'"2 A Guide for Evaluating Hi^^^^mmi

Reforestation 411,'''^

and

stand Improvement

Projects

In Timher Management Planning on the

Agriculture Handbook 304

U.S. Department of Agriculture Forest Service

NAL DIGITIZING PROJECT

MBP0000258

A Guide for Evaluating

Reforestation

and

Stand Improvement

Projects

In Timber Management Planning on the

By

Robert Marty, Project LecLder^

Forest Economics Research^ Northeastern Forest Experiment Station,

Upper Darby, Pa,

Charles Rindt, Chief, Silviculture Branch,

Division of Timber Management;

John Fedkiw, Chief, Forest Economics Research Branch,

Division of Forest Economics and Marketing Research,

U.S. Department of Agriculture Forest Service

Washington, D.C. April 1966

For sale by the Superintendent of Documents, U.S. Government Printing Office,

Washington, D.C. 20402—Price 15 cents
FOREWORD

This handbook describes a procedure for economic evaluation of

reforestation and timber stand improvement projects. It indicates

a method for scheduling available funds to projects that will yield

the highest rates of financial return.

Usually there are values in addition to timber that must be

considered on National Forest projects of this kind. These values,

and the cost of developing them to accomplish multiple-use objectives on a project area, should also be appraised to arrive at an

overall project evaluation. Economic evaluation for timber

production alone, however, provides a benchmark for rating project

priorities.

Economic evaluation of projects shows the significance of

inefiiciencies and resultant higher costs, which reduce the economic

justification for projects. The analysis of costs and expected returns

should thus guide efforts to improve treatment procedures and

encourage better project administration to reduce costs and increase

returns from expenditure of public funds.

In private enterprise, the profit motive provides the incentive

to produce with maximimi efficiency. To a large extent, economic

principles that apply to investment of funds for reforestation and

timber stand improvement on private land should apply to the

setting of priorities for such work on National Forest land.

This handbook was initially designed to develop economic criteria for the guidance of reforestation and timber stand improvement work on National Forests in the Appalachian Mountains, and

has been generalized to apply to this work on all National Forests.

Continuing research and field experience in the economic evaluation

of projects should lead to better local guides and more and better

accomplishment per dollar of public funds invested.

^iu^f-^

Chief9 Forest Service
CONTENTS

Introduction

Page

1

Basic concepts . 2

Measuring economic desirability 2

Comparing projects and allocating funds „.. 3

Choosing and rating projects „ . 4

Choosing modal projects for evaluation „ 5

Estimating added yield 7

Determining project cost 8

Appraising added yield 9

Computing rates of return 10

Two examples of modal project analysis 12

Limitations of return rate estimates ^ 18

The reliability of rate of return estimates 18

Rate of return sensitivity ^ ^ 18

Intangible factors I9

Interaction among management activities 19

Literature cited „ 20

Appendix 21

Compound interest formulas 21

A computer program for rate of return computation 21

111
INTRODUCTION

Timber stand improvement and reforestation projects are an important

and growing part of the total timber management program on the National

Forests. These projects are undertaken to increase timber growth and

quality, to reduce the risk of fire, weather, and pest losses, to transfer

growth from low to high value trees, to return denuded areas to production

quickly, and to enhance other forest uses and values as well. Economic

appraisals of the various opportunities for stand improvement and reforestation are helpful in deciding how much effort to devote to each aspect of

timber management, and what kinds of projects to favor. This handbook

outlines procedures for rating and comparing proposed stand improvement

and reforestation projects.

IV
BASIC CONCEPTS

Economic desirability, in terms of costs and returns, is a principal consideration in establishing priorities for reforestation and stand improvement

projects on the National Forests. This section summarizes basic economic

concepts used to estimate economic desirability, compare competing projects,

and to allocate funds among projects.

MEASURING ECONOMIC DESIRABILITY

The economic desirability of a project is measured by how much it adds

to the value of the timber stand, in relation to its cost and the length of time

required to bring the stand to harvest. Value is used, rather than volume

or some other physical quantity, because it is the only measure of output

that reduces all changes in timber yield to a common denominator. For

example, a 20-percent increase in the yield of select-grade lumber cannot

be compared directly with a 10,000 board-foot increase in per acre volume,

but the dollar values of these yield changes can be compared.

Both costs and values have to be considered because omitting either can

lead to erroneous priorities. Where differences in the value added by various projects are ignored, the least costly projects are likely to be favored,

even though slightly more expensive projects may add several times as much

value. When costs are ignored, projects adding the most value tend to be

favored without regard to their cost.

Time is the third important element that must be considered. When time

is ignored and both cost and value are taken into account, projects with equal

returns per dollar of cost are likely to be given equal priority. Yet some of

these projects might accomplish their value increase in only a few years,

whereas others require a longer period of time.

Cost, value added, and the time between investment and return vary from

one project to another, and each influences economic desirability. All three,

however, are taken into account by the value growth rate of a project. The

usual way of expressing value growth rate is the annually compounded

percentage increase—a compound interest rate.

Compound interest is the preferred measure of the rate of value growth

not because it is intrinsically better than any other measure, but because it

is used so commonly to describe investments that it is universally understood

and accepted. Economists call it the internal rate of return or the rate of

return to investment.

To summarize, the internal rate of return is a widely understood and

accepted measure of an investment's economic desirability. It measures the

rate at which an investment grows toward the return it eventually generates,

and takes into account the amount and timing of both costs and returns.

Methods of computing rates of return, and some comparisons with other

measures of economic desirability, are discussed later.
COMPARING PROJECTS AND ALLOCATING FUNDS

Each year funds available for reforestation and stand improvement must

be allocated among a large number of management units. There is opportunity to allocate these funds to areas and projects that will produce the

highest internal rates of return. How can these opportunities be identified?

