques that will be applied in the case studies are also introduced, including the rati onale of using the binomial lattice, Monte Carlo simulation, replicating po rtfolio, binomial lattice with jump diffusion process, and investment with private risk.

PAGE 72

72 CHAPTER 5 THE COMBINED APPROACH Chapter 5 and 6 present case studies that impl ement the principles of RERO described in Chapter 4. The two chapters describe the valua tion of two parts of one case: valuation of the building using the combined approach, and valuation of the infill land using the separated approach. Together, these two case studies demonstrate how the RERO framework can be applied to different scenarios in the real estate acquisition and development analysis. Case Description The case identified is 211 Perimeter in Atlant a. This property is located in the Central Perimeter submarket of Atlanta. Adjacent to the Perimeter Mall and a subway station, 211 Perimeter is located in one of the largest suburba n office markets in Atlanta. The property has an office building of 226,000sf rentable area, and 13 acres total land. The current owner has got approvals for over 1 million square feet of mi xed-use development on the 9.5 acres developable site, and has built a 6-storey parking garage with the intention to get as much value as the regulations allow from development of the ex cessive land (Figure 5-1). Furthermore, the property is strategically located within a la rger neighborhood redevel opment planning of 38 acres and nearly 3 million square feet mixe d-use development, although the timing of the neighborhood development is unknown. The land obviously has some value, but deve lopment might not break ground immediately. The real estate market in Atla nta is a commodity market, which means developments are spread out with few restrictions. As 2005, the Centra l Perimeter office submarket was over built, with several old office buildings torn down for new resi dential developments. It would be interesting to know how current bidders should price the land in addition to the building.

PAGE 73

73 Figure 5-1. 211 Perimeter site plan. Building Valuation In this chapter only the building is valuated using the combined approach with Monte Carlo simulation. The land valuation will be inves tigated in the next chapter using the separated approach. The following are the 6 steps used to perform the RERO valuation: Problem framing; Approach selection; Base case modeling; Risk drivers identification and estimation; Option modeling; and Sensitivity analyses. Problem Framing The property is located in a premium office mark et, with superior quali ty and tenant mix. Its strategic location within a larger neighborhood redevelopment plan makes real estate price

PAGE 74

74 appreciation in the future extremely promising, although the timing is still unknown. In short, the 211 Perimeter project is a sound investment that deserves further valuation. After the preliminary qualitativ e analysis, this project app ears acceptable for quantitative analyses. The 11-floor office building consists of 226,000sf rentable area. Current occupancy rate is 85%, with 15% upside pot ential to lease up the space. Major tenants collectively occupy 68% of the rentable square footage, which is deemed to be a sign of solid cash flow over the future. One of the major decisions to make is about the chiller system upgr ade. The existing chillers are still in wo rking condition but are at their maximum capacity, and consume far more energy than new ones. Preliminary research show s that replacement of the existing chillers will cost $950,000, and will increase the net cash flow by 5% per year. If both rental rates and occupancy rates are good, replacement of the chill ers can justify its cost, and add value to the property. Otherwise, the capital improvement may not break even, and keeping the existing chillers is more economical. Approach Selection The combined approach is selected since both th e rental rate and occupancy rate are market driven, and can be combined into the Monte Carlo simulation. Base case NPV calculation The following variables are typical in the NP V valuation model: rental rate, occupancy rate, rentable square footage, expense recovery operating expenses, capit al expenditure, tenant improvement, leasing commission, going-out cap rate, discount rate. Table 5-1 shows the assumptions used in the base case NPV calculati on. Figure 5-2 shows the cash flow output from Argus, a software package for real estate valuation.

PAGE 75

75 Table 5-1. Major assumptions for Argus. Average rental rate $17/sf Capital expenditure $75,000 Occupancy rate 85% Tenant improvement $18/sf Rentable sf 225,924 sf Leasing commission 6.0% Expense recovery $0 Going-out Cap rate 7.0% Operation expenses $7.75/sf Discount rate 9.0% From the Argus cash flow output, modifications are made so that the model can be used for Monte Carlo simulation using Risk Simulator. Rental rate and occupa ncy rate have been identified as the two major risk variables that need to be simulated. Annual average rental rate and annual average occupancy rate are calculat ed from the Argus output, which are used to derive annual net cash flow. Purc hase price is assumed to be fixed, so that we can compare the project value with and without flexibility. Operating expenses and expense recoveries are controllable variables. Capital items, such as capital expenditure, tenant improvement, and leasing commission, are also controllable. Cap ra te and discount rate ar e also assumed to be fixed. Ignoring the option of chiller replacement, th e project NPV has two components: (1) Total acquisition cost, including purchas e price and closing cost; (2) Pr esent value of annual net cash flow from operation and present value of net re sidual value (gross sale proceeds net out selling cost). These two parts are also called cost and benefit. The option of chil ler replacement will be modeled later. In real estate fundamental analysis, property value consists of residual value and net cash flow from operation. The residual value, or value when the project is sold, is the major part. It is determined by Net Operating Income (NOI) and Cap italization rate (Cap rate). NOI is the gross

PAGE 76

76 Figure 5-2. Base case NPV calculation.

PAGE 77

77 income from all sources (rental, storage, tenant reimbursement, antenna lease, etc) minus all operating expenses (common area maintenance, management fee, security, landscaping, insurance, real estate taxes, etc). For this reas on, NOI is also regarded as the net income of the property. This is different from what the inve stor actually gets, which is called the Net Cash Flow. Net cash flow is calculated by taking ou t capital items from NOI. These capital items, such as capital improvement, tenant improvement and leasing commission, are one-time-off in nature. All these analyses are on an unleveraged before-tax basis, meaning debt financing and taxation are not considered. Figure 5-3 shows the modified Argus cash flow output for NPV calculation. For simulation simplicity, modifications of the Argus output are made so that the net operating income and net cash flow are calculated by Equation 5-1 and Equation 5-2. OE ER Occ SF Q NOI (5-1) CapX LC TI NOI NCF (5-2) where NOI is the net operating income; Q is the average rental rate; SF is the rentable square footage; Occ is the actual occupancy rate; ER is the expense recovery and other income; OE is the operating expenses; NCF is the net cash flow; TI is the tenant improvement; LC is the leasing commission; CapX is the capital expenditure. The residual value at sales is calculated by Equation 5-3. SC Cap NOI Vn n 1 (5-3) where Vn is the net residual value at year n and n is the holding peri od of the project; Cap is the going-out Cap rate; SC is the selling cost.

