.--—' —n ~c‘a-

'.~"'s I" )3)“ "‘ A
A --

_- ' ‘ " ‘52:]
EIBRARY ‘r
Michigan State

I I“;‘1afc‘.m _

.---1

I]

      

This is to certify that the
thesis entitled
Capital Budgeting Formulas For Determining

Land Values With Programs For Hand—Held
Calculators

presented by

Ghanbar Kooti

has been accepted towards fulfillment
of the requirements for

M. S. degree in Ag. Economics

oéw» Mp

Lindon J. Robison

 

 

 

Major professor

Date May 1, 1980

 

0-7 639

CAPITAL BUDGETING FORMULAS FOR
DETERMINING LAND VALUES WITH
PROGRAMS FOR HAND-HELD CALCULATORS

By
Ghanbar Kooti

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Economics

1980

 

ACKNOWLEDGEMENTS

The author wishes to express his appreciation to
Dr. Lindon J. Robison, the Chairman of his Guidance Com—
mittee, for guidance, constructive criticisms and helpful
suggestions during the development of this research. Ap-
preciation is also extended to other members of the com-
mittee, Dr. Stive Harsh and Dr. Gerald Schwab who read
and made many helpful comments on the thesis. In addi-
tion, the author would like to express his thanks to Dr.
Anthony Koo who served as a member of the committee.

I would especially like to express my appreciation
to my girlfriend Lisa Gilbert for making the time spent
on this study as pleasant as it was. I would also like
to extend my appreciation to Sheryl McBride for her help

in editing the thesis.

 

 

TABLE OF CONTENTS (Cont'd)

Chapter Page
Subtracting the Cost of Risk. . . . 55
Sensitivity Analysis. . . . . . . . 60
Chapter Summary . . . . 63

VI. ABSOLUTE RISK AVERSION OBTAINED USING
TRIANGULAR DISTRIBUTION FUNCTION. . . 64

VII. PREDICTABILITY COMPARISON AND CON—

CLUSION . . . . . . . . . . . . . . 70

Comparing the Predictability of the
Models. . . . . 70
Summary and Conclusion. . . . . . . 72
APPENDIX . . . . . . . . . . . . . . . . . . . . 77

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . 98

ii

Figure

LIST OF FIGURES

Historical Index of Farm Real Estate
Value Per Acre and Percent Change
in Per Acre Value From Previous
Year.

Constant Payment Plan and Constant
Payment on Principal Plan

Equilibrium Between an EV Efficient
Set and a Decision Maker's Iso-
Expected Utility Function

Triangular Distribution Function.

iv

Page

40

56
64

CHAPTER I

INTRODUCTION

A REVIEW OF CHANGES IN LAND VALUES

The price of farm products rose from an index of
100 in 1914 to a peak of 225 in early 1920. They then
started to decline to an index of 124 in 1921. High farm
product prices during World War I, along with savings accum—
ulated by farmers in the form of Liberty Bonds and other
liquid assets, started a land boom in 1916 which lasted
through 1920 and raised land prices by 56 percent during
that period. After the four year boom, a decline began
that continued until 1933.

With the advent of World War II, agricultural com—
modity prices again increased dramatically. Then, like
the period from 1916 to 1920, they were followed by in—
creases in land values. During the years 1946, 1947 and

1948 land values increased by 13, 12 and 8 percent re-

spectively (U.S. Bureau of Census, U.S.D.A.zai

Two inflationary influences were largely respon-
sible for land price increases. The first was high
levels of domestic employment and income. The second was
an abnormally large foreign demand for United States agri-
cultural commodities, because of shortages brought about
by World War II and devastating droughts in the Southern
Hemisphere in 1945. These pressures on food production
along with large amounts of liquid funds accumulated in
the hands of farmers and non-farmers were translated into
increased demand for farmland.

It is interesting to note the similarity of conditions
that pushed up land values from 1916 to 1920 and in the
1940's. In both cases, increased farm commodity prices
and liquid funds in the hands of prospective purchasers
led to increased demand for land.

After the second major boom in land prices, which
peaked in 1949, income began to decline and land buyers
became more cautious. Land values continued to rise, but
at slower rates through the 1950's, except for a brief
period from 1953 to 1954.

During the early 1950's there were two important
developments which greatly influenced the farmland market
during the 1960's and 1970's. A revised price support

program was instituted which assured farmers minimum prices

for their products and reduced the risk of loss due to low
commodity prices. The second development was farm enlarge—
ments. Modern agricultural technology created situations
in which existing farm operations were deficient in land,
in relation to other farm inputs such as labor and capital.
To take advantage of economies of scale created by the new
technology, farm sizes had to increase. As a result, most
land purchases were for expansion purposes which, with price
supports, led to continued strong demand for farmland and
higher land prices. Beginning in 1972, land prices in—
creased more rapidly than in earlier periods. Because;
there was a large increase in foreign demand for american
food products; deficit spending by the federal government

led to inflation reflected in rising land values.

Figure 1 illustrates the historical pattern.

Factors Affecting the Price of Farmland

In this section several important variables which
affect the supply and demand of farmland are discussed.
First, the factors affecting supply will be considered.

The price at which farmland owners offer land for sale

is influenced by such seller characteristics as his
occupation, age and income. Colyer found that sellers who
are farmers, laborers, or retirees at the time of the land
sale tended to receive more per acre than those in other
occupations.

Colyer also found a positive relationship between
seller's income and the price per acre of land, possibly
because sellers with greater income have fewer economic
pressures and can bargain for a higher price per acre
than those who sell because they need the money.

0n the demand side, the expansion buyer has been
responsible for an increasingly large percentage of farm
sales. In 1977, these buyers purchased about 63 percent
of all farms transferred (U.S.D.A.lo). In most cases,an expan—
sion buyer is receiving above average net rent on acreage
he already owns. Therefore, he can often afford to pay
a higher than average price for additional farmland.

When technology creates a situation in which a farm
operation becomes land deficient in relation to other
inputs such as labor and machinery, the farmer needs to
increase the land input. Thus, it may be economically
feasible for him, if necessary, to pay a higher than
average price for land to increase the total land input
of the farm and spread his fixed costs over a larger land

area, while increasing only certain variable inputs,

 

his land becomes available. Thus, with an almost
constant supply of land, it may be assumed that price

changes are caused by shifts in demand for land.

Statement of the Problem

The question of how to determine the price of land
has received considerable attention (Boxley, Harris and
Nehring, Lee and Rask). Much of the interest in assessing
the value of land has been for taxation and mortgage
purposes. The old method for calculating'fluaprice of land,
called the capitalization formula, suggested that land
prices could be determined by dividing the average net
after-tax income per acre by the discount rate or return
from the next best alternative. For example, if after—tax
net return from land is $50.00 per acre and the rate of
return on the best alternative is 10 percent, dividing
$50.00 by .10 would price the land at $500.00 an acre.

The formula, unfortunately, has become hopelessly
outdated, yet it continues in use for lack of accurate and
easy to apply alternatives. It is outdated because it
assumes constant income from land and that land will be
valued the same after some planning period as it was at
the beginning. Historical data indicates that neither

land values nor income to land have remained the same.

 

 

10

During the last ten years land values have increased at
an average rate of 9.5 percent while income to land has
increased at an average annual rate of 7 percent. There—
fore, if the capitalization formula were to be used to
estimate land values using today's earnings, they would

likely fall below current land prices.

Purpose of the Study

It is the intent of this study to find more accurate
capitalization formulas to determine land values which
include changes in income attributed to land, capital
gains, variability of income, decision maker's attitudes
toward risk, available financing, and tax rates. In add-
ition to determining improved capitalization formulas,
this study also adapts the formulas for use with hand-
held calculators. That is, all of the models to be
developed will be programmed for use with the Texas

Instruments (TI-59) hand-held computer.

Objectives

More specifically, the objectives of this study are
as follows:
I. To develop an improved capital budgeting
formula to include such important variables
as inflation rates, time preference rates,

productivity changes of farmland, cost of

14

The technique of discounting is used to evaluate invest-
ments which generate a stream of income over time. That
is, for an investment to be made, the value paid for such
investment should be less than or equal to the present
value of the stream of income generated from the investment
in the future.

The purpose of this chapter is to review formulas and

methods for valuing assets that generate returns over time.

Valuing Assets Which Produce Returns Over Time

An investment project, such as the purchase of farm-
land, generates a stream of income over future time periods.
The value of these future returns may be converted to cur—
rent dollar values through discounting, so that the future
income stream can be compared to the cost in current
dollars of the investment. Thus the first step is to esti-
mate the income from the investment in each period and
convert this to current dollar equivalents. Let Ri denote
net income in the i—th time period. Three approaches can
be used to estimate the income attributed to an investment
in land. These three approaches are the landlord method,
the residual method, and the pro—rata share method.

The landlord method involves an estimation of the
income stream (R) to farmland based on the net rental

payments received by the landlord for the use of his farm—

15

land. Where land is rented and the rental fee is known,

as well as the costs associated with land ownership (such
as taxes), the net income stream to the landlord is also

the return on land.

For the residual approach, consider Table 1 which
illustrates net income for a typical corn grain farm which
yields an average of 85 bushels an acre. The income from
the land is the income earned from the sale of the corn
grain or its equivalent value if the grain is used on the
farm. From this gross income, we subtract all the operating
expenses associated with growing the corn, including seed,
fertilizer, fuel for machines, labor, interest charged on
short-term debt, herbicides and insecticides and taxes.
The difference between the gross income and farm operating
expenses equals net income-—the income expected from the

land purchase (Huff).