Capital budgeting is an analytical system developed by economists to

answer just this sort of question. It is so called because it budgets capital

funds among competing investment projects. There are several steps in

applying the capital budgeting system. For budgeting stand improvement

and reforestation projects within a Region it might work as follows:

1. In the course of periodic compartment examinations, areas would be

found where reforestation or cultural treatments would improve timber output. Type of treatment needed, acreage to be treated, project cost, internal

rate of return, and important nontimber effects would be estimated and

noted for each project area.

2. Compartment examination records would be reviewed once each year

by Forest staff. A listing would be prepared, for each working circle, of

the reforestation and stand improvement projects proposed for the ensuing

fiscal year. Separate lists might be made for work to be financed with

appropriated funds and with K-V^ funds. Projects would be listed in

descending order of internal rate of return, along with their cost and other

relevant data. Working circle lists would be forwarded to Regional staff.

Table 1 shows a hypothetical listing.

TABLE 1.—Hypothetical working circle list of scheduled reforestation and

stand improvement projects to be financed from appropriated funds

Project Return Project

Compartment Type Treatment area rate cost

Acres Percent Dollars

Sampson A36 Cove hdwd. Thinning 870 12.3 6,090

Logan F14 North, hdwd. Thinning 1,310 11.2 9,170

Logan F16 North, hdwd. Weed, release 2,100 9.7 10,500

Logan A24 Oak-hickory Thinning 1,745 9.7 12,210

Joshua B4 Cove hdwd. Thinning 315 9.3 2,200

Sampson D7 Conifer Weed, release 720 9.0 3,600

Sampson A14 Conifer Thinning 975 8.5 6,820

Joshua CIO North, hdwd. Thinning 150 8.1 1,050

Joshua Cll North, hdwd. Weed, release 1,380 8.0 6,900

Joshua C12 Cove hdwd. Thinning 865 8.0 6,050

Evans E4 Conifer Weed, release 2,400 2.1 12,000

Logan A28 Conifer Planting 310 1.9 6,200

Evans C12 Oak-hickory Weed, release 950 1.4 4,750

Snyder A17 Oak-hickory Thinning 705 1.4 4,930

Snyder A24 Oak-hickory Weed, release 1,430 1.0 7,150

Snyder D12 Conifer Weed, release 480 0.8 2,400

I BùiuUon-Vandenberg Act of June 9, 1930 (46 Stat. 527; 16 U.S.C. 576).

2
3. Region staff would arrange all projects in order of their return rates

on a composite list (table 2). A cumulative cost column would be added to

indicate how far down the project listing the funds available for the next

fiscal year would reach.

With this system each project is evaluated according to its economic

productivity as measured by an internal rate of return. Projects compete

for funds on the basis of their expected productivity. Those with the highest

internal rates of return are financed first; progressively less productive ones

are financed until available funds are exhausted. Exceptions could be made

where nontimber benefits are important.

TABLE 2.—Hypothetical composite list of scheduled reforestation and stand

improvement projects to be financed from appropriated funds

Working

circle Compartment

Return

rate Cost

Cumulative

cost

Sullivan

Franklin

Franklin

Franklin

Webster

Pendleton

Sullivan

Pendleton

Pendleton

Pendleton

Franklin

Pendleton

Pendleton

Webster

Webster

Pendleton

Sampson A36

Windham F23

Windham F18

Webster B2

Elk A22

Erie D12

Logan F14

Erie A28

Tioga F4

Tioga F14

Tucker D22

Erie B6

Wayne B18

Wyoming All

Roane C17

Wayne C31

Percent

12.3

12.1

12.1

12.0

11.7

11.6

11.2

6.2

6.2

6.2

6.1

6.0

5.8

5.8

5.7

5.5

Dollars

6,090

14,220

7,400

21,080

18,010

8,430

9,170

3,440

13,270

24,000

17,360

8,880

15,500

29,370

37,480

7,630

Dollars

6,090

20,310

27,710

48,790

66,800

75,230

84,400

1,336,480

1,349,750

1,373,750

1,391,110

11,399,990

1 Appropriated funds limit is $1,400,000, and Pendleton-Erie-B6 is the last fundable

project.

The capital budgeting approach is only as good as the basic evaluations

of the economic desirability of proposed projects. In addition to being as

accurate as possible, evaluations should be consistent to enable comparison

from one project to others. Furthermore, it is useful to have a standard

way of evaluating projects—a standard measure of economic desirability,

a standard method for determining which costs and returns to include, and

a standard way of computing required statistics—to enhance the validity of

comparisons. It is such a standard method of evaluation that is presented

in the remainder of this handbook.

CHOOSING AND RATING PROJECTS

The steps in project evaluation are choosing the project, estimating

added yield, determining project cost, valuing yield additions, and computing

rate of return.
CHOOSING MODAL PROJECTS FOR EVALUATION

Sometimes it is desirable to evaluate individual projects. An individual

evaluation may be particularly useful, for example, when a contemplated

project is large or unusual. In many cases, however, a single evaluation can

serve for a range of similar projects. This may be done by subdividing

projects into a limited number of fairly homogeneous groups, and by

choosing for evaluation the one project from each group that is most

representative of that group. The projects chosen are termed "modal"

projects because they will often be the modal or most frequently occurring

project of the group.

Many factors may ultimately play a part in defining project groups, but

it often helps to begin by determining the range and frequency of site and

stand conditions making up the timber type. Forest, or other management

unit chosen for study. National Forest compartment examination and timber inventory records are usually good sources of this information. Age,

size class, species composition, density of stocking, and site quality are

among the more important site and stand condition variables. Other characteristics that influence project cost or yield may also be important in

particular types.

The analysis begins by subdividing the type on the basis of site and stand

characteristics. Plot data are then sorted on this classification to gain some

idea of the acreage contained in each site-stand class. This initial classification may be modified, by either combining classes or subdividing them. It

is typical for the bulk of the acreage in a timber type to be concentrated

in a relatively small proportion of these site-stand condition classes. The

inventory data, thus, can give the analyst a good idea of the most important

site-stand condition categories.

