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The Impact of Range Improvement on the

Economic Success and Survivability of Ranches

in the Eastern Rolling Plains of Texas

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The Impact of Range Improvement on the
Economic Success and Survivability of Ranches
in the Eastern Rolling Plains of Texas

by

Larry W. VanTassell*
Assistant Professor
Department of Agricultural Economics
University of Tennessee

l. Richard Conner
Professor
Texas Agricultural Experiment Station
Department of Agricultural Economics
Texas A&M University

lames W. Richards
Professor
Texas Agricultural Experiment Station
Department of Agricultural Economics
Texas A&M University

*Formerly, Research Associate, Department of Agricultural Economics, Texas A&M University

Contents

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Production Technologies . . . . . . . . . . . . . . . . . 1

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Model Development . . . . . . . . . . . . . . . . . . . . 2

Representative Ranch . . . . . . . . . . . . . . . . . . . 2

Climatic Conditions . . . . . . . . . . . . . . . . . . . . . 3

Rangeland Stocking Capacity . . . . . . . . . . . . . . 4

Brush Control . . . . . . . . . . . . . . . . . . . . . . . . . 5

Cattle Production Parameters . . . . . . . . . . . . . . 7

Tax Accounting for the Livestock Herd . . . . . . . 8

Cattle Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Results and Discussion . . . . . . . . . . . . . . . . . . . 9

Evaluation Using Stochastic Dominance . . . . . . 11

Summary . . . . . . . . .  . . . . . . . . . . . .  12

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Appendix 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Overview

Uncertain forage production created by variation
in climatic conditions and encroachment of un-
desirable brush species account for much of the
business risk facing range livestock producers. This
study focuses on evaluation of range improvement
techniques which may decrease economic losses
associated with operating in this complex and un-
certain environment. The investment alternatives in
question were the implementation of grazing systems
and the control of mesquite infestations.

Nine scenarios were examined. They include the
combination of three grazing strategies (conventional
grazing, deferred rotational grazing, and rotational
grazing) with three mesquite control alternatives (no
treatment, aerial spraying with triclopyr, and aerial
spraying followed by maintenance burning). A repre-
sentative ranch developed for the eastern portion of
the Texas Rolling Plains was used for the study. The
simulation model developed for this analysis was
stochastic, dynamic, and recursive. Using Monte
Carlo techniques, several random variables were
simulated over a 20-year planning horizon for 100
iterations. The random variabTes included climatic
conditions, stocking rates, success of brush control,
cattle weights, conception and death rates, supple-
mentation rates, and labor requirements. Stochastic
cattle prices were also developed by projecting the
cattle cycle throughout the 20-year planning horizon
via harmonic functions.

Stochastic dominance was used to determine
efficient sets for ranchers who were risk averse, risk
neutral, or risk loving. Two conventional grazing
scenarios, aerial spraying and spraying plus burning,
were equally preferred by the risk neutral and risk
averse categories. The second most preferred strategy
included a rotational grazing system and an aerial
spraying practice. The risk lover's most efficient set
included only the conventional grazing strategy
coupled with aerial spraying.

Results showed it was economically prudent to
control mesquite infestations. The grazing strategies
studied obtained negative average net present values
when combined with the no brush control option.
Overall farm profitability and solvency were best
when implementing a conventional grazing strategy
and controlling mesquite using aerial spraying or
spraying followed by maintenance burns. With brush
control practices remaining constant, altering cattle
production by deviating from conventional grazing
was not profitable. These conclusions must be
qualified, though, because of the limitations of the
assumptions and data used in this study (e.g., the
production levels of grazing systems, response of
mesquite to treatment, and the economic environ-
ment assumed).

Introduction

Risks facing range livestock producers in the Texas
Rolling Plains stem from both economic and environ-
mental sources. Scifres (1985) summarized the major
business risks challenging Texas ranchers by stating
that excessive brush problems, scant and erratic
rainfall, and fluctuating livestock prices constituted
the major management issues facing range livestock
producers in Texas and that “all other issues seem
inconsequential compared to these management
concerns....” These three major business risks are
interactive and serve to make the decision environ-
ment uncertain and difficult.

To help alleviate the uncertainty in forage pro-
duction levels associated with erratic precipitation
levels and brush infestations, several grazing strategies
and mesquite control programs have been devel-
oped. These alternatives vary in implementation and
operating costs, and in their ability to increase total
beef production. Each alternative also responds
differently to changes in environmental conditions.

Objectives

The general objective of this research was to

"examine the feasibility of various range manage-
ment-beef production alternatives, and to assess

their effect on the stability and level of rancher’s
incomes. More specifically the objectives were the
following: 1) to evaluate the economic advantages
of three grazing systems, namely, rotational grazing,
deferred rotational grazing, and yearlong continuous
grazing, and 2) to examine the feasibilityof con-
trolling mesquite infestations by spraying with tri-
clopyr, combined with the possibility of extending
the benefits of the initial herbicide treatment by
controlled burning.

Study Area

The eastern portion of the Rolling Plains of Texas,
as defined by Bonnen (1960) (Figure 1), comprise
more than 5 percent of Texas’ land area or approxi-
mately 9 million acres. Farms and ranches comprise
almost 91 percent of the area, with 76 percent of the
land in farms and ranches consisting of pasture and
rangeland. The cow-calf enterprise is the principal
type of livestock production with wheat, cotton,
oats, and grain sorghum being the primary crops
(Texas Dept. of Agric. 1980-1984).

Clay loam range sites predominate the area, with
mesquite being most prevalent. Vegetation is a
mixture of mid- and shortgrasses. Climate is highly
variable, with warm, wet springs and falls, hot
summers, and mild winters. Rainfall is varied within
and between years with an annual average of 27
inches (Heitschmidt, et al. 1985).

Figure 1. Eastern Rolling Plains of Texas.

Production Technologies

Three common grazing systems utilized today are
rotational grazing (RG), deferred rotational grazing
(DR), and yearlong continuous grazing (CG). The CG
strategy is the least expensive and simplest of the
three grazing strategies to implement, maintain, and
manage. Livestock are simply allowed to roam at
large in one pasture year-round. The four-pasture,
three-herd DR strategy allows one pasture to be
unoccupied for four months following a one-year
grazing period (Merrill 1954). At moderate stocking
rates, the DR system provides more weight gain per
animal but less production per acre than the CG
system (Heitschmidt, et al. 1985). The RG strategy
uses a fencing design, whereby numerous grazing
paddocks radiate outward from a central watering
and handling facility (Savory and Parsons 1980). While
this strategy permits up to a 50 percent increase in
yearlong rates of stocking, individual animal per-
formance is hindered as a result of reduced weight
gains, conception rates, and weaned calf crops
(Heitschmidt, et al. 1985). Facility and labor costs are
also greater with the RG method than the CG grazing
method (Conner and Chamberlain 1985).

Increased forage production from controlling
mesquite is generally attributed to the increased
availability of moisture and sunlight to range forage.
Control of this invader also improves efficiency of
livestock handling and increases the availability of
grazing to livestock, especially if the plant is multi-
stemmed (Scifres 1980). Two of the more promising
methods for controlling mesquite infestations are
spraying with triclopyr, and spraying combined with
the possibility of extending treatment benefits by

controlled burning. The effectiveness of both control
methods depends upon environmental conditions
that are conducive to absorption and translocation
of the herbicide, as well as upon the effectiveness of
the burn.