__ _..h.._,1 “ a.

16

TABLE 1: Enterprise Budget for One Acre of Medium—Yield
Corn Grain

 

 

 

 

GROSS INCOME $191.25
(85 bu. X $2.25)
EXPENSES:
Labor (6.1 hrs. X $5.50) $ 33.44
Repairs and Maintenance 9.80
Seeds 11.33
Fertilizer 38.25
Insecticides and Herbicides 12.40
Fuel 6.00
Utilities 2.30
Harvesting, Trucking 6.20
Corn Drying 14.00
Other Expenses (including
interest on operating debt) $ 7.53
$141.25
NET INCOME (Gross Income — Expenses) $ 50.00
Source: Lindon Robison, ”The_Effect of Financial
Arrangements on the Maximum Biderice’for
Lgng". Paper presented at the Department of

Agricultural Economics, Michigan State
University, Oct. 24, 1979

17

The pro-rata share method involves estimating the
marginal value productivity for farmland, labor and capital.
This method requires that the total output be apportioned
among the inputs based on their productivity assuming the
capital as the total expense.

The difficulty, of course, is in determining the
marginal product of land. Euler's theorem directs that,
for homogeneous production functions of degree one, output
can be apportioned among the inputs by multiplying the
marginal product of each by the amounts of the input used
in the production process.

After having determined the income to land, we next
find its present value. To do so, we discount by the
opportunity cost of capital.

Consider an investment (an asset purchase) that
generates returns R in each of n future time periods.
Futhermore, assume that the opportunity cost of capital is r
and denote the asset's beginning and terminal value as V.
The present value of the investment can be written:

(11.1) v = R/(1+r) +.... + R/(1+r)n + V/(l+r)n.

That is, the assets' beginning value is equal to the
discounted present value of the income it produces, plus
its discounted salvage value. The value of the discounted
income alone can be written as:

(11.2) s = R/(1+r) + .... + R/(1+r)n

18

and after multiplying by (1+r) and sutracting from the
results , it can be written:
(11.3) S = R(1-(1+r)“n)/r.
Next, substituting into (II.1) for the discounted income gives:
(11.4) v = R(1-(1+r)‘n)/r + V/(l+r)n.
Then solving for V, by subtracting V/(1+r)n from both sides
of (II.4), we can write:
(11.5) v = R/r.
That is, V depends only on the discount rate r and net income
R.

Corsider now the effect of taxes on land values.
Taxes affect both income and the cost of capital. Tax
rates appear both in the numerator and in the denominator
of the capital budgeting formula. If we let t be the tax
rate on income, the land price V can be determined as the
following:
(11.6) v = R(1-t)/(1+r(l-t)) + .... + R(1-t)/(1+r(1-t))n +

V/(1+r(l-t))n.

Using the same method as was used to obtain (II.3), the
discounted income accounting for taxes can be written as:
(11.7) s = R t1—(1+r(1—t))'n J/r
Next, substituting into (II.6) for the discounted income
and solving for V by subtracting V/(1+r(1-t))n from
both sides of the equation, we can write:

(11.8) v = R/r.

19

This model which is the same one obtained in (II.5), we
refer to as the Basic Capital Budgeting (BCB) model.

This formula provides an accurate estimation only if
the following conditions are met:

1) The investment is expected to produce the same
annual net rent over time; that is, no inflation.

2) The capitalization rate used to discount future
net rent remains constant.

This model is examined using the net income to land
and the interest rate on mortgage loans (capitalization
rate for Michigan) Table 2 compares actual land prices
with those estimated using equation (II.8). Column 4 repre—
sents the estimated land values determined by R/r. This
estimate will be compared with the actual price of land
shown in the 5th column of the table. The differences
between columns 4 and 5 given in column 6 indicates the
accuracy of the BCB model.

The average error E was estimated by summing the
absolute differences between the predicted price of land
in the t-th year denoted P(t) and the actual value of land
in the t-th year denoted A(t). all divided by the number
of observations. That is:
(11.9) E =t§1| P(t)—A(t)| /n.
Where n is the number of observations.

The average error for this model was 91.50. This model

apparentLyunderestimates the price of land in periods

20

with high inflation rates. However, it performs better

in years with low inflation rates. That is, with inflation,
one assumption underlying the BCB model no longer holds

and as a result its accuracy is reduced.

Table 2 shows that neither net income to farmland,
nor the discount rate, which is approximated by the
intrest rate charged by the Federal Land Bank, are
constant. Thus violating both assumptions underlying the
BCB model.

To demonstrate that returns to farmland (R/fi is not a
constant r, the actual rate of return of the opportunity cost
of capital was calculated. Table 3 summarizes the results.
The estimated capitalization rate indicates that the assumption
of a fixed discount rate does not hold.

In the following chapter a more realistic model will
be derived to estimate land values which includes inflation
and productivity changes of farmland. This model will also be

tested for its ability to predict land values.

21

Table 2: Estimated Land Prices Obtained Using the BCB

 

 

 

model

Fed. Land Net Estimated Actual Estimated

Bank Int. Income Price of Price Minus

Rate 1/ to Land 2/ Land of Land Actual
Year % $/ac. $/ac. 3/ Price
1960 6.0 12.62 210.33 197.49 12.84
1961 5.6 12.46 222.50 207.73 14.77
1962 5.6 12.95 231.25 213.97 17.97
1963 5.6 13.04 232.85 209 85 23.00
1964 5.5 13.27 241.27 220.36 20.91
1965 5.5 13.88 252.36 230.36 22.00
1966 5.8 15.01 258.62 257.04 1.58
1967 6.0 17.16 286.00 273-59 12.41
1968 6.7 18.04 268.66 330.10 -61.44
1969 7.7 18.48 240.00 315-35 —75-35
1970 8.7 15.58 179.08 290.07 —110.99
1971 7.9 19.90 251.90 319-36 —67.46
1972 7.4 19.61 265.00 344-84 -79.84
1973 7.5 20.17 268.93 416.62 —147.69
1974 8.1 25.89 319.63 “86-00 -166 37
1975 8.7 28.03 322.18 552.00 -229.82
1976 8.7 30.72 353.10 617.00 -263.90
1977 8.4 36.81 438.21 757.00 —318.79

 

Average Error, E = 91.50

1. Source: Lindon Robison and David J. Leatham, "Intrest Rates
Charged and Amounts Loaned by Major Farm Real
Estate Lenders", Agricultural Economics Research,
vol. 30, no. 2, April, 1978, Table 5.

 

22

Source: Ralph Hepp, Michigan Agricultural Data,
Department of Agricultural Economics, M.S.U.

Source: Michigan Department of Agriculture, Michigan
Agricultural Statistics, 1978.

23

TABLE 3: Estimated Opportunity Cost of Capital Obtained
by Dividing Net Return to Land by Actual Land
Values (R/V) 1/

 

 

 

Opportunity Opportunity
Year COSt % Year COSt %
1960 6.40 1969 5.90
1961 6.00 1970 5.40
1962 6.00 1971 6.30
1963 6.20 1972 5.70
1964 6.00 1973 4.80
1965 6.00 1974 5.30
1966 5.80 1975 5.00
1967 6.30 1976 5.00
1968 5.45 1977 4.80

 

The Average Opportunity Cost for the 18 year Period is 5.67%
1/ Net returns to land and actual land values are those

reported in Table 2.

24

CHAPTER III

THE EFFECT OF INFLATION AND
PRODUCTIVITY CHANGES ON LAND PRICES

The BCB model, explained in Chapter II, shows that the
price of land can be estimated by dividing net returns to
land R by the discount rate r. However, if r is the oppor-
tunity cost of capital, then it has been changing. To
understand why it is changing, consider it being composed
of two parts: the time preference rate denoted r*, and the
inflation rate denoted i.

The rate of return required to induce savers to post—
pone consumption, assuming constant prices, is the time
preference rate which is sometimes referred to as the real
rate of return. This is usually assumed to be constant
over time. For the BCB model to be valid, the opportunity
cost must equal the constant time preference rate. The
second part is the inflation rate, a rate of return that
savers must receive in addition tothe time preference rate
to compensate them for losses of purchasing power due to
increased prices. Inflation means that the purchasing power
of the dollar declines. Dollars received one year from now
are not as valuable as current dollar because prices will
have increased and dollars at the end of a year cannot buy

as much as the dollar expended today. Thus savers demand

25

higher returns, and if inflation changes, so will the
oppertunity cost on investments, i.e. r* will change.

Inflation may be introduced into the BCB model by
assuming that expected net returns to land and the discount
rate increase by the same inflation rate. If the net returns
to land increase by the rate of inflation then the net income
to land in the first period becomes R(1+i) where i is the
inflation rate, and in the n'th period equals R(1+i)n.
Meanwhile, the discount rate which also is increased by the
inflation rate equals (1+r*) (1+i) in the first period and
in the n’th period equals (1+r*)n (1+i)n. Thus, the value
of a capital asset V with inflation rate i can be written as:
(111 1.) v = R<1+i)/(1+i)(1+r*) +...+ R(1+i)n/(1+i)n(1+r*)n

+ V(1+i)n/(l'+r*)n(1+i)n

Note that the inflationary impact on income and on the
discount rate cancel so that we can write:
(111 2.) v = R/(1+r*) +...+ R/(1+r*)n + Vt/(1+r*)n

This, however, is the BCB model except in place of the
opportunity cost of capital r, we have r* the time preference
rate. Hence, the value of an asset under inflation is the
current year's income divided by the time preference rate r*:
(111 3.) v = R/r*

It is obvious that inflation affects the purchase price
of land only as it affects current income. The formula R/r*

is used to estimate land value V given actual values for net

26

income to land R and the rate of pure time preference r*.
Moreover, returns R divided by V should equal r*. Thus,

Table 3 was, in essence an estimate of r*, equal to an
average of 5.67 percent and if the marginal tax rate were .25,
r*(1-t) equaled 4.25.