Each site-stand condition class will, of course, contain some variation in

actual conditions. The next task is to identify the modal site quality and

stand condition that will be used to represent the class. Plot data for the

more important stand classes will indicate the most frequently occurring site

index and stand condition for the class. Sometimes a class will be proposed

initially that turns out to include two conditions that are different with respect to some characteristic. The analyst may wish to subdivide such classes

so that he can deal with more homogeneous groups. Where the data are

inadequate, class midpoints can be used or additional sampling can establish

the particular set of site and stand conditions that should represent the class.

Additional field sampling may be needed for other reasons as well. For

example, a characteristic with an important influence on the type of reforestation or stand improvement practice needed, its cost or response, and that

was not measured by the inventory, may require a supplementary survey.

The next task is to prescribe a treatment for each site-stand condition

class, based on common practice on public and private forests, available

management guides, and research information. At the end of this procedure,

there should be a set of site-stand condition classes, an indication of the

extent of each class, a modal site index and stand condition reflecting the

most frequent situation within each class, and a treatment prescription

tailored to this modal condition. The modal site index and stand condition

for each class, together with its related treatment, define the modal project

that will be evaluated as representative of the class.

4
An evaluation study carried out for the George Washington National

Forest illustrates this process of defining modal projects. A primary classification or grouping of forest conditions was used that involved four factors:

Forest type, site class, main stand size class, and main stand age class. Three

forest types were included in the study: The conifer, the oak, and the cove

hardwood. Three levels of site quality were used to subdivide each type.

The four main stand size classes used were seedling and sapling stands, pole

stands, small sawtimber stands, and large sawtimber stands. Ten 20-year

age classes formed the final classification.

Five hundred and seventy-two survey plots were sorted on this primary,

four-way classification. These plots fell into 136 of the 360 primary classes.

The reason that so few of the primary classes actually exist on the Forest is

that several of the classification variables are correlated with one another.

For example, cove hardwoods are seldom found on poor sites, so there are

really only two site classes that this type occupies. Age class and stand size

class are also correlated in this way.

This primary grouping of forest conditions was not sufiicient to provide

groups homogeneous enough for analysis. Further subdivision was needed

in many primary classes. For example, one of the 136 primary classes was

"Oak type—medium site—poletimber—41-60 yr. old." This class contained 50 of the 572 survey plots, or about 8.7 percent of the total sample.

For the forest as a whole, this primary class encompasses about 65 thousand

acres, on the basis of its representation in the sample.

This class was further subdivided on the basis of basal area. Stands in

the class with less than 40 sq. ft. of basal area per acre in growing-stock

trees were considered candidates for a type conversion treatment.

Those with a growing-stock basal area above 40 sq. ft. per acre but a total

basal area of less than 80 sq. ft. per acre were to be retained, but were

considered to need no immediate treatment. Stands with growing-stock

basal areas above 40 sq. ft. per acre and total basal areas above 80 sq. ft.

per acre were considered to be candidates for a thinning treatment,

A subsample of the 50 survey plots that fell in the primary class showed

that about one-half of the area in this class had a stocking density that suggested thinning, about 35 percent needed no immediate treatment, and about

15 percent might benefit by a conversion treatment. The sample plots that

fell in the thinning subclass were much alike. The average d.b.h. for the

main stand was 8.4 in. in these sample plots; total basal area averaged

96 sq. ft., and growing stock basal area averaged 73 sq. ft. Optimal residual

basal area was determined to be 63 sq. ft. per acre, indicating a thinning

treatment removing 33 sq. ft. of basal area per acre on the average.

The listing below illustrates the definition of a modal project:

CLASS TITLE: Well-stocked oak poletimber on medium sites

CLASS DEFINITION:

Type.—50 percent or more of net cubic-foot volume in white,

black, scarlet and chestnut oaks, hickory and related

species.

Site class.—51-70 ft. at 50 yr. for oak.

Size class.—5.0-10.9 in. main stand average d.b.h.

Age class.—Age of main stand trees averages 41-60 yr«
Basal area class.—Total basal area exceeds 80 sq. ft. per acre, of which

at least 40 sq. ft. per acre is in growing-stock trees.

CLASS ACREAGE: 32,500 acres on the George Washington National Forest

MODAL CONDITIONS:

Site quality,—60 ft. at 50 yr. for oak.

D.bJio—8.4 in. average for main stand trees.

Age.—50 yr.

Basal area.—96 sq. ft. per acre total; 73 sq. ft. per acre in growingstock trees.

Species

composition.—37 percent red, black, and white oaks

34 percent chestnut oak

11 percent hard pines

4 percent yellow poplar

15 percent scarlet oak and other species

TREATMENT:

Type.—Thinning and cull tree deadening.

Intensity.—33 sq. ft. of basal area removed per acre.

Residual

stand.—63 sq. ft. of residual basal area.

—Average age and diameter not significantly changed.

—Residual species composition:

55 percent red, black, and white oaks

25 percent chestnut oak

15 percent hard pines

5 percent yellow poplar and other species

ESTIMATING ADDED YIELD

Reforestation and stand improvement projects are undertaken to increase

timber yield. The term "yield" as used here refers not just to volume, as

it does in most yield tables, but to any stand or tree characteristic that influences value and changes with time or stand management. Usually the timber

yield for a single species must be defined in three ways: A quantity measure

like volume or weight, a quality measure like tree grade or quality index,

and a measure of average unit size like average d.b.h,, because of the

influence of size on logging and milling costs.

Sometinîes practices exert most of their influence on a single yield factor.

For example, pruning primarily influences tree and stand quality. Most

practices, however, have multiple effects. A hardwood improvement cut, for

example, may increase volume, quality, and average d.b.h. at harvest by

retaining the larger, more vigorous, and better quality trees.

The analyst must adopt or develop a procedure for projecting timber

yields that is uniform for all projects in a given forest type. This procedure

should specify how yield factors are to be projected from a wide range

of initial stand conditions. It should take into account the possibility of

different rotation ages and alternate programs of subsequent silvicultural

treatment. Yield projection is usually the most complex analytical task in

preparing evaluations of reforestation and stand improvement projects.