PAGE 78

78 The total benefit of the project PVj, which includes the present value of net cash flow NCFi and residual value Vn, can be calculated by Equation 5-4. j n n n j i j i i jk V k NCF PV ) 1 ( ) 1 ( (5-4) where PVj is the project present value at Year j and n j 0, where n is the holding period. When j = 0 it is the present value at time 0, or PV0. NCFi is the net cash flow at Year i k is the discount rate of the project. The NPV of the project is the present value of total cost PP0 and total benefit PV0 at time 0, as calculated by Equation 5-5. 0 0 0PP PV NPV (5-5) Risk Drivers Modeling Among the variables, those that have th e most profound impact on the project NPV changes are rental rate and stabi lized occupancy rate, both are mark et driven. Rental rates differ lease-by-lease, but for simplicity we take the average rental rate ove r the entire building. Stabilized occupancy rate is subjective based on managements estimates In this case the 15% vacant space is assumed to be leased up within 2 years, after which a gene ral vacancy factor of 3% is taken out. Figure 5-4 shows the historical rental rates of the Central Perimeter Class A office market and the subject property in 15 years. The quarterly data is from CoStar. The change of rental rate is assumed to follow GBM. This means the logarithm of the rental rate Qi is normally distributed; and the return (also called the cha nge of rental rate) qi follows a random walk. Using Equation 5-6, a rental retu rn analysis was performed and th e scatter chart was plotted as shown in Figure 5-5, with market return variab les on X-axis and corres ponding subject property return variables on Y-axis. It shows negative corr elation (-0.1445), which indi cates that the rental

PAGE 79

79 Figure 5-3. Spreadsheet model for Monte Carlo simulation.

PAGE 80

80 rate change of the subject prope rty, 211 Perimeter, has very w eak, if not negligible, correlation with the market. $14.00 $17.00 $20.00 $23.00 $26.00 1990 3Q 1992 3Q 1994 3Q 1996 3Q 1998 3Q 2000 3Q 2002 3Q 2004 3Q Market Subject Property Figure 5-4. Historical market a nd subject property rental rates. Figure 5-5. Returns correlation betw een market and subject property. y = -0.3276x 8E-05 R2 = 0.0209-20.00% -10.00% 0.00% 10.00% 20.00% 30.00% -7.00% -5.00%-3.00% -1.00%1.00%3.00%5.00%7.00% Market Subject Property

PAGE 81

81 ) ln(1 i i iQ Q q (5-6) The seemingly controversial resu lt of weak or no correlation be tween the rental return of the subject property and that of the market can be explained as due to two reasons: (1) Data reliability. CoStar started as a se rvice portal mainly for commercial brokerage firms. In its early years data is derived fr om broker volunteer contributions. This would inevitably have led to data accuracy and timelines s issues. For example, from the first quarter of 1998 to the third quarter of 1999, the rental rates data of the subject property are missing, which are assumed to be $18.90/sf by the author for the purpose of data completeness. (2) The inelastic nature of real estate market. Compared to the financial market, the real estate market is lumpy and the performance is some what predictable, at least for the near term. Commercial lease terms are usually 3 to 7 years fo r office leases, 5 to 20 years for anchor retail leases, and even 100 years for ground leases. In most cases, the rental payment is set and documented in the contract througho ut the terms. Market rental rate changes can only slowly affect individual property ask rates, since the land lord can change rental rate only when a lease negotiation happens, usually before the lease expires. However, mark et rates can directly affect the rates for new construction, since all spaces are newly available. Nevertheless, the data set from CoStar is the most comprehensive and consistent data available in the real estate indus try. The characteris tics of real estate require a different method than the one used to estimate stock volatility in the financial industry. Thus the correlation between the market and the subject property was ignored on purpose, and only the subject property rental rate data was used to estimate its vol atility for acquisition.

PAGE 82

82 Risk Simulator is used to influence the di stribution of the populat ion from the available sample data. A lognormal distribution was chosen since the rental rates will never be negative. Due to the limitation of available data, the statisti cal significance of this distribution is low (PValue of 0.1625). Nevertheless, this is the most reasonable fit for the data. By fitting the sample data into a lognormal distribution (Figure 56), the following variables are determined: is 0.0056 and is 0.0548. Annualizing the quarterly and using Equation 5-7 and 5-8, mean of 18.0189 and standard deviation of 2.0218 for the re turn distribution are derived. To get the annual auto-correlation of the rental return, the qu arterly return data is annualized by taking the average of the 4 quarters of each year, which turn s out to be -0.0916. This auto-correlation of the samples is assumed to be the same as that of the population. ) 2 / (2 e X (5-7) 2 22 ) ( 2 e e SD (5-8) Figure 5-6. Normal distribution fi t for historical returns on rental. CoStar also provides historical occupancy rates data for th e market and subject property (Figure 5-7). Occupancy rate is assumed to follow the additive stochastic process. This means

PAGE 83

83 the change of occupancy rate oi between any two quarters is simply the difference of the occupancy rate Oi and Oi-1 (Equation 5-9). From the scatter plot of the change of occupancy data shown in Figure 5-8, it can be concluded that th e occupancy rate of the property also has very weak correlation with the market (0.1263). Thus, this correlation is also ignored on purpose and only the historical occupancy rates of the subj ect property will be relied on for forecasting. 1 i i iO O o (5-9) Using RiskSimulator, the population and the respective population mean and standard deviation of the normal distribu tion, are determined to be 0.0039 and 0.0471 respectively (Figure 5-9). Due to the limitation of available data, the sta tistical significance of this distribution is low (P-Value of 0.00004). Howe ver, this low P-value might be a limitation of the software itself, i.e., its estimation of data in a small range is inaccurate. Nevertheless, this is the most reasonable fit for the data. To preser ve accuracy, it was decided to keep the sample mean as the population mean (0.0026), and annu alize the sample standa rd deviation as the 20.0% 40.0% 60.0% 80.0% 100.0% 1986 4Q 1988 4Q 1990 4Q 1992 4Q 1994 4Q 1996 4Q 1998 4Q 2000 4Q 2002 4Q 2004 4Q Market Subject Property Figure 5-7. Historical market a nd subject property occupancy rates.

PAGE 84

84 y = 0.4502x + 0.0018 R2 = 0.016-30.0% -20.0% -10.0% 0.0% 10.0% 20.0% -10.0%-5.0%0.0%5.0%10.0% MarketSubject Property Figure 5-8. Occupancy changes corr elation between the local real estate market and the subject property. Figure 5-9. Normal distribution fit for historical occupancy rates.