In Table 4 actualland prices are compared with those
estimated using equation III.3 with r* = 5.67. Column 2
reports the estimated land values determined by the formula
R/r*. This estimated value compares with the actual value

of land for the period 1960—1977 reported in column 3.

27

Table 4: Estimated Land Prices Obtained Using the Model
with r* Equal to 5.67%.

 

 

 

Estimated Actual Estimated

Value of Value of Minus

Land Land Actual Price
Year $/ac. $/aC- 1/ $/ac.
1960 222.96 197.49 25.47
1961 220.14 207.73 12.41
1962 228.80 213.97 14.83
1963 230.39 209.85 20.54
1964 234.03 220.91 13.12
1965 244.80 230.36 14.44
1966 264.73 257.04 7.69
1967 302.64 273.59 29.05
1968 318.17 330.10 —11.93
1969 325.93 315.35 10.58
1970 274.78 290.07 -15.29
1971 350.97 319.36 31.61
1972 345.86 344.84 1.02
1973 355.73 416.62 ~60.89
1974 456.61 482.00 -29.39
1975 494.37 552.00 —57.63
1976 541.80 617.00 -73.20
1977 650.00 757.00 —107.00

 

Average Error, E = 29.90

1. Source: From Table 2.

28

We now introduce productivity changes into the BCB
model. The BCB model ignores the effects of productivity
changes in land which alter income streams and land values.
If land becomes more productive by the use of technologies
such as new seed varieties, insecticides and fertilizers, they
can be expected to increase the net returns to land. There—
fore the productivity of farmland will affect land prices.
An increase in the productivity of land will also explain why
farmers accept a lower rate of return on farm real estate
investments, than on nonagricultural investments.

The question now is how does changes in productivity of
land affect the purchase price of land. Changes in the
productivity of land can be positive, zero, or negative. If
we assume positive productivity changes in land over time
then the net income to land will increase by the rate of the
productivity increase. That is, the net income to land in
the first period will be R(1+g), where g is the productivity
change)and in the n-th period net income will equal R(1+g)n.
Assuming the price of land also increases at rate g, we can
write the value of land Vg with productivity changes as:
(III. 4) Vg = R(1+g)/(1+r*) +-.-+ R(1+g)n/(1+r*)n +

V (1+g)n/(1+r*)n

8

and solving for V as it was done before gives:

8
(III. 5) Vg = R(1+g)/(r*-g)

For purposes of comparison, the above model was used

29

to estimate the land values given the actual data for net
income to land, length of planning period, and productivity
changes of farm land. Productivity changes were obtained

from U. S. D. A. compiled statistics (see U. S. D. A., c, 1978)
Table 5 compares actual values of farmland with those esti-
mated by equation (III. 5) given an estimate of g equal to

the average productivity changes during the previous three
years. Given g, net returns R and land value V, a new average
for r* was obtained equal to 7.5 percent. Then using (III. 5)
estimated values of Vg obtained with an average error of

105.00.

30

Table 5: Estimated Price of Land by Equation (III-5).

 

 

 

Productivity Estimated Actual Estimated

Changes Price of Price of Price Minus

% 1/ 2/ Land Land 3/ Actual Price
Year $/ac. $/ac. $
1960 3.90 364.00 197.49 166.51
1961 5-07 538-75 207.73 331-02
1962 2.30 255.00 213.97 41.03
1963 3.80 365.82 209.85 155.97
1964 2.50 272.00 220.91 51.10
1965 1.10 219.00 230.36 —11.36
1966 1.77 266.60 257.04 9.56
1967 0.07 231.00 273.59 —42.59
1968 1.73 318.00 330.10 -12.10
1969 1.67 322.00 315.35 6.65
1970 3.00 356.60 290.07 66.53
1971 1.40 330.80 319.36 11.44
1972 2.27 383.00 344.84 38.16
1973 2.83 444.00 416.62 27.38
1974 3.80 726.00 486.00 240.00
1975 —2.10 285.85 552.00 —266.15
1976 —0.43 386.00 617.00 —231.00
1977 1.06 577.50 757.00 ~179.50

 

Average Error, E = 105.00

1. Source: U. S. D. A., "Changes in Farm Production and
Efficiency 1977", Economic Statistics, and
Cooperative Service. Statistical Bulletine
no. 612.

2. Productivity changes for each period as reported in
Column 2 of this table is estimated as equal to the
average productivity changes for the previous three years.

3. Source: From Table 2.

31

The average error of Table 5 is greater than the average
error without productivity gains suggests that either (1) the
model incorrectly incorporates gains into the model or (2)
that the gains series reported by U. S. D. A. does not match
the actual gain incorporated by decision makers into their
land pricing model.

The later explanation seems more reasonable, because
the productivity changes series were fluctuating. Looking at
the net income to land series, it is obvious that the growth
in income was positive throughout the series with the
exception of 1970. To demonstrate that the productivity
change used in the study may not explain the growth rate in
income, a new productivity change were estimated given r* of
5.67, from Table 3. This was estimated by solving the
equation for g in (III. 5):

(111. 6) g = (r*.v-R)/(R+v)

Table 6 summarizes the results of equation (III. 6).

32

Table 6: Estimated Productivity Chan ' '
ges USlng E uatlon
(r*.V—R) / (R+V). q

 

 

 

Actual Actual Net Estimated
Land Income To Productivity
Year gaigésl/ Land 2/ Changes
1960 197.49 12.62 -.007
1961 207.73 12.46 —.003
1962 213.97 12.95 -.0036
1963 209.85 13.04 —.005
1964 220.91 13.27 —.003
1965 230.36 13.88 —.003
1966 257.04 15.01 -.001
1967 273.59 17.16 -.006
1968 330.10 18.04 .002
1969 315.35 18.48 —.002
1970 290.07 15.58 .003
1971 319-36 19-90 --005
1972 344.84 19.61 .000
1973 416.62 20.17 .008
1974 486.00 25.89 .003
1975 552.00 28.03 .006
1976 617.00 30.72 .007
1977 757.00 36.81 .008

 

1/ From Table 2

2/ From Table 2

33

The results of Table 6 indicate that productivity changes
are small, given a rate of time preference equal to 5.67
percent. It is obvious from Table 6 that the productivity
changes estimated are significantly different from those used
in estimating land vlaues reported in Table 5. In fact the
results reported in Table 6 indicate that productivity

changes are unimportant in estimating land values.

Chapter Summary

In this chapter, two factors beleived to be affecting
land prices were discussed. Those two factors were inflation
rate and productivity changes. Starting out with the BCB
model, changes were made to allow for inflation and produc-
.tivity changes. The final model (III. 5) showed that changes
in productivity affect land prices but did not improve our

ability to explain changes in land values.

34

CHAPTER IV

THE LEE-RASK MAXIMUM BID PRICE MODEL

The Importance of the Maximum Bid Price for Land:

Determining the maximum bid price is an important task
for a real estate buyer and his lender. It is important
because the opportunity to purchase a particular parcel of
land occurs infrequently and the number of farms being sold
has declined in recent years. Thus, if the buyer's bid
price is not close to the seller's asking price, another
buyer may acquire the real estate. On the other hand, a bid
price above what the real estate can repay may mean financial
difficulties for the buyer that may finally result in liqui-
dation of his entire assets.

The Effect of Financial Arrangments on the Maximum Bid Price:

Land purchases are usually financed with borrowed money.
A downpayment from 10 to 50 percent of the purchase price is
usually required: with the remaining amount paid over a num—
ber of years. Financial arrangements such as interest rates,
downpayments, and the length of the loan amortization period,
should be considered in evaluating the agricultural land values,
along with the marginal tax rate of income, a factor which is
often overlooked. Expected costs and returns will be reduced
by the amount of taxes. Historical data also indicate that

land prices continue to increase in the U.S. and that a

35

capital gain will be realized when the land is sold at the
end of the investment period.

Nevertheless, even when all of the above mentioned fac-
tors are included in determining the maximum bid price for
land, a purchase should only be made if the asking price is
not above the maximum bid price and the buyer can meet cash
flow requirements. These cash flow requirements are deter-
mined by constructing a cash flow statement.

Cash Flow Statements:

The major cash inflow associated with an investment in
agricultural land consists of annual net return to the land
(usually estimated from the rental rates on comparable land
in the area) and returns from selling land at the end of
the investment period. The cash outflow associated with an
investment consists ofthe required downpayment, principal
and interest payments on the mortgage loan, and income taxes.

Using the cash flow statement, the present value of the
projected after-tax net cash inflow from added land can be
compared to the initial cost outflow for purchase. In this
case, since the cash outflow for purchase is spread over
several years because of financing terms, the present value
of this cash flow must be measured and compared to the present
value of cash inflow arising from the land purchase.

In purchasing land by a loan there are at least two

alternative loan amortization methods.

35

capital gain will be realized when the land is sold at the
end of the investment period.

Nevertheless, even when all of the above mentioned fac-
tors are included in determining the maximum bid price for
land, a purchase should only be made if the asking price is
not above the maximum bid price and the buyer can meet cash
flow requirements. These cash flow requirements are deter-
mined by constructing a cash flow statement.

Cash Flow Statements:

The major cash inflow associated with an investment in
agricultural land consists of annual net return to the land
(usually estimated from the rental rates on comparable land
in the area) and returns from selling land at the end of
the investment period. The cash outflow associated with an
investment consists ofthe required downpayment, principal
and interest payments on the mortgage loan, and income taxes.

Using the cash flow statement, the present value of the
projected after—tax net cash inflow from added land can be
compared to the initial cost outflow for purchase. In this
case, since the cash outflow for purchase is spread over
several years because of financing terms, the present value
of this cash flow must be measured and compared to the present
value of cash inflow arising from the land purchase.

In purchasing land by a loan there are at least two

alternative loan amortization methods.