6
Yield tables are a good starting point for relatively pure, even-aged stand

conditions. Yield tables alone seldom suflSce, however, and additional information will often be required. The stand table projection approach is often

best for mixed and uneven-aged stand conditions. Projections should not

ignore available research results. Studies that give estimates of yield,

growth, or treatment response can be used directly in stand table projections,

and indirectly in adapting yield tables to various conditions. Available

research data, then, can serve as checkpoints in developing or extending

available yield table and stand table projections.

Projection of quality may sometimes be dijGScult because information

about the eifect of time and treatment on quality is less abundant than information on volume and size. Yet it is necessary to make these projections,

even when the basis is at best doubtful. An objective estimate, even though

based on limited data, is better than a completely subjective one. Estimates

can and should be revised as better data become available.

Yield must be measured as of some future date and with a particular

intensity of future management in mind, since both subsequent management

and harvest date influence yield. And it may be necessary to assume different management programs depending on whether or not the project is

undertaken. In types where commercial thinning is assumed as a future

practice, thinning yields as well as the final harvest yield must be included

in the projections. Timber management guides and timber management

plans will indicate typical rotation ages and subsequent management plans

for the type. Both are frequently related to site quality. Select the most

likely rotation age and future management regime for each modal project,

and the most likely rotation age and future management regime that would

apply on the same area without stand treatment.

Having developed a yield projection technique and made estimates of

future management, it is now possible to estimate added yield. First, estimate yield without treatment for each modal project. Then, depending on

the projection procedure used, either estimate directly the yield added by the

project, or estimate total yield with treatment and let the difference between

the yield estimates with and without treatment define yield added.

In summary, a standard yield projection technique is developed and

applied to all modal projects in a single timber type, insofar as possible,

to avoid the inconsistencies of using different methods for different prqjects.

Future management is set for each project, with and without treatment,

according to silvicultural guides and management plans. Yield without

treatment is estimated for all modal projects, as well as yield with treatment

or yield added by treatment,

DETERMINING PROJECT COST

Project cost includes all the costs incurred because the project was undertaken, just as project yield includes all the yield added because the project

was undertaken.

The analyst will be interested primarily in estimating direct costs. Direct

charges include those for the labor, equipment hours, materials used to complete the treatment, and other costs that can be directly assigned to the

project and are not included in overhead, such as transportation to and
from the project area, professional planning, and supervision. The indirect

or overhead costs must also be included as a part of project cost. This is

most easily done by adding to direct cost a fixed percentage that reflects

the average relation between direct expenditure and overhead for the Forest

or Region.

Direct costs can be estimated by determining the physical inputs needed

to accomplish the required treatment and by multiplying each input by its

current unit cost. These data can come from cost studies or records of the

man-hours, equipment, and materials used on recent reforestation or stand

improvement projects. Accounting records of dollar cost may require careful scrutiny before use, because they often group heterogeneous projects and

may include charges for activities not directly related to stand treatment.

Project costs may be spread over several years. There are projects that

must be carried out in two or more steps spaced several years apart. Twostage pruning, for example, means pruning perhaps 10 feet of bole initially

and the remaining 7 or 8 feet some years hence. Such projects are undertaken in the expectation that subsequent treatments will be carried out in

later years. Compute costs for each treatment separately and estimate the

date of each treatment. Use the present prices of labor, equipment, and

materials to determine the cost of all treatments, unless there is suflScient

evidence indicating price change.

Costs, even for identical treatments under identical stand conditions, can

vary from project to project because of accessibility, crew efficiency, and

other factors that the analyst cannot take into account. Those who use

modal project evaluations as a guide to the rates of return that can be anticipated on actual projects may wish to recompute a return rate to reflect a

cost level for an actual project different from that assumed in the modal

project evaluation.

APPRAISING ADDED YIELD

Added yield ordinarily increases the stumpage income from the treated

compartment. Needed now is an estimate of what this income increase will

be for each modal project. Yield additions can be valued by applying current sales data or, where these are not available, the standard Forest Service

stumpage appraisal procedures.

Whatever unit price estimates are used, begin by computing the value

of the yield assortments expected if the modal project is not undertaken.

Prices, costs, and profit margins can be adjusted to reflect average conditions where necessary. Next, value the yield assortment expected with treatment and compute the difference between the two appraisals. The second

appraisal need not be made when the only significant effect of a project is

to increase volume (e.g., some regeneration projects). Here the percentage

increase in volume can be applied to the base appraisal to give value added.

There may be significant changes in product price and conversion cost

levels by the time added yields are harvested. Changes in the general level

of pulp or lumber prices and harvesting and processing costs—influencing

all timber types and treatments to a similar degree—usually do not influence comparisons among projects importantly. Differential price and cost

changes do. If conversion efficiency or product demand rise more rapidly

8
for some kinds of timber than for others, then projects yielding these kinds

of timber produce more value relative to other projects than is apparent

when yield additions are appraised at present prices. However, current

prices should be used in valuing yield until more reliable projections of

future prices are available.

COMPUTING RATES OF RETURN

The costs and added values for each modal project are used to compute

its internal rate of return. The procedures for making these calculations

are simple variations of the familiar methods of present worth and future

value computation used in forest finance.

One common problem in forest finance is to determine the present worth

of a future value discounted at a given rate of compound interest. For

example, consider a modal project with an added yield valued at $73 per

acre, and due 40 years after treatment. The present worth (i.e., at the time

of treatment) of this added value depends on the interest rate chosen. For a

5 percent discount rate,

?r = $73/(1.05)^«

= $10.37 per acre

where PW = present worth. In this problem the interest rate and future

value are given; present worth is the unknown.