PAGE 85

85 population volatility (0.1409). To calculate the au to correlation, the change of occupancy rate data is annualized by taking the average of the 4 quarters of each year, which turns out to be 0.1185. The correlation between rental re turn and change of occupancy rate is similar to the autocorrelation of the two, which comes out to be -0.1575. For Monte Carlo simulation, the project volatilit y is the volatility of percentage changes in the value of the project from one time period to the next, defined by the forecasting variable z (Equation 5-10). This value is computed using the simulated present value of the project in Year 1 divided by the expected present value of the project in Year 0. In other words, PV1 is dynamic, while PV0 is static. 0 1PV PV z (5-10) Option Modeling In the previous step the rental rate, occupa ncy rate, their respective volatilities, autocorrelations, and the correlation be tween the two have been identifie d and quantified. With these variables, rental rates and occ upancy rates for each year can be set as risk variables for the project value simulation. A total of 8 risk va riables are defined and highlighted as shown in Figures 5-43, 5-10, and Table 5-2. The cash flows go through Equa tions 5-1 to 5-5 to generate annual net cash flow for the first 3 years. PV0 and PV1 are calculated based on the annual net cash flow. The forecasting variable z is defined in Equation 5-10. Setting PV0 to be static and PV1 to be dynamic, and running the simulation for a 1000 times, the simulation result of z is obtained as shown in Figure 511. Table 5-3 also shows the statistical summary of z with a mean of 1.079 and standard a deviation of 0.3283.

PAGE 86

86 Figure 5-10. Snap shot of M onte Carlo simulation assumptions. Figure 5-11. Monte Carlo Simulati on Result of Forecasting Variable z The statistical distribution fit for Variable z is then performed. By plotting the 1000 z values from the simulation output, as shown in Figure 5-12, it is determined that they are normally distributed with P-Value of 0.8737. Th is result fits quite we ll with the theory

PAGE 87

87 Table 5-2. Correlation between random variables. Yr 1 return Yr 2 return Yr 3 return Yr 4 return Yr 1 Occ Yr 2 Occ Yr 3 Occ Yr 4 Occ Yr 1 return 1.00 Yr 2 return -0.09 1.00 Yr 3 return 0.00 -0.09 1.00 Yr 4 return 0.00 0.00 -0.09 1.00 Yr 1 occ -0.16 0.00 0.00 0.00 1.00 Yr 2 Occ 0.00 -0.16 0.00 0.00 0.12 1.00 Yr 3 Occ 0.00 0.00 -0.16 0.00 0.00 0.12 1.00 Yr 4 Occ 0.00 0.00 0.00 -0.16 0.00 0.00 0.12 1.00 Table 5-3. Statistical summary of Monte Carlo simulation result. Description Value Number of data points 1000 Mean 1.0797 Median 1.0569 Standard deviation 0.3283 Variance 0.1078 Average deviation 0.2561 Maximum 2.4431 Minimum 0.0977 Range 2.3454 Skewness 0.3787 Kurtosis 0.7041 25% percentile 0.8722 75% percentile 1.2831 Error precision at 95% 0.0188 Figure 5-12. Normal distribution fit of forecasting variable z

PAGE 88

88 developed by Samuelson and adopted by Copela nd and Antikarov (2001), as discussed in Chapter 4, that changes in correct ly expected asset prices follow Geometric Brownian Motion. From the Monte Carlo simulation, the mean and the volatility of forecasting variable z are calculated as 1.0797 and 0.3283 respectively. This means the expected average project return is 7.97% (1.0797 minus 1), and the volatil ity of the project is 30.4% (0.3283 divided by 1.0797). Using the assumptions in Table 5-4, with 30.4% volatility, and $24,963,000 PV derived from the base case analysis, a value tree is constr ucted as shown in Figure 5-13. Net cash flows are modeled as dynamic dividend yield times PV in the base case (Refer to Chapter 4 for details of binomial lattice with divi dend). For example, in Year 1, the PV can go up to $34,664,000 with an up factor of 1.3886, the post dividend cash flow is therefore $33,638,000 (after taking out 2.96% yield from the $34,664,000 before dividend cash flow). Table 5-4. Event tree assumptions (Dollars in $1,000). Assumptions Intermediate computations PV of asset value $24,963 Stepping time (dt) 1.0000 Implementation cost $24,205 Up step size (up) 1.3886 Maturity (years) 3.00 Down step size (down) 0.7201 Risk-free discount rate (%) 5.00% Volatility (%) 32.83% Lattice steps 3 Option type Call NCF as percentage of PV Year 1 2 3 NCFi $805 ($511) $1,828 PVi $27,210 $28,781 $31,928 Percentage 2.96% -1.78% 5.73%

PAGE 89

89 Figure 5-13. Event tree present value w ithout flexibility (N umber in $1,000). With the event tree of PV without flexibility the chiller replacement option can now be modeled. An event tree of PV with flexibility is constructed (Fi gure 5-14). At the end nodes, the decision is whether to keep the existing chillers or replace them with new ones. For example, the value of Node A` is calculated as follow. Max (Replace, Keep) = Ma x (Present Value 1.05 Cost, Present Value) = (62234 1.05 950, 62234) = 64396 (Replace) At the intermediate nodes, the decision is a bout whether to leave the option open or to execute it immediately. To calculate the valu e of leaving the option open, the replicating portfolio method developed in Chapter 4 must be used, but not the discounting method, since risk-adjusted probability and risk-a djusted discount rate are used to construct the spread sheet and event tree. Equation 4-7 is the replication portfolio formula to be applied. 34,664 33,638 17,977 17,445 12,563 12,786 9,208 8,681 17,755 16,738 34,235 32,275 66,014 62,234 46,710 47,540 24,224 24,655 24,963

PAGE 90

90 Figure 5-14. Present value with fl exibility (Numbers in $1,000). For example, the value of keepi ng the option open at Node C` is 48877 ) 7201 0 3886 1 ( 68175 7201 0 34889 3886 1 7201 0 3886 1 34899 681751 05 0 e C Therefore, the value of node C` is Max (Replace, Open) = Max (47540 *1.05-950, 48877) = 48967 (Replace) The decision is to replace the chiller syst em immediately. Usi ng Equation 4-14 to add back the implied net cash flow of negative $830,000, the before dividend present value is $48,137,000. Working backward the value at eac h node can be similarly calculated and the optimal action can be selected to maximize th e present value, and eventually the maximum present value can be derived at time 0. Th e present value increases from $24,963,000 (without 35,486 34,461 18,124 17,593 12,563 12,786 9,208 8,681 17,755 16,738 34,899 32,939 68,175 64,396 48,137 48,967 24,537 24,967 25,421 Replace Replace Keep Keep Replace Open Open Open Open Open A A` B` B C C`