Methodology

Most economic studies assessing the viability of
grazing systems and brush control practices have
used a deterministic partial budgeting approach to
develop the appropriate cash flows, which are then
analyzed using a net present value, internal rate of
return, or payback approach (Lundgren, et al. 1984;
McBryde, et al. 1984; Whitson and Scrifres 1980;
Conner 1985). The other methodology commonly
used is multi-year linear programming (Sharp 1964;
Freeman, et al. 1978; Garoian and Conner 1986;
VanTassell and Conner 1986). The major drawback to
both of these methods is that they ignore the business
and financial risks involved in undertaking range
improvement investments. Motad and quadratic
programming have been used more sparingly to
address these problems (Whitson, et al. 1982; Whitson
1974). While motad and quadratic programs address
some risk issues, the lack of flexibility in specifying
the model and the size of the matrix involved are
major drawbacks.

To evaluate the objectives of this study, a proper
accounting of several uncertain economic and phy-
sical forces acting upon a ranching enterprise was
essential. The major sources of risk needed to be
quantified and combined appropriately to adequately
describe the interacting relationships which exist
between the uncertain environment and the pro-
ductive processes of a livestock operation in order to
evaluate the relative risk involved with each proposed
project.

The methodology chosen to examine this problem
was simulation analysis. Simulation provides the
flexibility for dealing with dynamics and stochastics
that are too complex to be represented by more
rigid mathematical models such as linear and qua-
dratic programming (Anderson.1974). Although the
flexibility and autonomous analytical structure of
simulation modeling relinquishes the advantage of
determining an optimal solution, it does provide an
estimate of the true answer via probability distri-
butions (Johnson and Rausser 1977). Therefore, a
representation of possible outcomes which could
result in actual performance is supplied.

Model Development

A simulation model, Ranch Simulator (RANSIM),
was developed to examine the effect of several
existing uncertain conditions upon the success and
survivability of a representative ranch. The model
was dynamic, stochastic, and recursive in nature.

Using Monte Carlo techniques, random climatic
conditions, stocking rates, cattle weights, weaning
dates, cow conception rates, cow and calf death
rates, supplementation rates, labor requirements,
and cattle prices were simulated throughout a 20-
year planning horizon for 100 iterations. These
stochastic production parameters, input levels, and
output prices were then combined with depreciation,
taxes, and capital requirements to compute the firm’s
income, cash flow, and balance sheet statement. At
the end of each year, a solvency test was made to
determine if the firm was still viable. After each 20-
year iteration, the model records information nec-
essary to estimate the empirical probability distri-
butions for several key output variables.

The model was basically driven by the simulated
climatic environment which directly influenced sup-
plementation levels, cow and calf weights, weaning
dates, and range conditions (including the possibility
of undertaking brush control practices and deter-
mining their success). March 15, lune 15, August 15,
and October 15 were identified as important dates in
the decision-making process for ranchers in the
Rolling Plains (Riechers 1986). The model assessed
cumulative environmental conditions (e.g., precipi-
tation and temperatures) at each decision date,
generated production parameters, and made pro-
duction decisions given the generated conditions.

Representative Ranch

Evaluation of the alternative production systems
under consideration necessitated describing a repre-
sentative ranching operation for the eastern portion
of the Rolling Plains. It was desirable to define a
ranch large enough to employ a full-time operator
who would have the expertise and capital base
necessary to invest in and manage the production
practices under examination. Area financial con-
sultants, bank managers, experiment station per-
sonnel, and ranchers were consulted in defining the
representative ranch.

The representative ranch consisted of 10,240 acres
of rangeland that was in fair condition. One-half of
the acreage was operated on a long-term cash lease
at $4 per acre. The lessee was responsible for repair
of all fences and shared in one-third of the fence
replacement costs. The lessee also paid for implemen-
tation of all brush control and grazing system
improvements. At the end of the lease or in case of
insolvency, the lessee was reimbursed a salvage
value for such improvements.

In its original condition, the total acreage supported
515, 640, and 439 crossbred cow-calf pairs for the CG,
RG, and DG systems, respectively. Cows were bred
to calve from late December to early February. Dry
cows were sold in lune if an adjustment downward
in stocking rates was needed. At weaning, open
cows, 13-year-old cows, and a minimum of 1 percent

of the bottom of the herd were automatically culled.
If conditions necessitated a further reduction in
livestock numbers, pregnant cows or cow-calf pairs
were sold. Spring replacements were assumed to be
purchased as cows with calves at side, and bred
heifers were purchased for fall replacements. All
calves were sold after weaning at the prevailing
market prices. Bulls were purchased as 2-year-olds
and sold after they reached 8 years old.

Beginning long-term debt to asset ratio was 0.70
and the intermediate-term debt to asset ratio was
0.50. Existing and current long- and intermediate-
term debts were assumed to be financed with 30-and
5-year loans, respectively. Beginning net worth was
$538,351. Minimum equity requirements for solvency
were 0.20 for long-term assets and 0.30 for inter-
mediate-term assets.

Family living expenses were set at a minimum of
$18,000 and a maximum of $36,000, with a marginal
propensity to consume 25 percent of disposable
income. Personal income and self-employment taxes
for each year of the planning horizon were computed
under provisions of the Tax Reform Act of 1986.

The operator and his family provided a total of 40
hours of labor per week above the amount required
for financial, marketing, and other management
concerns. Additional labor was provided at a cost of
$10 per hour.

Assumed inflation rates and interest rates for the
20-year planning horizon are found in Appendix 1.
All rates for 1987 through 1990 were obtained from
the Commodity Specific General Equilibrium Model
(COMGEM) using a high federal budget deficit
scenario (Hughesfet al. 1987). After 1990, interest
and inflation rates were assumed to remain at their
1990 levels for the remainder of the planning horizon.
Costs were increased annually to reflect the assumed
inflationary environment.

Machinery complements and livestock facilities
were valued on a current market basis and replaced
at the end of their economic (useful) life. Replace-
ment price was based on 1986 prices and inflation
rates which reflect the assumed economic conditions.
Depreciable items were recovered using a 5-year
double declining balance schedule. First-year ex-
pensing was also assessed on purchased livestock
and machinery.

Initial costs of production for each grazing system
were adopted from enterprise budgets developed by
Conner and Chamberlain (1985). The ranch was
already cross-fenced, so no additional facilities were
needed for the DR system. An investment of $58,518
was required for fences, corrals, and watering systems
required to set up two circles (six paddocks each) for
the RC system. Operating costs for repairs, insurance,
etc., were assumed to be equal for the CG and DR
systems, but were increased almost $2,100 for the RG

Table 1. Yearly operating fixed input costs for the Conventional (CG),
Deferred (DG), and Rotational (RG) Grazing Systems.

CG DC RG

Fence Repair $ 128.30 $ 128.30 S 128.30
Electric Fence Repair 63.36
Equipment, Fuel,
and Lube 2,112.90 2,112.90 ' 2,853.80
Water Facilities Repair 110.00 110.00 660.00
Equipment Repair 2,295.00 2,295.00 3,060.20
Accountant and Legal
Fees 2,500.00 2,500.00 2,500.00
Insurance 600.00 600.00 600.00
Miscellaneous Costs 1,000.00
Total $8,746.20

1,000.00

$10,865.66

1,000.00

$8,746.20

Table 2. Average production parameters for the Conventional (CG),
Deferred Rotational (DC), and the Rotational (RG) Grazing
Systems.

CG DC RC
Acres/Animal Unit 12.00 14.00 9.50
Cows/Bull 25.00 25.00 30.00
Weaning Weight, Steers (lbs)- 580.00 595.00 550.00
Death Rate, Calves (Z) 7.80 7.00 8.50
Death Rate, Cows (Z) 1.90 1.60 2.20
Conception Rate (Z) 90.00 94.00 88.00
Labor/Acre (hours) 0.17 0.17 0.31
Labor/Cow (hours)a 1.40 1.70 2.1.0

a . . .
Increased as a function of brush infestations.

system (Table 1). Operating inputs per cow were
assumed to be equal for all systems. They included
$6.85 for veterinary and medicine, $2.30 for salt, and
$0.50 for miscellaneous expenses, for a total of $9.65
per head. Marketing costs were $11 per animal sold,
and supplemental feed in the form of range cubes
was priced at $11 per hundredweight of feed. Labor
requirements were included on both a per acre (for
facility and fence repair) and a per cow basis. Average
production parameters for each grazing system are
found in Table 2.