The problem at hand is a variation of the above: to determine the interest

rate that makes present worth zero, given an initial cost and a future added

value. All the elements of the problem are given except the balancing interest rate, which is the unknown. Using the previous example and introducing

a project cost of $6.40 per acre, the equation becomes:

PW = 73/(1 + î)^^ - 6.40

Substituting zero for PW and rearranging terms:

6.40(l + £)^o=:73

(l + ¿)4o^ 73/6.40

(1 + 1)^0 = 11.41

and by consulting the 40 year line in a (1 + î)** interest table (Marty and

Neebe 1966) :

i = 6.3 percent

Rephrased, the problem is to determine the rate at which project cost

grows toward the additional stumpage income it produces. In the example

above the problem can be stated: If $6.40 were invested at compound interest, what would the rate of interest have to be to realize exacüy $73 40 years

hence? When the project cost is incurred during a single year and the

added return accrues at harvest—the simplest case—^then the balancing rate

of interest or internal rate of return can be computed in two simple steps:

by first calculating the value of (1 + i)** and then by finding the i that has

a corresponding value for n years in a (1 + i)** compound interest table.

The formula for finding the value of (1 + i)** is simply:

a + iy = R/C (1)

where R = per acre value added

C = per acre project cost
Some projects have more than one cost or more than one income or value

added. Indeed, a project may call for a whole series of costs and generate

a whole series of returns. Here is a general formula for any project.

Cx(i + i)^ + c^a + i)---^ + Cad + 0^"' +...

+ Cn-i(l + i)' + Cn{l + 0 = fiid + ¿)^-' + Ä2(l + 0*^-'

... + fin-i(l + 0 +Rn. (2)

There is provision for a cost and return item for every year between initial

treatment and final harvest in this equation. The unknown is the interest

rate, i, that will equate the future value of costs with the future value of

returns.

By convention, all costs occurring within a given year are considered to

have been incurred at the beginning of the year, and all returns occurring

within a single year are assumed to have accrued at the end of the year.

în most practical applications many of the yearly cost and return items

will be zero, for few projects have costs and returns in every year. Consider

a pruning project that calls for two treatments 10 years apart, with a single

return in 50 years. For this project the equation above simplifies to:

If each pruning costs $17 per acre and the added value at harvest is estimated

to be $128 per acre, then substituting these values we have:

17(1 + i)'' + 17(1 + i)^^ = 128

or (1 + £)'' + (1 + ¿)^o = 128/17 = 7.53

Since more than one cost is involved, there is more than one value of exponent n in the expression (1 + i)\ Thus i cannot be solved for by the

direct, two-step method. Instead it must be found by a process of successive

approximation, in which various values for i are substituted in the formula

until one is found that satisfies the equation.

The process can be begun with any interest rate. If 6 percent is substituted in the pruning example, the equation becomes:

18.420 + 10.268 = 7.529

28.706^^7.529

Since the cost side is far too high, the internal rate must be lower than

6 percent. Three percent gives:

4.384 -f 3.262 = 7.529

7.646:7^7.529

This is still a little high. 2.9 percent gives:

4.176 + 3.138 = 7.529

7.314 7^7.529

Since 2.9 percent is too low and 3.0 percent is too high, the balancing rate

must be somewhere between the two, and is probably closer to 3.0 percent

than to 2.9. In this way the analyst can determine the internal rate of

return within narrow limits. This basic method of successive approximation

must be used whenever the cost-return equation contains more than one value

for the exponent n.

The appendix provides additional compound interest formulas for simplified handling of various regular series of costs and returns. Also included

10
in the appendix is a description of a computer program for interest rate

computation (Row 1963). Where many interest rate analyses have to be

made by the method of successive approximation, this program can save

much time and expense.

TWO EXAMPLES OF MODAL PROJECT ANALYSIS

Examples may help the reader to a better understanding of project evaluation. The first example ^ involves precommercial thinning in ponderosa

pine, for which initial site and stand conditions can be summarized as

follows:

Type,—Pure, even-aged ponderosa pine

Site index,—120 ft. at 100 yr.

Size class,—Sapling stand

Stand age,—12 yr. after regeneration cut

Density,—^2,500 stems per acre

This specific set of conditions might be considered representative of densely

stocked stands of young ponderosa pine reproduction on medium sites.

A precommercial thinning is to be applied to the stand immediately, and is

expected to accelerate the growth rate enough to attain the product objective

20 years sooner than would otherwise be so.

Frequently, the project influences future management as well as rotation

length. If the stand receives a precommercial thinning now, at age 12,

future management will include a thinning for pulpwood at age 25, another

pulpwood thinning at age 40, saw log thinnings at ages 55, 70, and 85, a

shelterwood harvest at age 100, and shelterwood removal at age 110.

If the stand is not thinned now, its future management will involve pulpwood thinnings at ages 40 and 55, saw log thinnings at ages 70, 85, and 100,

and shelterwood reproduction cuts at ages 120 and 130. Tables 3 and 4

show these two management schedules, with project cost and output volumes

and values. A $50-per-acre cost for reproduction treatment is deducted

from the value of the final harvest in both programs. Unit values for both

pulpwood and sawtimber increase with stand age, reflecting increases in

average size and quality of timber.

Table 5 repeats the income and expense schedules for each program and

adds a schedule ("Marginal") that indicates the dijfference between the two

programs. Incomes in this schedule are those received in the precommercial

thinning program beyond those available in the alternate program, or expenses without precommercial thinning that are avoided in the precommercial thinning program. Similarly, expenses in the marginal schedule are

either those occasioned by precommercial thinning or incomes forgone.

The rotation age assumed, if precommercial thinning is employed, is 110

years; without this treatment rotation age is assumed to be 130 years.