PAGE 91

91 flexibility) to $25,421,000 (with flex ibility), or an increase by $458, 000. The NPV of the project is now $1,216,000. In other words, the option to replace the chillers system creates $458,000 value. If the building could be purchased at $24,205,000, the NPV increases to $1,216,000. Sensitivity Analyses Sensitivity analyses are conducted using option value as dependent variable, and present value, replacement cost, discount rate and vola tility as independent variables. Table 5-5 summarizes the effect of each independent variab le as well as their combined effects on the option value. Present value has positive effect on the opti on value (Figure 5-15). Replacement of the chiller system increases the annua l net cash flow by 5%. And pres ent value is pos itively related to net cash flow. Therefore, the higher the present value is, the highe r the additional net cash flow would be when exercising the replacement option, and hence the higher the option value would be. Table 5-5. Summary of vari able effect on option value. Present value Replacement cost Discount rate Volatility Present value Positive Uncertain Positive, most Sensitive when inthe-money Positive, most Sensitive when atthe-money Replacement cost Negative Uncertain, most Sensitive when atthe-money Uncertain, most Sensitive when atthe-money Discount rate Positive Positive, most Sensitive when atthe-money Volatility Positive

PAGE 92

92 200 400 600 800 1,000 -10,00020,00030,000 Present ValueOption Valu e Figure 5-15. Option value in relation with present value. As shown in Figure 5-16, the replacement cost has negative effect on the option value. The higher the replacement cost is the less likely the replacement is breakeven, and hence the less likely the option would be exercised. 200 400 600 800 1,000 1,200 -5001,0001,5002,000 Replacement CostOption Valu e Figure 5-16. Option value in relation with replacement cost. Volatility also has positive effect on the option value (Figure 5-17). The higher the volatility, the wider the present value spread be comes in later years, but the replacement option is only exercised in those scenar ios with positive net cash flows. Therefore, the more uncertain the future cash flow is, the more valuable the option becomes.

PAGE 93

93 200 400 600 800 1,000 -10,00020,00030,000 Present ValueOption Valu e 20% Volatility 33% Volatility 45% Volatility Figure 5-17. Option value in relation with present value and volatility. Risk-free interest rate has positive effect on the option value. But the effect is not significant. After examining the effect of each independent variable on the option value, combinations of each two independent variables can be looked at The combination of present value and Riskfree interest rate has positive effect on the option value. The two pairs of (1) present va lue and volatility (Fi gure 5-17), (2) volatility and risk-free rate (Figure 5-18) both exercise positive effect on option value, and are most sensitive when the option is at-the-money. The three pairs of (1) replacement cost and volatility (Figure 5-19) (2) replacement cost and risk-free rate, (3) present value and repla cement cost (Figure 5-20) all display uncertain effect on the option value. This conclusion is best illustrated in Figure 5-20. The 3-dimensional curve indicates that the higher the present valu e and the lower the replacement cost, the higher the option value. However, this effect is non-linear. With higher present value and higher

PAGE 94

94 replacement cost, the option value may be hi gher or lower, dependi ng on whether the option value is in-the-money. 300 350 400 450 500 550 600 0%10%20%30%40%50% VolatilityOption Valu e 3% Risk-Free 5% Risk-Free 7% Risk-Free Figure 5-18. Option value in relation with volatility and discount rate. 200 400 600 800 1,000 1,200 -5001,0001,5002,000 Replacement CostOption Valu e 20% Volatility 33% Volatility 45% Volatility Figure 5-19. Option value in relation with replacement cost and volatility.

PAGE 95

95 200 1,200 2,200 2,000 12,000 22,000 32,000 42,000 500 1,000 1,500 2,000 2,500 Option Value Replacement Cost Present Value Figure 5-20. Option value in relation w ith present value and replacement cost. Summary This chapter applies the combined approach to determine the building value of the 211 Perimeter property in Atlanta. Re ntal rate and stabilized occupancy rate are identified as the two major risk drivers and their volatilities are estima ted using historical data. The risk variables are combined in a spread sheet. Monte Carlo si mulation is performed to estimate the project volatility. Event tree is constructed, in whic h the option to replace the chiller system is incorporated. The RERO appro ach indicates that the buildin g is worth $25,421,000, and the value of managerial flexibility is worth $458,000.

PAGE 96

96 CHAPTER 6 THE SEPARATED APPROACH This chapter is the second part of the case st udy described in Chapter 5. In the previous chapter the RERO fr amework is applied to analyze the building structure and a managerial decision of chiller replacement. The combined approach with Monte Carlo simulation is used as the major methodology. This chapter, however, is about valuation of the infill land using the separated approach, with jump diffusion process and decision tree analysis techniques. Together, these two parts demons trate how the RERO framework can be applied to different scenarios in the analysis of real estate acquisition and development. Case Description The previous chapter has full description of the case 211 Perimeter in Atlanta. This chapter only repeats the infill land portion. Be sides the existing office building and the 6-story garage, the current owner has got approvals for over 1 million square feet of mixed-use development on the 9.5 acres developable site. Fu rthermore, the property is strategically located within a larger neighborhood redevelopment planning of 38 acres and nearly 3 million square feet mixed-use development, although the timing of neighborhood deve lopment is unknown. The land obviously has some value, but deve lopment might not break ground immediately. The real estate market in Atla nta is a commodity market, which means, with little control of urban sprawl, developments are spread out easily as far as market demand exists. The Perimeter office submarket is currently overbuilt, with several old office buildings torn down for new residential developments. It would be interest ing to know how current bidders should price the land in addition to the building.

PAGE 97

97 Land Valuation The value of the infill land (9.5 acres out of the 13 acres total) de pends on the value and cost of the improvement should it be developed. The value of the improvement is determined by a function of its annual rental in come and operating cost, just like the existing building. The cost of development includes hard cost s and soft costs. Since ever y project is unique, development cost is assumed to be a private risk that does no t correlate with the traded financial market. Problem Framing The addition of a 6-story garage has freed th e infill land from its original function as surface parking. With the 1 million square feet mix-used development approval, the land can be sold for $4.75 million at anytime during the holding period. Its best value for the investor is being either developed or spin-off for $4.75 million. Table 6-1 shows the development assumptions. Assume the land allows for 1 million square feet to be built, gross re nt is $24.5/sf, stabilized occupa ncy rate is 85%, operating expense is $8.5/sf, required cap rate is 8%, risk-free intere st rate is 5%. Expected development cost is $227.5/sf. Land carrying cost is assumed to be negligibly small compared to the development value. The land can be sold for $4.75 million at anytime. This can be viewed as the exercise price of a put option to the investor. Table 6-1. Development assumptions. Rentable sf 1,000,000 Site acres 9.50 Gross rent psf $24.50 Land $4.75 Occupancy rate 85.0% Value $154.06 Operating expenses psf $8.50 Cost $177.50 Net rent psf $12.33 Riskfree rate 5.0% Cap rate 8.0%