Estimated costs for brush control were $11.25 per
acre for spraying, which included $7.25 for chemicals
and $4 for application. Cost of the first burn was
assumed to be $6 per acre, including the development
of fire lanes. Cost of the second burning was
estimated at $3 per acre. To accommodate the
temporary decreases in carrying capacity due to
brush treatment, additional acreage was leased at
$6.67 per cow per month.

Climatic Conditions

Monthly precipitation and average minimum
temperatures were determined by VanTassell, et al.
(1987 to be the most crucial climatic variables in
evaluating production relationships in the Rolling
Plains, with each forage production year beginning
in August of the previous year and extending to each
decision month. Historical monthly data for the
Texas Rolling Plains area covering 1936 through 1985
were obtained from the National Oceanic and

Atmospheric Administration (NOAA 1985). These
data were checked for long-run cyclical trends, but
none were significant.

To stochastically generate alternate sequences of
monthly climatic data, multivariate empirical prob-
ability density functions (pdf’s) for each month’s
precipitation and January through May temperatures
were developed (Richardson and Condra 1978;
Clements, et al. 1971). Stochastically drawing the
monthly climatic variables in this manner for each
year maintains the interyear correlations. Because
data needed to be aggregated across years into
production periods, two problems existed with this
method. First, was the correlation problem. For
example, the correlation coefficient between Feb-
ruary and December in year t was -0.01, while the
correlation coefficient between February in year t
and December in year t-1 was 0.411. To maintain the
intertemperal correlation, the correlation matrix was
expanded to include the lagged (t-1) August through
December climatic variables (August t-1 thru
December t climatic variables were generated for
each year.). A second problem then arose, because
the precipitation generated in year t for August
through December precipitation by definition must
be the same level generated for the lagged August
through December precipitation in year t+1. There-
fore, to assure identity in the overlapping precipi-
tation variables, the empirical correlation method
used to obtain the correlated deviates was modified
to include intertemperal correlation and provide
identical overlapping data.‘

Rangeland Stocking Capacity

Forage availability was a function of total precipi-
tation accumulated during a forage production
period which began in August of the previous year
and extended to each decision point. To account for
the variability in forage levels, subjective probability
distributions for carrying capacity, conditional upon
rainfall, were elicited from range scientists. Precipi-
tation levels associated with percentages of 90, 70, 50,
30, and 1O percent of the maximum precipitation
received for each forage production period through-
out the 5O years of historical data examined were
used as the elicitation points.

A conditional cumulative distribution function (cdf)
was estimated for each decision month using the five
elicited density functions as observations (one for
each precipitation level). The cdf’s were estimated
using a hyperbolic tangent transformation procedure
described by Taylor (1984). The procedure estimates
a cumulative distribution function as

‘See Appendix 2 for a complete explanation of this method.

(1) F(YlX) + .5 + .5tanh [P(Y, x)].

Where Y is the stocking rate, X is accumulated
precipitation throughout the production period, F(Y}
X) is the cdf of Y conditional on X, and P (Y, X) is a
third degree polynomial function of Y and X. A
program, SECANT, developed by Taylor (1983) was
used to search for maximum likelihood (ML) estimates
of (1). Stepwise regression procedures were used to
specify which initial variables and coefficients from a
third degree of polynomial were to be included in
P(X, Y). A likelihood ratio test (Theil 1971) was used
to determine which remaining polynomial terms
were included in the ML estimates of P(X, Y).

Final ML estimations (and accompanying asymptotic
t-statistics) for the CG strategy at the June, August,
and October decision points, respectively are:

(2) F(Y : x) = .5 + .5tanh[-5.04 +18.24Y2 - 2.13xv2]
(-8.44) (8.01) (-8.91)

(3) F(Y : x) = .5 + .5tanh[-4.95 + 16.08Y2 - 1.9OXY2]
(-8.45) (7.93) (-7.01)

(4) F(Y : x) = .5 + .5tanh[-0.34 + 25.39Y2 - 1.94x +

(0.115)(5.472) (2.143)
0.41X2Y - 4.59XY2]
(2.585) (-4.087)

Final ML estimations (and accompanying asymptotic
t-statistics for the RG strategy at the June, August,
and October decision points, respectively, are:

(5) F(Y : x) = .5 + .5tanh[-8.47 + 20.93Y - 4.80xY +
(8.53) (8.38) (3.88)

0.41X2Y]
(2.81)

(8) F(Y l X) = .5 + .5tanh[-7.64 + 26.18Y - 8.78xv +
(8.55) (8.05) (4.45)

0.58x2Y]
(3.80)

(7) F(Y : x) = .5 + .5tanh[-8.31 + 32.83v - 8.o5xv +
(8.84) (5.79) (4.35)

0.82x2v]
(3.75)
The expected values of Y given X are then defined
3S1 x
(8) E(Yl x) = .5 y P’ (y,X) sech2[P(y,X)] dy.

Given the leve-l of precipitation occurring during the
production period, (8) was numerically integrated to
obtain the carrying capacity for each decision period.

Twenty percent of the historic precipitation levels
fell outside the range of the elicited density functions.

For most of the extreme levels of precipitation, the
hyperbolic tangent functions did not remain stable,
but gave stocking levels which were unrealistic.
Stocking rates at levels outside the elicited range of
precipitation were therefore assumed to be distri-
buted empirically using the elicited density functions
estimated at the 10 percent and 90 percent levels.

Because the DG strategy varies stocking rates only
minimal amounts, carrying capacity was not con-
ditional upon precipitation in the hyperbolic tangent
functions. Carrying capacity was therefore assumed
to be empirically distributed for the DG strategy,
with the elicited density functions (dependent upon
precipitation levels) being used as historical data.

Several factors usually cause a rancher to not
completely utilize the full range of carrying capacity
each grazing strategy affords. Among these are the
expense of selling and buying cows, the disruption in
the ranchers culling and breeding schemes, the
availability of suitable replacements, and the lack of
available funds for restocking. To partially account
for the rigidity which exists in utilizing the full range
of carrying capacity, stocking rates were obtained
from a dampening function defined as:

(9) SR = ASR - (ASR -CP)/AD].

Where SR is the finalstocking rate, CP is the carrying
capacity obtained from the respective functions, ADJ
is an adjustment factor, and ASR is the average
stocking rate for each grazing strategy (12.0 for CG,
14.0 for DC, and 9.5 for RG). AD] was assumed to be
2.0 unless accumulated precipitation was below
(above) that which occurred 20 (80) percent of the
time for the given decision point. For these later
levels, the adjustment factor was changed to 1.75 to
allow for more drastic stocking rate changes due to
continual drought or excessive forage.

Brush Control

Two major sources of uncertainty exist when
mapping changes in stocking rates over time via
response curves. First, uncertainty exists about what
the response from brush control will actually be.
Second, is the effect the level of precipitation will
have upon the carrying capacity of the range. To
account for the first uncertainty, traditional response
curves (Workman, et al. 1985; Whitson and Scifres
1980) were modified, after consultation with range
scientists, to provide several response paths. Figure 2
presents the estimated response curve for spraying
mesquite with triclopyr for normal precipitation
levels. The range was assumed to be in fair condition
with a mesquite canopy cover of 25 percent to 30
percent and a stocking rate of 20 acres per animal
unit. Without treatment (Paths 1, 2, and 3), the
stocking rate decreased to either 22, 24, or 26 acres
per animal unit throughout the 20-year planning
horizon, dependent upon several unmeasureable

environmental factors. Each path was assigned a
subjective probability of occurrence equal to 33.3
percent and a random draw determined which of
the three lines were followed.

