THE EFFECTS OF VARIOUS TENURE A'ND TAX MANAGEMENT
STRATEGIES ON ORGANrIZATION OF BEEF CATTLE RiANCHES
IN THE GULF COAST AREA OF CENTRAL FLORIDA
HENRY DOSS BROD:'AX, JR.
A DISSERTATION PI:.ESErFED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLOR;DA
IN PARIIAL FULFILLUIElI OF ;-H.- REQ IJIRENENtrS FOR THE
DEGREE CI- DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
The author wishes to express appreciation to the Department of
Food and Resource Economics, University of Florida, and the Economic
Research Service, United States Department of Agriculture, for making
the joint research effort possible. Indebtedness is acknowledged to
Dr. B. R. Eddleman, Chairman of the Supervisory Committee, for his
valuable supervision and assistance during the author's graduate pro-
gram, and to Drs. H. B. Clark, R. E. L. Greene, and C. H. Donovan, who
served as committee members.
Grateful acknowledgment is extended to Mr. Gene Harris for his
programming assistance, and appreciation is expressed to
Dr. K. R. Tefertiller, Chairman, and members of the Department of Food
and Resource Economics. A special word of thanks is expressed to
Dr. John G. Stovall and to other fellow workers in the United States
Department of Agriculture for their help and encouragement.
The author wishes to thank Mrs. Christine Ward for her valuable
assistance in typing and checking the dissertation and to
Mrs. Carolyn Coker for her clerical help.
The greatest debt is due the author's wife, Martha, for her
unselfish devotion and help during his graduate program.
TABLE OF CONTENTS
ACKNOWLEDGMENTS. . . . . ... .. ii
LIST OF TABLES . . . .. . . vi
LIST OF FIGURES. ... . . . . xi
ABSTRACT . . ... .. . . . . xii
INTRODUCTION . . . . . .
Statement of Problem . . . . 2
Scope of the Study . . . .... .5
Purpose and Specific Objectives. . . 5
Plan of Presentation . . .... .. .. 7
CHAPTER I I
CONCEPTUAL MODEL. . . . ... . . 10
Firm Theory. . . . . . 11
Dynamic Nature of the Problem. . . ... 13
Mathematical Programming Model . . . 14
METHOD OF ANALYSIS. . . . . . .18
Model Assumptions. .... . . . 19
Typical Resource Situation. .... . . 19
Enterprise Organization ..... .. . . 22
Restrictive Production Resources. . 24
Land . . . . . .24
Labor. . . . . 30
Capital. . . . . 32
Management ..... .. .. .. 33
Planning Horizon. ... . . 33
Tax Structure ... .. ........... 36
Gross income . . . 36
Adjusted gross incom.e. ..... .. . 3 37
Taxable income .... . . 37
Tax Management Strategies . .
Ranch organization . .
Nonranch income levels . .
Programming Matrix . . . .
Coding . . . .
Restrictive Constraints of the Model.
Objective Function . ... .
Activities of the Model . .
Livestock enterprises . .
Land activities . .
Financial components . .
Summary . . . . .
OPTIMAL PRODUCTION ORGANIZATION FOR ALTERNATIVE TENURE
ARRANGEMENTS . . . . .
Owner-Operator Situation .
Land Activities .
Labor Activities. .
Renter Situations .
Land Activities .
Labor Activities. .
Land Activities .
Labor Activities. .
Summary of the Optimal Tenu
. ... .. .
. .. .. .
. .. .
. . ... .
. . .
- . .
- . .
. .. e .
. ..... .
. .. .
.re Arrangements .
OPTIMAL RANCH ORGANIZATION FOR VARIOUS TAXABLE INCOME
SITUATIONS . . . . .
Owner-Operator Situations . .
Zero Nonranch Income . .
Livestock enterprises. .
Land activities . .
Financial components .
Positive Nonranch Income Levels .
Livestock enterprises. .
Land activities . .
Financial components .
Tenant-Landlord Situations . .
Maximization of Landlord's Income
Tenant's Income . . .
Renter Situations. ... . . . . 127
Summary of Tax Situations. . . . ... 129
SUMMARY AND CONCLUSIONS . . . ... 131
Summary. . . . . .... 131
Conclusions. . . . . ... 139
Need for Further Research. . . . ... 145
APPENDIX . . . . ... . . .148
EXPLANATION OF INFORMATION CONTAINED IN TABLES IN APPENDIX 149
LIST OF CITED REFERENCES . . . .... 174
ADDITIONAL REFERENCES. . . . . ... 176
BIOGRAPHICAL SKETCH. . . . . ... . 178
LIST OF TABLES
1 Initial resources available on the representative
ranch used in the programming analysis . .
2 Average (1966-70) cattle prices adjusted for trend
by months, 16 Florida livestock auctions . .
3 Animal unit equivalents, annual expenses, and cash
receipts per head for each class of livestock. .
4 Per acre capital requirements for purchasing land,
including annual appreciation of 6 percent;
machinery and equipment; and building, fencing,
and other permanent land improvements for beef
herd . . . . . .
5 Estimated per acre cost and labor requirements
for establishment of improved pasture . .
6 Annual per acre maintenance costs and grazing
produced by specific periods for alternative
forage producing systems . . . .
7 Annual labor requirements by production periods
for all alternative livestock and forage systems
available to be included in optimal ranch
organizations . . . . .
8 Percentage share of costs, returns, and available
resources for various tenure situations .
9 Taxable income, tax payments, and marginal tax
rates . . . . . .
10 Code key, row types, and right-hand-sides of
row elements for one submatrix (one year) of
the multiperiod linear programming model . .
11 Code key for column activities for one submatrix
(one year) of the multiperiod linear programming
mode I. . . . . . .
12 Restrictive bounds used each year for specified
column activities of the rultiperiod linear
programming model . . . .
13 Linear programming tableau specifying the brood
cow activities of the multiperiod model for
year t . . . . . .
14 Linear programming tableau specifying the feeder
and stocker activities of the multiperiod model
for year t . . . . .
15 Linear programming tableau specifying the land
activities of the multiperiod model for year t
and each tenure situation . . .
16 Linear programming tableau specifying the land
purchasing and clearing activities of the multi-
period model for year t . . .
17 Linear programming tableau specifying improved
pasture establishment activities of the multi-
period model for year t . . .
18 Linear programming tableau specifying the improved
nonirrigated and irrigated permanent pasture
activities of the multiperiod model for year t .
19 Linear programming tableau specifying the hay
purchasing, paying overhead, temporary grazing,
and unimproved grazing activities of the multi-
period model for year t . . .
20 Linear programming tableau specifying labor
purchasing and capital borrowing activities
of the multiperiod model for year t. . .. 70
21 Linear programming tableau specifying property
tax and certain fixed activities of the multi-
period model for year t. . . . 71
22 Linear programming tableau specifying income tax
paying activities of the multiperiod model for
year t . . . . . .. .73
23 Enterprise combinations, resource allocations,
and net returns for a full-equity owner-operator
ranch organization . . . ... .77
24 Enterprise combinations, resource allocations,
and net returns for ranch organization for a
complete renter (paying $2.55 annual rent per
acre) . . . . . .
25 Enterprise combinations, resource allocations,
and net returns for ranch organization for a
complete renter (paying $3.15 annual rent per acre)
26 Enterprise combinations, resource allocations,
and net returns for the 50-50 tenant-landlord
ranch organization, maximizing tenant's income . 90
27 Enterprise combinations, resource allocations,
and net returns for the 50-50 tenant-landlord
ranch organization, maximizing landlord's income 91
28 Livestock numbers for full-equity owner-operator
organizations when maximizing before-tax and after-
tax incomes with zero nonranch income. . ... 99
29 Improved pasture acreage for full-equity owner-
operator organizations when maximizing before-tax
and after-tax incomes with zero nonranch income. 100
30 Before-tax and after-tax incomes for full-equity
owner-operator when maximizing before-tax and
after-tax incomes with zero nonranch income. ... 102
31 Livestock numbers for full-equity owner-operator
ranch organizations with various levels of nonranch
income . . . . . 104
32 Improved pasture acreage for full-equity owner-
operator ranch organizations with various levels
of annual nonranch income. . . . ... 107
33 Capital gains and net ranch income for full-equity
owner-operator ranch organizations with various
levels of annual nonranch income . . .. 110
34 Before-tax and after-tax incomes for full-equity
ranch owner-operator including various levels of
annual nonranch income . . . 114
35 Total income and taxing components for optimal
owner-operator ranch organizations and for nonranch
income levels without the ranch organization .... 115
36 Annual depreciation and net worth for full-equity
owner-operator ranch organizations with various
levels of annual nonranch income . . .. 117
37 Livestock numbers for 50-50 tenant-landlord ranch
organizations when maximizing landlord's after-
tax income with two levels of annual nonranch
income . ... . . . . 120
38 Improved pasture acreage for 50-50 tenant-landlord
ranch organizations when maximizing landlord's in-
come with two levels of annual nonranch income . 122
39 Total net ranch income and landlord's share of
ranch income for 50-50 tenant-landlord ranch
organizations when maximizing landlord's income
with two levels of annual nonranch income. . ... 123
40 Net worth, before-tax income, and after-tax
income for landlord in 50-50 tenant-landlord
ranch organizations when maximizing landlord's
after-tax income with two levels of annual
nonranch income. . . . . ... 125
41 Share of ranch income and after-tax income for
tenant in 50-50 tenant-landlord ranch organiza-
tion when maximizing tenant's after-tax income
and landlord's after-tax income with two levels
of annual nonranch income. . . . ... 126
42 Comparisons of landowner's and tenant's incomes
with high and low rent payments and under a
50-50 tenant-landlord arrangement, landowner
with two levels of annual nonranch income. . ... 128
43 Percent of farms under some form of tenant
arrangement and average age of farmers by
counties in Central Florida. . . ... 142
44 Number of beef cattle farms, number of beef cows
that have calved, by counties in Central Florida 144
45 Number of farms and acreage of improved pasture-
land and irrigated pastureland, by counties in
Central Florida. . . . . 146
46 Optimal ranch organization when maximizing after-
tax income for a full-equity owner-operator with
zero nonranch income . . . ... .152
47 Optimal ranch organization when maximizing after-
tax income for a complete land renter paying an
annual rental rate of $2.55 per acre . .. 154
48 Optimal ranch organization when maximizing after-
tax income for a complete land renter paying an
annual rental rate of $3.15 per acre . ... .156
49 Optimal ranch organization when maximizing tenant's
after-tax income (50-50 cost-revenue tenant-
landlord share arrangement). . . .. .158
50 Optimal ranch organization when maximizing land-
lord's after-tax income (50-50 cost-revenue
tenant-landlord share arrangement) with $5,000
annual nonranch income . . . ... .160
51 Optimal ranch organization when maximizing
before-tax income for a full-equity owner-
operator with zero nonranch income . ... 162
52 Optimal ranch organization when maximizing
after-tax income for a full-equity owner-
operator with $5,000 annual nonranch income. ... 164
53 Optimal ranch organization when maximizing
after-tax income for a full-equity owner-
operator with $15,000 annual nonranch income .... 166
54 Optimal ranch organization when maximizing
after-tax income for a full-equity owner-
operator with $25,000 annual nonranch income .... 168
55 Optimal ranch organization when maximizing
after-tax income for a full-equity owner-
operator with $50,000 annual nonranch income . 170
56 Optimal ranch organization when maximizing
landlord's after-tax income (50-50 cost-revenue
tenant-landlord share arrangement) with $25,000
annual nonranch income . . . ... .172
LIST OF FIGURES
S Livestock areas in Florida, shaded area is study
area. .......................... 6
2 Multiperiod programming matrix configuration. ... 44
3 Influence of various tax provisions on effective
tax rates for optimal full-equity owner-operator
ranch organizations . . . . 138
Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy
THE EFFECTS OF VARIOUS TENURE AND TAX MANAGEMENT
STRATEGIES ON ORGANIZATION OF BEEF CATTLE RANCHES
IN THE GULF COAST AREA OF CENTRAL FLORIDA
Henry Doss Brodnax, Jr.
Chairman: Dr. B. R. Eddleman
Major Department: Food and Resource Economics
This study examined the effects that selected institutional
factors (tenure arrangements and income tax structure) have on the eco-
nomic organization of beef cattle firms. The relative advantage to an
owner-operator, tenant, or landlord of a tax-sheltered investment in a
beef breeding herd was evaluated.
A multiperiod decision model for a beef cow-calf firm was formu-
lated as a dynamic linear programming problem. Decisions made during one
production period were binding on alternatives in subsequent production
periods. Features of the model included provisions for maximizing after-
tax income of the ranch organization for full-equity owner-operator
situations, complete renter situations, and 50-50 revenue-cost sharing ar-
rangements between landlord and tenant. Income tax-paying activities were
included that required capital for paying taxes in proportion to annual
taxable income. The model was designed to maximize after-tax income to
owned resources over a 15-year planning horizon. Landowner situations
(owner-operator and landlord) were optimized with varying levels of non-
A representative ranch firm formed the resource basis of the
analysis. The ranch operator could add to the breeding herd with raised
heifers and had the option of selling weaned calves or feeder steers and
heifers. Available grazing could be increased by purchasing more land or
by establishing improved pasture.
Tax regulations included in the study were paying capital gains
income taxes on sales from cull cows (allowing 50 percent deduction on
taxable income); capitalizing land-clearing costs over a 10-year period,
or charging land clearing-expenses as ordinary business expense up to 25
percent of taxable ranch income (maximum of $5,000 per year); and
charging soils and water conservation expenses as ordinary expenses in the
year incurred, up to a maximum of 25 percent of gross ranch income, with
any excess expenses carried over to succeeding years. Nonranch income
was included as available capital to the firm and was assumed to be com-
The effects of various tenure arrangements on optimal ranch orga-
nization were evaluated for situations without any nonranch income.
After-tax income was maximized for each of the three resource ownership
situations. The basic solutions for the different tenure situations
showed many similarities. No additional land was purchased and approxi-
mately one-third of the initial 3,500 acres of rangeland was established
in permanent pasture. However, after-tax incomes varied among the three
types of tenure situations.