PAGE 98

98 In addition, management believes that th e groundbreaking for the larger neighborhood redevelopment will have significant impact on the demand for new office space, and hence drive up rental rate of this development by 20%. This is a one-time event, bu t once the rental rate rises, it will remain at that level during the entire analysis period. Approach Selection The separated approach is selected because th e impact when the rental rate jumps up by 20% is significant, and the chance is uncerta in, depending on the timing of the neighborhood redevelopment. This is an exam ple where one risk driver (the re ntal rate) does not get resolved smoothly, and must be modeled sepa rately from the other risks. Risk Drivers Identification and Estimation The risk drivers are rental rates and developm ent cost. Unlike the existing office building, the new building does not have a historical track r ecord. For income, the building rental rate is assumed to have some premium over the average ma rket rental rate. Changes in rental rate are assumed to follow the GBM movement, with a jump-diffusion process corresponding to the groundbreaking of the neighborhood proj ect. Figure 6-1 shows the historical market average rental returns for Class A office properties in th e Central Perimeter submarket. Using the Risk Simulator, the quarterly lognormal returns are plot ted into a normal fit as shown in Figure 6-2. Converted into annual data, the market rental rate volatility is 4.84%. As explained in Chapter 5, individual property is far more volatile than the market aver age. The management estimate doubles and becomes 9.68% per year for the infill land development project. The current gross rental rate is $21/sf for the average Cl ass A building in the Central Perimeter submarket. According to manageme nt experience, a $3.50/sf premium for a brand new building can be secured.

PAGE 99

99 $0.00 $5.00 $10.00 $15.00 $20.00 $25.00 $30.00 1990 3Q1992 3Q1994 3Q1996 3Q1998 3Q2000 3Q2002 3Q2004 3Q -8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% Rental Return Figure 6-1. Historical market average rental rates and return volatility. Figure 6-2. Normal distri bution fit for historical market rental returns. Rental rate changes are assumed to follo w the GBM movement. A Poisson distribution jump-diffusion process corresponds to the groundbreaking of the neighborhood residential project, with 10% annual probability. The op tion value is calculated using Equation 4-15 developed in Chapter 4, where is 10% and y is 1.2 (1 plus 20%). Figure 6-3 shows how to get rental rate change s from one period to the next period. At Year 0, gross rental rate is $24.50/ sf. It could have three values in the next year: $29.40/sf (1.2

PAGE 100

100 times $24.50/sf) if the neighborhood developmen t breaks ground, $26.99/sf (up movement) or $22.24/sf (down movement) if the neighborhood development does not break ground, with probabilities of 0.10, 0.5895, and 0.3105 respectively. In year 2, it could have five values. If the neighborhood development breaks ground in Year 1, the rental rate $29.40/sf will follow the GBM movement with possible va lue of $32.39/sf or $26.69/sf, w ith probabilities of 0.7402 and 0.2598 respectively. If no development breaks ground in Year 1, the rental rates of $26.99/sf and $22.24/sf each follows the GBM with jump diffusion process and has three values, which combine into 5 possible values. In Year 3 the re ntal rates follow the same process and can have seven values. Notice, however, the probabilities to get to these values are different with and without the jump diffusion process. Figure 6-3. Gross rental rate movement and probabilities.

PAGE 101

101 Taking out revenue lost from the 15% vacant space, $8.5/sf operating expense, and capping the net cash flow at 8% Cap rate, we can get the corres ponding per square foot building value contingent upon the gross re ntal rate, stabilized occupanc y, operating expenses, cap rate, and the likelihood of the neighborhood re sidential development (Figure 6-4). Figure 6-4. Building value movement and probabilities. There is no direct comparable data on devel opment cost. Development cost includes hard and soft costs. For hard cost, the RS Mean s Building Cost Data manual (RS Means, 1998-2006) can be used. The cost per square foot data fo r high-rise office buildings from Year 1998 to Year 2006 is shown in Figure 6-5. The historical data shows an upward trend, at a pace generally consistent with the inflation rate from inflati odata.com (Figure 6-6). RS Means compiles market average data nation wide, which does not reflect th e volatility of local mark ets. More over, there are no data about the soft cost. Each project is unique in some soft cost items, such as land acquisition cost, permit application cost, unexpected cost, etc. The best estimate would be from

PAGE 102

102 experienced managers. The development cost is assumed not to change with the financial market. It is a private risk that depends on the geological condition of the site, material and labor condition of the local market, etc. Management has estimated that with 50% probability the development cost would be $175/sf, with 20% to be $150/sf, and with 30% to be $200/sf, or 70.00 90.00 110.00 130.00 150.00 170.00 199819992000200120022003200420052006$ psf Low Mid High Figure 6-5. Historical c onstruction cost for high-rise office building. 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 19992000200120022003200420052006 Cost Inflation Figure 6-6. Construction cost chan ge rate and inflation rate.

PAGE 103

103 expected cost of $177.50/sf (Fi gure 6-7). Cost increases by 3% annually, consistent with the average inflation rate over the past 7 years. For simplicity, the buildable square footage is assumed to be the same as the rentable square footage. Figure 6-7. Developmen t cost assumptions. Base Case Modeling The expected PV without any flex ibility is calculated as shown in Figure 68. It is better represented in matrices. Each table in Figure 69 is a matrix of possible PVs for a given year. Starting from Year 3, the possible outcomes of building values are listed in the first row, and the possible outcomes of development costs are listed in the first column. The values inside the rectangle are all possible combinations of costs and values. The same applies to the values for Year 2, Year 1 and Year 0. In Year 0, the expected value is ca lculated as the sum of the three values times the respective probabilities of their development cost. Option Modeling There are three possible kinds of decisions at each node: (1) to develop the land, (2) to keep the land as-is, and (3) to sell it for $4.75 million. Figure 6-10 depicts the decisions and payoffs corresponding to the matrices in Figure 6-11. In this lattice, the notation below the value represents the optimal decision to be made: D for developing th e land; K for keeping the option alive; and S for selling the land.

PAGE 104

104 Figure 6-8. Payoff and proba bilities without fl exibility (Dollars in $1,000,000).

PAGE 105

105 Figure 6-9. Payoff matri ces for project values without fl exibility (Numbers in $1,000,000). In Year 3, the decision will be either to develop the land or to sell it for $4.75 million, whichever generates the higher payoff. For example, the PV of Node A is calculated as follows: Max (Develop, Sell) = Max (Buildi ng Value Cost, Salvage Value) = (206.13 163.61, 4.75) = 42.22 (Develop) Working backward, in Year 2, the payoff is the greatest of the three: (1) the payoff of developing the land, which is the building valu e minus development cost; (2) the payoff of keeping the option open, i.e., th e corresponding payoff in Year 3 di scounted at risk-free interest rate using the binomial or jump diffusion probabilitie s calculated in Table 62; (3) the payoff of