Paths 4, 5, and 6 map carrying capacity after
spraying (Figure 2). No increase in forage production
occurred the first year of spraying. By the second
year, the majority of foliage was assumed to have
been removed from the trees and maximum forage
production was reached by the third year. The main
source of forage variation from spraying was the rate
of decline once maximum carrying capacity was
reached. To account for this uncertainty, three paths
of descent were assumed.

A major factor influencing the success of spraying
mesquite was the physiological activity of the plant.
Accumulated precipitation 3 months prior to spraying
(April through June) was used as an indicator of plant
viability. The decision about whether to spray and
the subjective probabilities used for assigning a path
of descent were changed depending upon the
precipitation occurring prior to spraying. If precipi-
tation was below 6.6 inches, which historically
occurred 30 percent of the time, spraying was
assumed to not be a successful investment and was
not undertaken. If accumulated precipitation was
above 8.7 inches, which historically occurred 50
percent of the time, probabilities of success for Paths
4, 5, and 6 were 20, 40, and 40 percent, respectively. If
precipitation was between 6.6 and 8.7 inches, pro-
babilities of success were changed to 25, 50, and 25
percent for Paths 4, 5, and 6, respectively. Once the
range condition again deteriorated to 20 acres per
animal unit, the range was eligible for respraying.

Sprayed land was eligible for burning in February
during the sixth year after spraying, assuming suf-
ficient fine fuel was available to carry the fire (Figure
3). To accumulate fuel, a grazing deferment of 5
months, from September until February, was re-
quired. Total precipitation during the deferment was
used as a barometer for the amount of accumulated
grass. If precipitation was below 6.6 inches, burning
was not allowed. Since the amount of forage dictates
the intensity of the fire, which in turn determines the
extent of mesquite control, probabilities about the
success of the burn were assigned to each path
dependent upon the level of precipitation received
during the deferment. Probabilities of following Paths
4, 5, or 6 were 25, 50, and 25 percent, respectively,
when precipitation was under 8.7 inches; and 20, 50,
and 30 percent, respectively, when precipitation was
over 8.7 inches. A grazing deferment was continued
for 3 months after the burn to allow proper regrowth
of the forage.

Assuming the first burn occurred, the range was
eligible for a second burn 6 years hence. The same
rules used to determine eligibility and success of the
first burn applied to the second burn except that
probabilities were changed for Paths 7, 8, and 9, to

5

S
IO

H

C

H

E

S

P

E

H

H

N

I

H

H

L Legend: l I No Treatment, Path 1
ll 25__ 2 I No Treatment, Path 2
N 3 I No Treatment, Path 3
I 4 I Spray, Path 6

I 5 I Spray, Path S

6 I Spray, Path 6
30 <
35 ~

TEHH

Figure 2. Response curves for the spray and and no treatment alternatives.

30, 50, and 20 percent, respectively, for precipitation
between 6.6 and 8.7 inches; and 25, 50, and 25
percent, respectively, for precipitation levels over 8.7
inches for the same paths. The decreased success of
the second burn was due to increased size and
foliage of the mesquite plants.

The range was only eligible for burning during the
sixth and seventh years following the previous
treatment. After the seventh year, mesquite foliage
was assumed to be sufficiently dense and the stems
large enough to reduce the effectiveness of burning
below its marginal value. If financing was not available
or if drought had prevented implementing a burn
prior to the seventh year, the range was resprayed
when carrying capacity reached 20 acres per animal
unit or more. The rancher also had to resort to
spraying as the only means of treatment the fourth or
fifth year following a successful second burn because
of the increased size and viability of the mesquite
plants.

The ranch was assumed to be divided into parcels
one section in size for brush treatment. In the first
year of every iteration, each section was randomly
assigned a stocking rate path to follow. Sections were
then evaluated separately on brush control needs.
Spraying was allowed in a maximum of four sections
each year and burning was permitted in three
sections, depending on environmental conditions
and the rancher’s financial condition. Sections quali-

fying for the first maintenance burn were given first
priority for financing. Second burn sections were
given second priority, and spray or respray sections
were given last priority.

A secondary advantage of controlling mesquite
infestations was the reduction in labor required for
gathering, handling, feeding, and inspecting the
cattle. To account for these increased economies,
labor requirements per cow were altered depending
on the degree of mesquite infestation. Labor require-
ments for relatively clean-pastures were assumed to
be 1.4, 1.7, and 2.4 hours per cow for the CG, DG,
and RG strategies, respectively (Conner and Cham-
berlain 1985). As carrying capacity was reduced to
between 16 and 19 acres per animal unit, labor
requirements increased to 1.89, 2.61, and 2.66 for the
CG, DG, and RG strategies, accordingly. For infes-
tations which reduced carrying capacity to more
than 19 acres per animal unit, labor requirements
were assumed to increase to 2.37, 3.51, and 2.78 for
the CG, DG, and RG strategies, respectively.

Response curves were consolidated with the sto-
chastic stocking rates developed for each grazing
system via the hyperbolic tangent or empirical
distributions discussed earlier using:

(10) SRi= 1 /[ (1 /SAJ- * BSR) /cci].
Where SRi is the final stocking rate for the ith

IO»
H
C
'8
I5-
S
P
E
H
n 20 _ \
w \\\\___“‘"IIIIIIlIIIIdl@"' ___-
n I
n I
L
II 25' Legend: 1 I No Treatment, Path I
N 2 I No Treataent, Path 2
I 3 I No Treatment, Path 3
I b I lat Iurn, Path I
S I lat lurn, Path S
6 I lat lurn, Path 6
3U * 7 I 2nd Iurn, Path 1
8 I 2nd Burn, Path I
9 I 2nd_lurn, Path 9
3S <
I 'I* I I I ‘I* I I I I I “I'*I I I I I I
I 2 3 U 5 7 B 9

I I I I I I I I ‘I I I I I I I ' 'T'“'_'T
II, I2 I3 I" IS I6 I7' I8 I9 20

IEHR

Figure 3. Response curves for the no treatment and burn-after-spray alternatives.

section, SA» is the stocking rate (conditional upon
precipitatioln) derived for the jt grazing system, BSR
is the stocking rate for the response curve (assuming
low brush infestations and average precipitation,
e.g., 12 acres per animal unit), and CC is the carrying
caIpacity determined from the response curve for the
it section.

Discounted terminal values were used to assess the
productive potential of the range at the end of the
planning horizon, or in case of insolvency, by valuing
each animal unit available above the untreated
carrying capacity level at $60. This rate corresponded
to a yearly per head grazing fee associated with a
conservative $3 per acre lease.

Cattle Production Parameters

To account for the variability in cattle production
levels, steer and heifer calf weights, cull and dry cow
weights, cow and calf death rates, and conception
rates were developed for each grazing system. These
data were developed using historical production
data collected at the Texas Experimental Ranch in
Throckmorton County, Texas.

Cattle weights were developed for both the June
and weaning decision periods. Table 3 contains the
weight equations used in the study, along with their
accompanying statistics. The calf weight equations
were obtained from VanTassell, et al. (1987), while
the cow weight equations were developed using
these same data and methods. All weights were
stochastically simulated by adding the respective
standard deviation multiplied by a random normal
deviate to each equation.

Differences between steer and heifer weights
(adjusted for age differences) were independent of
all other variables, and thus were determined by
their mean difference (34 pounds) plus their standard
deviation (20 pounds) times a normal random deviate.
This difference was added to the estimated average
calf weights to obtain steer weights and subtracted to
obtain the final heifer weights. Purchased replace-
ment heifers and young cows were assumed to
weigh 850 pounds and cull bulls were assumed to
weigh 1,750 pounds.