The effects of various tax management strategies on the optimal
ranch organization were evaluated for four levels of nonranch income
($5,000, $15,000, $25,000, and $50,000 annually). The results indicated
that present capital gains provisions in the tax law provide an incentive
for individuals in the beef cow-calf industry with large nonranch incomes
to sell calves and increase the breeding herd. Individuals with little
x I I
or no nonranch income would find it more profitable to sell feeders and
maintain a smaller cow herd.
Beef cattle production is continually becoming relatively more
important as a source of farm income in Florida. Total cash farm re-
ceipts from the sale of cattle and calves in Florida increased from $41.3
million (6.5 percent of total cash farm receipts) in 1955 to $163.9 mil-
lion (11.5 percent of total cash farm receipts) in 1971. Beef cattle and
calves on Florida ranches totaled 1,681 thousand head as of
January 1, 1972. This represents an increase of 392,000 head since 1960
[1, pp. 1-2]. According to the 1969 U. S. Census of Aqriculture [2, p. 2]
there were 14.03 million acres of land in farms in Florida but only 2.23
million acres were used for harvested crops. Thus, Florida has a great
potential for growth of the beef industry with large acreages available
for cattle production in a mild climate suitable for year-round grazing
in parts of Central and Southern Florida.
Even with this ideal climate and abundant water for the produc-
tion of forages, Florida still has many problems to solve in beef
production. Most of these problems are due to variations in soil, ter-
rain, and management practices. Brodnax and Eddleman  found that
grazing land requirements per mature cow ranged from 3.33 to 8.1 acres
and for some ranches this figure was as high as 20 acres per cow'. on na-
tive pasture. Beef produced per acre ranged from 41 pounds to 143 pounds,
but some of the top cattle producers and research units have already ob-
tained 400 pounds of beef per acre. In that study five representative
cow-calf organizations were identified which ranged in size from 100
acres to 17,000 acres of grazeable land with a herd size of 43 animal
units to 3,131 animal units. Florida is unlike most states in the south-
east; a large segment of the beef industry is located on large ranches
similar to the western states.
The beef cattle industry in Florida is expected to continue to
grow. According to the 1969 DARE Report [4, pp. 123-125], cattle numbers
are expected to increase to 1.8 million head by 1975 and 2.1 million head
by 1980. The trend is toward increasing ranch size,with an estimated
10,000 ranches in 1980 as compared to over 17,000 in 1969. Most of the
increase in beef production is expected to be related to improved pastures
and a larger calf crop weaned.
Florida produced 35 percent of the total beef consumed in the
state in 1968. It is predicted that Florida can produce only about 42
percent of its beef needs in 1980 due to a rapidly growing population and
increasing per capital beef consumption in relation to production capacity
[4, p. 124]. However, the Florida beef industry has great potential for
Statement of Problem
The large investment capital requirements of ranch units, as
characterized by many of Florida's beef producers, raises many questions
with respect to the growth potentials of firms. What are the best alter-
natives afforded ranchers in expanding their operations? What effect
d o various decisions related to capital investmentand income flows
have on organization of the firm?
Beef cattle producers are continually making production decisions
that affect their incomes over time. These decisions are usually con-
sidered to be based on the ultimate objective of net revenue maximization,
but a rancher's goal may be governed by something other than maximum net
revenue. Many of the larger ranches in Central Florida are operated by
hired managers,with the owner having other sources of income. Thus, the
beef cow-calf enterprise may be an alternative for accomplishing some ob-
jective other than net revenue maximization. These objectives might
include maximization of after-tax income, asset accumulation through
land appreciation, or even personal satisfaction derived from owning a
Adjustments are taking place among beef producers in Florida but
these changes are not in terms of new producers. Land ownership is rela-
tively stable even in the face of possible high speculative value of land.
Also, large acreages are owned by wood products companies, mining firms,
and land speculators. These large land owners can greatly influence the
future of beef production (cow-calf system) in the Gulf Coast region of
Central Florida. The usual leasing arrangement is short-term (one year)
but if longer term leases were offered to cattlemen the rangeland acre-
age might be made more productive. Under a short-term lease the
cattleman grazes the native range with little consideration for the
future. Thus, many leases have a stocking rate clause in them that
limits the number of animals that can be grazed during the year. Native
pastures might be improved and even improved pastures established if the
net returns were large enough to meet specified goals for both the land-
owner and the cattleman.
Another crucial factor that is faced by ranchers, and especially
large-scale producers, is their after-tax position. The question of in-
come tax policy as it may affect ranch management decisions is very
relevant for the Florida cattleman. Many producers in the study area
have nonranch income ; thus, beef breeding herds could be a means for
a tax-sheltered investment. Carman  discusses the after-tax returns
for a tax-sheltered investment in beef cattle. His analysis shows how
taxpayers in the highest tax brackets benefit from investment in beef
cattle operations while incurring apparent large cash losses from their
The problems of financial management are important considerations
when analyzing a firm's growth pattern. Ranches in this area of the
state seem to be characterized by an internal capital rationing. Rela-
tively low use of intermediate and long-term credit was found with the
largest proportion of credit needs being annual operating capital .
From a random survey of ranches in the study area, less than 40 percent
of the ranchers interviewed admitted using any type of credit for their
ranch. On ranches with over 2,000 head, no intermediate or long-term
credit was used. Thus, growth opportunities may be available to warrant
use of more capital.
Previous firm growth studies have dealt almost entirely with
variations in technical production and market structures and not with
the institutional structures that this study considers. It is believed
that ranches in Central and South Florida are not as responsive to price
variations as they are to changes in some institutional structures. This
suggests that decisions might be based on such considerations as maxi-
mizing after-tax returns to the owner-operator rather than maximizing
the gross net returns to the firm per se.
Scope of the Study
The scope of this study includes beef cattle ranches in a nine-
county area in the Gulf Coast area of Central Florida (Figure 1). The
soils are predominately sandy and imperfectly to poorly drained. These
counties are below the normal freeze line and a killing frost is likely
in half the years. Average annual normal rainfall is 56 inches and the
mean temperature is 730 F.
Climatic factors are important to ranchers in the study area.
With the mild climate and high rainfall, year-round grazing is possible
throughout the area. Thus, very little forage is produced and stored
for use in the winter months. The warm climate and heavy rainfall in-
crease the hazard of diseases, insects, and leaching of soil fertility.
Farming in this area is usually highly specialized in either
citrus, vegetable crops, or beef cattle. Beef herds in this area are
usually large, with large areas over which to graze. Citrus and vege-
table production are usually separate farming operations from the beef
enterprise and compete very little with beef for resources. Vegetable
and citrus production in some instances have been replaced with cattle.
This has occurred when excessively large disease problems emerged in vege-
table production or when a large acreage of citrus was lost during a
freeze. The analysis of this study deals with representative ranches
which are assumed to be completely independent from other farming
Purpose and Specific Objectives
The general purpose of this study was to develop an economic de-
cision model that identifies optimal ranch investment and production
L1. [A Aa
J~~~ ~ Hh.<[i~OLt
1 *u a rte
T3.TI (J~T A-
^./ v^.^ .
Figure 1. Livestock areas in Florida, shaded area is study area.
strategies required to fulfill specified entrepreneurial goals. This
study dealt more with growth patterns and organizational change of the
ranch firm due to institutional conditions rather than with growth in the
sense of increased net worth or acreage.
Specific objectives were (1) to develop a multiperiod production
model for a beef cow-calf operation, (2) to analyze the effect of various
tenure arrangements on the organizational structure of the firm, and (3)
to compare the effects of various tax management situations on the op-
timal ranch organization.
When ownership and management of ranch firms were assumed to be
by the same individual the objective was to maximize after-tax net income,
given certain tax regulations and a specified amount of nonranch income.
Another aspect was the combining of leasing structure with tax manage-
ment. The tenant and landlord had the sane objective function
(maximize after-tax net income), but their optimum organizations were dif-
ferent due to their marginal rates of taxation being different. Under a
share-lease arrangement, the landlord with outside income emphasized
minimizing income tax payments,with such tax strategies as the capital
This study should be helpful in answering questions pertaining
to organizational arrangements conducive to firm survival, the aggre-
gate effect of tax-sheltered investment in beef cattle, and the effect
of tax incentives on the flow of capital into the beef industry of
Plan of Presentation
The thesis is presented in six chapters. Chapter II provides a
general discussion of previous work in the study of firm growth. This
brief review provides a background for this study and the need for
research in the general area of firm growth. In addition, the dynamic
nature of the problem is discussed in terms of a planning horizon for
firm decisions. The theoretical model is presented emphasizing possible
objectives for the decision-maker other than gross net revenue maximiza-
tion For the firm.
Chapter III provides a detailed description of the multiperiod
linear programming model used in the analysis. The representative re-
source situation is discussed in terms of sources and types of data.
The assumptions of the analysis are presented in a discussion of the
time period, tenure arrangements, taxing structure, and nonranch income
situations. A brief presentation of the programming matrix includes
the coding procedure for both activities and constraints. The last
part of Chapter III presents detailed information about the specific ac-
tivities of the decision model. All activities in the model are
characterized under one of the following main categories: livestock,
land, labor, capital, or tax.
Results from empirical applications of the decision model are
presented in Chapters IV and V. In Chapter IV, the optimal ranch orga-
nizations are given and discussed for the Full-equity owner-operator
situations, the complete renter situations, and the 50-50 cost-revenue
sharing between landlord and tenant situations. This chapter deals only
with the firm when nonranch income is not a factor influencing entre-
preneurial decisions. Optimal firm organizations considering various
tax situations are discussed in Chapter V. These tax situations are
analyzed for the four different nonranch income levels for the landowner
in both full ownership and cost-revenue sharing situations.
Chapter VI summarizes the results and the major conclusions of
the study. The industry implications of changes in institutional factors
with regard to aggregate beef production in the study are discussed.
Growth might be defined as the gradual development toward
maturity. Penrose indicated that growth has two different connotations,
"It sometimes denotes merely increase in amount; for example, when one
speaks of 'growth' in output, exports, sales. At other times, however,
it is used in its primary meaning implying an increase in size or an im-
provement in quality as a result of a process of development" [6, p. I].
This study's primary concern is not with total ranch size (e.g.,
total acres of land or total capital investment) as the growth alterna-
tive but more emphasis is placed on the method of obtaining the optimal
size of firm consistent with specified goals of the operator. This size
was based on the selection of the optimal combinations of alternative
activities possible for the ranch organization.
Several factors influence the process of economic growth of the
firm. These factors include price and yield variability, managerial
ability, resource supply, and institutional factors related to the ranch
firm. Most firm studies have dealt primarily with firm factors such as
price and yield variability and resource supplies. The conceptual frame-
work of this study may be summarized under three headings: (1) the role
of institutional factors in firm theory, (2) the dynamic nature of the
problem, and (3) specification of the mathematical programming model
used in the analysis and review of some related studies.
The theory of the firm involves determination of the optimum
combination of different forms of output, the optimum combination of
variable factors for any given output, and the optimum rate of output.
Relevant functions required in the solutions of problems are the pro-
duction, cost, and revenue functions. These relationships are utilized
to obtain an optimum level of production which will maximize an objec-
tive, usually assumed to be the highest level of net revenue. This
section discusses the problems of compatibility among the goals of the
total ranch firm and the goals of the individuals comprising the ranch
Let P. = the price of product j
Y. = the output of product j
P. = the price of resource i
X. = the input of resource i
F = unallocated fixed costs
TR = total revenue
TC = total cost
Net Revenue = TR TC = Z P.Y. 7 P.X. F
J j I
For a specific analysis, inputs are assumed to be either variable
inputs or fixed inputs. The technical relationships can then be written
Y. = f(X. X ) where i = 1, 2, k, and n = k+l, k+2, ,r
J n '
In the above expression X. represents the variable resource inputs, and
X represents given levels of specified fixed inputs. Carlbon [71,
Henderson and Quandt , and Leftwich  state that,by substituting
the technical production function [Y. = f(X.IX )] into the net revenue
equation and solving the equation, the optimal levels of the variable
resources, X., and products, Y., can be determined which will maximize
net revenue. Thus, variations of product and input prices would affect
the optimal arrangement of resources and production for net revenue maxi-
mization of a firm.
When considering the individual's aspect of net revenue maximiza-
tion, not all of the variables are endogenous to the total firm
organization. All of the total disposable income of the firm is not
available for investment in capital goods for future production. A
specified proportion of disposable income must be used to satisfy the
family goals of consumption and to pay an individual's federal income
tax. Therefore, the amount of disposable income available for obtaining
control of additional resources is limited by the consumption level of
the family, the amount of income generated through the operation of the
ranch firm, the amount of nonranch income available for firm use, and
the capital requirement for paying income taxes. The interrelationship
between the ranch firm and the family and the relative importance of
institutional variables such as tax and tenure structures will have an
impact on the growth process of the ranch firm.
The net revenue function of an individual needs to be examined
with these institutional factors included. Variable rental rates, share
arrangements, and nonranch income levels would affect the individual's
optimal economic unit. Rental charges could be included in the price
for the land resource,but the tenant-landlord cost and revenue share ar-
rangement is in addition to the firm's resource system. Firm net revenue
maximization might not maximize either tenant's or landlord's net income
because of the division of income and certain exogenous variables such
as the marginal rate of taxation on taxable income.
Let an individual's after-tax net revenue be:
Y = TR TC = SI (E P.Y. Z P.X.) S F + NRI Z(TI)
S, = share of gross ranch income and variable costs
S2 = share of unallocated fixed costs
NRI = nonranch income
Z = effective tax rate
TI = taxable income (gross income minus allowable tax deductions)
TI = f(EP.Y. ZP.X. F + NRI)
J J I
Z = f(TI)
The optimum level of variable resources, X., and products, Y., for
optimizing the individual's net revenue is determined by the technical
production function, share of ranch net income received, nonranch income
level, and marginal rate of taxation. For a full-equity owner-operator
with no nonranch income the individual's net revenue equation would not
be affected by the S or NRI variables. However, when the individual's
total income is composed of ranch and nonranch income, taxable income is
a function of this total income and the allowable tax deductions. It
would be expected that products of the firm that were given tax-sheltered
advantage would add relatively more to the after-tax net revenue of the
optimum organization as the total income level increased (ranch plus non-
ranch income). Therefore, individual producers might be more sensitive
to their marginal rate of taxation than they would be to the firm's
marginal rates of substitution among inputs, and the marginal rates of
transformation among products.