PAGE 106

106 Figure 6-10. Decision payoff and probabilities with flexibility (Dollars in $1,000,000).

PAGE 107

107 Figure 6-11. Payoff matrices of project value with flexib ility (Numbers in $1,000,000). Table 6-2. Probabilities of jump di ffusion and binomial processes. Jump diffusion No jump Jump Up Down Up Down (1) p ~ (1)(1p ~ ) p 1-p 0.1000 0.5895 0.3105 0.7402 0.2598 the put option, which is to sell the land for $4.75 million. For the normal stochastic process, the payoff of keeping the option open at Node B, for example, is calculated using Equation 3-19 as follows: 90 30 ] 75 4 2598 0 22 42 7402 0 [ ] ) 1 ( [1 05 0 e C p pC e Cd u rt

PAGE 108

108 Consequently, the PV of Node B is calculated as follow. Max (Develop, Keep, Sell) = Max (Building Value Cost, Payoff of Keeping Option Open, Salvage Value) = (177.30 159.14, 30.90, 4.75) = 30.90 (Keep) For the jump diffusion, the payoff of keeping the option open at Node C, for example, is calculated using Equation 4-15 as follows: 73 14 } 75 4 3105 0 61 16 5895 0 22 42 1 0 { ]} ) ~ 1 ( ~ )[ 1 ( {1 05 0 e C p C p C e Cd u y rt Consequently, the PV of Node C is calculated as follows: Max (Develop, Keep, Sell) = Max (Building Value Cost, Payoff of Keeping Option Open, Salvage Value) = (154.06 159.14, 14.73, 4.75) = 14.73 (Keep) Working backward to Year 0, the PV of the pr oject is expected PV of each cost scenario times its corresponding probability. The PV of Node D is calculated using Equation 4-17 as follows: 14 22 21 13 3 0 99 21 5 0 91 35 2 0 )] ( [ ) (1 0 m j j jPV E p PV E The PV of the project increases from negativ e $23.44 million without flexibility to positive $22.14 million with the development and se ll-off flexibility. The option value is 57 45 $ ) 44 23 $ ( 14 22 $ million. Sensitivity Analyses Sensitivity analyses are conducted using gross re ntal rates, occupancy rates, volatility, Cap rates, and development cost as independent vari ables, and on two depende nt variables: project value and option value. Project value is the PV of the project with the flexibility of deferred development, spin-off the land, and immediate development. Option value is the difference

PAGE 109

109 between PV with flexibility and PV without flexibility. Since th e PV without flexibility also changes with variables, the project value and op tion value analyses have quite different results and implications. As shown in Figure 6-12 the rental rate has a pos itive effect on project value. Rental rate is directly linked to revenue. Th e higher the rental rate is, the hi gher the income the project will generate, and hence the higher the project value is. However, as shown in Figure 6-13 it has a negative effect on option value. This is because the higher the rental rate is, the more likely the project will be developed imme diately, hence the option to wa it or abandon the development by selling off the land is less worthy. In other wo rds, higher rental rate not only increases the project value with flexibility, it also increases the value without fl exibility at even higher pace. These two values cancel out each other, resulting in minimal option value. The combination of rental rate and occupancy rate has the same result: positive effect on the project value (Figure 6-12), and negative effect on the option value (Figure 6-13). Note that the option value is sensitive to stabilized o ccupancy rate when the option is at-the-money. 50 100 150 200 250 369121518212427303336 Gross RentPV with Flexibili t 60% Occ 85% Occ 100% Occ Figure 6-12. Present value in relation with rental rate and occupancy rate.

PAGE 110

110 50 100 150 200 250 300 369121518212427303336 Gross RentOption Valu e 60% Occ 85% Occ 100% Occ Figure 6-13. Option value in relation with rental rate and occupancy rate. Just opposite to the effect of rental rate, as shown in Figure 6-14, development cost has a negative effect on project value, but positive effect on option value (Figure 6-15), for the same reason as explained above. 3 9 15 21 27 33 100 200 300 20 40 60 80 100 120 140 160 180 200 PV with Flexibility Gross Rent Development Cost Figure 6-14. Present value in relation with rental rate and development cost.

PAGE 111

111 3 9 15 21 27 33 100 200 300 50 100 150 200 250 300 350 400 Option Value Gross Rent Developmen t Cost Figure 6-15. Option value in relation w ith rental rate and development cost. As shown in Figure 6-16, cap rate has negative effect on project value. This is because cap rate is inversely related to property value. (Property value is dete rmined by dividing net operating income by cap rate.) However, the effect of cap rate on option value is more profound. Figure 6-17 shows that at normal rental rate ra nge ($11/sf to $31/sf), cap rate has a positive impact on the option value; however, in the low rent al rate range ($0/sf to $11/sf), its impact is the opposite. Figure 6-18 illustrates how the combin ation of rental rate and cap rate results in different option value. Unlike most situations where a variable has monotonic impact on the option value, the shape of cap rate on option valu e is convex. For example, at $20/sf gross rent, the option value at 2% cap rate is $71 million, at 4% cap rate the option value drops to $47 million, and at 8% cap rate the option value comes back to $77 million.

PAGE 112

112 50 100 150 200 250 369121518212427303336 Gross RentPV with Flexibili t 6% Cap 8% Cap 10% Cap Figure 6-16. Present value in relati on with rental rate and Cap rate. 50 100 150 200 250 300 369121518212427303336 Gross RentOption Valu e 6% Cap 8% Cap 10% Cap Figure 6-17. Option value in relation with rental rate and Cap rate. As shown in Figures 6-19 and 6-20 volatility has positive impact on both project value and option value. This finding is consistent with ma ny observations in real options research (Titman, 1985; Williams, 1991; Quigg, 1993) that greater volat ility increases option value, which is also the reason why the real options methodology should be applied to projects with high uncertainty.

PAGE 113

113 2 8 14 20 26 32 1% 3% 5% 7% 9% 100 200 300 400 500 600 700 800 900 Option Value Gross Rent Cap Rate Figure 6-18. Option value in relation w ith rental rate and Cap rate in 3D. 50 100 150 3%6%9%12%15%18%21%24%27%30%33%36%VolatilityPV with Flexibili t 6% Cap 8% Cap 10% Cap Figure 6-19. Present value in relation with volatility and Cap rate.

PAGE 114

114 20 40 60 80 100 3%6%9%12%15%18%21%24%27%30%33%36%VolatilityOption Valu e 6% Cap 8% Cap 10% Cap Figure 6-20. Option value in relation with volatility and Cap rate. Summary This chapter applies the separa ted approach to value the in fill land of the 211 Perimeter property in Atlanta. Rental ra te and development cost are id entified as the two major risk drivers. Rental rate is assumed to have jump di ffusion effect due to the uncertainty of the larger neighborhood redevelopment project. Development co st is assumed to be a private risk with no corresponding traded twin asse t and it is estimated subjectively based on managements experience. DTA methodology is app lied and an event tree is constr ucted, in which three options are incorporated: the option to develop immediately, the option to delay development, and the option to sell the land. The RERO approach indicates that the land is worth $22,140,000 and the value of managerial flexibility is worth $45,570,000. In Chapter 5, the building is estimated to be worth $25 million; in this chapter, the land is estimated to be worth $22 million, totaling $47 million. This is very close to reality, because the property was actually sold for $43.5 million in 2005.