VanTassell, et al. (1987) showed that cumulative
probability distributions of the historical calf weights

Table 3. Cow and calf weight (lbs) ordinary least square equations for
the June and weaning decision periods.

WT2 = -242.35 + 1.97 AGE + 0.20 SUP - 19.80 cc - 40.29 RG + 81.92 08 +
(-5.21)“° (12.80)“" (4.20)"" (-5.09)"" (-4.22)“" (19.80)“"

15.19 All - 0.27 A112 + 0.58 J4 + 0

(0.99)** (-0.42)** (1.70)*

R2 = .83 o = 19.38

WT3 = -220 20 + 0.05 WT2 + 1.09 DAY + 0.081 sup - 9.10 cc - 22.08 RG
(0.47) (10.73)"" (8.07)"‘ (1.11) (2.03)"‘ (1.80)"

+ 62.71 CB + 14.75 F7 - 0.44 F72 + 1.26 J5 + 6

(9.84)** (2.51)** (2.53)** (3.44)**
2

R = .89 0 = 20.25

wc2 = 959.12 + 0.18 WT2 + 111.85 DRY + 0.87 SUP - 02.28 cc - 70.73 RG
(21.74)7‘ (1.72)" (9.40)"“ (2.09)““ (-4.52)"" (-5.70)""
+ 87.57(DRY*DG) - 0.11(DG*WT2) + 0

(3.82)“‘ (-2.94)""

R2 = .70 0 = 41.24

WC3 = -21.69 + 0.78 CFG + 3.79 DRY - 1.15 DAY + 6

(-0.99) (4.39)** (3.52)** (-3.00)**

R2 = .25 0 = 42.20

¢t-values for each parameter are in parenthesis below the parameter

estimate.

* and ** imply significantly different from zero at the 902 and 95Z
level, respectively.

Where, 0 = standard deviation, WT2 = average calf weight in June; WT3 =
average calf weight at weaning; WC2 = average cow weight in calf
between June and weaning; AGE = age of calf in days at weighing;
DAY = days between the June and weaning weigh dates; SUP = supple-
mentation level of cow herd in pounds of total crude protein; CG =
'1 if CG strategy, 0 o.w.; RG = 1 if RG strategy, 0 o.w.; DC = 1 if
DG strategy, 0 o.w.; CB = 1 if crossbred, 0 o.w.; DRY = 1 if cow
was dry, 0 o.w.; All = accumulated precipitation from August in the
previous year through June; F7 = accumulated precipitation from
February through August; and J4(J5) = accumulated average minimum
monthly temperatures from January through April (May).

were relatively steep at the upper and lower tails
(i.e., a ceiling and floor on the range of weights),
while distributions created from simulating the
respective equations tailed off more slowly. All
weights were therefore bounded, with the range
dependent upon the grazing system involved. The
ranges for calf weights were 450 to 590, 475 to 625,
and 480 to 630 pounds for the RG, CG, and DG
strategies, respectively. The ranges for-lune dry and
weaning cow weights, respectively, were 990 to 1,215
and 890 to 1,140 pounds for RG; 1,000 to 1,225 and
900 to 1,150 pounds for CG; and 1,050 to 1,275 and
950 to 1,200 pounds for DG. Weight range limits were
increased by 0.75 pounds per year to allow for any
technical progress which may have occurred.

Cows were supplemented a 20 percent crude
protein range cube at varying levels for up to 120
days during the winter depending on the assumed
forage levels as determined by accumulated precipi-
tation. The difference in supplementation rates
between the grazing strategies corresponded to the
stocking pressures on the rangeland. For the sim-
ulated data, average yearly supplementation rates
were 164.50, 50.15, and 164.50 pounds for the CG,
DG, and RG strategies, respectively.

Probability distributions were developed for con-
ception rates and death rates for cows and calves by

combining the historical observations (1981 through 1985)
with subjective probability distributions obtained
from range scientists working at the Texas Experi-
mental Ranch. No historical correlations were found
among these performance variables, or with other
variables such as supplementation, weight, or
weather. The distributions were therefore modeled
as independent empirical, from which stochastic
conception and death rates were obtained. Ninety
percent of the yearly death loss for calves was
assumed to occur prior to the lune decision period,
while 75 percent of the cow death loss was assumed
to occur by this period.

Tax Accounting for the Livestock Herd

Because some depreciable breeding stock were
assumed to die or be sold before the end of their
economic life, extra consideration was given in
modeling the tax implications of prematurely dis-
posing of assets. To accomplish this task, cattle were
classified by age in the initial period according to a
representative age mix for the cow herd. Given this
initial cow age distribution, a depreciable basis was
established for each age group under the assumption
that cows were purchased as 2-year-old heifers.
Cows purchased prior to 1980 were valued according
to historical prices, given a salvage value of $200, and
depreciated using a 150 percent declining balance
schedule. Cows purchased from 1980 through 1986
were recovered using a 5-year acceleratedschedule,
electing first-year expensing, and taking a 10 percent
investment tax credit. Investment tax credit recapture
was taken on all qualified breeding stock disposed of
prematurely. Bulls purchased during these same time
periods received the same tax treatment.

Casualty loss was taken on the remaining depreci-
ation and salvage value (if applicable) of any cows or
bulls which died during the year. Depreciation
recapture was accumulated on all open cows sold
using their respective remaining depreciable basis.

For accounting and salvage value purposes, breed-
ing herd value was determined at the end of each
year. Cows were priced at an average of utility and
replacement cow prices. Bulls were valued at 80
percent of their current replacement price. Federal
income taxes were calculated using the provisions
for the 1986 Tax Reform Act, assuming the livestock
producer was a sole proprietor.

Cattle Prices

Cyclical price paths were projected for 400-500,
500-600, and 600-700 pound steer and heifer calves;
cull cows and bulls; and replacement heifers, cows,
and bulls using harmonic regressions (Franzmann
andWalker 1972; Gutierrez 1985). Data were collected

on a monthly basis for the years 1972 through 19852
(Texas Dept. of Agric. 1972-1985; American Hereford
journal 1972-1986; USDA 1972-1985). Table 4 contains
the ordinary least squares equations for each class of
cattle using the following cyclical trend model:

(11) Pit = BO + B127rt - B2SlN(27Tt/L1) + B3COS
(27rt/L1) + B4SIN(27Tt/L2) + B5COS(27rt/L2) + 5

Where Pit is the predicted price for the ill‘ class of
cattle in time period t, B’s are parameter estimates, L
is the specified cycle length, and 5 is the residual
error term. Following Franzmann and Walker, a 12

zSlaughter bull prices were only available for the years 1972,1973,
and 1980 through 1985. Ordinary least square regressions showed
that slaughter bull prices over that period were almost exactly 1.25
times utility cow prices (R2 = 0.99). Slaughter bull prices were
therefore determined by multiplying the predicted utility cow
pncesby'L25.

Table 4. Ordinary legst square equations for the cyclical trend cattle
price model .