36

(1) Constant payment, where the total payment in each
period remains constant over the term of the loan,
with varing proportions allocated to interest and
principal as payments are made.

(2) Constant payment on the principal, in which an equal
payment in each period is made on the principal plus
a varying amount of interest. In both cases, inter—
est is calculated on the remaining balance.

The pattern of annual payments on a loan of $757 amortized
over 25 years will be compared using the constant payment and
the constant payment on principal methods of repayment. To
complete the example assume the loan is repaid over 25 years,
the borrower is in the 25 percent tax bracket, income in the
first year is $36.81 which increases at a rate of 5 percent
and that capital gains accure at 6 percent per year.

Notice that the total payments (principal and interest)
during the early years of the loan are lower for the constant
payment method. Beginning with the 9th year, however, pay—
ments become lower in the constant payment on the principal
method. Figure 2 shows the curvilinear and linear relation—
ships. The comparative results of the constant payment
method and the constant payment on principal method are shown
in Tables 7 and 8, respectively.

Although the length of time required to amortize the

loan is the same under both methods, the outstanding loan

37

balance for any particular year will be greater for the con-
stant payment method, as illustrated in Figure 2. Thus, the
total interest paid during the life of the loan will be greater
for the constant payment method. This method may seem less
attractive to cost—conscious farmers who are operating under
severe capital constraints. However, the higher payment obli-
gation during the early years using the constant payment on
the principal method reduces the amount of cash flow available
for other uses. It especially reduces the cash available for
servicing non real estate loand, and thus tends to reduce the
availability of such loans. a reduction in non realestate
credit may severely limit growth for expansion minded farmers.

The total interest will be less for shorter term loans.
However, the cash required each year to repay principal and
interest on the loan will be greater, thus adversely affect—
ing non realestate credit.

Table 7, column 9 shows the present value of net cash
flow for each period. The total present value of the net
cash flow over the amortization period is $29.66. Table 8,
column 9 shows the present value of net cash flow for each
period during the constant payment on the principal payment
method. The total present value of net cash flow over the
amortization period is $9.00. In both cases, the present
value of net cash flows are greater than zero, thus the land

purchase is profitable.

38

 

 

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Figure 2-a Constant Payment Plan.

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Figure 2-b Constant Payments on Principal Plan.

41

Effect of Capital Gains:

Equation (III. 3) demonstrates that inflation has no effect
on the discounted after—tax income associated with land: how—
ever, the capital gains associated with farmland will be
affected by the rate of inflation. Capital gain in farmland
accrues over time but is realized only when the asset is sold.

The question is how does inflation affect capital gains
and therefore the price of land. If the price of land in the
first period is V(o) and it increases by the rate of inflation,
then n periods later equals V(o)(1+i)n. If n is the planning
horizon, after—tax capital gain realized at the end of the
planning period is (V(o)(1+i)n — V(o))(1—t*), the difference
between the beginning and ending value of land where t* is
the tax rate applied to capital gains income. This value
should be discounted by the after—tax discount rate
[1+(i+r+ir)(i—t)] to determine its present value. Only if the
income tax rate was equal to the capital gains tax rate,
and the rate of increase in land prices equalled the rate of
increase in income from farmland, then equation (III.3)
correctly estimates land prices.

A Summary List of Factors Affecting Land Prices Include:

The factors influencing or determining the maximum bid
price for land include‘the following:

(1) the average price per acre of recent sales of

comparable parcels in the area.

(8)
(9)

(10)

(11)

42

the after-tax opportunity cost of capital.
the expected annual net cash income per acre
before taxes.

the expected annual rate of growth in annual
net cash income per acre.

the buyer's marginal income tax rate.
downpayment (the proportion of the purchase
price paid down).

the rate of interest charged on the mortgage
loan.

the amortization period on the loan.

the expected annual rate of inflation in land
values.

planning horizon, years.

the capital gains tax rate.

The first stepin.determining'uuemaximum'bid price for

land is to estimate the income to be earned from the land.

As mentioned earlier, there are at least two methods for

determining the net income to land. One is the rental

method where the annual net income to land equals the net

rent received bythe landlord minus his share of production

costs. In another approach, the residual method, net income

to land is calculated as a residual after subtracting the

operating expenses from the gross income of one acre of land.

The subtracted operating expenses include seed, fertilizer,

43

fuel for machines, labor, interest charged on short-term
loans, and herbicides and insecticides. As an example, a
sample budget is described in Table 1. In that budget after
subtracting operating expenses, net income to land equaled
$50-

The next step in determining the maximum bid price for
land is setting the planning horizon. The horizon should
at least equal the life of the mortgage loan and is important
because, as the length of the planning horizon increases, the
importance of income from the land also increases relative
to capital gains. Since the capital gains are realized at
the end of the planning period, the further away the end of
that period, the less important are the capital gains to be
realized. The converse is also true; the shorter the planning
period is, the more important are the capital gains.

The after—tax opportunity cost of capital is used to
convert future income to its equivalent value in the present.
The before—tax opportunity cost of capital is made up of two
parts, the rate of the pure time value of money and the ex-
pected rate of inflation. The rate of pure time preference
is the cost of postponing consumption. However, if prices
are increasing, as they are now, the saver must be compensated,
not only for his time preference rate, but also for the loss
of purchasing power. Thus income earned in all future time

periods is divided by or discounted by the discount rate which

44

includes both time preferences and inflation.

Next, the present value of future after-tax income should
be summed together with the present value of after-tax capital
gains income. The result is the return to land. A maximum
bid price is determined by equating the returns to land to the
cost of purchasing the land. The cost of the land purchase
is the downpayment plus the present value of the mortgage
loan payment minus the tax deductible interest payments.

Thus, the cost of acquiring land is: the downpayment plus the
remaining repayment due after the downpayment minus the interest
savings attributable to the interest deducted against income,
respectively.

The remaining portion of the model consists of two parts:
the discounted after-tax income and the capital gains which are
equated to the return. Lee and Rask have constructed a maximum
bid price model which includes all the factors discussed so
far. This model was used to predict the maximum bid price for
land in the period 1960—1977 given a downpayment required of
25 percent of the cost; a marginal tax rate on income of
25 percent, and a capital gain tax rate of 12.5 percent,

a planning horizon and amortization loan period of 20 years
while before tax opportunity cost of capital is assumed to be
equal to the interest rate on the mortgage loan.

Table 9: Summarizes the result of this model:

45

Table 9: Estimated the Maximun Bid Price for Land Using
the Lee and Rask Model: Assuming a 20 year
planning horizon and loan amortization period,
a 25 percent marginal tax rate, income from land
and price of comparable tracts reported in Table 2.
Interest rate of loan also reported in Table 2.

 

 

Growth Rate Opportunity Estimated Actual Estimated

 

 

of Income g Cost of Land Value Value Minus
and in Land Capital ;/ Values of Actual
Year Values 1/ % $/ac. Land Value
% $/ae.
1993 1-00 5-60 231.43 208.89 21.54
1964 1.23 5.50 249.50 220.36 29.1”
1965 2.17 5.50 295.82 230.36 65.45
1966 5.17 5.80 472.43 257.04 214.3
1967 7.60 6.00 719.10 273.59 445.51
1968 11.77 6.70 1222.00 330.10 891.90
1969 9-13 7-70 786-50 315-35 471-15
1970 7.26 15.58 466.22 290.07 176.22
1971 -2.70 7.90 177.18 319.36 —142.19
1972 4.90 7.40 486.10 344.84 141.26
1973 3.60 7.50 444.62 416.62 28.04
1974 9.80 8.10 1208.10 486.00 722.10
1975 9.90 8.70 1215.00 552.00 663.00
1976 13.00 8.70 2052.70 617.00 1435.70
1977 15.00 8.40 3839.70 757.00 3082.70
Average Error, E = 569.00
1. It is assumed that average growth rate in income equals

to average inflation rate in land values. The inflation
rate reported in this column is calculated as the aver—
age growth rate in the previous three years net income
to land for each period.

2. Source: From Table 2, Column 2.

46

To calculate land values using the Lee and Rask model,
this author wrote a program for the Texas Instruments (TI—59)
programmable calculator (for details refer to Appendix A,
Table A:1). This program estimates the maximum bid price for
land, annual loan payment, unpaid balance remaining on loan
in any year, net cash flow in any period, market value of the
land and equity, given the variables discussed earlier. To
test the sensitivity of the program, a sample problem was

first solved with input data equal to:

(1) Income growth rate of 8 percent.
(2) Before-tax opportunity cost of capital of
11 percent.
(3) Annual net income to land, 36.81 $/Ac.
(4) Marginal tax rate of income, 25 percent.
(5) Expected rate of inflation on land values of

6.5 percent.

(6) The market value of land 757 $/Ac.

(7) The capital gain income tax, 12.5 percent.

(8) Downpayment, 25 percent.

(9) Interest rate on mortgage loan, 10 percent
annum.

(10) Planning horizon, years, 20 years.

(11) Amortization period on the loan, years, 20
years.

The resulting maximum bid price = 1091.00

47

Table 10 summarizes the cash flows per acre for the

basic case with a maximum bid price of $879.00.

48

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49

Sensitivity Analysis:

The solution for the base case will serve as the point

of departure to examine the sensitivity of the maximum bid

price to changes in the input variables. The sensitivity

of the maximum bid price was tested by altering the input

variables one at a time. Each variable was examined over a

range.

In every case the values for all variables, other

than the one being tested, were fixed as specified in the

original
The

case are

(1)

(5)

case.

results of the sensitivity analysis from the base

summarized below:

An increase in the mortgage loan interest rate
from 10.00 to 10.00 percent, reduces the maximum
bid price for land by $100.00.

Increasing the precent of loan paid as a down—
payment from 10.00 to 50.00 percent, decreases
the maximum bid price for land by $21.00.