PAGE 115

115 CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS Conclusions Three main conclusions are drawn from this research: (1) acquisition and development has different characteristics and deserv e different kinds of attention; (2) consideration of managerial flexibility can change investment decisions; a nd (3) many unconventional real option valuation problems can be realized by using binomi al lattice and Monte Carlo simulations. Acquisition and development have different characteristics and thus deserve different kinds of valuation. The option value of acquisition is usually on a mu ch lower scale than that of development, but by no means is it less significant. In the case studies, th e option in the existing building is replacement of the chiller system. Its value is $496,000, or 52% of the replacement cost of $950,000. On the other hand, the opti on on the infill land is development timing and abandonment. The option value is as high as $45.65 million, but only 26% of the development cost of $177.5 million. Due to the scale of the valu ations, it is better to have the option in the building and the options in the la nd valued separately. But the im pact of management flexibility on acquisition and operation is as significant as, if not more than, that on development. The consideration of operating flexibility in ac quisition is important. It adds competitive value to the bid for a property. In the case st udies, the building is worth $25 million, and the land is worth $22 million, totaling $47 million. In other words, the infill land is worth almost as much as the building. This is very close to reality, because the prope rty was actually sold for $43.5 million. Note that the present value of th e development project wit hout any flexibility is negative $23 million. With negative NPV, the pr oject will not break ground. This means if management does not incorporate the flexibilities into the land valuation, the development is deemed worthless, and so is the land.

PAGE 116

116 The RERO framework explores a few unconventi onal real option cases, including (1) jump diffusion process that does not go back to normal diffusion, (2) risk drivers that do not follow the multiplicative stochastic movement, (3) private ri sk that has no market equivalent and hence violating the no-arbitrage option pricing assumption. All of thes e can be implemented through a binomial lattice with Monte Carlo simulations or the DTA approach The RERO framework is a simple yet powerful tool, intuitiv e to the practitioners, yet math ematically correct and precise. Recommendations for Future Research There are at least three direct ions that future research can go in: model perfection, game theory and phase investment. Model perfection is to improve the precisen ess of outcome from the RERO models. Lattice is a discrete-time method for option pr icing. The smaller the time step, the closer the result will be to that calculated by continuous-time methods. At the same time, the development cost is assumed to have three values in our case study: the optimistic value, the most likely value, and the pessimistic value. More branches can be added to produce a more precise result. By dividi ng the lattice into more time step s, and breaking the development cost into more branches, a more pr ecise result will be generated. A significant factor not considered in this study is competition. Without the consideration of competition, in most cases it is optimal to defer exercising an option until the end of the holding period. However, competition erodes the valu e of waiting, affects the value of option as competitors enter or exit the market place and changes the market dynamics (Williams 1993; Myerson, 1991). Should game theory be incorporat ed into the RERO fram ework, we predict the option value would be slightly lower, and hence even closer to the closing price. The other direction is stage i nvestment and phased investment. Real estate development is a lengthy process, and it usually takes 2 to 3 years, if not longer. During this period, a lot of uncertainties can change the managerial strategies Stage investment refers to dividing a real

PAGE 117

117 estate development project into di fferent stages: planning, design, c onstruction, sales, etc. This process can be valued similar to pharmaceutical re search and development. Phased investment refers to dividing a large real estate development project into different phases, for example, Phase I retail corridor, Phase II residential condominium, Phase II I office and hotel towers, etc. Decisions at later phases are contingent upon the out come of earlier phases. However, there can be timing overlaps between two phases. While this problem is best solved by decision tree analysis, the combination of real options and decision analysis could be beneficial.

PAGE 118

118 LIST OF REFERENCES Adams, Andrew, Philip Booth, and Bryan MacGre gor. (2001). Lease Terms, Option Pricing and the Financial Characteristic s of Property, City Univers ity Business School London. Retrieved September 2005, from http://www.cass.city.ac.uk/refig/papers/LeaseTermsOptionPricing.pdf Amin, Kaushik. (1993). Jum p Diffusion Option Valuati on in Discrete Time, The Journal of Finance 48(5), 1833-1863. Arnold, Tom, and Timoth Falcon Crack. (2003) Option Pricing in the Real World: A Generalized Binomial Model with Applications to Real Options, Seventh Annual International Conference on Real Options: Theory Meets Practice Washington, DC, 10 12 July. Retrieved March 05, 2007, from http://www.realoptions.org/abstracts/ abstracts03.html Black, F. and M. Scholes. (1973). The Prici ng of Options and Corporate Liabilities, Journal of Political Economy 81 (May-June), 637-654. Bellalah, Mondher. (2002). Valui ng Lease Contracts Under Inco mplete Information: A RealOptions Approach, The Engineering Economist 47(2), 194-212. Borison, Adam. (2005). Real Options Anal ysis: Where Are the Emperors Clothes? Journal of Applied Corporate Finance 17 (2) (Spring), 17-31. Brigham, Eugene F., Louis C. Gape nski, Michael C. Ehrhardt. (1999). Financial Management: Theory and Practice 9th Edition. Dryden Press, Fort Worth, TX. Bulan, Laarni, Christopher Mayer, and C. Tsur iel Somerville. (2004). Irreversible Investment, Real Options, and Competition: Evidence fr om Real Estate Development, unpublished manuscript, Faculty of Commerce, Univer sity of British Columbia, Vancouver, CA. Retrieved March 05,2007, from http://p eople.brandeis.edu /~lbulan/Vanc.pdf Capozza, Dennis, and Robert W. Hels ley. (1990). The Stochastic City, Journal of Urban Economics 28, 187-203. Capozza, Dennis, and Gordon Sick. (1991). Valuing Long Term Leases: The Option to Redevelop, Journal of Real Esta te Finance and Economics 4, 209-223. Cederborg, Andreas, and St efan Ekeroth. (2004). Real Options and Real Estate: A Master Thesis About The Option To Convert Offices To Flats Goteborg University, Sweden. Retrieved December 2005, from http://www.hgu.gu.se /files/cff/uppsats%20cff%20-%20se%20ac.pdf Childs, Paul D., Timothy J. Riddiough, and Alex ander J. Triantis. (1996). Mixed Uses and the Redevelopment Option, Real Estate Economics 24 (3), 317-339.