R4 = 37.39 + 0.0301 + 1.66181 - 1.47001 - 10.14982 + 8.70402 + 6
(24.70)"“ (12.31)"" (1.58) (-1.39) (-9.51)"" (7.99)‘“
R2 = .67 6 = 9.49

H5 = 36.04 + 0.0281 + 1.62481 - 0.73301 - 9.07982 + 8.33002 + 6
(28.64)““ (13.98)"“ (1.85)" (-0.84) (-10.23)"" (9.21)""

R2 = .71 o = 7.89

H6 = 34.69 + 0.0291 + 1.57481 - 0.56501 - 8.23982 + 7.93102 + 6
(30.71)""(16.14)”“ (2.00)“" (-0.72) (-10.34)"“ (9.76)""
R2 = .75 6 = 7.08

84 = 44.64 + 0.0351 + 1.68481 - 1.44701 - 12.15482 + 9.63902 + 6
(27.48) "(13.42)““ (1.49) (-1.28) (-10.61)“" (8.25)"“

R2 = .70 0 = 10.20

85 = 42.02 + 0.0331 + 1.58381 - 0.51901 - 10.25582 + 8.92502 + 6
(30.23) "(14.53)“" (1.64) .(-0.54) (-10.47)““ (8.93)""
R2 = .72 6 = 8.71

86 = 40.10 + 0.0311 + 1.43481 - 0.08101 - 9.01382 + 8.39702 + 6
(32.96)“2(15.82)"" (1.69)" (0.10) (-10 51)"" (9.60)""

R2 = .75 0 = 7.62

u1 = 25.88 + 0.0171 + 1.95081 - 1.72201 - 5.37582 + 4.72602 + 6
(34.40)“‘(14.38)“" (3.72)“" (-3.30)"" (10.13)"“ (8.73)""
R2 = .72 6 = 4.72

PR = 348.25 + 0.2691 + 5.21781 - 21.15901 - 93.73082 + 108.6202 + 6
(24.22)““ (11.58)"“ (0.52) (-2.12)““ (-9.25)"“ (10.51)""
R2 = .68 6 = 90.10

RP = 33.39 + 0.152T + 1.51081 - 0.222C1 - 8.616S2 + 7.42C2 + 6

‘k >'< 7': 7': a’: i a‘: i: 3': ‘k
(30.22) (8.49) (1.96) (-0.29) \-11.06) (9.34)

R2 = .65 6 = 6.92

BL = 813.28 + 1.l06T + 160.77S1 - l17.028C1 - 38.46582 + l59.454C2 + 6

(11.21)““ (9.43)““ (-3.18)”“ (-2.32)““ (-0.75) (3.06)““

R2 = .43 6 = 454.57

a . . .
t-values for each parameter are 1n parenthesis below parameter estimates.

* and ** imply significantly different from zero at the 90% and 95%
level, respectively.

Where, 0 = standard deviation, H4, H5, H6, S4, S5, and S6 = Heifer (H)
and Steer (S) price per cwt. for 400-500(4), 500-600(5), and
500-600(5), and 600-700(6) pound calves, respectively; UT = price
per cwt. for utility cows; PR = price per pair for cow-calf pairs;
RP = price per cwt. for replacement heifers; BL = price per head for
replacement herd sires; t = time trend (e.g., 1, 2, 3...); t = time
trend (1.6., 1, 2, 3...); 1 = Znt/L1); 81 = SIN(2nt/L1); 01 =
COS(2nt/L1); S2 = SIN(2nt/L2); C2 = COS(2nt/L2); L1 = cycle length
of 12 months; L2 = cycle length of 120 months.

month seasonal component was specified for L1, and
a 120-month cycle was used for L2. The prediction
equations were stochastically simulated using cor-
related random normal deviates developed from the
covariance matrix of the harmonic function residuals.

Two different starting points in the cattle cycle
were assumed for the simulation as shown in Figure
4. Following the harmonic functions through time,
the position for 1987 prices would be at the beginning
of Path A. To follow closely with the COMGEM high
deficit scenarios, in which average cattle prices
decline slightly from 1987 through 1990, and because
several conditions pointed to continued soft cattle
prices (e.g., decreased demand for beef and dairy
buyout program), Path B was also assumed. Subjective
probabilities of 0.70 for Path B and 0.30 for Path A
were given for determining which path was followed
each iteration. Using a 0.725 transmission coefficient
between inflation rates of costs of production and
farm output prices (Tweeten 1980), and assuming a
6.0 percent general rate of inflation, average annual
cattle prices were increased by an annual rate of 4.35
percent after the fourth year in each iteration.

While the random normal deviates used to simulate
cattle prices were correlated between classes, they
were not correlated between months. To maintain
this correlation in the stochastic simulation, monthly
prices from each equation were averaged into yearly
prices and then seasonalized using seasonal indices
developed from the historical cattle prices.

Results and Discussion

To obtain a representative sampling of the sto-
chastic process inherent in the model, a 20-year
planning horizon was simulated for 100 iterations.
Nine scenarios, CN, CS, CB, DN, DS, DB, RN, RS, and
RB, were designated for the CG (C), DG (D), and RG
(R) grazing strategies, combined with no mesquite
treatment (N), spray (S), and spray-burn (B), respect-
ively.

The ranch’s probability of success (the probability
that the ranch would return at least an 8 percent
after-tax net return to initial equity), and the pro-
bability of survival (the probability that the rancher
would remain solvent over the 20-year planning
horizon) under each scenario are contained in Table
5. Also presented are simple statistics for discounted
net present values (NPV’s), discounted ending net
worths (ENW’s), and average size of cow herd
maintained.

Continuing Scenario CN, a rancher in the Rolling
Plains would have a 24 percent chance of surviving
during the 20-year planning period, and a 26 percent
probability of success. Income from an average of
477 cows did not allow the rancher to maintain the
necessary cash flow to remain in business past an
average of 16 years. This scenario did, however, have

Q4
L)
...J

1DO~

ec- A
.   l

D

c l

L l

g I

a 70-

S

P

E 5111

G

u

l _ LegenchA-PathA

110- B-PachB

l-IU-

30-

20-—

steers.

the greatest probability of success and survival of all
the no mesquite treatment scenarios. NPV averaged
-$138,660 and ENW diminished to $80,750, down
from the original $538,356 under Scenario CN.
Controlling mesquite, the probabilities of success
and survival were increased to 93 percent and 92
percent, respectively, for Scenario CB, and 9O percent
under the Scenario CS. These probabilities were the
highest obtained of the nine scenarios examined.
Scenarios CS and CB had equal probabilities of
survival until the twelfth year when the relatively
inexpensive second burn of Scenario CB began to
pay off. Scenarios CS and CB also had the highest
average NPV of all scenarios ($976,550 and $909,670,
respectively), and the highest average ENW ($876,190

10

1

l

1-1' "r

1.1 12 1a 111 1s 1s 1v 1a 1's 2o

TERH
Figure 4. Starting points and associated cycles for the simulated prices for 500-600 pound

and $843,360, respectively). Scenario CB obtained
the lowest and Scenario CS the second lowest positive
relative variance of NPV and ENW, as measured by
their coefficients of variation.

The number of mother cows operated by Scenarios
CS and CB averaged 185 head more than under the
CN strategy. Average number of sections treated for
mesquite infestations were the highest of all Scen-
arios, with a yearly average of 0.75 sections first
sprayed, and 0.84 sections resprayed under Scenario
CS; and a yearly average of 0.64 sections first burned,
and 0.29 second burned under Scenario CB.

_A rancher using Scenario DN under the stated
assumptions would have had a zero probability of

success and survival, while remaining in business an
average of 9.6 years. This strategy operated the
smallest average size cow herd (420 head), but had
the lowest variation in the number of cows main-
tained. Scenario DN had the lowest average NPV (-
$327,820), with ENW decreasing $500,000 from the
initial $538,351. While each scenario started with the
same net worth, Scenario DN was not able to produce
enough calves to maintain its equity position.

Utilizing mesquite control methods, the prob-
abilities of survival and success were improved from
zero under Scenario DN to 38 percent and 43 percent
each under Scenarios DS and DB, respectively. While
the NPV and ENW positions were better than any no
mesquite treatment scenario, they were the lowest
of all mesquite treatment scenarios. The number of
cows operated under these two scenarios were
increased by approximately 80 head over the number
maintained by Scenario DN, with the variation in
average number of head run increasing because of
brush control. Insufficient cash flow and the low
number of years in operation left Scenarios DS and
DB with the fewest number of sections treated for
mesquite of the treatment scenarios.