Dynamic !Jature of the Problem
With static firm theory, the problems associated with capital ac-
cumulation and variable institutional factors cannot be solved without
removing the realism. A time span is involved in organizing resources to
take maximum advantage of the given situations. In developing a dynamic
model, Plaxico states,
By omitting time as a variable, one may greatly simplify
conceptual and empirical models. At the same time, one
tends to ignore (assume away) certain practical important
problems of production timing, capital acquisition and
accumulation, transitory resource efficiency, and the im-
pact of a decision in one time period on production,
opportunities and choices during subsequent periods.
[10, p. 12]
A ranch firm represents an organization that requires several
years to reach optimum resource efficiency. Two years are needed for a
heifer to become a producing cow and improved pasture requires at least
two years for sustained high levels of forage production. For tenure
arrangements to be effective, each party in the firm needs to be able
to plan for several years.
The Internal Revenue Code also places the beef firm in a time-
wise dynamic situation with requirements such as keeping breeding stock
at least two years before the sales can be included as capital gains in-
come. This makes it necessary to employ a framework for the analysis
that is dynamic in the sense that time is explicitly included in the pro-
duction and decision process.
Mathematical Programming Model
Linearity was assumed to describe the production and cost rela-
tionships involved in this analysis. The static firm theory described
previously can be transformed into a standard linear programming form.
Maximum net return = E C.Y. (j = 2, n)
subject to: E a..Y. < B. (i = 1, 2, m)
and Y. > 0
Where C. = the net return from producing one unit of product j
Y. = the number of units of product j produced
a.. = the amount of resource i used to produce one unit
Sof product j
B. = the total amount of resource i available
Multiperiod linear programming as used in this analysis is an ex-
tension of static linear programming where the transformation from the
static to the "dynamic" model is produced by the use of submatrices.
The usual one period static model in vector form may be stated as
[10, p. 13]
Maximize C' X = Z
8 > AX
X > 0
Here, A is a matrix of input-output coefficients; X represents
the alternative ways that resources might be transformed into alter-
native products. The vector C describes the net revenue from each unit
of the alternative products which may be produced. The factor B speci-
fies the availability of scarce resources.
The above model can be made "dynamic" if the input-output matrix
A represents submatrices corresponding to the time periods of the
planning horizons (Al, A2, An). Overlapping in rows and columns
of the submatrices adds the time dimensions to the analysis. Resources
required or produced in one time period affect available resources in
some future time period (Bt) Maximum net revenue over time is repre-
Net return = E C. Y. t = r
C. = the net return from producing one unit of product
j during time period t
Many studies have used the above framework in analyzing the
process of firm growth. The early studies dealt with only one period of
production. One of the first studies that considered the multiperiod
problem was by Martin [1l]. His analysis incorporated the longer run in-
vestment aspects of firm growth, and various starting equities were
determined in relation to specified growth conditions.
Fewer studies have been made of the effects of the progressive
income tax system on net income and organization of the farm firm.
Martin and Gatz  analyzed the possibility of high income nonfarm
persons using cattle ranches as a tax-sheltered investment. They con-
cluded that the use of cattle ranches as a tax shelter does not greatly
affect cattle prices. In another study by Dean and Carter , total
revenue and total cost curves were used to determine optimum output
under varying conditions. Results showed that when the economic costs
are equal to the tax deductible costs, the income tax has no effect on
The effects of selected Federal income tax regulations on after-
tax net income from farming and ranching were compared in a recursive
type analysis by Vieth and Epp . A five-year decision-making horizon
was involved, based on specified amounts of tax-sheltered incomes. This
study showed that capital gains provisions of the Internal Revenue Code
(tax year 1967) provided an incentive for the absentee beef herd in-
vestor to replace the breeding herd more often than the owner-operator.
Baker  presented a method for specifying personal income taxes, con-
sumption, and saving in a decision model. His model specified a
progressive tax structure within a linear programming tableau, assuming
two situations: no capital gains and capital gains.
The multiperiod model in this study presents several economic
aspects not handled by any previous beef cattle firm analysis. These in-
clude the partitioning of total income into ordinary and capital gains
incomes for tax purposes, inclusion of many alternative forage producing
systems, payment of annual income taxes on both ranch and nonranch in-
comes, and maximization of after-tax incomes of the ranch firm for three
different tenure arrangements.
METHOD OF ANALYSIS
In this section, three closely associated topics are discussed
in detail. First, an explanation of the basic assumptions of the analy-
sis is presented. This includes an identification of the basic resource
situation for the typical firm. Second, the model structures are re-
lated to the programming matrix. Coding procedures, resource
restrictions, objective functions, and economic activities are presented.
Third, detailed presentation of all column activities of the model are
discussed with emphasis on transfers and tax paying activities.
In general, the framework of the analysis and construction of the
model used in this study portrayed characteristics of a typical ranch
firm. The ranch operator provided management ability and controlled
ranch resources such as capital, land, labor, equipment, and livestock.
Types of resources controlled depended on the tenure arrangement: full-
equity owner-operator, complete renter, or tenant-landlord cost-revenue
share arrangements. The full-equity owner-operator organization is pre-
sented as the typical situation and modifications are specified for the
other tenure arrangements. These modifications occurred primarily in
land and labor resources.
Division of the expenses and returns into categories suitable
for the taxpaying activities was a critical factor in specifying the
programming model. These tax activities were structured according to
existing federal tax regulations. For example, the annual allowable
soil and water conservation expenses were restricted by total gross
ranch income. Thus, these conservation expenses required a separate
programming activity from the pasture establishment enterprise. The
programming matrix was developed to represent the beef production alter-
natives in terms of existing tax structures for the individual operator.
Optimum ranch organizations were based on the objective of maximizing
The multiperiod linear programming model was solved with proce-
dures available in the Mathematical Programming System/360 (MPS/360).
MPS/360 procedures deal only with strategy for solving a linear program-
ming problem. Solutions were obtained with the use of an IBM 360/65
The typical ranch in the Gulf Coast area of Central Florida used
as the basic resource situation was identified by Brodnax and Eddleman
. Data applicable to the area were obtained from agricultural experi-
ment station results at Gainesville, and the Range Cattle Station at
Ona; farm surveys; and consultations with scientists of the Florida Ag-
ricultural Experiment Stations.
Enterprise budgets based on production coefficients, costs, and
returns for above-average management levels were used in the programming
analysis. Copies of these enterprise budgets are on file in the Food
and Resource Economics Department.
Typical Resource Situation
Usually a large number of farm enterprise alternatives exist in
a producing area, but only a relatively small number of alternative
enterprises are relevant to a typical ranch in Central Florida. As
pointed out in Chapter I, beef cattle ranches in this area of Florida
are characterized as rather large specialized operations. Approximately
30 percent of total cattle numbers in Central Florida are located on
ranches with 500 or more brood cows . Also, previous research re-
sults have indicated that most economies to size are achieved with a
500-cow herd size . Net ranch income (returns to investment, oper-
ator's labor, management, and risk) for representative ranch budgets,
consisting of 480, 900, and 2,100-cow herds, were $17.73, $20.31, and
$19.74 per cow, respectively.
The levels of resources available for the initial year of the
programming analyses are shown in Table 1. This basic ranch organization
was based solely on a cow-calf operation. Calves were sold when weaned
and all replacement heifers were selected from the calf crop.
Rangeland required for the cow-calf herd was 3,500 acres. The
initial ranch unit was based on full equity in this acreage for either
an owner-operator or a landlord. The full-time operator had 2,700 hours
of labor available annually, divided equally between three production
periods for the year. Additional labor could be purchased in unlimited
amounts for each production period.
Land was initially valued at $150 per acre plus an additional
$7.21 per acre for land improvements. These land improvements included
corrals, barns, wells, feed boxes, and fencing needed for 3,500 acres of
rangeland. The complement of machinery and equipment required for oper-
ating 3,500 acres of rangeland had an average total value of $22,855
($6.53 per acre). Net value of livestock was $105,700 (based on $197
per cow unit including proportional value of a bull and $120 per replace-
Table 1. Initial resources available on the
in the programming analysis
representative ranch used
Item Unit Total
Brood cows head 500
Weaned calvesa head 400
Replacement heifersb head 60
Bulls head 20
Rangelandc acres 3,500
Period I (November-February) hours 900
Period II (March-June) hours 900
Period III (July-October) hours 900
Total available labor hours 2,700
Land dollars 525,000
Buildings, fences, and improvements dollars 25,235
Machinery and equipmentf dollars 22,855
Livestock dollars 105,700
Total initial net worth dollars 678,790
Borrowing capacity (50 percent of net worth) dollars 339,395
Eighty percent of the brood cows wean calves.
Sixty heifers are kept each year for replacement of cows
culled and for death loss.
CThree thousand five hundred acres of rangeland was needed for a
Initial value of land was $150 per acre.
eAverage investment in buildings, fences, and other improve-
ments was $7.21 per acre.
Average investment in a complement of machinery and equipment
needed for 3,500 acres was $6.53 per acre.
The initial net worth position varied according to the tenure
arrangement. For the full-equity owner-operator all the above items
were included in the net worth of the firm. Value of land, buildings,
fences, and other land improvements was excluded from the net worth of
the firm for the complete renter and tenant-landlord cost-revenue share
arrangements. These land and improvement values were added to landlord's
The expense and income of the ranch firm included only those re-
sources that were directly related to production activities of the ranch.
With a complete renter situation, the operator paid a fixed sum to the
landowner for use of the land and the landlord assumed all expenses di-
rectly related to land. The tenant-landlord cost-revenue share
arrangement delegated fixed land expenses entirely to the landlord to be
deducted from his share of ranch income. Thus, fixed land expenses
(real estate taxes and depreciation on improvements) were considered as
a direct firm expense for only the full-equity owner-operator situation.
The programming analysis of this study considered four beef
cattle production alternatives. In addition to the basic cow-calf system
with weaned calves sold in October, the calves could be kept for an ad-
ditional six months on winter grazing and sold as feeders in April.
Also, feeders could be purchased in October and sold in April. Another
livestock alternative was buying stocker steers (375 pounds) in April
with supplemental feeding on pasture until October. These feeder alter-
natives allowed flexibility in selling during months when prices are
normally high and in utilizing excess forage from pastures. Culled cows
were sold in March after the calving season. Prices received for cattle
during the 1966-70 period are presented in Table 2.
Table 2. Average (1966-70) cattle prices adjusted for trend by months,
16 Florida livestock auctions
I Monthly prices
Class Grade Weight Monthly
March April October
---cwt.--- ------dollars per cwt.--------
Cows Commercial 8.75 20.24 20.88 18.34
Calves Good 4.00 31.50 33.07 27.68
Feeder steers Choice 6.25 27.21 27.36 26.28
Source: Florida Crop and Livestock Reporting Service, Florida
Agricultural Statistics Livestock Summary, 1966-70.
Cattle prices are generally higher during the spring months than
during the fall, but a majority of calves produced in Florida are sold
during the fall period. Calves purchased as feeders were assumed to
weigh the same as calves raised (400 pounds).
The weaning percentage for calves was 80 percent. Thus, 20 per-
cent of the brood cows either did not wean a calf or died during the
year. Death loss was equal to 2 percent for brood cows. The average
number of years that a mature cow remained in the herd was ten. Thus,
to maintain herd size an approximate replacement rate of 12 percent per
year was required. An additional 8 percent of the brood cows (without
calves) was available for culling to improve the quality of the herd.
Brood cow numbers were maintained and increased only by keeping
weaned heifer calves. Fifty percent of the weaned calves were assumed
to be heifers and could be kept for herd replacement and expansion. The
minimum number of replacement heifers kept each year was 60 head to
maintain at least 500 brood cows in the herd. Two years are required
for a heifer to mature. Thus, a heifer born in March produced a calf
two years later.
The livestock enterprise summary shown in Table 3 reflects the
animal unit equivalents, annual expenses, and cash receipts for each
class of livestock. Animal unit equivalents were used in determining
the grazing requirements for the entire herd. One animal unit month
(AUM) of grazing represents the amount of forage or grazing required to
maintain one mature cow (approximately 950 pounds in weight) for one
month. Yields for each forage enterprise were measured as animal unit
months of grazing. The annual cost of production for each enterprise
was not included as an annual expense to a specific class of livestock.
The livestock inventory added to the firm's net worth. One
brood cow and a twenty-fifth share of a bull was valued at $197. Re-
placement heifers increased the beginning year inventory by $120.
Personal property taxes were paid on livestock at a rate of 3.5 mills.
Thus, the ranch firm was taxed at an annual rate of $.70 per brood cow
and $.42 per heifer.
Restrictive Production Resources
The assumptions related to the restrictive resources of the re-
presentative ranch firm (land, labor, capital, and management) are
presented in this section.
The livestock enterprises (cow-calf system and feeders) were in-
come-producing activities and required varying amounts of resources.