An increase in the before-tax opportunity cost
of capital from 10.00 to 14.00 percent, reduces
the maximum bid price by $217.00.

An increase in average price of comparable

tract of land from $700.00 to $800.00, increases
the maximum bid price for land by $68.00.

Increase in the expecede rate of inflation from

5.00 to 10.00 percent, increases the maximum bid

50

price for land by $593.20.

(6) If the expected net income to land increases from
$30.00 to 50.00 , the maximum bid price for land
increases by $199.00.

(7) Income growth rate of 6.00 percent instead of
2.00 percent, increases the maximum bid price by
$142.75.

(8) An increase in the income tax rate from 20.00 to
40.00 percent and capital gains tax rate from
10.00 to 20.00 percent, increase the maximum bid
price for land by $156.65. This result occurs
because reduction in the expected annual net
income per acre, due to income taxes is more than
offset by the tax deductible interest payments
and the decrease in after tax opportunity cost
of capital.

(9) An increase in loan amortization and planning
horizon from 20 to 30 years, increase the maxi—
mum bid price for land by $11.00.

The accuracy of the maximum bid price developed by Lee
and Rask and reported in Table 9 has an average error of
569.00 making it the least accurate of all the models examined
thus far.

Chapter Summary:

In this chapter the effect of financing and taxes on the

51

price of land weredemmnstrated. The chapter began with two
cash flow statements and ended by demonstrating the effects
of financing arrangements and taxes on land values, using
the maximum bid price developed by Lee and Rask.

The two cash flow methods examined were: (1) constant
payment where the total payment in each period remains con-
stant over the terms of the loan; (2) constant payment on the
principal where an equal payment in each period is made on
principal, plus varying amounts of interest.

Finally, the maximum bid price for land was discussed
using a model incorporating eleven variables. Those variables
were the average price per acre in recent sales of comparable
tracts of land, the after-tax opportunity cost of capital,
the expected annual net income to land, the expected annual
rate of growth in annual income, the buyer's marginal income
tax rate, downpayment, the rate of interest on mortgage loan,
the amortization period of the loan, inflation rate in land
values, planning period, and the capital gains tax rate.

This model demonstrated the sensitivity of land prices to
changes in any of the variables discussed above (refer to

sensitivity analysis for more detail).

52

CHAPTER V

THE EFFECT OF RISK 0N FARMLAND VALUES

Thus far, all the models used to estimate land prices
assumed perfect knowledge. The future net incomes to land
in each period have been assumed known with certainty.
However, the value of the future net income which determine
land prices is rarely known with certainty.

There are several different opinions as to what con-
stitutes risk and uncertainty (Robison, 1979,a). In this
thesis, risk and uncertainty will be used interchangeably.
Robison describes risk as "actions with more than one pos—
sible outcome; where the likelihood of all possible outcomes
is described by a probability density function".

The net return to land is a function of the price of
the agricultural output and the cost of agricultural input.
The market environment provides risk in price and in other
terms of trade. The organized activities of the government
and otherjyunjtutions add uncertainty to the market expecta-
tions. Commodity price support programs are an example of
the factors affecting the price of inputs and agricultural
products. Weather and biological environment introduce
risk and uncertainty in the production output of crops and

livestock. The effect of uncertainty is more pronounced in

investment decisions because of the long term nature of real

53

estate investments; the effects of a wrong decision may be
felt for many years. One means of reducing risk is to improve
the planning information of the decision maker through effec—
tive capital budgeting.

In the following sections ways of handling risk in the
capital budgeting analysis will be discussed.

Adjustment of Discount rate:

A simple method of accounting for risk in capital budget—
ing models is to vary the discount rate. For investments which
involve greater risk, the cost of capital is higher than those
investments which involve less risk. That is, let the cost of
capital consists of three parts:

(V.1) co = r*+i+Y.

where: r* = pure time value of money
i = the inflation rate
T = the risk factor

Investment with a higher degree of risk leads to greater
cost of capital and this reduces the value of an acre of land.
The weakness of this approach lies in determining the appro-
priate discount rate for an investment. This determination is
rather subjective and arbitrary. The difficult question be—
comes: How much should the discount rate be changed for an
investment which involves a greater risk? This is a hard
question because the present value of a sum to be received in

the future may be dramatically changed by a few percentage

54

point changes in the discount rate.

Another weakness of this approach is that this method
conceptually adjusts the wrong element. It is the future in—
come of an investment which is subject to risk, not the cost
of capital. Yet this method adjusts the discount rate and
does not adjust the variable income. Finally, this approach
does not use all the information available from the probability
distribution of an investment. This model in its simplist
form is:

(v.2) VY = R/(1+r*+Y) + --- + R/(1+r*+Y)n + VY/(1+r*+Y)

and after summing geometrically it gives:

(V-3) VY = R/(r*+Y)

H

where: VY the value of one acre of farmland estimated

by (V'3)o
R = the annual net income to farmland.
r* = the time preference of money rate.
Y =

the risk factor.
Multiplicative Risk coefficient:

A second method is to reduce income to its certainty
equivalent by multiplying income by some coefficient a- The
advocates of this method argue that any adjustment of risk
should occur in the numerator of the present value equation
in the form of a coefficient with a value which varies between

zero and one according to the degree of risk. This model can

be written as:

55

(v.4) v“ = aR/(1+r*) + ... + aR/(1+r*)n + Va /(1+r*)n
After summing geometrically it gives:

(V-S) Va = uR/r*.

The coefficient a is called the risk coefficient. This
coeficient leads the investor to regard the expected annual
net return to investment as equal to a certain return. For
example, consider an expected net return of $1,000.00 from

a specific investment. The investor must choose a certain
income, which he would accept in lieu of this expected in-
come. If the investor chooses $1,000.00, then a equals 1.00
and the investment is called riskless. If he chooses $800.00,
then a equals 0.80. The smaller the value of a, the larger
is the risk associated with the income.

The weakness of this method is that the risk measure—
ment u is still subjective and arbitrary. The multiplicative
risk coefficient avoids the problem that investors cannot
ignore: the investor's attitude toward risk and uncertainty.
Clearly the investor's attitude toward risk and uncertainty
must be considered in decision making. In the following
section a procedure that takes the investor's attitude into
account will be discussed.

Subtracting the Cost of Risk:

Another way to adjust income R to its certainty equiv—

alent is to subtract the cost of risk. This method is based

on the expected utility hypothesis. Consider an individual

56

with asset X and utility function U. The risk premium n is

such that the decision maker is indifferent between a random

variable Z with expected value 0 and variance 02 and the

certain income X-n. Then, the utility of a certain U(X—n)

equals the expected utility of the random variable EU(X+Z):

(v.6) U(X—n) = EU(X+Z).

By taking the Taylor expansion around both U(X—n) and EU(X+Z),

Pratt has shown that:

(v.7) n = oZU"(X)/2U'(x).

Where -U (X)/U'(X) equals the absolute risk aversion coeffi-

cient which most economists argue decreases with income X.
Another commonly used risk measure is the equilibrium

trade—Off between expected returns and variance On an Expected

Value - Variance (EV) efficient set (see figure 3).
W(X) E1

woo = I: + A 0200/2

(3|

 

2 4!

o (X)

Figure 3. Equilibrium between an EV efficient set and a
decision maker's isoexpected utility function.

57

Let AB be the EV set, U U1 be fits isoexpected utility
lines and let:
(v.8) mm = W + >. o2(X)/2
be the linear tangent drawn to the equilibrium point with
slope A.
Rearranging (V-8), gives:
mm» mm - W = A cflow/.2.
The amount W(X)—W by definition is the risk premium m. If
U"(X)/U'(X) is constant, then (V-9) is equivalent to (V-7)
and the equilibrium is the amount of risk aversion.

Let the expected value of land,E(V) equals to R/r*, then
the certainty equivalent of land value,CE(V) is:
(v.10) CE(V) = R/r* — n.
Where CE(V) is the certainty equivalent value of one acre of
land.

To determine the risk premium H, first the total variance
Var(V) must be estimated.

The variance of the sum U = aX, is o2 = a2 02(X), where
a is constant and X is a random variable. Using the above
concept, the variance of land values Var(V), is derived as:
(v.11) VarW) = Var<R)/<r*>2.
Where Var(R) is the variance of annual net income to land and
r* is the rate of pure time preference which equals 5.67 per-
cent as calculated earlier in the thesis. However, this is

not the end of the story, because Var(R) also needs to be

58

estimated before n can be calculated. Empirically, the var—
iance of net income to land, Var(R) is estimated first by
regressing the previous three year values of net income against
time. Then, the variance is estimated by squaring and summing
the difference between the observed value and those predicted
by the regression equation. If Y(t) is Observed and ?(t) is
Predicted by the regression equation; then, the variance esti—
mate is §(Y(t) - Tit))2/3

Finaily, the certainty equivalent of land value CE(V) is:
(v.12) CE<V> = R/r* - x Var(R)/2(r*)2.

The model was examined given the data for cash rent to
land as reported in table 2, variance of net income to land
as reported in table 11, risk aversion coefficient of 0.003,

and the rate of pure time preference of 5.67 percent. The

results are given in table 11.

59

Table 11: Estimated Land Prices Using EquatiOn (V-12).