The probability of success and survival for Scenario
RN (5 percent) was slightly above Scenario DN, but
below that of Scenario CN. This scenario maintained
the fifth highest average number of cows at 593, but
remained in business 14.7 years, the second lowest of
all scenarios. Average NPV (-$230,300) was second
lowest, and ENW ($14,580) was the lowest of the all
scenarios considered. The poor financial showing of
Scenario RN was attributed to the initial investment
needed to establish the grazing system and the
outflow of cash needed for maintenance.

Mesquite control enhanced the survivability and
success of the RG strategy, with Scenario RS exhibiting
an 81 percent probability of success and survival and
Scenario RB a 76 percent probability of each. Average
NPV’s and ENW’s for Scenario RS ($626,370 and
$634,640) and Scenario RB ($488,810 and $539,400)
were the third and fourth highest, respectively, of all
scenarios. Scenarios RS and RB were more subject to
increased variation in NPV and ENW than Scenarios
CS and CB, because of the high number (790) and
extreme variation of herd size, plus the large debt
load maintained. Scenario RS also provided the lowest
single iteration NPV of any scenario examined (-
$516,700). While Scenarios RS and RB first sprayed
approximately the same number of sections per year
as their counterpart CG strategies, fewer sections
were resprayed or burnt, presumably because of the
decreased equity position and fewer number of
years in operation.

The pre- and post-burn deferment proved to be a
detrimental factor in the economic success of the
spray-burn scenarios. Because of the smaller herd
size operated (i.e., lower deferment bill) under the

DG strategy, Scenario DB was more profitable than
Scenario DS. As the number of cows operated
increased, i.e., under the CG and RG strategies, the
economic advantages shifted toward the spray scen-
arios with the difference in NPV’s between the spray
and spray-burn alternatives increasing with the
number of cows operated.

Evaluation Using Stochastic Dominance

Cumulative probability distributions of ending
NPV’s for each scenario (Table 5) were compared
using stochastic dominance with respect to a function.
Absolute risk aversion intervals of -.00001 to 0, 0 to
.00001, and -.00001 to .00001 were used to distinguish
producers who are risk loving, risk averse, and risk
neutral, respectively.

Cumulative probability distributions of ending NPV
for all nine scenarios are plotted in Figure 5. The
distributions for Scenarios CS and CB clearly domin-
ated (i.e., were always preferred by all risk aversion
groups) all other distributions because they were
always below and to the right. Scenarios RS and RB
always dominated the scenarios associated with no
brush treatment and those associated with the DG
grazing strategy. The distribution for Scenario DN
was dominated by all other scenarios. While NPV
distributions for Scenarios DN, DS, DB, CN, andRN
followed each other closely up to the 0.5 probability
level, a distinct branching was obtained afterwards.
After separating, these five scenarios were ordered
roughly based on the number of cows they operated,
except for Scenario RN, which had the highest fixed
grazing system costs. The ordering of all distributions
from right to left at the 1.0 probability level, was
identical to ordering the scenarios by their average
NPV.

The preference ordering of the nine scenarios for
each risk aversion group is summarized in Table 6.
For a risk loving rancher, the strategies could be
ordered by second degree stochastic dominance
because a clear preference was indicated by all risk
lovers. This ordering was the same as would have
occurred from ranking the scenarios by their average
NPV’s.

The ordering of scenarios was identical for risk
neutral and risk loving ranchers. Their most efficient
sets were basically the same as the risk loving
producer's, except that Scenario CS and Scenario CB
were both included in their most efficient set. Both
these CG strategies engaged in mesquite control,
and while Scenario CS had the higher average NPV,
it also had a higher probability of lower returns and
thus did not dominate Scenario CB.

Scenarios CN, DS, and DB were also equally
preferred under the risk averse and risk neutral
ranges given. These scenarios were able to be ordered
by the risk loving rancher because of the higher

11

Table 5. Selected statistics for the Conventional (CG), Deferred (DG), and Rotational (RG)
Grazing Systems under the nine scenarios examined.a
Scenario
CN CS CB DN ' DS DB RN RS RB

Probability

of Survival 24.0 90.0 93.0 0.0 38.0 43.0 5.0 81.0 76.0

Probability

of Success 26.0 90.0 92.0 0.0 38.0 43.0 5.0 81.0 76.0

Net Present Value ($1000)

Mean -138.66 976.55 909.67 -327.82 -64.14 -21.06 -230.30 626.37 488.81

Std. Dev. b 192.86 512.26 461.06 65.14 324.39 382.16 133.77 533.46 522.46

Coef. Var. -139.09 52.46 50.68 -19.87 -505.73 -1,814.95 -58.09 85.17 106.88

Minimum -432.53 -387.25 -332.51 -498.58 -432.92 -509.09 -433.70 -516.70 -500.24

Maximum 350.85 1,857.94 1,577.90 -96.56 751.66 983.94 218.69 1,439.33 1,433.94

P.V. of Ending Net Worth ($1000)

Mean 80.75 876.19 843.36 40.72 159.72" 201.46 14.58 634.64 539.40
4 Std. Dev. 119.25 355.92 325.39 67.42 217.52 253.10 89.53 394.89 383.79

Coef. Var. 147.68 ' 40.62 38.58 165.56 136.19 125.64 614.15 62.22 71.15

Minimum -114.72 -80.16 -68.42 -141.62 -118.31 -149.95 -145.27 -203.76 -213.75

Maximum 405.80 1,553.68 1,325.93 163.90 731.97 913.65 286.09 1,218.77 1,223.99

Number of Cows

Mean 477.0 662.0 663.0 420.0 500.0 513.0 593.0 790.0 790.0

Std. Dev. 55.8 111.6 108.3 17.6 74.7 86.8 63.0 156.9 160.4

-Coef. Var. 11.7 16.9 16.3 4.2 14.9 16.9 11.4 19.9 4 20.3

Minimum 354.0 388.0 396.0 369.0 379.0 375.0 393.0 450.0 . 427.0

Maximum 633.0 1,004.0 983.0 450.0 707-0 734.0 719.0 1,281.0 1,281.0

12

aCN=CG system with no brush control, CS=CG system with spraying, CB=CG system with spray-burn.
DN=DG system with no brush control, DS=DG system with spraying, DB=DG system with spray-burn.
RN=RG system with no brush control, RS=RG system with spraying, RB=RG system with spray-burn.

bCoefficient of variation is expressed as a percentage.

probability of receiving a big payoff, regardless of

the increased variation

Summary

Uncertain forage production created by variation
in climatic conditions and encroachment of un-
desirable brush species provide much of the business
risk facing range livestock producers. This study
focused on the evaluation of range improvement
techniques which may decrease economic losses
occurring from operating in this complex and un-
certain environment. The investment alternatives in
question were implementation of grazing systems
and control of mesquite infestations.

For the representative ranch, results showed that it
was economically prudent to control mesquite in-
festations. All three grazing systems studied obtained
negative average net present values under the no
brush control options. The increased productive
capacity obtained from mesquite control increased

both the NPV and ENW for each grazing strategy,
while decreasing the relative variance of both eco-
nomic measures. Probabilities of success and survival
were also increased when mesquite control was
undertaken.

Spraying mesquite-infested land returned the
highest NPV’s for the CG and RC] strategies. The
deferment seemed to be a detrimental factor for the
burn options, especially for the grazing strategies
with high stocking rates.