PAGE 119

119 Clarke, Harry R., and William J. Reed. (1988). A Stochastic Analysis of Land Development Timing and Property Valuation, Regional Science and Urban Economics 18, 357-381. Copeland, Thomas E., and Vladimir Antikarov. (2001). Real Options: A Practitioners Guide Texere, New York. Copeland, Thomas E., and Vladimir Antikarov. (2005). Real Options: M eeting the Georgetown Challenge, Journal of Applied Corporate Finance 17 (Spring), 32-51. Cox, J., S. Ross, and M. Ribinstein. (1979) Option Pricing: A simplified Approach, Journal of Financial Economics 7, 229-263. Childs, Paul S., Steven H. Ott and Timothy J. Riddiough. (2001). Noise, Real Estate Markets, and Options on Real Assets: Theory. Unpub lished Manuscript, MIT, 2001. Retrieved 03/15/2007, from http://www.bus.wis c.edu/realestate/pdf/pdf/ NoisyAssets_%20Theory__3_01.pdf Feinstein, Steven, and Diane M. Lander. (2002). A Better Unders tanding of Why NPV Undervalues Manageri al Flexibility, The Engineering Economist 47 (4), 418-435. Geltner, David, Timothy Riddiough and Srdjan Stojanovic. (1996) Insights on the Effect of Land Use Choice: The perpetual Option on the Best of Two underlying Assets, Journal of Urban economics 39, 20-50. Ghosh, C, and CF Sirmans. (1999). An Introduction to Real-Options Analysis for Corporate Real Estate The IDRC Foundation, Research Bulletin No. 24. Grenadier, Steven R. (1995). Valuing L ease Contracts: A Real -Options Approach, Journal of Financial Economics 38, 297-331. Grenadier, Steven R. (1996). The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets, The Journal of Finance 11(5), 1653-1679. Grenadier, Steven R. (2003). An Equilibrium Analysis of Real Estate Leases, Working Paper, Stanford University. Retrieved September 2005, from https://www.gsb.stanford.edu/news/pdf/grenadier_leasing.pdf Grenadier, Steven R., and Neng Wang. (2005) Investment under Uncertainty and TimeInconsistent Preferences, Working Paper #1899, Stanford University. Holland, A. Steven, Steven H. Ott, and Timot hy J. Riddiough. (2000). The Role of Uncertainty in Investment: an Examination of Competi ng Investment Models Us ing Commercial Real Estate Data, Real Estate Economics 28 (1), 33-64. Hull, John C., (2006). Options, Futures, and Other Derivatives 6th Edition. Prentice-Hall, Upper Saddle River, New Jersey.

PAGE 120

120 Lander, Diane M., and George E. Pinches. (199 8). Challenges to the Practical Implementation of Modeling and Valuing Real Options, Quarterly Review of Economics and Finance 38 Special Issue, 537-567. Luenberger, David G., (1998). Investment Science Oxford University Press, New York. Miller, Luke T., Chan S. Park (2002). Decisi on Making Under Uncertainty Real Options to the Rescue? The Engineering Economist 47 (2), 105-150. Myers, S. (1977). Determinants of Capital Borrowing, Journal of Financial Economics 5 (2), 147-175. Mun, J. (2002). Real Options Analysis: Tools and Techni ques for Valuing Strategic Investments and Decisions John Wiley & Sons, New York. Myerson, R.B. (1991). Game Theory: Analysis of Conflict Harvard University Press, Cambridge, Massachusetts. Ng, Frances P., and Hans C. Bjornsson. (2004) Using real option and decision analysis to evaluate investments in the architecture, construction and engineering industry, Construction Management and Economics 22, 471-482. Ott, Steven H. (2002). Real Options and Real Estate: A Review and Valuation Illustration, Real Estate Valuation Theory, an Am erican Real Estate Society Monograph 8, 411-423. Pindyck, Robert S. (1991) Irreversibility, Uncert ainty, and Investment, Journal of Economic Literature 29, 1110-1148. Quigg, Laura. (1993). Empirical Tes ting of Real Option-Pricing Models, The Journal of Finance 48 (2), 621-640. RS Means. (1998-2006). Building Construction Cost Data Kingston, Mass. Sivitanidou, R., and P. Sivitanide s, (1999). Office Capitalization Ra tes: Real Estate and Capital Market influences, Journal of Real Estate Finance and Economics 18, 297-323. Smith, James E., and Robert F. Nau. (1995). Val uing Risky Projects: Opti on Pricing Theory and Decision Analysis, Management Science 41(5), 795-816. Smith, James E., and Kevin F. McCardle. (1999). Options in the Real World: Lessons Learned in Evaluating Oil and Gas Investments, Operations Research 47(1), 1-15. Titman, Sheridan (1985). Urban Land Prices Under Uncertainty, American Economic Review 75, 505-514. Trigeorgis, Lenos. (1996). Real Options: Managerial Flexibi lity and Strategy in Resource Allocation MIT Press, Cambridge, Massachusetts.

PAGE 121

121 Trigeorgis, Lenos. (2005). Making Use of Real Options Simple: an Over view and Applications in Flexible / Modular decision Making, The Engineering Economist 50, 25-53. Wheaton, William C., Raymond G Torto, Petros S Sivitanides, Jon A Southard, Robert E. Hopkins, James M. Costello. (2001). Real Es tate Risk: a Forward-Looking Approach, Real Estate Finance 18(3), 20-28. Williams, Joseph T. (1991). Real Estate Development as an Option, Journal of Real Estate Finance and Economics 4, 191-208. Williams, Joseph T. (1993). Equilibrium and Options on Real Assets, The Review of Financial Studies 6 (4), 825-850. Williams, Joseph T. (1997). Redevelopment of Real Assets, Real Estate Economics 25 (3), 387-407. Yao, Junkui, and Ali Jaafari. (2003). C ombining Real Options and Decision Tree, The Journal of Structured and Project Finance 9 (Fall), 53-70.

PAGE 122

122 BIOGRAPHICAL SKETCH Nga-Na Leung earned her PhD degree in build ing construction from the University of Florida, Gainesville, FL. While earning this de gree, she worked as an acquisition analyst for Parmenter Realty Partners in Miami, FL later fo r Acadia Realty Trust in White Plains, NY, and now for Antares Investment Partners in Greenwich, CT. She also holds a master of science degree in re al estate from the University of Florida, a master's degree in building from the National Univ ersity of Singapore, Singapore, and a bachelor's degree in architecture fr om Tongji University, Shanghai, China. Nga-Na worked as an assistant project ma nager in the Environetics Design Group in Shanghai, China prior to coming to the US. At UF, she was supported by the Alumni Fellowship, the highest merit-based award for gr aduate students. After graduation Nga-Na will continue her career in commercial real estate investment, including acquisitions, development, and management.