Land.--Since most of the feed requirements for the herd were
obtained from grazing, the land base for forage production was a restric-
tive factor in livestock production. The representative resource
situation consisted of 3,500 acres in rangeland that supported the 500-
cow herd. Some of this acreage had to be in improved pasture to support
Table 3. Animal unit equivalents, annual expenses, and cash receipts
per head for each class of livestock
Class Animal unit Annual Cash
equivalents expenses receipts
Cow, with calf 1.25 18.18
Cow, culled 1.0 6.51 170.90
Bull 1.25 49.00a
Calf .50 -- 106.84
Feeders (October-April) .65 134.58 163.36
Stocker steer (April-
October) .65 143.57 156.91
Heifer, coming 1 .50 2.06
Heifer, coming 2 .75 10.74
aCash expenses of maintaining a bull were included in the annual
expense of a cow. The $49.00 was annual bull depreciation obtained by
subtracting the salvage value adjusted for expected death loss from the
purchase value and dividing this total by the years of useful life.
one cow on seven acres. The programming analysis assumed that the
initial land resource was unimproved native rangeland. To provide the
forage requirements for a 500-cow herd, either forage had to be purchased,
additional acreage of rangeland purchased or rented, and/or some of the
owned native range put into improved pastures. Growth in the size of
the beef herd (more cows, feeders, and stockers) also required additional
graz i ng.
Hay could be purchased to help maintain the herd during the
winter months (November-February) at a cost of $30 per ton. Land was
available for purchase during any year of a 15-year planning period.
Land values based on annual appreciation of 6 percent are shown in
Table 4. For each additional acre of land above the initial 3,500 acres,
Table 4. Per acre capital requirements for purchasing land, including
annual appreciation of 6 percent; machinery and equipment; and
building, fencing, and other permanent land improvements for
aThe value of land initially was $150 per acre.
include $3 per acre closing cost when purchasing land.
This does not
capital requirements for fencing and other improvements were $14.29 per
acre and machinery and equipment required an additional capital invest-
ment of $11.74 per acre.
Two methods of purchasing land were considered. Land could be
purchased for cash in any year. The second method of purchasing land
was through a 10-year loan which required a one-third down payment at
the beginning of the first year and equal annual principal payments at
the end of each of the ten years. The annual interest rate on the
loan was 7 percent on the unpaid balance. Miscellaneous costs of pur-
chasing land were $3.00 per acre. For example, land purchased during
the fifth year required $229.76 of capital ($226.76 plus $3.00). If
the land was bought on loan, the initial down payment per acre equaled
_ ~ __
$66.91 (one-third of $200.73) plus the additional per acre capital
requirements of $29.03 (equipment $11.74; fencing and other improvements
$14.29, miscellaneous closing costs $3.00). Loan payments were $13.38
per year plus interest on unpaid balance for ten years.
An annual fixed charge of $2.49 per acre was made for land. The
charge included $.37 for insurance and repair of machinery and equipment;
$.36 for insurance and repair of buildings, fencing, and other beef
equipment; $.93 depreciation on machinery and equipment; and $.83 depre-
ciation of buildings, fencing, and beef equipment. Real estate taxes
were $1.57 per acre based on a land use value of $80 per acre plus $7.21
For land improvements, and a tax rate of 18 mills ($18 per thousand dol-
lars of evaluation). Personal property tax was $.02 per acre based on
an average investment of $6.53 per acre in machinery and equipment. An-
nual insurance costs were .38 percent of average value and annual repair
costs were computed as initial cost times 2 percent.
The ranch organization had available the alternatives of grazing
land as unimproved native range, cleared land, improved temporary pas-
ture, improved nonirrigated pasture (bahiagrass or Pangola digitgrass)
or improved seepage irrigated pasture. Before land could be transferred
from native range to improved pasture, land had to be cleared and the
improved pasture established. Costs and labor requirements for estab-
lishment of improved pastures are presented in Table 5.
Temporary pasture consisted of an annual winter grass (ryegrass)
with the acreage planted converted back to cleared land after the
grazing season. All other improved pastures were perennials and re-
mained in the farm organization for 15 years,at which time the grass had
to be reestablished. As shown in Table 6, several alternatives were
Table 5. Estimated per acre cost and labor requirements for
establishment of improved pasture
Item Expense required
Clearinga 33.93 2.1
Irrigation system (seepage):
Capitalized expense 27.14
Conservation expense 47.52
Establishment of grass 39.75
Total 114.41 8.3
Conservation expense 7.60
Establishment of grassd 21.53 -
Total 29.13 2.2
Conservation expense 19.47 --
Establishment of grassd 21.53 --
Total 41.00 3.3
aInitial clearing involved removing brush and undesirable
growth, leveling, and breaking the land.
Seepage irrigated acreage was restricted to 25 percent of total
acreage in ranch.
Capitalized expenses were for pumps and other equipment that
could be depreciated during the years of use.
Conservation expenses were separated from other establishment
costs because of the income tax regulation restricting the total amount
of allowable conservation expenses per year.
available for maintaining improved perennial pastureland. These alter-
natives were based on different levels of fertilization. The cost of
maintaining unimproved native range was $.13 per acre. The acreage of
native range remained in the ranch organization unless it was improved
at an additional expense to meet increased grazing requirements of the
The AUM's of grazing produced per acre was an estimate of the
number of animal units that could be grazed for one month, or
Table 6. Annual per acre maintenance costs and grazing produced
forage producing systems
by specific periods for alternative
Annual Grazing produced (AUM)
Item maintenance Period 1 Period II Period III I
cost (Nov.-Feb.) (Mar.-June) (July-Oct.)
Unimproved native range .13 .28 .38 .32 .98
Cleared land .13 .36 .46 .40 1.22
Temporary pasture 35.57 4.3 3.9 0 8.2
Medium fertilization 18.36 .50 3.0 2.5 6.0
High fertilization 27.63 .80 3.6 3.5 7.9
No maintenance (idle) .13 .48 .48 .48 1.44
Medium fertilization 18.46 .50 2.70 3.10 6.3
High fertilization 27.82 .80 3.50 3.90 8.2
Grass topseeded with ryegrass 45.12 3.7 3.8 3.0 10.5
Grazing and hay 44.86 6.5a 2.5 2.0 11.0
No maintenance (idle) .13 .48 .48 .48 1.44
Irrigated perennial grass: b
High fertilization 21.73 1.6 4.7 4.0 10.3
No maintenance (idle) 3.98c .48 .48 .48 1.44
aThis represented 2.5 tons of hay produced in addition to grazing during the other two periods.
blncluded depreciation ($3.48), annual repairs ($.94),
taxes ($.28), and insurance ($.09 charges for
Concluded depreciation ($3.48), taxes ($.28), and insurance ($.09) for irrigation system.
alternately, the number of months one animal unit could be grazed on one
acre. For example, assume that the .32 AUM of grazing produced during
Period II by unimproved native range was equally distributed among the
four months (July-October). Thus, .08 AUM of grazing was available for
each month. The acres required per animal unit can be determined by
Acres AU (animal unit) 1_ l
Acres = -----: 12.5
AUM grazing per acre .08
This calculation indicates that 12.5 acres of unimproved native range
would be required each month during Period III to support an animal unit
(one mature cow). During the same Period III an acre of irrigated peren-
nial pasture (high fertilization) produced 4.0 AUM of grazing which would
support one animal unit per month.
Labor.--Labor requirements for livestock and pasture activities
were grouped according to the production periods: Period I (November-
February), Period II (March-June), and Period III (July-October). These
time intervals reflect the seasonal components of production activities
for a beef herd. Period I is the winter season requiring supplemental
feeding and miscellaneous ranch repairs. The calving season occurs
during Period II and the roundup and selling activities are carried out
in Period III.
Labor requirements by production periods are presented in Table
7 for the livestock and forage-producing activities. The ranch operator
provides 900 hours of labor each period to meet these labor requirements.
Hired labor could be obtained during each period at a wage rate of $1.85
per hour. This wage rate included the base rate ($1.75 per hour) plus
$.10 (5.2 percent) for the employer's contribution to Social Security
taxes. No restrictions were placed on the amount of hired labor that
could be purchased in any period.
Table 7. Annual labor requirements by production periods for all alternative livestock and
available to be included in optimal ranch organizations
Labor requirements (hours)
Item Unit Period I Period II Period III
(Nov.-Feb.) (Mar.-June) (July-Oct.)
Cow with calfa
Heifer, coming I
Heifer, coming 2
Stocker steers (April-Oct.)
Unimproved native range
Cleared land grazed
No maintenance (idle)
Grass topseeded with ryegrass
Grazing and haymaking
No maintenance (idle)
Irrigated perennial grass:
No maintenance (idle)
aLabor requirements for bulls were averaged in the total required
for a brood cow.
Capital.--The annual capital requirement consists of operating
capital (cash expenses), capital improvements (establishing improved pas-
ture), land investment, principal repayment on borrowed capital, payment
of income taxes, and family consumption at a level of $5,000 per year.
Total capital generated within the ranch firm consisted of cash receipts
from sale of weaned calves, culled cows, feeders, and stocker steers.
Additionally, nonranch income added to the total available capital. Bor-
rowed capital could be used to meet any capital requirements that exceeded
total available capital. Unused capital in any given year could be
transferred to the next production year. Accumulated capital was the
progressive total of the yearly transfers of unused capital.
Three methods of borrowing were available. As previously dis-
cussed, land could be bought with a one-third down payment and the
balance paid off over 10 years at an annual interest rate of 7 percent.
Annual operating capital could be borrowed for one year or on a three-
year loan basis. Money borrowed and paid back the beginning of the next
year with interest charges constituted the one-year loan. Under a three-
year loan only interest charges were paid on the principal during the
first and second years, then the total amount borrowed plus annual in-
terest charges for the third year were paid at the end of the third year.
The three-year loan extended the capital requirements to later years in
the program analysis. The annual interest rate on operating loans was
8 percent and was included as a cash expense for the ranch firm.
Security provided the only restriction on the amount of capital
that could be borrowed. Security, or net worth, was the sum of the
values of land, livestock and equipment. The amount of capital that
could be borrowed was $1 for each $2 of security.
Management.--The tenure situations considered in this study were
full-equity owner-operator, complete renter, and 50-50 cost-revenue
sharing between tenant and landlord. The management level for each sit-
uation reflected in the production coefficients for livestock and forage
enterprises was assumed to be above the state average.
All resources were controlled and managed by the owner-operator
in the full-equity owner-operator situation. Enterprise returns were
based entirely on the owner-operator's objectives. The renter controlled
all resources except land in the complete renter situation. He paid an
annual charge for use of land for a specified number of years through a
lease and then made organizational decisions according to his objectives.
With the 50-50 cost-revenue sharing tenant-landlord situation, the net
returns were equally divided between the tenant and landlord. The land-
lord (landowner) paid real estate taxes and incurred the depreciation on
buildings and fencing. The tenant furnished his labor (2,700 hours per
year) for operation of the ranch. Consumption capital and the extra
landowner's expense were not included in the firm's annual capital re-
quirement for the tenant-landlord cost-revenue share arrangement.
Percentage shares of costs, returns, and resources for each
tenure situation are shown in Table 8. A complete renter contributed 100
percent and a tenant 50 percent of the cost of capital improvements to
land, but the landowner reaped the full increase in net worth.
The duration of time to be included within a firm's planning hor-
izon is one of the major problems pertaining to multiperiod programming
models . A planning horizon is defined as the time span for a plan
that is necessary to make a decision for the first period. Uncertainty
Table 8. Percentage share of costs, returns, and available resources
for various tenure situations
Full- Complete Cost-revenue
Item equity renter sha
owner- situation situation
_operator Renter Landowner Tenant Landlord
Real estate taxes 100 0 100 0 100
ments to land 100 100 0 50 50
Land purchased 100 0 100 0 100
Other firm operating
expenses 100 100 0 50 50
Bull 100 100 0 50 50
equipment 100 100 0 50 50
Buildings and fences 100 0 100 0 100
Net ranch returns 100 100 0 50 50
Livestock 100 100 0 50 50
equipment 100 100 0 50 50
Land 100 0 100 0 100
Buildings and fences 100 0 100 0 100
available for ranch
use 100 100 0 100 0
Management decisions 100 100 0 50 50
Capital improvements included land clearing and establishment of
nonirrigated or irrigated pasture.
Included purchase of land plus capital required for buildings
complicates decision-making at a specific point in time because as more
information becomes available through time, confidence increases.
Ideally, short time periods are preferable for the planning hor-
izon because more detailed information can be used in optimizing the
specific objective function. The multiperiod model developed for this
study has a planning horizon composed of 15 one-year time periods. Most
previous multiperiod studies dealt with more than one year for each
planning period primarily because of the limited computer capabilities
for solving a large matrix. The size problem comes from the necessity
of setting up a submodel for each time period of the planning horizon.
If each submatrix was m x n (number of rows and columns) and the number
of time periods within the planning horizon equaled T, then the number of
rows and columns for the total matrix would be T x m and T x n,
respectively. The computation requirement grows at the rate of T
The shortest time period considered reasonable for this study
was one year. This time period is based on the requirement of paying in-
come taxes on an annual basis. Thus, the ranch operated on a January
through December basis with yearly transfers of cattle, land, and
A planning horizon of 15 years was chosen for three reasons.
First, improved pastureland would have to be reestablished after 15 years
in a maintenance program. This would require additional activities for
the model which substantially increase the matrix size. Second, ac-
cording to the 1969 U. S. Census of Agriculture [2, p. 3], the average
age of farmers in Florida was approximately 53 years. Assuming that the
average age of ranchers in the study area was the same, the additional
15 years in the planning horizon would put the ranch operator at
retirement age. The cost of computer services for solving a larger prob-
lem was also prohibitive. Approximately one hour of computer time was
required for the initial solution of an optimum ranch organization.
This section discusses federal income tax laws that were incor-
porated into the analysis. All possible alternative tax regulations
could not be included in the analysis,but the major tax laws that affect
the ranch organization (individual and firm) were included. The tax
rules applicable to the 1971 tax year were assumed effective for this
The sole proprietorship form of tax regulations was applied as
the tax structure for the ranch operator. The rancher (owner-operator,
renter, tenant, or landlord) f-iled a joint return with a wife and two
children included as dependents. Each individual taxpayer was allowed a
personal exemption deduction from his adjusted gross income of $650. In
addition, another $650 per dependent was allowed resulting in personal
exemptions of $2,600 per year. The individual is allowed either a stand-
ard deduction or an itemized total deduction to be subtracted from his
adjusted gross income. This analysis assumed $1,400 for itemized de-
ductions. Thus, annual total personal exemptions and deductions were
Gross income.--Gross income is defined as all income from what-
ever source derived such as  gross income derived from business;
interest, dividends, and royalties; compensation for services (wages);
pensions; capital gains; and rents. Two sources of gross income were
included for some aspects of the analysis. First, the ranch firm was a
source of income for every optimal organization. This ranch income was
derived from two income categories (ordinary income and capital gains in-
come). The ordinary income includes receipts from the sale of weaned
calves, feeders, and stockers. Sales of culled brood cows contributed
to the capital gains income. A second source of income for an owner-
operator or landlord situation was from nonranch activities.