 

 

 

Variance Estimated Actual Estimated

of Income Price of Price of minus Actual
Year Var(R).l/l Land, $/ac. Land, $/ac. Price ,$
1963 0.023 230.00 209.85 20.15
1964 0.005 234.00 220.36 13.64
1965 0.004 244.80 230.36 14.44
1966 0.006 264.55 257.04 7.51
1967 0.015 302.60 273.59 29.01
1968 0.014 317.45 330.10 -12.65
1969 0.026 325.90 315.35 10.55
1970 0.130 274.72 290.07 -15.35
1971 0.620 350.70 319.36 31.34
1972 0.800 345.30 344.84 0.46
1973 0.700 355.40 416.62 —61.22
1974 0.500 456.40 486.00 -29.60
1975 0.400 493.60 552.00 —58.40
1976 0.400 541.60 617.00 —75.40
1977 0.270 645.00 757.00 —112.00

 

Average Error = 32.80

1— Those series were estimated by regressing net income
against time (for detail refer to page 57).

60

The results as given in table 11 indicate that inclusion
of risk in the model did not improve the predictibility of
the model. The average error of the estimated values of land
from the actual values is 32.80, while the average error of
the simple model R/r* was 29.90.

Sensitivity Analysis:

The sensitivity of land prices to change in most of the
variables was discussed in Chapter IV. However, in this chap—
ter the effects of changes in risk coefficient A, variation
in income, and net income on land values will be demonstrated.

Mathematically to demonstrate such effects the partial
derivatives of land prices (V.12) with respect to expected
net returns to land R, risk aversion coefficient A. and the
variation in income Var(R) were obtained.

The partial derivative with respect to net income to
land equals:

(v.13) ov/eR = 1/r* > o
The above derivative is greater than zero, since r* is greater
than zero.

The derivative of land prices with respect to variation
in income equals:

(v.14) ov/ ¢Var(R) = —A/2(r*)2 < 0.
That is, the effect of variation in income to land prices is
negative, since both A and r* are positive.

The derivative with respect to the risk aversion coeffi—

61

cient A equals:

(v.15) aV/ax = -var(R)/2(r*>2 < 0.

Which is also less than zero, because the cost of risk increases
with risk aversion. To examine the effect of net income to
land, variation in income and risk aversion coefficient on

land value, equation (V.12) was used. Table 12 summarizes

the results of the sensitivity analysis.

62

 

 

 

 

 

 

 

Table 12: A Sensitivity Analysis of Land Values with
respect to Changes in Income, Variation in
Income and Risk Aversion.
A: The sensitivity of land values to net income:
*-
given rate of pure time preference r equal
to 5.67 percent, A equal to 0.003 and Var(R)
equals 5
Net Land
Income Values,$/ac.
10.00 174.00
20.00 350.00
40.00 703.00
80.00 1408.60
160.00 2819.50
B: The sensitivity of land values to variation in
9(-
income: given rate of pure time preference r
equals 5.67 percent, A equals 0.003 and net
income to land R equals $10.
Variance Land
of Income, Var(R) Values, $/ac.
5.00 174.00
10.00_ 171.70
20.00 167.00
40.00 157.70
80.00

139.00

 

63

Table 13 continued:

C: The sensitivity of land values to risk aversion
coefficient x : given rate of pure time preference

r* equals 5.67 percent, net income R equals to $10
and the variation in income equals 5.

 

 

 

Risk Aversion Land
Coefficient, A Values, $/ac.
0.003 174.00

0.006 171.70

0.012 167.00

0.024 157.70

0.048 139.00

 

Thus, while changing R, has a positive effect and
changing Var(R), A have negative effect, land prices

appear most sensitive to changes in income.

Chapter Summary:

 

In this chapter discussion centered on the effect
of risk on land prices. The model discussed was (V 12).
Sensitivity analysis demonstrated that any increase in
variation in annual net income would decrease the amount
the buyer is willing to pay. Increasing the risk aversion

coefficient A, decreases the maximum bid price for land.

6L:

CHAPTER VI

ABSOLUTE RISK AVERSION OBTAINED USING TRIANGULAR
DISTRIBUTION FUNCTION

The risk was included in the BCB model in Chapter V.
Using Pratt's formula which defined the cost of risk to be
equal to a function of: a risk aversion coefficient, the var—
iation in income and the mean of the probability distribution
of returns. Often, reliable data on probability distribution
is not available; requiring instead a subjectively determined
triangular probability distribution. The triangular distrib-
ution (figure 4) can be determined by setting three values:
the pessimistic value X1, the most likely value X2 and the
optimistic value X3. Then the expected value of X and the
variance can be calculated. It is of course, recognized
that the sum of the area in figure 4, must equal one—-the sum

of probabilities for an event must equal one.

 

. i \

X1 X2 X3

Figure 4. Triangular Distribution Function.

 

65

To calculate the area of the triangle is the height h multi—
ply by one-half of the base. Setting the total area of the
triangle equal to one (since probability must sum to one)
and solving for height, h, gives:

(v1.1) h = 2/(X3 - X1).

Then the slope, m of the triangle over the range Xl to X2 is
simply the height, h, divided by the distance (X2 - X1).

h/(X2 - x1)

m

0].”

(v1.2) m = 2/(x3 — X1)(X2 - X1).

Thus, the height at any point along the X1 - X2 range is
determined by multiplying the slope, m, and the distance of
the random variable X from the point, X

(v1.3) f(X)

1. That is:

1 = 2(X - X1)/(X2 - X1)(X3 — X1). for X15 X 5 X2

Using the same procedure, the height or the probability

of occurrence over the range X2 to X was determined as:

3
(VI.u) f(X)2 = 2/(x3 - X1) — 2(X — X2)/(x3 — X1)(X3 - x2)

for X25 X i X3

Next the expected value for a random variable X is

determined by taking the integral of the product X.f(X) over

the range of X1 — X3. That is:

(v1.5) E(X) = J X f(X)dX for X j x j x
X

1 3'

Where E(X) is the expected value of the random variable X,

f(X) is the probability that X will occur. Thus the expected

66

value was found equal to:

3 2 3
(V1.6) E(X) (2/(x3-x1)(x2_x1))(x2/3 - xlxz/z + xl/é)

H

2 2 3 2
+ (g/(XB- X1))(X3 - x2) - 2(X3/3 - X2X3/2
X2/6)/(X3 - X1)(X — X2).

+

3

To calculate variance, we solve for the expression;
2 2 2
(VI 7) 0 = E(X ) - (E(X))

The first part of which equals:
2
(V1.8) E(X )

H

L: 3 L:
(2/(X3- X}(X2- Xi)(X2/h - X1X2/3 + X1/12)

+

3 3
<2/<x3— x3><x3/3 - x2/3> - <2/(X3 - x1)

4 4

3
x (X3 - X2))(X3/u — x2x3/3 + X2/12).

Then the variance is calculated as the difference between
(V1.8) and the square of the expected value.

The cumulative density function, that is the probability
that X less than or equal to some given value over the ranges
X1 — X2 and X2 - X3 are determined by taking the integrals of
f(X)l, f(X)2, respectively. That is:

2 2
(v1.9) F(x)l = 2(X2/2 - xix2 + X1/2)/(X3 - X1)(X2 _ x )

1

Where X1 is the lowest value, X2 is the most likely, and X3

is the highest value given.

For X2: X : X3, the cumulative density function is:
2

2
(v1.10) F(X)2 = 1 — (X - 2x3x + X3) / (x3 - x1)(x3 - X2 )

Knowing the expected value, variance, and the certainty

67

equivalent of income derived from a risky investment, the
absolute risk aversion for a particular investor can be
determined using Pratt's formula as:

(v1.11) A = 2(E(V) — CE(V))/o2

Where X is the absolute risk aversion, E(V) is the expected
value, CE(V) is the certainty equivalent, and ozis the var—
iance.

A program has been provided to estimate the expected
market price of land (or other investments), variance, ab—
solute risk aversion, and the probability that the market
price, P, is going to be less than or equal to a given price.
The probability that the market price is going to be greater
than a given value can also be determined. Thus, this pro-
gram enable the buyer of land or other investments to estimate
probability density functions by specifying the lowest, most
likely, and highest price of land. Then, if they specify the
random variable, certainty equivalent, their average risk
aversion can be calculated. For example, if the lowest, most
likely and highest price and their certainty equivalent were
$10,000.00, $30,000.00, $100,000.00 and $29,000.00, respec—

tively, the result using the program would be the following

1. Expected Value = $46,666.70
Variance = $3.70 x 108
= $19,293.00

H

2
3. Standard Error
L;

Absolute Risk Aversion 0.0009

The probability that the value of investment is less
than or equal to some value in the range of X,

mined by pressing the value for the input X and then D.

68

can be deter-

Table

13 summarizes the results of that probability for different

values of X.

 

 

 

 

Table 13: Summary of the Cumulative Density Function:
that is, the probability that X: x.
Cumulative

' Density

$X Function
9,000.00 0.0000
15,000.00 0.0139
20,000.00 0.0550
25,000.00 0.1250
30,000.00 0.2220
5,000.00 0. 300
0,000.00 0. 286
45,000.00 0.5190
50,000.00 0.6000
55,000.00 0.6785
60,000.00 0.7460
65,000.00 0.8050
70,000.00 0.8570
75,000.00 0.9000
80,000.00 0.9360
85,000.00 0.9600
90,000.00 0.9800
95,000.00 0.9960
100,000.00 1.0000

Note: The program to estimate the above table is given in

table A:2 in the appendix.

69

Chapter Summary:

This Chapter introduced one way of estimating the prob—
ability distribution of returns -- the subjective triangular
probability distribution. This is necessary to estimate the

risk premium of an investment.

70

CHAPTER VII
PREDICTABILITY COMPARISON AND CONCLUSION

1. Comparing the predictability of the Models

All the models discussed throughout the thesis are
maximum bid price models. Maximum bid price models for
land are determined by equating returns from land to the
costs. The maximum bid price should be correlated with
the actual price of land. So, to determine which model
was the best predictor, the actual price of land V was
regressed against the estimated price of land V using the
simple linear regression described below:
(VII.1) v = a + .t
where u and B are estimated parameters 0f the Simple re—

gression model. If the actual price was equal to the esti—
mated price 3 would equal one and 4 would equal zero.
Instead, for the BCB model we obtained the following

estimates:

(VII.2) V = -710.00 + 3.07 V
The correlation coefficient R2 is 0.67 indicating that 67
percent of the variation in land prices is explained by the
linear relationship with independent variable V.