Table 5 shows the schedules of both treatment alternatives for 130 years,

and so the schedule for the precommercial thinning program is extended

20 years into the second rotation, having incurred a second thinning expense

2 Harmon, Wendell H. Does precommercial thinning pay? U.S. Forest Service, Region

6. Portland, Oreg. 2 pp. mimeographed. 1963.

11
TABLE 3.—Management program for ponderosa pine on medium sites^ with'

out precommercial thinning

Stand Management

activity

Per acre yields Unit

value

Per acre values

age Pulpwood Sawtimber Expense Income

Years

An Pulpwood thinning

Pulpwood thinning

Saw-log thinning

Saw-log thinning

Saw-log thinning

Shelterwood cut

Shelterwood removal

Reproduction treatment

Cords

10

27

Mbdjt, Dollars

4

6

15

25

28

32

35

Dollars Dollars

40

55

70

162

13

14

12

22

13

195

350

100

120

130

130

336

704

455

50

TABLE 4.—Management program for ponderosa pine on medium sites, with

precommercial thinning

Stand Management

activity

Per acre yields Unit

value

Per acre values

age Pulpwood Sawtimber Expense Income

Years

19 Precommercial thinning

Pulpwood thinning

Pulpwood thinning

Saw-log thinning

Saw-log thinning

Saw-log thinning

Shelterwood cut

Shelterwood removal

Reproduction treatment

Cords Mbd.ft. Dollars Dollars

30

Dollars

25 8

27

4

6

15

25

28

32

35

32

AO 162

c;c; 13

14

12

22

13

195

70 350

ft«^ 336

TOO 704

no 455

lift 50

TABLE 5.—Individual and marginal schedules of program expenses and

incomes

[Dollars]

Individual schedules

Stand

age Without early thinning With early thinning Marginal schedule

Expense Income Expense Income Expense Income

Years

12 30 30

25 32

162

195

350

336

704

455

32

40 40

162

195

350

336

122

55 33

70 155

85 14

100 368

110 50 405

190 704 704

30

321

122 30

130 50 455 184

^The present value of incomes and expenses during the remainder of the second

rotation, when they are discounted at 7.9 percent.

12
but no second-rotation incomes as yet. A terminal value of $84 per acre is

shown here and is the discounted value, at stand age 20, of subsequent

second-rotation incomes.

Table 6 shows the calculations that demonstrate that the rate of return to

precommercial thinning, in this case, is very close to 7.9 percent. This is

shown by discounting the expenses and incomes of the marginal schedule

to the present and comparing them. Various discount rates were tried until

one was found that balanced costs and returns. In the actual computations

procedure, the terminal value for the precommercial thinning program was

recomputed each time a new interest rate was tried on the marginal schedule.

The second example presents the evaluation of a pruning project in eastern

white pine, adapted from Marty.^ Pruning is a frequently recommended

treatment for white pine since it improves timber quality markedly. The

site and stand conditions assumed for this project are as follows:

Type,—Pure, even-aged eastern white pine

Site index.—60 ft. at 50 yr.

Size class.—^Poletimber stand

Stand age.—30 yr. from seed

Density.—Fully stocked

The diameter distribution and total height by diameter class for this stand,

based on yield table data, are shown in table 7.

3 Marty, Robert. Timber investment decisions. 1961. (Ph.D. dissertation, Yale University, New Haven, Conn.)

TABLE 6.—Computation of present worth for incomes and expenses related

to precommercial thinning in ponderosa pine

[DoUars]

Time Discount

factor 1

Marginal schedule Present values ^

henoe

Expense Income Expense Income

Years

0 1.0000

2.6871

8.4062

26.298

82.270

257.37

805.16

1722.3

3683.9

4289.0

7880.0

30 30.00

13 32

122

33

155

11.91

28 14.51

43 1.25

58 1.88

73 14 0.05

88 368

405

0.46

98 0.24

108 704

30

321

0.19

0.01

0.04

110

118

Total« 30.29 30.25

1 Given by 1.079** when n is years hence.

2 Given by the expense or income divided by the discount factor indicated.

13
TABLE 7.—Stand table for a fully stocked, pure white pine stand of 30 years

on a medium site

D.b.h.

class

Number

of trees^

Range in

total heights

Inches

1.0-2.9

3.0-4.9

5.0-6.9

407

1463

280

Feet

18-24

25-30

31-34

1 Based on average diameter and number of trees above 1 inch d.b.h. (table 19) and a

general diameter distribution for fully stocked white pine stands (table 24) reported

by Gevorkiantz and Zon (1930).

2 Based on a percentage diameter-height distribution (table 178) reported by Brown

and Gevorkiantz (1934).

The treatment chosen for analysis involved pruning 150 well-distributed

pine per acre, all from the 6-inch d.b.h. class. Pruning was to be carried to

17^ ft. above the ground and accomplished in a single operation. A rotation age of 60 yr. was assumed for the stand. No other intermediate treatments were contemplated. Approximately 250 merchantable trees per acre

were expected at harvest.

The response to pruning over a given period is closely related to the rate

of tree growth. The expected diameter distribution 30 years hence at harvest age 60, for trees now in the 6-in. class, is shown in table 8. This estimate

again is based on normal yield data (Gevorkiantz and Zon 1930).

The second stage in predicting the response to pruning was to estimate

the expected increase in tree value for trees of various harvest diameters.

Three steps were involved: Predicting the change in butt log quality index

(QI), predicting the volume of butt logs at harvest, and predicting the value

of the increase in QI for butt logs of the predicted volume.

TABLE 8.—Diameter distribution 30 years hence for trees now in the 6-inch

d.bJi, class ^

D.b.h. class

Expected

number of

trees

Inches

Less than 9 or mortality

. 9.0-10.9

11.0-12.9

13.0-14.9

15.0-16.9

30

158

74

17

1

Total 280

1 Based on average diameter and number of trees above 1 inch d.b.h. (table 19) and a

general diameter distribution for fully stocked stands (table 24) reported by Gevorkiantz

and Zon (1930).

14
Table 9 shows the derivation of the prediction of change in QI for trees

of different harvest diameters. The second column shows the percent of

total butt log volume outside the knotty core. These estimates assume that

(1) pruning occurs when the tree is 6 inches d.b.h., (2) that 2 inches d.b.h.

growth are required to enclose branch stubs and pruning wounds, and (3)

that the scaling diameters of both the log and its knotty core are 2 inches

less than their diameters at breast height.