Nonranch income levels for the owner-operator were $5,000,
$15,000, $25,000, and $50,000 per year. The landlord in the tenant-
landlord situation was assumed to have two levels of nonranch income
($5,000 and $25,000). The renter and tenant received income only from
the ranch organization.
Adjusted gross income.--The adjusted gross income for the indi-
vidual is generally gross income minus business deductions. The
allowable deductions as specified by the Revenue Code  that were
used in the beef analysis were
1. deductions encountered by the business carried on
by the taxpayer, if such business does not consist
of the performance of services by the taxpayer as
2. fifty percent of the excess of net long-term capital
gain over net short-term capital loss;
3. losses from the sale of property;
4. deductions attributable to rental property; and
5. depreciation allowed on property.
Taxable income.--Taxable income is defined as adjusted gross in-
come minus itemized family deductions and personal exemptions. The
taxable income is the amount for which the federal income tax is deter-
mined by using the income tax rates. The taxable income levels and tax
rates used in the tax paying activities of the model are shown in
A total of 24 marginal tax rates (14 percent to 70 percent) are
included in the IRS tax table for a married taxpayer filing a joint re-
turn. Only nine tax-paying activities are represented in the program-
ming model because the additional 15 marginal tax rates would have
expanded the matrix size by 225 column activities. The procedures used
in the programming routine to select the correct income level for tax
paying activities are discussed later.
Tax Management Strategies
The terms before-tax incomes and after-tax incomes are used
throughout the presentation. Before-tax income is defined as net income
(total receipts minus total cash expenses). The objective function used
in the analysis was to maximize after-tax income (before-tax income
minus tax obligation for the taxable income level). Minimizing taxes
does not necessarily give the same result as maximizing after-tax in-
come. If a decision was made strictly to reduce the tax burden, but a
larger amount of money is lost by selling at a lower product price, the
net after-tax income would be less.
Ranch organization.--Tax management strategies available to a
rancher were developed according to regulations specified in the Farmer's
Tax Guide . Farmers may file their tax returns using either the cash
basis or the accrual basis for accounting. The cash method of accounting
was used for this analysis because taxes can be postponed for the farmer
who is in a period of year-to-year increases in inventory. The accrual
method would have increased the matrix size because of yearly inventory
Table 9. Taxable income, tax payments, and marginal tax rates
Taxable Tax Marginal
income levels obligation tax obligation
4,000 620 19
12,000 2,260 25
20,000 4,380 32
28,000 7,100 39
36,000 10,340 45
52,000 18,060 53
76,000 31,020 58
100,000 45,180 62
200,000 110,980 70
Adjusted gross income minus exemptions and deductions.
Increment of added tax at the specified taxable income levels.
Source: 1971 Instructions from Internal Revenue Service.
accounts. A farmer makes his choice of filing his return on the cash or
accrual basis when he files his first return.
Under the cash method of accounting all taxable income, whether
received as cash or property, is included as income for the year it is
actually received. Income for the beef firm was derived from the sale
of culled cows, weaned calves, feeders, and stocker steers. Ranch busi-
ness expenses were deductible only in the tax year in which they were
paid. Allowable expenses included ranch operating expenses paid during
the year and depreciation allowances on ranch improvements, machinery,
equipment, and bulls.
For income tax purposes, everything the individual owns is
either a capital asset or a noncapital (ordinary) asset. Noncapital or
ordinary assets included items held for sale in the normal operation of
the farm business, such as livestock, livestock products, and crops.
Under certain provisions, gains and losses from sales or other disposi-
tions of ordinary assets used in the farming business and held more than
six months (two years for breeding livestock) are often treated as gains
and losses from sales of capital assets.
Capital assets for income tax purposes are all the property an
individual owns for personal purposes or investment. Capital assets are
treated differently from ordinary assets when computing income taxes on
the income derived from such assets. Capital assets held for six months
or more are classified as long-term assets. Income from short-term as-
sets are taxed at the same rate as noncapital assets. When the net
long-term capital gains exceeds the short-term capital loss, an income
tax deduction equal to 50 percent of the excess can be subtracted from
the gross income.
Income from the sale of weaned calves, feeders, and stocker
steers was taxed as ordinary assets (held less than two years). Since
gains and losses were computed by the cash accounting method, brood cows
raised on the ranch and kept in the herd for two years or more were
taxed as capital gains during the year they were sold. For tax purposes
the selling price was reduced by any sale costs. Cost of sale included
hauling costs, commission charges, and other similar expenses. The costs
of raising an animal were deducted as ordinary expenses during the years
the animal was being raised.
Farm producers are allowed current deductions (ordinary expenses)
of land-clearing expenditures and certain soil and water conservation ex-
penses. Previous tax laws allowed ordinary assets to be converted into
capital assets at the time of land sale. The Tax Reform Act of 1969
reduced the advantages of claiming these expenses as current deductions,
if the land is sold in less than ten years. If land is sold within any
of the nine years after these costs are claimed as ordinary expenses, a
specified percentage of the claimed expense must be reported as ordinary
income. The allowable percentage reclaimed depends on the year the land
Land-clearing costs are expenditures for clearing land to make it
suitable for farming. These expenditures are for such operations as
eradication of trees, stumps and bushes, and the moving of earth. The
annual deduction of land-clearing expenses for tax purposes cannot ex-
ceed 25 percent of the taxable income from farming up to a maximum of
$5,000. If clearing expenses exceed either of these limitations, the
balance must be capitalized, and taxable income would not include the
expenditures for clearing land. Both methods of handling land-clearing
expenses were included in the programming analysis by imposing the spec-
ific limitations of the Internal Revenue Code.
Ranchers were allowed annual deductions for certain soil and
water conservation expenses as specified by law. The ranch operator
could deduct expenditures up to 25 percent of the gross income from
ranching in any one year. Conservation expenses in excess of 25 percent
of gross income could be deducted in later years within the general
limitation that no deductions in excess of 25 percent of the gross in-
come from ranching in each of these years could be taken. Soil and water
conservation activities included leveling, grading, ditching, and resto-
ration of fertility for establishment of nonirrigated and irrigated
The analysis did not have a land-selling activity. Thus, the
capital gains section of the tax regulations on land sales was not
applicable. Capital gains from land appreciation were reflected in the
net worth of the landowner.
The straight line method of figuring depreciation was used in the
analysis. Depreciation for each year was estimated by dividing the
value of the property less salvage value by years of useful life. De-
preciation was deducted as an annual expense for purposes of computing
taxes and maximizing after-tax income. Sources of annual depreciation
in the study were bulls ($1.96 per mature cow); machinery and equipment
($.93 per acre operated); buildings, fences, and other capital improve-
ments ($.83 per acre operated); and seepage irrigation system ($3.48 per
Other expenses associated with the operation of the beef herd
were deducted for income tax purposes during the year the expense was in-
curred. An example is expenses associated with feeders bought in
October of one year and sold in April of the following year. Expenses
from October through December were deducted the first year and expenses
for January through March were deducted the second year, even though all
income from sales of the Feeder animals was reported the second year.
Nonranch income levels.--Nonranch incomes were introduced into
the analysis to determine the effects on the optimal ranch organization
and tax management strategies. The tax consequences of farm decisions
have a greater impact on cash flows and the net income when nonranch in-
come is available. The optimum tax management strategies for the ranch
firm with nonranch income were developed for the farm tax regulations
discussed in the previous section. Thus, the ranching operation was as-
sumed to be the only tax-sheltered investment available for maximizing
A maximum nonranch income of $50,000 per year was included in the
analysis. The Internal Revenue Code adds restrictions or provisions for
offsetting individual income with farm losses when nonfarm adjusted
gross income is greater than $50,000 per year.
A prototype of the multiperiod programming matrix used in the
analysis is shown in Figure 2. The matrix consisted of column activities,
row elements, right-hand-side constraints, restrictive bounds, and ob-
jective functions. One submatrix, as represented by either C, E, G, or
I in Figure 2, was composed of 40 rows and 62 columns. Therefore, the
total matrix (15 submatrices) consisted of 600 rows and 930 columns. The
programming model is a composite of submodels. The year t represents any
submodel year which is linked to other years by resource transfers for
t + 1, t + 2, t + n years.
The size and complexity of the multiperiod linear programming
tableau required a very carefully planned coding system to identify con-
straints and column activities. An eight-digit code was used to specify
both rows and columns. The time period (year) occupied two digits and
the title (identification) filled the other six spaces.
Table 10 provides a list of all row codes (constraints). The
period (year) was coded as the last two digits of the eight digits in
the code. For example, INCOWSOI specified the first year and INCOWS15
specified the fifteenth year of the analysis. Column activities were
coded with the first two digits of the code as the year designation. The
cow-calf activity was coded as OICOWCAL and 15COWCAL for the first and
Figure 2. Multiperiod programming matrix configuration.
A. Column identification
B. Row identification
C. Input-output submatrix for year I
D. Year I resource transfer
E. Input-output submatrix for year 2
F. Year 2 resource transfer
G. Input-output submatrix for year t
H. Year t resource transfer
I. Input-output submatrix for year 15
J. All matrix elements right of main diagonal are zero
K. Type of constraint (equality; less than or equal,
greater than or equal, or no constraint)
L. Right-hand-side restrictive vector
M. Restrictive bounds
N. Objective function I, maximize before-tax income
0. Objective function 2, maximize after-tax income for
full-equity owner-operator situation
P. Objective function 3, maximize after-tax income for
complete renter situation
Q. Objective function 4, maximize after-tax income for tenant
in 50-50 cost-revenue tenant-landlord share arrangement
R. Objective function 5, maximize after-tax income for land-
lord in 50-50 cost-revenue tenant-landlord share arrangement
Code key, row types, and right-hand-sides of row elements for
one submatrix (one year) of the multiperiod linear programming
Explanation Rowb RHS Unit
Receives transferred cows from the
Cows in herd available to calve
Cows that are required to be culled
Cows that are culled in excess of
Heifer calves kept for breeding
Transfer weaned calf to either
breeding herd, sell weaned calf,
or raised feeder calf
Transfer feeders from raising ac-
tivity to selling activity
Transfer stocker steers from
raising activity to selling
Total land operated
Transfer cleared land to improved
pasture establishment activity
Land available for establishment
of irrigated pasture
Improved nonirrigated land
Improved irrigated land
Transfer bahiagrass pasture
Transfer Pangola digitgrass
Transfer grass-clover irrigated
Grazing available Period I
codesa Explanation Rw b RHS Unit
GZP2MJ Grazing available Period II
(Mar.-June) L Oe AUM
GZP3JO Grazing available Period III
(July-Oct.) L Oe AUM
LBP1NF Available labor Period I
(Nov.-Feb.) L 900 hour
LBP2MJ Available labor Period II
(Mar.-June) L 900 hour
LBP3JO Available labor Period III
(July-Oct.) L 900 hour
CONSER Transfer all conservation expenses
to one column activity E 0 dollar
RSCSEX Restrict soil and water conserva-
tion expenses L 0 dollar
RSLACL Restrict land clearing as direct
expense L 0 dollar
OVERHD Transfer all overhead expenses to
one column activity E 0 dollar
CAPITA Available capital for owner-operator
and renter situations L 0 dollar
CAP5OL Available capital for landlord in
50-50 tenant-landlord situation L 0 dollar
CAP50T Available capital for tenant in
50-50 tenant-landlord situation L 0 dollar
SECURI Security restriction for borrowing
capital L 0 dollar
NETWOR Net worth accounting row L 0 dollar
PEPREV Transfer personal property evalua-
tion to column paying activity E 0 dollar
REESEV Transfer real estate evaluation to
column paying activity E 0 dollar
ORDINC Ordinary income accounting row N dollar
Row Row .
R a Explanation b RHS Unit
CAPGAN Capital gains income accounting row
RANINC Ranch profit transfer row
RANLOS Ranch loss transfer row
TAXINC Owner-operator or renter's income
tax paying row
TXI50L Landlord's tax paying row
TX15OT Tenant's tax paying row
ACCEQU Accounting equality for tax paying
PRETXINC Objective function 1 (before-tax)
POSTXINC Objective function 2 (after-tax) for
owner-operator or renter
50LANLOR Objective function 3 (after-tax) for
landlord in 50-50 tenant-landlord
50TENANT Objective function 4 (after-tax) for
tenant in 50-50 tenant-landlord
N max. dollar
N max. dollar
N max. dollar
aThe period (year) was coded as the last two digits of the eight
digits in the code. For example, INCOWSOI signified the first year and
INCOWS5I signified the fifteenth year. The objective functions were not
coded by years.
E, equality; L, less than or equal; G, greater than or equal;
and N, no constraint.
cFirst year RHS equaled 500 because program was assumed to start
with 500 brood cows.
dEqualed 600 first year and 300 second year.
equaled 1,000 first year and 500 second year.
fRow type was "N" when specified tenure situation was not the
gAllowed for personal tax exemptions and deductions of $4,000
fifteenth years, respectively. Title codes and explanations for the
columns of a submatrix are presented in Table 11. Identification of rows
and columns was simplified with the system of placing the year code on
opposite ends of the title code.
Restrictive Constraints of the Model
Restrictions were placed on the model with constrained right-
hand-sides (rows) and restrictive bounds on column activities. These
constraints helped make the model more realistic in terms of a typical
beef cattle firm. The type of row constraints and right-hand-side
levels are presented in Table 10. Row constraints restrict the factors
of production (land, labor, and capital). Bounds were placed on some of
the column activities (Table 12) to restrict these activities at equality,
upper, or lower levels. Reasons for planning restrictions on certain ac-
tivities of the model are discussed in following sections of this chapter.