For the second model, which expresses land values as
net income to land in current R, over the rate of pure time

*
of money, r , the following regression was obtained:

71

(VII.3) v = —85.95 + 1.28 v

The correlative coefficient determination R2 is 0.98. This
regression indicates that 98 percent of the variation in the
actual values of land is explained by the variation in the
model which depends on net income and the preference rate.

The third model examined includes productivity changes
(see equation III.5). The regression estimated using the
data for the independent variable V and the dependent var—
iable V was:

(VII.4) v = 128 + 0.59 V.
The correlation coefficient R2 is 0.68

The fourth model is the maximum bid price model. The
following regression was obtained, using estimated values,
by this model:

(VII.5) V = 235 + 0.15 V.
The correlation coefficient R2 in this model is 0.80.

The fifth model is equation (V.12) which was adjusted
for risk. The certainty equivalent method was used to de—
termine the risk premium and obtain the following regression
for this model:

(VII.6) v = -92.60 + 1.30 V.
The correlation coefficient R2 was 0.98. Thegnxnmaregression

does not show good predictability of the actual price of

land. This can be explained by fluctuation in productivity

72

changes, especially low and sometimes negative during the

recent years.

2. Summary and Conclusion:

The objective of this thesis has been to build models
of increasing complexity, in order to help explain the max—
imum bid price for land. Factors such as the time preference
rate, marginal tax rates, capital gains tax rates, and risk
are included.

The process began with the Basic Capital Budgeting model;
one which expressed land values as equal to net return to
land, divided by the opportunity cost of capital. According
to the formula, the net return to land and the opportunity
cost of capital were the only tow factors affecting the land
value. It ignored such factors as the inflation rate, pro-
ductivity of land and risk. Consequently, results with this
formula showed large discrepancies between predicted value
of land and the actual value of land.

The second model expressed land value as net returns
to land over the rate of pure time preference. This model
was the best predictor among all the models.

The third model, which included such factors as the
income to land, the rate of time preference, the inflation
rate, the productivity changes of land. The average error

of this model is significantly higher than the second model.

73

It is concluded that this model is not a good predictor
given the productivity changes used in the study.

The Maximum Bid Price Model,-discussed in Chapter IV
incorporated such financial arrangements as downpayments,
interest rates on mortgage loans, and the length of the in—
vestment period. This model showed that an increase in the
downpayment decreases the maximum bid price, and an increase
in amortization period of the loan increases the maximum bid
price of land. This model also yielded a large discrepancy
between the predicted and the actual value of land. The
major contribution of this study was to adopt this program
for use on TI-59 hand held calculator.

Tow kind of loan payments were discussed; the Constant
Payment Method in which the total payment each period re—
mains constant over the term of the loan, and the Constant
Payment on Principals Method in which an equal payment in
each period is made on the principal, plus a varying amount
of interest. The total payments(interest and principal),
during the early years of the loan, are lower in the Constant
Payment Method. They increase during the second half of the
term of the loan. Total interest paid over the life of the
loan was greater using the constant payment method.

The Maximum Bid Price Model demonstrated that mortgage
loan.interestrates have considerable impact on land prices.

An increase in interest rate decreases the value of land.

74

Downpayment size had an inverse impact on land prices. The
length of amortization period had a direct positive effect
on land prices.

Adjustment of the discount rate for risk was discussed
and it was concluded that this method did not provide any
objective way of estimating the risk factor. The adjustment
for risk cost was subjective and arbitrary. The second meth-
od of adjusting the Capital Budgeting Formula for risk, the
Certainty Equivalent Multiplicative Coefficient of risk, was
also found to be arbitrary and subjective. Both adjustment
of the discount rate for risk and the multiplicative coeffi—
cient of risk avoid the problem that investors can not ignore,
the investor's attitude toward risk.

A third method of adjusting the Capital Budgeting For—
mula for risk is the Certainty Equivalent Method, based on
the expected utility hypothesis. The results to this model
indicate that inclusion of risk does not improve the predicta—
bility of the model. Variation in income to land was shown
to have a negative impact on land values. That is, as var-
iation in income increases, land value decreases. Absolute
risk aversion coefficient also has a negative impact on land
values. There is a positive relationship between the ex-
pected income to land and the value of land.

The Maximum Bid Price model first developed by Lee and

Rask at Ohio State University, was adapted here. The model

75

was adjusted for risk by subtracting the cost of risk from
the expected maximum bid price. This demonstrated that
there is a negative relationship between the variation in
income to land determined by variance and the maximum bid
price of land. Investors with greater absolute risk aver-
sion indicated lower maximum bid price than those who had
less absolute risk aversion. Variation in market price of
land had a small negative effect on the maximum bid price
for land.

In this thesis, it was made available a program for
the hand-held programmable calculator to estimate the ex—
pected value of land, variance, absolute risk aversion of
the investor, and the probability that market price is going
to be greater than the maximum bid price, given lowest market
price, most likely price, the highest market price, and the
one that is their certainty equivalent. Program to estimate
market price and maximum bid price for different models are
discussed. In addition, a program was provided, not only
to estimate the maximum bid price, but the buyer's annual
loan payments, loan balance remaining in each period,taxable
income, net cash flow, market value of land, equity, and
after—tax capital gains income.

In general, it is concluded that terms of financing
such as downpayment required, interest rate and length of

the loan repayment period and expected inflation rate of

76

land price are very imporant in determining the price of
farmland. However, inclusion of risk in the capital budget-
ing model does not improve land price predictability, because
the cost of risk is too small given the value of the risk
aversion coefficient.

The effect of increases in the cost of factors of
production such as fertilizer, labor, capital and fuel on

land prices are currently the subject of the auther's Ph. D.

thesis.

77

APPENDIX A

PROGRAMMING THE HAND-HELD CALCULATOR

The models and the mathematical operations involved
throughout the thesis can be complicated, and determination
of land values using any of the models discussed may be dif—
ficult and time—consuming. Recent developments in computer
technology led to the development of the hand-held computer
which has provided a powerful compilation capacity that can
solve problems that formerly could be solved only by large
computers. These programmable calculators are currently
available at reasonable prices which seem to be decreasing
as technology advances.

The hand-held programmable calculator, like any com-
puter, can carry out the following:

1. Read in both data and instructions.

2. Store the data and instructions in a memory.

3. Perform calculations in manner prescribed by

the instructions.

4. Read out the results.

5. Control all aspects involved in getting an

answer.

The advantages of these hand-held programmable cal-

culators to a large number of.decision-makers and pro—

78

fessionals are clear—cut. Its use helps speed up busi-

ness decisions and eliminates manual calculations.

The TI-59:

Many of the principles of programming are common
to large computers and programmable calculators of all
manufacturers. However, each manufacturer's equipment
requires the user to follow some specific rules and con-
ventions that are unique to that particular line. Since
the Texas Instruments-59 line of programmable calculator
was used to solve for land values throughout the thesis,
some of their features will be discussed briefly.

The TI-59 is one of the recent programmable cal—
culators made by Texas Instruments and capable of handling
problems that formerly could be solved only by large com-
puter. The most striking feature of the TI-59 is the use
of removable solid—state modules for the storage and
execution of library programs.

Program steps are entered into the memory of the
calculator by pressing keys on the keyboard. The program
will be stored in the memory and can be used repeatedly
with different data. If a given program is to used only
once, it can be erased from the program memory when the
power is turned off. However, if needed again, the same

program can be saved by recording it on a magnetic card.

79

Then when it is needed the card containing the program can

be read into the calculator memory and the program reused.

The Tables in this Appendix:

 

Table A:1. Lists the Maximum Bid Price and Cash Flow
program.

Table A:2. Lists the procedure to follow once the
program (table Azl) is read into the
computer.

Table A:3. List the program for the Subjective
Probability Distribution.

Table A:4. Lists the procedure to follow once the
program (table A:3) is read into the

computer.

80

Table A. 1: Maximum Bid Price and Cash Flow Program.

 

 

1. is Line No. 2. is Key Code 3. is Key

5.;
N
\b
H
N
h)
3...:
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tw

 

 

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Table A.

 

 

 

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83

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85

1 Cont.

Table A.

 

 

 

ad

 

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Table A:2.

86

Procedure to follow for the Maximum Bid Price

model.

 

 

Objective:

To determine: (1) The maximum amount one can
afford to pay for one acre of land, (2) Annual
loan payment, (3) Unpaid balance remaining on
loan at year j; (4) Netcash flow at period j,
(5) Market price of land at period j, (6) Equity
at year j; j=1 . . . . m, where m is the amorti-

zation period of the loan.

INPUT DESCRIPTION INPUT VALUE PRESS

1. Turn calculator off, and
back on, to clear program
and memory.

2. Partition memory (Note 639.39 (H) (2nd)
should appear on the screen. (op) (17)
If not, return to step 1.)

3. Clear Display (CLR)

U. Insert side 1 of the card

containing the program (A:1).
If the calculator has read
the card successfully, a "1"
will appear and remain sta—
tionary. If a flashing "0"
appears, repeat step 3 and M.

Clear Display (CLR)

Insert side 2 of the card.

If the calculator reads side
2 successfully, a "2" will

87

Table A:2 continue.

 

 

STEP

10.

11.

12.

13.

14.

15.

16.

INPUT DESCRIPTION INPUT VALUE

 

appear and remain stationary.
If a "0" appear, repeat steps
5 and 6.

Clear Display

Insert side 3 of the card
containing the program.