The third column shows the QI of unpruned butt logs. It is based on an

average of figures given for lumber grade recovery of second-growth New

England white pine (Davis 1940; Holland 1960). For unpruned trees, the

differences in butt log QI among the several diameter classes are assumed.

As pine increases in size more and more butt log branches die, causing the

formation of "loose" rather than "green" knots and thus a reduction in

lumber grade recovery. Further size increases tend to reverse this downward trend as dead Umbs drop and a clear shell develops. Because of the

persistence of dead limbs, however, litüe or no clear shell develops until pine

exceeds 16 inches d.b.h.

TABLE 9.—Change in butt log quality index (QI) due to pruning ^

Harvest

d.b.h. class

Clear volume

with pruning without pruning with pruning

Change in QI

due to pruning

Inches

10

12

14

16

Percent

25

40

54

63

74

72

71

72

90

98

107

114

16

26

36

43

^ See text for sources, assumptions, and derivations.

Column four shows the QI of logs that have been pruned. These estimates

were derived by taking the weighted (by volume) average of the QFs of the

knotty core and the clear shell. It was assumed that the knotty core would

produce lumber with a QI like that for an unpruned log of the same size,

and that the clear shell would produce select lumber with a QI of 138.

Column five shows the increase in QI due to pruning the butt log, given

by the difference between columns three and four.

Table 10 shows the derivation of butt log volume. Volumes are according to the International log rule with separate allowance for expected cull

due to weevil injury and other loss factors.

TABLE 10.—Butt log volumes for white pine

Harvest

d.b.h.

Girard

form class

But log

volume 1

Inches

10

12

14

16

Percent

83

83

82

82

Board-feet

23

38

56

78

1 Based on Bickford (1951) and represents International one-fourth-in. volume corrected for average reductions due to weevil injury and other defect factors.

15
The increase in value for pruned logs stems from the improvement in

lumber grade yield. The cost of conversion is assumed to be unchanged by

pruning. Lumber price for the base lumber grade (No. 1 and 2 Common)

is predicted to be $215 per M bd.-ft. in 1960 dollars 30 years hence. The

estimate is based on a published price projection for white pine lumber

(Holland 1960) and indicates that each board foot that is raised one point

on the QI will increase tree value by $0.00215. This multiplied by the

product of increase in QI due to pruning (table 9, column 5) and butt-log

volume (table 10, column 3) gives the value added per tree by pruning.

The results of these calculations are shown in the second column of table 11.

The average return per pruned tree is calculated in table 12. This computation, being a weighted average of value added of all trees in the 6-inch

d.b.h. class at time of treatment, assumes that pruned trees will have the

same diameter distribution at harvest as all trees in the 6-inch d.b.h. class.

On a per-acre basis the 150 trees yield an added value at harvest of $193.50.

TABLE 11.—Value response to pruning

Harvest

d.b.h.

Value added

per tree^

Inches

10

Dollars

0.79

12 2.12

14, 4.33

16- - 7J21

1 Based on tables 9 and 10, and Holland (1960).

TABLE 12.—Computation of average value added per pruned tree when

pruned trees have the same diameter distribution at harvest as all trees

D.b.h. class

Relative

frequency

Value added

per tree

Value added

per class

Inches

T^ftss tban Q nr mortality

Percent

10.7

56.4

26.4

6.1

.4

Dollars

0

.79

2.12

4.33

7.21

Dollars

0

QO-IOQ 45

71.n-19 0 55

l.^.O-U.Q 26

ISO-lfiQ 03

Averagft valuft per pruned tree. 1J29

Two studies that report white pine pruning costs (Meyer 1940; Ralston

and Lemmien 1956) for particular operations give physical performance

rates of 176 and 130 bole-feet per hour. A range in performance rates from

50 to 200 bole-feet per hour has also been reported (Cline and Fletcher

1928). A performance rate of six trees per man-hour (approximately 105

bole-feet per man-hour) was assumed in the example.

If the average cost per man-hour is $1.75 for the pruning crew, then the

16
direct labor charge amounts to $43.75 per acre. Supervision, transportation, equipment maintenance, and other overhead expenses might bring the

per-acre cost to $55 or $60 for a compartment of average accessibility.

The return/cost ratio for this project, at a cost of $60 per acre, amounts

to 3.225. This indicates an internal rate of return of about 4 percent for

the 30-year period. A $50 cost per acre would produce a return rate of about

4.6 percent, whereas a $70 per acre cost would yield a return of about 3.4

percent.

LIMITATIONS OF RETURN RATE ESTIMATES

Project evaluations are neither perfectly reliable nor unaffected by other

management activities and thus should be interpreted and used with care.

This section contains a brief discussion of some of the limitations of rate

of return estimates.

THE REUABIUTY OF RATE OF RETURN ESTIMATES

It has been stressed in several places that the data used to determine rates

of return for modal projects are not completely reliable. Physical cost data,

yield response data, and dollar prices are estimates that ordinarily will not

always be exactly correct; thus, the rate of return estimates for modal

projects may not always be exactly correct.

If all the information used were accompanied by statistical variance statements, the analyst could compute a variance estimate for each rate of return,

and in this way present some information on the reliability of each estimate.

Relative reliability can be an important consideration in ranking projects.

Which should be ranked highest: a project that is almost sure to have a

4-percent rate of return, or one that might fall between 3 and 6 percent?

There are differences of this sort within most groups of projects.

Unfortunately, the analyst seldom has the statistical information with

which to objectively estimate these differences in reliability. However, it

may be worthwhile sometimes to see how the return rate fluctuates under

various assumptions about uncertain factors. A description of this analytical approach can be found in Marty (1964).

A second source of error in rate of return estimates comes in the application of guides. Rate estimates for modal projects will often be applied in

situations somewhat different from that assumed for the modal project. So

even if the modal project rate were exactly correct, when applied to nonmodal conditions it may overestimate or underestimate the rate of return

somewhat. This second type of error can be partly reduced by increasing

the number of modal projects analyzed. The more stand conditions and

treatment variations investigated by the analyst, the more probable will be

a modal project that closely approximates each actual project.