The objective function was to maximize after-tax income for the
ranch operator during the planning horizon (15 years). Several other
objective functions could have been used. They include maximum net
worth, maximum herd size, maximum acreage, maximum before-tax income,
and maximum sales. Maximization of after-tax income was chosen for this
study because it was considered to be more closely related to the goals
of the ranch firm. Ranch operator decisions are usually compatible with
the assumption of profit maximization made in studies using static
models. But profit maximization in this study includes payment of the
individual's income taxes.
The eight-digit code POSTXINC was used in the matrix to identify
the objective function row (maximizing after-tax income). When the
Table 11. Code key for column activities for one submatrix (one year) of
the multiperiod linear programming model
Codea Explanation Unit
COWCAL Cow-calf activity head
COWCUL Cull cow activity head
COWLIQ Liquidating cow activity in excess of cows culled head
COWSTR Transfer remaining cows to next time period head
HERDEX Heifer calf activity, kept for breeding herd head
SWCALF Sell weaned calf head
FCALFR Feeder calf raised head
FCALFP Feeder calf purchased in October head
SFCALF Sell feeder calf in April head
BUYSTC Buy stocker steers in April head
SELSTC Sell stocker steers in October head
PURLAC Purchase land on cash basis acre
PURLAL Purchase land on long-term loan acre
INITLAb Initial land for owner-operator situation acre
USOWLAb Total land (initial land plus purchased land) for
owner-operator, method of paying ownership land
UNIMLR Land rented for complete renter situation acre
LEASLAc Total acres leased, used to pay leasing cost
(rent), overhead, depreciation, and personal
property evaluation acre
LALOLAd Initial land owned (3,500) by landlord for
tenant-landlord situation acre
SHARLAd Total land in operation (initial land owned plus
land purchased by landlord) for tenant-landlord
situation used to pay overhead, depreciation, and
personal property and real estate evaluation acre
GZNALA Grazing native unimproved land acre
LACLEX Land-clearing expenses that can be charged in
year performed acre
Table 11 (Continued)
Codea Explanation Unit
LACLCA Land-clearing expenses that must be capitalized acre
BUYFOR Hay-buying activity tons
GZCLLA Graze cleared land acre
CLLATR Cleared land transfer for establishment of
permanent pasture acre
IRLATR Transfer of land suitable for seepage irrigation
SEEPIR Investment in seepage irrigation system acre
RYEGTM Temporary grazing (ryegrass) acre
ESTBAH Establish bahiagrass pasture acre
MTBAMF Maintain bahiagrass pasture at medium fertiliza-
tion level acre
MTBAHF Bahiagrass, high fertilization acre
IDLEBA Idle bahiagrass pasture, no maintenance acre
ESTPAN Establish Pangola digitgrass pasture acre
MTPAMF Maintain Pangola digitgrass, medium fertilization acre
MTPAHF Pangola digitgrass, high fertilization acre
PARYEG Pangola digitgrass topseeded with ryegrass during
PANHAY Pangola digitgrass pasture grazed and cut for hay acre
IDLEPA Idle Pangola digitgrass acre
ESTPCI Establish perennial grass-clover irrigated pasture acre
MPCIHF Maintain perennial grass-clover, high fertilization acre
IDLPCI Idle perennial grass-clover irrigated (no
CONSEX Pay soil and water conservation expenses dollar
LABEPI Buy labor, Period I hour
LABEP2 Buy labor, Period II hour
Table 11 (Continued)
LABEP3 Buy labor, Period III hour
BORCAP Borrow capital for one year dollar
BORCA3 Borrow capital for three years dollar
CAPTRA Capital transfer dollar
PEPRTX Pay personal property taxes dollar
REESTXe Pay real estate taxes (owner-operator and landlord) dollar
PYLEAS Pay lease (renter) dollar
FIXCOS Pay fixed costs dollar
FAMCON Family consumption dollar
OTHINC Income other than ranch (nonranch income) dollar
TXRINC Taxable ranch income dollar
LOSITI Ranch loss dollar
PYTXOO Pay income tax at zero level (no taxable income) dollar
PYTX04 Pay income tax at 4,000 level dollar
PYTX12 Pay income tax at 12,000 level dollar
PYTX20 Pay income tax at 20,000 level dollar
PYTX28 Pay income tax at 28,000 level dollar
PYTX36 Pay income tax at 36,000 level dollar
PYTX52 Pay income tax at 52,000 level dollar
PYTX76 Pay income tax at 76,000 level dollar
PTXO00 Pay income tax at 100,000 level dollar
PTX200 Pay income tax at 200,000 level dollar
aThe period (year) was coded as the first two digits of the eight
digits in the code. bIncluded only for full-equity owner-operator situa-
tions. Concluded only for complete renter situations. dlncluded only
for 50-50 tenant-landlord share situations. elncluded only during owner-
operator and tenant-landlord situations. included only during renter
Table 12. Restrictive bounds used each year for specified column
activities of the multiperiod linear programming model
ole a Explanation Unit bTys b Amount
COWCALC Cow-calf activity head LO 500
HERDEX Herd expansion head LO 60
FCALFP Feeders purchased head UP 250
BUYSTC Buy stocker steers head UP 250
BUYFOR Buy forage (hay) tons UP 500
LACLEX Land clearing as direct expense acres UP 147.25
LACLCA Land clearing with expense capitalized acres UP 500
RYEGTM Temporary grazing acres UP 500
PANHAY Pangola digitgrass pasture grazed and
cut for hay acres UP 300
FAMCON Family consumption dollar FX 5,000
OTHINC Nonranch income level dollar FX d
aAll columns not listed in this table were unconstrained by the
Type bounds were LO, lower limit; UP, upper limit; and FX,
CThis bound did not become effective until the fifth year of the
Values were fixed at zero, $5,000, $15,000, $25,000, and $50,000
depending on objective function.
objective functions for the tenant or landlord situations were imposed,
the codes 50TENANT and 50LANLOR were used. With the 50-50 cost-revenue
tenant-landlord share situation, the POSTXINC entries were divided
equally between the partners.
Activities of the Model
Activities of the multiperiod programming model are discussed by
categories: livestock enterprises, land activities, and financial com-
ponents of the model. The presentation in this section describes the
activities included for these categories for one submatrix (one-year
period). A submatrix included the input-output coefficients for a
specific year (t) with activities for resource transfers to future years.
The year t signifies any year of the planning horizon.
The programming matrix is constructed with the column activities
across the top and the constraint rows down the side of the page. Co-
efficients are placed in position (cells) according to the specified
column and row. For the row constraints a negative sign with a coeffi-
cient indicates an addition to the right-hand-side. The positive or no
sign signifies a subtraction. Expenses are indicated as negative in the
objective function row and receipts are positive. Thus, sale of a culled
cow adds to after-tax income and expenses, such as raising a heifer, sub-
tract from the objective function.
The coefficients in the matrix represent a one-unit segment. For
example, the coefficients in the COWCAL column are based on one cow unit
of the cow-calf activity. The requirements for purchasing an acre of
land with cash are depicted in the land purchase column (PURLAC). If
the optimum organization required 100 acres of purchased land, the
total requirements of a resource would be 100 times the coefficient in
the purchase land column.
The actual coefficients used in the analysis are included in the
tables. The discussion of the programming matrix primarily represents
the matrix formulation for the owner-operator situation. When the renter
and tenant-landlord situations vary from the owner-operator, these dif-
ferences will be discussed. The expense and receipt coefficients, when
maximizing for the tenant or landlord with the 50-50 cost-revenue share
arrangement, were usually 50 percent of the owner-operator coefficients.
Therefore, the rows pertaining specifically to the tenant or landlord
were excluded from the matrix presentation unless the 50-50 cost-revenue
share situation did not apply. These rows were capital (CAP50T and
CAP50L), taxable income (TXI50T and TXI5OL), and objective functions
(50TENANT and 50LANLOR).
Livestock enterprises.--The livestock production activities con-
sidered in the analysis are presented in Tables 13 and 14. The activities
related to the brood cow production system and transfers depict a typical
cow-calf system. All mature brood cows are entered in the cow-calf ac-
tivity (COWCAL) at the beginning of the year. Total annual requirements
for a mature cow with a calf and a twenty-fifth of a bull are re-
flected in the COWCAL coefficients. Cows could either be culled (COWCUL),
liquidated (COWLIQ), or transferred (COWSTR) to the cow-calf activity for
next year (t+l). The COWCUL activity is constrained by an equality row
(CULCOW) at the specified culling rate. Additional cows can be culled
(COWLIQ) to a rate specified by the less-than row (LIQCOW). Resources
are added to the constraint levels by the COWCUL and COWLIQ activities
because these cows would not remain in the herd (COWCAL) a full year.
Receipts from the culling activities are included in the taxing row
(TAXINC) at the capital gains income level (one-half of sales value).
Table 13. Linear programming tableau specifying the brood cow activities
of the multiperiod model for year t
Row Coded activities related to breeding herd
codes COWCAL tCOWCUL tCOWLIQ tCOWSTR HERDEX SWCALF
Table 13 (Continued)
Row Coded activities related to breeding herd
codes COWCAL tCOWCUL COWLIQ tCOWSTR HERDEX SWCALF
SECURI t+ -120.00
PRETXINC -20.14 184.53 184.53 -12.80 106.84
POSTXINC -20.14 184.53 184.53 -12.80 106.84
Table 14. Linear programming tableau specifying the feeder and stocker
activities of the multiperiod model for year t
Row Coded activities related to feeders and stockers
codes FCALFR tFCALFP SFCALF tBUYSTC tSELSTC
STOCKSt -1.0 1.0
GZPINFt 1.40 1.40
GZP3JOt .65 .65 2.30
LBPINFt .48 .48
LBP3JOt .36 .36 .70
RSCSEXt -42.32 -40.65
CAPITAt 11.93 122.65 -163.36 143.57 -156.91
ORDINCt -163.36 143.57 -156.91
TAXINCt -163.36 143.57 -156.91
TRFEEDt -1.0 -1.0
GZPINFt+1 1.5 1.5
GZP2MJt+ .8 .8
LBPINFt+ .48 .48
LBP2MJt+ .34 .34
CAPITAt+1 11.93 11.93
ORDINCt+ 23.86 134.58
TAXINCt+ 23.86 134.58
PRETXINC -23.86 -134.58 163.36 -143.57 156.91
POSTXINC -23.86 -134.58 163.36 -143.57 156.91
The COWSTR column transfers cows to the next year (INCOWSt+l) and allows
for 2 percent death loss.
A lower bound of 500 brood cows was set on the COWCAL activity
for the fifth year through the fifteenth year of the planning horizon.
Since each tenure situation started with 500 cows, the possibility of
increasing income by selling cows below this level was eliminated with
the bound restriction. The bound did not become effective until the
fifth year to allow for adjustments in the cow-calf activity. These ad-
justments were needed because of the two years required for raising a
brood cow from a heifer calf.
Calves weaned from the COWCAL activity are made available through
the equality row (TRCALF) for herd expansion (HERDEX), selling (SWCALF),
or the feeder operation (FCALFR). Heifers kept for the breeding herd
are constrained with the HEIFER row to a maximum of 50 percent of weaned
calf crop. Requirements for raising a heifer are presented for years t
and t+l, then the heifer is included in the brood cow herd (INCOWSt+2
in the third year with an adjustment for death loss. Weaned calves sold
(SWCALF) add to gross receipts as ordinary income.
Table 14 illustrates the feeder and stocker activities of the
matrix. Two sources of feeders were available for the organization:
transfer of weaned calves from cow-calf herd (FCALFR) and calves pur-
chased for feeders (FCALFP). Both of these systems had the same grazing
and labor requirement for the period October through March. Thus, re-
source requirements, costs, and returns were included for both year t
and year t+l depending on the year involved. The selling activity
(SFCALF) occurred in year t+l and was accomplished through the transfer
with the equality row (TRFEED). All the gross sales from feeders were
taxed as ordinary income in year t+l. The other livestock alternative
was grazing of purchased stocker steers (375 pounds) from April to
October. Resource levels and costs are shown in the purchase stocker
activity (BUYSTC) and the sale activity(SELSTC) reflects the gross sales
from a stocker steer.
There were several reasons for separating the livestock selling
activities (COWCUL, COWLIQ, SWCALF, SFCALF, and SELSTC). One important
reason was the tax regulations pertaining to allowable conservation ex-
penses and capital gains income. Allowable conservation expenses are
restricted by total gross sales and capital gains income is taxed at a
lower rate than ordinary income. The two alternatives for acquiring
feeders were raising them and a cash purchase. Each alternative was con-
sidered separately because of different capital requirements.
Land activities.--Fixed charges such as real estate taxes, de-
preciation, and miscellaneous overhead expenses were based on an acre of
land. The proportion of an item charged depended on the type of tenure
situation being considered. This required that each tenure arrangement
have different land activities (Table 15). Land activities (columns) for
a tenure group were deleted from the matrix when the specific tenure ar-
rangement was not being considered.
The activities that specified alternatives for land use were
INITLA (for the owner-operator), UNIMLR (for the renter) and LALOLA
(for the tenant-landlord). For the owner-operator and tenant-landlord
arrangements the initial land owned (INITLA and LALOLA) was fixed at
3,500 acres. The renter's land activity was unrestricted. Any amount
of land could be rented during a year but once the land was leased
(UNIMLR) it had to remain in the firm for the remaining years in the
planning horizon. The equality row (TOLAOW) transferred the total
Table 15. Linear programming tableau specifying the land activities of
the multiperiod model for year t and each tenure situation
Coded activities related to total land operated
Row Owner-operatora Renterb Tenant-landlordc
codes INITLA USOWLA UNIMLR LEASLA LALOLA SHARLA
TOLAOWt -1.0 1.0 -1.0 1.0 -1.0 1.0
RALAOWt -1.0 -1.0 -1.0
IRRLANt -.25 -.25 -.25
OVERHDt -.73 -.60 -.73
SECURI -x -6.53 -6.53
NETWOR -xd -6.53 -6.53
PEPREVt -6.53 -6.53 -6.53
REESEVt -157.21 -157.21 -157.21
ORDINCt 1.76 .93 1.76
TAXINCt 1.76 .93
TOLAOWt+1 -1.0 -1.0 -1.0
PRETXINC -1.76 -.93
POSTXINC -1.76 -.93
These columns were deleted from the matrix except when the full-
equity owner-operator situation was considered.
bThese columns were deleted from the matrix except when the
complete renter situation was considered.