If the calculator has read

the card successfully, a "3"
will appear and remain station-
ary. If a "0" appears, repeat
steps 7 and 8.

Clear Display

Insert side A of cards contin-

ing the program. If the calcu-
lator has read the card success-
fully, a "4" should appear and
remain stationary. If "O" flashes
on the display after the card

has been read, steps 9 and 10
should be repeated.

Clear Display

Growth rate of annual net
income to land, % annum

 

Before tax opporunity cost
of capital, % annum

 

Annual Net Income to land;
$ per acre.

 

Marginal tax rate on annual
income, %.

 

Expected rate of inflation

 

(CLR)

(CLR)

(CLR)

(STO)

(STO)

(STO)

(STD)

10

11

13
1h

88

Table A:2 continue.

 

 

STEP

17.

18.
19.
20.
21.

22.

Note:

INPUT DESCRIPTION INPUT VALUE

 

Price of comarable tract,
per acre.

 

Capital gain tax rate, %

 

Down payment. %

 

Interest rate, % annum.

 

Planning horizon, years.

 

Amortization period, years.

 

 

OUTPUT
OUTPUT DESCRIPTION PRESS VALUE
The maximum bid price $/ac. A

INPUT DESCRIPTION

 

Enter the price $/acre that

will be used in the cash

flow analysis. (STO) 21
OUTPUT DESCRIPTION

 

Annual loan payment (prin—
cipal and interest). B

CASH FLOW ANALYSIS

 

PRESS

 

(STO) 15
(STO) 16
(STO) 17
(STO) 18
(STO) 19

(STO) 20

RESULTS

To prepare an annual cash flow chart, enter the year

you want to examine in (STO) 22. Then press

(C) to

get the unpaid balance at the end of that year.

Press (D) and you will see the taxable income. Press
(E) for income tax paid and (2nd) A for the net cash
flow that year. Press (2nd) B for the inflated invest-
ment (market price) and press (2nd) for the equity
(cost less principal paid plus inflation) use the

chart as shown in the next page to record your data.

Table A:2 continue.

89

CASH FLOW CHART

 

 

Year

Unpaid
Balance

Taxable
.Income.

Income
Tax.

Net
Cash
Flow

Market
Price

Equity

 

 

 

 

 

 

 

 

 

 

 

Table A. 3:

90

The Program for the Subjective Probability
Distribution.

 

 

 

 

"1" is Line No. "2" is Key Code "3" is Key

1 2 3 1 2 1 2 3
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fig; %é LEI OéO S4 0?? 54

CE: :8 EE U41 PS BBQ 55

C53 4? CH3 U4: 53 us: 53

GE; 25 CLE U45 53 us: 53 a
055 g; Egg U44 43 333 43 EC;
B55 :5 LEL 345 51 fig; 33 03
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use F? 2' U47 53 i 036 5; p
ufié ii 3 343 43 REL BS? 75 —
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0.4 03 [5: 853 ES as: 54

8:5 75 — U54 03 use 54 3
8:6 43 PCL 355 54 094 75 —
8;? E: n? 058 BB 3?5 53

his F: EST 53 395 33 g
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GE: 02 as Ubl 45 108 43 ELL
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335 E; " 065 as :84 a: a:
RF7 5: 056 54 EOE is

Egg 5; 06* 5; :05 as

1:; E .:__: E r:- C' if. E? E' E i if} “ E .:

DE? E2 378 Si 30? $3 33
CE? 5% r D71 55 118 TE ’
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335 $3 3 U75 T5 1:4 54
037 E; 376 43 EL? 54
His ES 4 57— O: 1;g if

 

 

91

(cont'd)

3:

Table A.

 

 

 

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Table A.

fifflw;?ffiia.;tt;_;t.::;_;::;:_:tin;:f:m;c.$53.;itfia;2.9T;.;:t;.;:.:.

 

 

93

(cont'd)

3..

Table A.

 

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94

(cont'd)

3

Table A.

 

 

 

 

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94

3: (cont'd)

Table A.

 

 

 

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_HL. ..:... 7.. _ _w._.._ “3“ _HI._ .H... “a“ .V... _...... .._: ma... .H. .... : _.-... ......

E. ....m E 2... _.h -...- _...... F.

_...... _...... .H. ._...“. _.-”. _...... _...... _....H. ...... _...”. 5...”. _H. _..... .5... ..-. _....H. ....._.. :1. _...... a: ....
.._..H. 51 ..:... 3...“. 7... .H. ...—H. .d- _..“... ...—n. ..n_.. ...2. .....H. d: .H. _H...H. CA. D... an... 1... D...

tun. G... .Hu. _...... _H.. ._ .3. ..u: _...”. ...—n. 7.. _H. G... mm. ...... .w..._ _H...H_ S: _....u ...—.:.. 7.. OH.
.1. h. ...—.... 7... 7... 7.. 7 a. 7.. 7... _..... 7... 7... _H. _H. .....H. OH. OH. .Hfl. .H. .H. _H.

74 Jun—z Jun—x .:.—z ..n—: ..H—1 4%.. Jun-I gnu: 5...: ..H—: ..H—.. .57 AB: 4.35.. Jun—x ..H—: .35.. ....u: ..n..—l dun.

 

 

Table A:h.

95

Probability Distribution.

Procedure to follow for the Subjective

 

 

Objective:

STEP

To determine expected market price of land,

variance, risk aversion coefficient of the

investor and the probability that the market

price is less than or equal to a given price.

INPUT DESCRIPTION

Turn calculator off, and
back on, to clear program
and memory.

Partitioning memory (Note
639.39 should appear on
the screen. If not ,
return to step 1.)

Clear Display

Insert side 1 of the cards

containing the program (Az3).
If the calculator has read the
card successfully, a "1" will
appear and remain stationary.
If a flashing "0" appear repeat

steps 3 and A
Clear Display

Insert side 2 of the cards
containing the program.

If the calculator reads
side 2 successfully, a "2"
will appear and remain
stationary. If a "0"
appears, repeat steps 5
and

INPUT VALUE

PRESS

(4)(2nd)
(OP)(17)

(CLR)

(CLR)

96

Table A:u continue.

 

 

STEP

CD\7

10.

11.
12.

13.

14.

15.

INPUT DESCRIPTION INPUT VALUE

 

Clear Display

Insert side 3 of the cards.

If the calculator has read

the card successfully, a "3"
will appear and remain
stationary. If a "O" flashing
repeat steps 7 and 8.

Clear Display

Insert side u of cards

If the calculator read

the card successfully, a
"u" should appear and
remain stationary. If a
"O" flashes on the display
steps 9 and 10 should be
repeated.

Clear Display

Lowest price of one acre
of land, $ per acre.

 

Most likely price of one
acre of land, $ per acre.

 

Highest price of one acre
of land, $ per acre.

 

What the investor would
like to pay for one acre
of land, $ per acre.

 

(CLR)

(CLR)

(CLR)

(STO)

(STO)

(STO)

(STO)

PRESS

Ol

02

03

OH

97

Table A:4 continue.

 

 

STEP

RESULTS

OUTPUT DESCRIPTION

Expected Value of one acre
of land, $ per acre.

Variance of price of land
Risk aversion coefficient
Probability that the
market price is less

than or equal to some
value $ X.

PRESS

RESULTS

BIBLIOGRAPHY

98

BIBLIOGRAPHY

Boxley, Robert Fox Jr. The Relationship between Land
Values and Flood Risk in the Wabash River Basin
Unpublished Ph. D. thesis, M. S. U. 1969

Colyer, Dale, Socio-Economic Determinants of Rural Land
Values in Greenbrier County, West Verginia,
Journal of the Northeastern Ag. Econ. Council
Vol. VII, No. 2, Oct. 1978

Harris, D. G, and R. F. Nehring, Impact of Farm Size on
the Bidding Potential for Agricultural Land,
American Journal of Agricultural Economics,

May 1976

Hepp, Ralph, Unpublished Michigan Agricultural Data,
Department of Agricultural Economics, M. S. U.

Huff, Harry, Bruce, Land Values and Valuation: A
Landlord Approach. Unpublished M. S. Thesis,
Mo So U0, 19670

Lee, W. F. and Norman Rask, Inflation and Crop Prof-
itability: How Much can Farmers Pay for Land?
American Journal of Agricultural Economics
Dec. 1976.

9

Michigan Department of Agriculture, Michigan Agricultural
Statistics, 1978.

Pratt, J. W. Risk Aversion in the Small and in the large,
Econometrica, 32(1964). p 122-136.

Robison J. Lindon, Decision Making Under Uncertainty,
Lecture notes for Agricultural Economic 906,
Department of Agricultural Economics, M. S. U.

1979 a.

99

Robison, J. Lindon, The Effect of Financial Arrangements
on Maximum Bid Price for land. Memo presented at
the Department of Agricultural Economics, Oct. 24,

1979.

Robison J. Lindon and David J. Leatham, Interest Rates
Charged and Amounts Loaned by Major Farm Real
Estate Lenders. Agricultural Economics Research,
Vol. 30, No. 2, April 1978, table 5.

Rossmiller, George E. Farm Real Estate Value Patterns in

the U. s. 1930-1962. Unpublished Ph. D. Thesis,
M. s. U., 1965.

U. S. D. A. Agricultural Statistics, Washington: Govern-
ment Printing Office, 1978 a.

U. S. D. A. E. R. S. , Farm Real Estate Market Development,
1978 b.

U. S. D. A. Changes in Farm Production and Efficiency 1977.
Economic Statistics, and Cooperative Service.
Statistical Bulletine no. 612, U. S. D. A. c, 1978

U. S. Bureau of Census, Historical Statistics of the U. S.

Colonial Time to 197Ql Washington: U. S. Goverment
Printing Office, 1971.