Holding brush control practices constant, it was
not profitable to alter cattle production by deviating
from the CG strategy. When the representative ranch
was changed to a DG grazing strategy, it suffered
disastrous financial results and obtained the lowest
average NPV of all scenarios. The increased per-
formance per animal unit could not compensate
financially for the decrease in total numbers. Com-
bining brush control practices with the DG strategy
increased the average NPV and ending net worth
above those obtained by Scenario CN, but these

1.01
4
0.9-
0.8<
0.7-
P 0.6-
H
C
B 4
R
B 0.5-
I
l- .
I _ e
T ,
YUJ-l" I. _;‘
0.:-+ if
Y Legend: 1 I Scenario CN
i 2 I Scenario CS
J 3 I Scenario CB
0.2 4 I Scenario DN
5 I Scenario DS
1 qr 6 I Scenario DB
Y 7 I Scenario RN
0 1 _ a 8 I Scenario RS
' 9 I Scenario RB
0.0-i_ _ _f_ _ Y V v
-1000000 C 1000000 2000000

NET PHESENT VRLUE

Figure 5. Cumulative probability distributions for net present values for the nine range

improvement scenarios.

scenarios were still unable to obtain an average NPV
_ _ _ I _ or build on beginning net worth.
Table 6. Preference ordering by risk aversion intervals for the nine
range improvement scenarios examine

Increasing stocking rates by investing in a RG

Rank, L,‘ Averseb Risk Neutral Risk Levin system was more economically viable than divesting
in cows for a DG strategy, but was not as profitable as
1st Most Preferred CS, CB CS, CB CS . . . h d .  b h
2nd Mos. Pmfened RS Rs CB maintaining t e CG system un er simi ar rus
jig :32: gjijjijg 0N,  DB 6N,  DB  control techniques. The increased number of cows
5th More Preferred RN RN DB did not compensate for the increased debt or
6th Most Preferred DN DN DS d d f - I - B f
m, Mos, pmfened CN ecrease per ormance per anima unit. ecause o
gt“ "m Pmerre“ R“ the increased available debt incurred from esta-
th Most Preferred DN bl‘ h'ng the RG s stern less capital emaned a ailable
IS i y , r I v
aScenarios are the same as defined in Table 3. to invest in brush control-
bRisk aversion coefficients were: —0.00001 to 0.0 for risloloving, 0.0 AS  rnost Comparative analysis 0f range improve-
to 0.00001 for risk averse, and -0.00001 to 0.00001 for risk neutral.

ment methods, results are applicable only to the area

‘l3

14

under study because of the differences in climate,
soil, and vegetation. Caution should also be taken
when interpolating the results of this study to
individual ranch situations. While conditions repre-
sentative of the Eastern Rolling Plains area were
utilized for this study, they individually and col-
lectively are not identical to any of the actual ranches
in the area. The assumptions made for obtaining the
production responses of the individual grazing
systems and mesquite control practices will vary
immensely as the designated climate, soil, and
vegetation differ. The results are also sensitive to the
assumed economic conditions which may occur
during the life of these investments. While the results
may not be applicable to all situations, the meth-
odology used to quantify the risks inherent in range
livestock production should prove helpful and trans-
ferable to similar studies.

References

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15

Appendix 1

Annual interest rates, inflation rates, and self-employment tax rates for 1987-2006.

1987 1988 1989 1990 1991 1992 1993 1994 1995 1996

Annual Interest Rates (fractions)

Long-term Loans 0.131 0.141 0.156 0.172 0.172 0.172 0.172 0.172 0.172 0.172
Intermediate-term Loans 0.127 0.134 0.139 0.154 0.154 0.154 0.154 0.154 0.154 0.154
Received for Cash Reserves 0.087 0.094 0.099 0.114 0.114 0.114 0.114 0.114 0.114 0.114

Annual Fractional Change in Prices (fractions)

New Farm Machinery 0.033 0.040 0.053 0.065 0.065 0.065 0.065 0.065 0.065 0.065
Used Farm Machinery -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040
Fixed Costs, Insurance 0.043 0.049 0.055 0.060 0.060 0.060 0.060 0.060 0.060 0.060
Chemicals 0.112 0.015 0.034 0.069 0.069 0.069 0.069 0.069 0.069 0.069
Fuel 6 Lube Costs 0.040 0.045 0.055 0.069 0.069 0.069 0.069 0.069 0.069 0.069
Repairs on Machinery 0.043 0.049 0.055 0.060 0.060 0.060 0.060 0.060 0.060 0.060
Other Production Cost 0.043 0.049 0.055 0.060 0.060 0.060 0.06077 0.060 0.060 0.060
Labor Costs 0.054 0.069 0.086 0.108 0.108 0.108 0.108 0.108 0.108 0.108
Purchase Livestock Inputs -0.024 0.016 0.047 0.076 0.076 0.076 0.076 0.076 0.076 0.076
Farmland Values 0.027 0.026 0.030 0.036 0.036 0.036 0.036 0.036 0.036 0.036

Consumer Price Index and Self-Eggloymgnt Tax Rates

Consumer Price Index 312.9 328.2 346.3 367.1 389.1 412.5 437.2 463.5 491.3 520.7
Self-Employment Tax Rate .1302 .1302 .1530 .1530 .1530 .1530 .1530 .1530 .1530 .1530
Maximum Income Subject to

Self Employment Tax ($) 43218.0 44016.0 46441.0 49274.0 52231.0 55364.0 58686.0 62208.0 65940.0 69896.0

16

Appendix 2

To illustrate the method used, assume quarterly
precipitation data is to be stochastically generated
and then aggregated into various production periods
beginning with Quarter 3 in the previous year and
going through the first three quarters in the current
year (e.g., Qg + Qk + Q1 + Q2 + Q3, with L
signifying precipation lagged 1 year). The 6x6 upper
triangular correlation matrix of Q1, Q2, Q3, Q4, Qg»
Qi- would normally be factored into a unique upper
right triangular matrix via the “square root method”
and multiplied by a vector of random normal deviates
"d "to obtain the vector of correlated random normal
deviates"c"ais =

(1) "OH-i
¢2t
¢3t z
¢4t
¢5t
L¢6r_
'11 '12 '13 '14 '15 '16‘ 111,1
'22 '23 '24 '25 '26 d2,
'33 '34 '35 '36 * d3t
'44 '45 .r46 d4t
r55 r56 dst \
l. '66_ Ld6t_

where t = the current year.

The correlated random normal deviate used to
determine Q4t, with t=1, would be calculated as

6
(2) C41 =2 f4j * 
i=1

In year two, 94'} would be determined by c52
as

6
 C62 =2  * 
i=1

Because QL = Q41, it follows that e52 = c41.
Therefore, sustituting c41 for c52 gives

(4) ¢41=§ r6i*dj2
i=1
='66*d62,

with

(5) d62 = ¢41/ '66-

Thus the random normal deviate d52 needed to
assure that c52 is defined so that Q41 = 0&2 can be

determined by using c41.
Using the same logic, Q31 ___ QL impnes c =
.   32 31
c52. Solving for d52 we get:

6
(6) C31 =2 r54 * djz.
i=1
='55 * d52 t '56 * d5;
with
l7) d52 = '31 - '56 * d62/ '55-
Therefore, instead of all normal deviates being

randomly drawn, d5t and d5t are calculated con-
ditional upon the correlated deviates obtained for

c3t_1 and c4t_1 to have Qi-Z = Q41 and Qgz = Q31.
At the beginning of each iteration (year 1), initial

values are given to d62 and d52 to start each iteration
at the same point.

17

18

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All programs and information of The Texas Agricultural Experiment Station are available to everyone without regard to race, color, religion,
sex, age, handicap, or national origin.

Mention of a trademark or a proprietary product does not constitute a guarantee or a warranty of the product by The Texas Agricultural
Experiment Station and does not imply its approval to the exclusion of other products that also may be suitable.

1.4M—7-89