These columns were deleted from the matrix except when tenant
or landlord (50-50 tenant-landlord share) situation was considered.
Coefficient equals the appreciated value of land based on the
formula V = $150 (l+.06)t plus $6.53; V (appreciated value), $150
(initial value of land), .06 (appreciation rate), and t (year in the
acreage to an annual expense activity for each tenure group: USOWLA
(owner-operator), LEASLA (land leased by renter), and SHARLA (land in
tenant-landlord share arrangement). Land available for seepage irriga-
tion was restricted to a maximum of 25 percent of total land (IRRLAN).
Annual land expense activities varied among tenure groups. For
the full-equity owner-operator, all fixed costs were charged as a firm
expense. The renter firm only paid S.60 of the per acre overhead charges
and $.93 for depreciation of machinery and equipment. But the renter
did pay a rental rate to the landowner based on real estate evaluation
(REESEV). Under the tenant-landlord arrangement the firm paid all over-
head and depreciation costs per acre except for real estate taxes and
buildings and fencing depreciation which were incurred by the landlord.
These land activities added to security (SECURI), net worth (NETWOR),
personal property tax evaluation (PEPREV), and real estate tax evaluation
(REESEV) rows for the firm. With the renter and tenant-landlord situa-
tions, land value was not counted in the firm's security or net worth.
Increases in land value were fully attributed to the landowner's
(owner-operator or landlord) net worth.
The size of the basic ranch acreage could be increased by pur-
chasing land (Table 16). The two methods of purchasing land were
PURLAC (cash buy) and PURLAL (loan basis). When land was purchased, it
entered the total land activity (TOLAOW) and increased the land available
for irrigation. Land purchasing activities were only relevant for the
full-equity owner-operator and the landlord in the tenant-landlord
The capital requirement for purchasing land with cash depended
on the year bought since land increased in value at a rate of 6 percent
per year. For tax purposes the only cost that could be charged against
Table 16. Linear programming tableau specifying the land purchasing and
clearing activities of the multiperiod model for year t
Row Coded activities related to adding grazing
codes PURLAC PURLAL LACLEX LACLCA CLLATR IRLATR
t t t t t t
TOLAOWt -1.0 -1.0
RALAOWt -1.0 -1.0 1.0 1.0
TRCLLAt -1.0 -1.0 1.0
IRRLANt -.25 -.25 1.0
LBPINFt 2.1 2.1
CAPITAt xa x3.93 33.93
ORDINCt+, .30 x 3.39
TAXINCt+I .30 x 3.39
NETWORK t+n xc
ORDINCt+n .30 xe 3.39
Table 16 (Continued)
Row Coded activities related to adding grazin
codes PRLAC PURLAL LACLEX LACLCA CLLATR IRLATR
TAXINC .30 xe 3.39
ORDINCt+O .30 x 3.39
TAXINCt+O .30 x 3.39
PRETXINC -3.00 x -33.93 -33.93
POSTXINC -3.00 x -33.93 -33.93
aTotal cost of purchasing land for year t (Table 4).
One-third of total cost of purchasing land.
CTotal of unpaid loan.
Payment of principal plus interest on loan.
eAnnual interest expense plus $.30 for prorated closing cost for
Total interest charge over life of loan plus $3.00 for closing
the beef firm was a $3 per acre closing cost (legal fees). This cost
was capitalized over 10 tax years. For land purchased under a 10-year
loan, both the closing cost and the yearly interest charge were counted
as a tax deductible expense. Thus, the total expense included in the
objective function was closing cost plus total interest on the loan.
Total net worth and available security were reduced each year by the
total amount due on the loan. Once land entered the program it was
counted in the USOWLA column (Table 15) as being fully owned.
Land was classed either as unimproved native range or improved
pasture. Since all land in the initial resource situation was assumed
to be unimproved native range, several alternatives were available for
improving land. The first alternatives were basic land clearing require-
ments (Table 16). Two column activities were available for land clearing
(LACLEX and LACLCA). Land-clearing costs were charged as a tax deduction
on ordinary income (LACLEX) in amounts up to 25 percent of taxable in-
come in a specific year, or a maximum of $5,000. The row RSLACL
constrained the activity to 25 percent of taxable income and the $5,000
limit was imposed on the column by an upper bound of 147.25 acres
(147.25 x $33.39 = $5,000). Any land-clearing costs that exceeded the
direct expense deduction allowance were handled as capital assets in the
LACLCA activity (expense capitalized over 10 tax years).
Cleared land could either be grazed, planted in temporary
grazing, or established as improved nonirrigated or irrigated permanent
pasture. The CLLATR column and TRCLLA row allowed for transfers of
cleared land. The IRLATR column transferred land available for irriga-
tion through time (year t to year t+l).
Nonirrigated permanent pasture could be established on cleared
land (Table 17). Acreages of irrigated pasture had to be transferred
Linear programming tableau specifying improved pasture estab-
lishment activities of the multiperiod model for year t
Row Coded activities related to establishing permanent pasture
codes SEEPIR ESTBAH ESTPAN ESTPCI CONSEX
through the seepage irrigation activity (SEEPIR) before it could be
established as permanent pasture (ESTPCI). The seepage irrigation system
consisted of capital improvements such as ditching, wells, pumps, etc. A
$20 per acre cost of leveling and ditching was included as conservation
expenses. Part of the expenses for establishing the three types of per-
manent pasture were charged as conservation expenses. The equality row
(CONSER) accumulated the conservation expenses and they were charged to
the firm by means of the conservation column (CONSEX). During the year
of establishment the improved pasture required labor and furnished some
grazing. These establishment requirements were only for one year in the
planning horizon. Pasture acreage established in year t was transferred
to an annual pasture maintenance activity for each remaining year of the
planning period (t+l, t+2, tl)
The annual maintenance activities for improved permanent pasture
are presented in Table 18. Once pasture was established, several alter-
native levels of maintenance (fertilization) were available each year.
For example, established bahiagrass pasture (ESTBAH) had maintenance al-
ternatives of medium fertilization (MTBAMF), high fertilization (MTBAHF),
or no maintenance (IDLEBA). The established acreage could be allocated
in any proportion in any year by the transfer row (TRBAHG). Each main-
tenance activity increased available grazing (e.g., row GZPINF) and
required labor according to the type of pasture and level of fertiliza-
tion. Improved pasture increased the landowner's capital asset value
(SECURI and NETWOR). All expenses related to maintenance were allowed
as taxable deductions for the beef firm. The irrigated pasture activi-
ties (MPCIHF and IDLPCI) included overhead expenses (OVERHD) for taxes,
insurance, and annual repairs on the irrigation system. Overhead was
SCO COCO CO J00----
I- -1 I I I I Ln LA (t f c c
S0 LA I I
S- 1 1
C 0 '.0 0 r- LA O 0 0 .. ." -." 4.
C L 0 4.4 0 0 0 0
Sl I I I L C0 Ca i
L i < O 1 O CO 0 0 CO J 0 0 0O ( r
" 3 0- 0 0 O 0 0 -- --
4J < 0 .
( Q I I I
C 0 0 C0 0 \D \O \ D \D \
C < C 1
0 > LL 0 0 0 00- c- '0 0 0 '.0 '. '.
cn o u I
0) a a
L- a) CC 0 0 0 00 D- ( 0 c i CJ CN CN
Ui 0U o O O o 0 r -00- -
o 1 I I I I -3 -1 -T C -: -
C 0)- 4
0 E LL. o o o M s O o o f f f
a I 2 i I i i
I- 4 L 000 0 \ 0', 0w 0 C) a m w
0)>- 0 < -
a- ) D D- m CO O 0 0 \D \CO CO CO
> L I cn ar 0 I 0 Ln L\n 00 0 co 00
'-- C- T H I I C- -3D -
OC- 0 CO C O CO \ 0a0 \D \D \D c
3C co 0 -t -. -. 00 0- -
1) I I I I
0 4-' I I ss
C0) EL 0 0 0 t l L00 A C
0- 2 0 0 0 0 .J IC 0 00 U CF
C < < | | -- -rT -
0 0 C ELL CL 0 EL 0 w CL Uu -x
-U < < ) OJ rsl c = -
(C)!: c oc rc: i r-j rj m m 'm >.j
H- H H O L L C -io a Ln Z O CL CL
less for idle irrigated pasture (IDLPCI) because no repair costs were
charged. Annual depreciation on the irrigation system ($3.48 per acre)
was included in the objective functions but not in the capital row. An
upper bound of 300 acres was set on the Pangola digitgrass pasture
grazed and cut for hay (PANHAY).
Cleared land that was not established in permanent pasture was
either grazed as cleared land (GZCLLA) or grazed as temporary pasture
(RYEGTM). Acreage not cleared remained in the graze native land activity
(GZNALA). These three activities, hay buying (BUYFOR), and fixed cost
(FIXCOS) activities are shown in Table 19.
Financial components.--The labor purchasing, capital borrowing,
and capital transfer activities are given in Table 20. Labor require-
ments were separated into three periods to correspond to the production
periods for beef herds. When labor requirements for any period exceeded
900 hours, labor could be purchased at a cost of $1.85 per hour. Capital
could be borrowed by two methods (BORCAP and BORCA3). The first method
was to borrow capital one year (t) and repay it the next year (t+l) with
the interest charged as a firm expense. The other method (BORCA3) was to
assume a three-year loan. Annual interest charges were deducted as tax-
able expenses each year of the loan and the total loan was repaid the
third year (t+3). Total capital borrowing was restricted by the security
row (SECURI)with $2 of security backing required for each dollar borrowed.
Excess capital could be transferred from year t to year t+l through the
capital transfer activity (CAPTRA).
Personal property taxes (PEPRTX) and real estate taxes (REESTX)
were considered as separate activities because they were taxed at differ-
ent rates (Table 21). Personal property taxes on livestock, machinery,
Table 19. Linear programming tableau specifying the hay purchasing,
paying overhead, temporary grazing, and unimproved grazing
activities of the multiperiod model for year t
Row Coded activities related to forage systems and overhead
codes BUYFOR GZNALA GZCLLA RYEGTM FIXCOS
GZPINFt -7.5 -.28 -.36 -4.3
GZP2MJ -.38 -.46 -3.9
GZP3JOt -.32 -.40
LBPINFt .08 .08 .14
LBP2MJt .02 .02 .07
CAPITAt 75.00 .13 .13 35.57 1.0
SECURIt -30.00 -30.00
NETWORt -30.00 -30.00
ORDINC 75.00 .13 .13 35.57 1.00
TAXINCt 75.00 .13 .13 35.57 1.00
TRCLLAt+1 -1.0 -1.0
PRETXINC -75.00 -.13 -.13 -35.57 -1.00
POSTXINC -75.00 -.13 -.13 -35.57 -1.00
Table 20. Linear programming tableau specifying labor purchasing and
capital borrowing activities of the multiperiod model for
Row Coded activities related labor and capital
codes tLABEPI tLABEP2 tLABEP3 tBORCAP tBORCA3 tCAPTRA
CAPITAt 1.85 1.85 1.85 -1.0 -1.0 1.0
SECURI 2.0 2.0
NETWORt 1.0 1.0 1.0
ORDINCt 1.85 1.85 1.85
TAXINCt 1.85 1.85 1.85
CAPITAt+1 1.08 .08 -1.0
S t+l 2.0
ORDINCt+l .08 .08
TAXINCt+I .08 .08
PRETXINC -1.85 -1.85 -1.85 -.08 -.24
POSTXINC -1.85 -1.85 -1.85 -.08 -.24
*4c' *N (
0 0 0
U-\ U-\ Lt\ 0 00 0
C0 C0 0D 0 0D 0
-J < --l )- > > O O
-u w- o o 0 0 U z z 0 z 0 0 x
<- L\ L -- L u\ 1-\
- Q. w' z z 2X w
) < < < w L oa < < X < -
la: U U ) u 0 w C l w C- h-C-
0 0 0
and equipment were considered as ordinary firm expenses. Real estate
taxes were entirely the landowner's expense. Real estate taxes were a
firm expense for the owner-operator, a landlord expense for the tenant-
landlord situation, and were not considered in the complete renter
situation except that taxes formed part of the charge for the land lease
in the objective function. The renter paid an annual lease payment
(PYLEAS) based on the landowner's real estate tax evaluation (REESEV).
The taxable ranch income activity (TXRINC) was used with the
RSLACL row to restrict the land clearing cost that could be charged as a
direct expense to a maximum of 25 percent of taxable ranch income. The
ranch loss activity (LOSITI) and the rows RANINC and RANLOS were re-
quired for the TXRINC activity to be feasible. The family consumption
(FANCON) and nonranch income (OTHINC) activities were fixed with equality
bounds at specified levels. Family consumption represents a withdrawal
from the available capital supply and nonranch income added to available
capital and taxable income.
The income tax payment row (TAXINC) and the accounting equality
row (ACCEQU) shown in Table 22 allow the model to pay income taxes. The
income tax paying activities are also shown in Table 22. In considering
the capital and tax accounting rows, the following relations are
required. Given the notation,
Y = total ordinary income from the ranch
CAGA = capital gains income from the ranch
EX ranch expenses
RY = Y + CAGA EX = net ranch income
BC = borrowed capital
TC = capital transferred from previous year
T = income taxes
(0 .0 U 0 -0 U 0 0: F-
44 44 4' 44 44 4.' 4 Z 0 2
< -J F- 0 -J i- D -J <
1- o O Z o o 0' x Z z
L- U"\ L U \ U" \,_- w <
Q- -. .- X 0 (nJ -o o-
< < < < X X ) 0 0 0 0
u 0 0 L- I- I- < a Q. il LPl
0 00 0 0 0 0 0 0
O0 00 0 0 0 -C 0
00 0 0 0 0 0 0 0
- -0 0 0 -
- (N (N ( -
00 0 00 0 0 0 0
cO OC co 0 0 0 CO aO O0
- 0 0 0 -
0o 00000 0 o
-M C 0 0 M- -
I I I
o o o 0 o0 0 )o co c
I I I
0 0 0 0 0 0 0 0 0
0 C 0 0 0 0 0 0 0
r-N O O O D r
0 0 0 00 C C0 C C
P I I I
C0 CD Co 0 0 0 C0 CD CD
0000000 o 000
0 O OOO 0 0 0
I I I
0 0 0C 00 0 0 0 0
(N (N (N 0 C0 0 ( (
-C M I I I
CM M M O C C C
o o 0
(- 0 4
4 C C
S C 4
0 0 0
0 0 a
S C C
<) N N
3 E E
-c E E
*- *- *-
S o0 0
C = family consumption capital
TY = total taxable income
TRY = taxable ranch income
A = personal tax exemptions and deductions
NRY = nonranch income
t = increment in time
f = progressive tax structure (see Table 9)
RY = Y + CAGA EX
TRY = Y + 1/2 CAGA EX
TY = TRY + NRYt A
Tt = f(TY)t
Required linear programming specifications:
(1) CAPITA = RY NRY BC TC + C + 620 + + 110,980 0
t t t t t t
(2) TAXINC = TRY NRY + PYTXOO + PYTX04 + + PYT200 > A
t t t t t t t
(3) ACCEQUt = + 1 + 1 + + =
(4) POSTXINC = RY + NRY 620 110,980 (N) Max.
Equation (1) represents the capital activity of the model. Equa-
tion (2) requires the organization to pay income taxes when taxable
income exceeds A (allowable personal exemptions and deductions). The
ACCEQU equation (3) restricts the tax paying activities to the required
amounts. After-tax income (POSTXINC) for year t is represented by
The presentation of this chapter emphasized structuring a beef
cattle firm as a workable multiperiod linear programming model.
Assumptions and activities of the model were developed to realistically
portray a typical beef cattle firm. A focal interest was to maximize
after-tax income considering specified tax regulations pertaining to a
farm business and alternative tenure arrangements.
OPTIMAL PRODUCTION ORGANIZATION FOR
ALTERNATIVE TENURE ARRANGEMENTS
This chapter presents the results from applying the decision
model with the initial ranch conditions and three tenure situations.
These basic situations assumed zero nonranch income for the owner-
operator, renter, or tenant-landlord arrangements. The objective
function was to maximize after-tax income for each individual. The as-
sumptions of the model were presented in detail in Chapter III. These
assumptions must be kept in mind when interpreting the results. De-
tailed information for each of the optimal ranch organizations is
presented in the Appendix. Optimal organizations for the three tenure
situations are compared and variations in ranch organizations due to
tenure arrangements are emphasized.
The optimal solution for the owner-operator situation is pre-
sented in Tables 23 and 46. All resources were owned by the operator
and he received all of the net ranch income. He furnished 2,700 hours
of labor annually to the ranch.
The number of brood cows in the cow-calf herd ranged from 462
head during the second year to a high of 613 head for the thirteenth
year and then decreased to 500 head the last year of the organization.
-0 1- -
0 0 C
00 "o M rM C,4U\-3--7-.-. CM m- 00
Oc '-0O rNO 0
C)O r- 00r-L r--.-.r Ir0 r c.-- rn 0-
I \N A -T -C r-
o- 0 0000000- 00o 00
S00 Mo 0 o.- "O P CO W O l
a 00 00 000000 0 0 000
. ..r .. ., . .
0a) O 0" C 0" C" C" C 0" C C" 0" 0"
m ( O'~ O .0 r ( Lm (N Q)n m" mr O O r ('-
L'"0 0'..-D--~- O0 00
0 Om~~m N. -t r-OOO CJ -TO
-mC 00oc nD.- D0O CCLAOC
C"r4 -7 0 G") 0' 0'% 0% 00 3 \", 3_3- 0 3 3'
o0-0-oo' o0 oo 00
0 \-0 m^ m^ "0 m \ 0 m 0 F C) U 0C
oo rn -T-3 'D r- 00ao 0 -\ (D m-T LAr
r~i M C ^ ^ M C C f rOC CNM CM ^
Cows were culled to the maximum allowed (18 percent of mature cows) in
most years. The number of bulls required varied from 20 to 27 depending
on the number of cows.
The only way to increase herd size or replace culled cows was
with heifer calves kept from the weaned calf crop. Thus, in some years
a substantial number of heifer calves were kept for the cow herd. This
number varied from a high of 218 calves the eleventh year to the mini-
mum of 60 head for several of the latter years. Weaned calves sold
varied from zero to a maximum of 360 head in the 13th year. In general,
more calves were kept for growth of the herd during the first half of the
15-year planning horizon.
The alternatives for steer calves,and for heifer calves that did
not go into the brood cow herd, were sell as weaned calves or sell as
feeders after an additional six months on grazing. Feeder numbers
reached a peak of 294 head during the fifth year. Feeders gained 225
pounds during the six months on grazing (October through March). Stocker
steers were purchased only during the last year of the planning period.
Seventy stocker steers were bought to utilize the excess grazing that
occurred during the months April through September from the reduction
in the brood cow herd.
Initial land owned was 3,500 acres of native range and no ad-
ditional land was purchased by the rancher during the planning period.
Of the total acres operated, 554 acres were cleared and established in
improved pasture. Five hundred acres of this land were cleared the
first year with the expense capitalized over 10 years. Three hundred
acres of improved nonirrigated pasture and 254 acres of seepage
irrigated pasturevere established by the third year of the planning
period. Thus, 2,946 acres of unimproved native range were also used for
grazing the beef herd.
Improved nonirrigated pasture was completely planted in peren-
nial grass with no temporary grazing. The perennial grass was used for
grazing,with haymaking in the fall. Some of the nonirrigated pasture
was idle during the latter part of the planning period, depending on the
grazing requirement for the year. For example, during the fourteenth
year 188 acres were maintained for grazing and haymaking and 112 acres
were not maintained (idle). The 254 acres of irrigated pasture were
maintained at a high fertilization level for the entire planning period.
One hundred and fifty tons of hay were purchased only during the first
year to meet the feed requirements of the herd. Total feed require-
ments for the remaining years were supplied by native range and improved
Labor requirements were separated into three periods within a
production year. The operator had available 900 hours of his labor in
each period. Additional labor requirements could be met with hired
Total hours of hired labor are presented in Table 23. Most
hired labor was required during Period I (November-February) for hay-
making, feeding, repairing fences, etc. Hired labor was needed only
during the first two years for the March to June period (approximately
500 hours each year). This extra labor was used mainly for the estab-
lishment of improved pasture.
The operator's labor was utilized at the maximum of 900 hours
during Period I for every year of the organization. An excess of oper-
ator labor occurred for the other two production periods in years three
through fifteen. The amount of unutilized operator's labor never ex-
ceeded 300 hours during either of these four month production periods.
Soil and water conservation expenses total $17,904 for the first
three years of the organization. Overhead expenses were $2,888 each
year. This fixed expense included insurance premiums and other miscel-
laneous costs. Personal property taxes on livestock and equipment
ranged from $425 to $528 per year. Real estate taxes remained constant
at $5,502 per year. This included taxes on the land, fences, and
buildings required for the beef enterprises. Four sources of depreci-
ation occurred: depreciation on bulls ($1.96 per brood cow), equipment
($.93 per acre of total land), land improvements ($.83 per acre of total
land), and irrigation system ($3.48 per acre of irrigated land). Total
annual depreciation charges ranged from $7,140 to $8,245.
Total operating capital requirements included total cash ex-
penses, repayment of borrowed capital, payment of income taxes, and
family consumption. Total operating capital requirements reached a
peak of $77,523 during the fourth year. Slightly more than $23,000 was
borrowed for both the first and second years of the ranch operation.
This borrowing activity was needed since small amounts of capital were
generated from livestock sales. During these years a large number of
the heifer calves were kept for the cow herd. After the seventh year no
capital was borrowed since internally generated capital met all oper-
ating capital requirements. During the tenth year, the ranch firm
began to accumulate operating capital in excess of requirements and
depreciation allowances. By the end of the fifteenth year $29,915 of
excess operating capital had been accumulated.
Total net worth of the ranch was $653,006 in the beginning year.
This included 500 brood cows, 3,500 acres of unimproved native rangeland
with buildings and fences, and a complement of machinery and livestock
equipment. Considering the additional value for each acre of improved
pasture and a 6 percent annual appreciation value for all land, the net
worth of the ranch organization increased to $1,439,468 in the fifteenth
year. This represented an average annual increase in net worth of
Net ranch income before taxes totaled $117,478 for the 15 years.
Total sales of weaned and feeder calves less production expenses resulted
in an income loss of $123,345 for the 15 years. However, when receipts
from culled cows were added to returns, net ranch income was $117,478.
This represented an average before-tax income of $7,832 per year. The
after-tax income for the owner-operator totaled $110,098, or an average
of $7,340 per year. Annual incomes ranged from a $23,841 loss for the
second year to an after-tax income of $21,430 for the last year of the
planning period (Table 23).
None of the depreciation allowance for buildings and improvements
was assumed to be reinvested. Under this assumption the total capital
accumulation was $86,750 and total available cash for the rancher was
$166,933, or an average of $11,129 per year. The ranch operation pro-
vided the rancher and his family with at least $5,000 each year for
personal consumption and an additional $30,000 during the 15-year period
for personal use.
Two renter situations with different rental rates for land were
analyzed. The first situation was based on an annual lease rate of
$2.55 per acre. This lease rate was composed of charges for real estate
taxes, depreciation on buildings and fences, and insurance and miscel-
laneous expenses (Tables 24 and 47). For the second situation (Tables
25 and 48), an additional $.60 per acre was paid to the landowner for a
total lease rate of $3.15 per acre.
In the following sections comparisons are made for the two op-
timal ranch organizations when the objective was maximization of
after-tax income of the renter. The renter furnished all resources ex-
cept land and received all of the net returns from the ranching opera-
tion. His full-time labor was available for use on the ranch.
Both renting situations initially started with 500 brood cows.
The low land-rent situation resulted in a few more cows being maintained
each year of the planning period. For example, the low land-rent orga-
nization included 39 more cows in the ninth year and 11 more cows in the
thirteenth year. In both situations cows were culled to the maximum
number allowed each year.
Heifer calves kept for replacement and expansion of the cow
herd varied from a low of 60 head to a high of 190 to 194 head for the
renter situations. A major difference occurred in the years that heifer
calves were kept. For the first year 122 heifers were kept for the
low land-rent situation,but only 60 heifers were kept for the high
land rent situation. More of the calves were sold by the high land
Table 24. Enterprise combinations, resource allocations, and net returns for ranch organization for a
complete renter (paying $2.55 annual rent per acre)a
Brood cows Weaned calves Pasturelandb Operating Ni
SImproved L capital
Year Heifers rt
Total Culled Sold Feeders Native Nonir- Irri- hired require-
kept rigated gated ment tci
---_-------------__ _- ka--n--------------------- ---------rrs---- ------ -hmirc-- -------- rnl lar-.
aRenter furnished all resources
(equal to landowner's expenses).
except land, buildings, and fences.
Paid landowner $2.55 per acre
Leased a total of 3,525 acres.
Acreages of grazed cleared land are not shown but equal 153 acres
the first year, 25 acres the second year, and one acre the third year.
cTotal of cash expenses, repayment of borrowed capital, income taxes, and family consumption.
Net ranch income minus Federal income tax. Minus sign indicates a loss or negative income.
eSteers were purchased the second (22 head) and fifteenth (85 head) years.
Table 25. Enterprise combinations, resource allocations, and net returns for ranch organization for a
complete renter (paying $3.15 annual rent per acre)a
Native Nonir- Irri-
furnished all resources except land, buildings, and fences. Paid landowner $3.15 per acre
($.60 per acre above landowner's expenses).
bLeased a total of 3,325 acres. Acreages of grazed cleared land are not shown but equal 234 acres
the first year, 68 acres the second year, and five acres the third year.
CTotal of cash expenses, repayment of borrowed capital, income taxes, and family consumption.
dNet ranch income minus Federal income tax. Minus sign indicates a loss or negative income.
eSteers were purchased the second (37 head) and fifteenth (67 head) years.
rent rancher during the beginning of the planning period since larger
operating capital requirements were necessary. Some additional stockers
were purchased by both optimal organizations during the second and fif-
teenth years. Purchased stockers utilized grazing the second year
before maximum expansion of the breeding herd and the fifteenth year
with the reduction in size of the breeding herd.
In the low land-rent situation 200 more acres of native range-
land was rented than for the high land-rent situation. No restrictions
were placed on the acreage of land that could be leased, but once the
acreage was brought into the optimal organization it had to remain for
the duration of the planning period.
In both situations approximately 550 acres of land were cleared.
The low land-rent organization included a maximum of 296 acres of non-
irrigated pasture compared to 288 acres for the high land-rent situation.
The high land-rent situation included a few more acres of irrigated
pasture. The low land-rent organization grazed a total of 2,974 acres
of native pasture and 551 acres of improved pasture. For the high land-
rent situation 2,773 acres of native range and 552 acres of improved
pasture were grazed. Nonirrigated pasture was used for grazing and hay-
making. Cattle were grazed on the improved pasture from March to
October and then in later months the pasture was cut for hay.
The high land-rent organization generally required less hired
labor than the low land-rent organization. This was primarily due to
the smaller acreage operated and fewer cows in the herd. The high land