RATE OF RETURN SENSITIVITY

The analyst should be aware that the sensitivity of a return rate, as

a measure of economic desirability, decreases as the investment period

lengthens. It requires only a 10-percent increase in returns, or decrease

in costs, to cause a 1-percent increase in rate of return when the investment

period is 10 years. When the investment period is 50 years, it requires a

17
60-percent increase in the return/cost ratio to cause a 1-percent increase

in internal rate of return. Seventy-five-year investment periods, typical of

many projects, require doubling of the return/cost ratio to increase a return

rate 1 percent. What this means is that there may not always be large differences in the rates of return among modal projects, so that even small

differences between rates are significant when investment periods are 30

years or more.

INTANGIBLE FACTORS

Rate of return estimates are based on dollar costs and returns of timber

production. But there are other factors that influence the desirability of

projects. These are often the intangible or unmeasurable aspects of a project. Frequently they relate to other products or services of the compartments being treated. What will the influence of a project be on wildlife

habitat, on water yields, on scenic values? For most projects these effects

may be negligible. Some projects, however, do cause marked changes in

the flow of other products, sometimes increasing them, sometimes decreasing

them. The analyst could consider these changes as additional costs or returns to the project if they could be evaluated in dollar terms. When, as

often happens, they cannot be so measured, they cannot be included in calculations to determine internal rates of return. For the present, consideration

of these intangible effects is left to those who apply the modal project

evaluations. The guides described in this handbook do not take these effects

into consideration.

INTERACTION AMONG MANAGEMENT ACTIVITIES

A regeneration or stand improvement project can significantly influence

the value of future management activities. For example, pruning in a young

pine stand increases the quality and value of volume growth. Therefore,

subsequent cultural treatments that save or increase this growth produce

more value than they would in unpruned stands. Improvement cuts in

young hardwood stands also make subsequent management practices more

profitable for similar reasons.

The analysis of single regeneration or stand improvement treatments does

not take these interactions into account. Most projects probably do increase

the value and profitability of subsequent treatments, but this is not counted

as one of the returns or added values of the initial project. Thus, return

rates for modal projects in young stands may underestimate true economic

benefits

Strictly speaking, individual projects should not be the unit of management evaluation. Rather, series of treatments—entire management regimens

—should be compared. This would allow assessment of the combined economic benefit of a series of interdependent treatments, which could be

summarized by the net or average rate of return to the entire series of

practices scheduled.

To summarize, return rate estimates for modal projects are not perfectly

reliable, and there is an additional source of error in applying them under

nonmodal conditions. The important things for the analyst to remember

are that users should be made aware of any marked differences in the reliability of various modal project return estimates, and that application error

18
can be reduced by increasing the number of modal projects so that more

treatment variations and stand conditions are evaluated. Also, return rates,

although not the only valid measure of economic desirability, are easily used

and understood, but become less sensitive measures as investment period

increases. Small changes in return rates are significant where the investment

period is 50 years or more.

Rates of return measure only the net effect of tangible costs and returns to

projects. Intangible effects, which may sometimes be important and even

overriding, are not taken into account. Users should be made aware of this,

and they must judge the effect of intangibles. Finally, guides that consider

only single treatments ignore the relationships and interdependence among

sequences of treatments. It may sometimes be necessary to undertake subsidiary analyses of treatment series when individual analysis may significantly misrepresent the real contribution of a treatment.

LITERATURE CITED

Bickford, C. Allen.

1951. Form-class volume tables for estimating board-foot content of

northern conifers. U.S. Forest Serv. Northeast. Forest Expt.

Sta. Station Paper 38. 33 pp., illus.

Brown, R. M., and Gevorkiantz, S. R.

1934. Volume, yield and stand tables for tree species in the Lake States.

Minn. Univ. Agr. Expt. Sta. Tech. Bui. 39. 208 pp., illus.

Cline, A. C, and Fletcher, E. D.

1928. Pruning for profit as applied to eastern white pine. Harvard

Forest and Mass. Protective Assoc. Bui. 24 pp., illus.

Davis, E. M.

1940. Lumber from old-growth versus lumber from second-growth in

Pinus strobus. Jour. Forestry 38: 877-880.

Gevorkiantz, S. R., and Zon, Raphael.

1930. Second-growth white pine in Wisconsin. Wis. Univ. Agr. Expt.

Sta. Res. Bui. 98. 40 pp., illus.

Holland, I. Irving.

1960. A suggested technique for estimating the future price of eastern

white pine stumpage. Forest Sei. 6: 369-396, illus.

Marty, Robert.

1964. Analyzing uncertain timber investments. U.S. Forest Serv. Res.

Paper NE-23, 21 pp., illus.

and Neebe, David J.

1966. Compound interest tables for long term planning in forestry.

U.S. Dept. Agr., Agr. Handb. . pp.

Meyer, WiUiam H.

1940. Pruning natural pine stands.

Jour. Forestry 38: 413-414.

Ralston, Robert A., and Lemien, Walter.

1956. Pruning pine plantations in Michigan. Mich. State Univ. Agr,

Expt. Sta. Cir. Bui. 221. 27 pp., illus.

Row, Clark.

1963. Determining forest investment rates-of-retum by electronic computer. U.S. Forest Serv. Res. Paper SO-6. 13 pp., illus.

19
APPENDIX

COMPOUND INTEREST FORMULAS

Formulas Dealing With Single Values

1. Future value of a current cost or income:

F„ = F.(l + Í)»

2. Present value of a future cost or income:

Vo = VJ{l + i)-

Formulas Dealing With Series of Equal and Annual Values, Beginning 1

Year Hence

3. Present value of a perpetual series:

Vo = V/i

4. Future value of a terminable series:

Vn==V[{l + i)-^l]/i

5. Present value of a terminable series:

F, = F[(l + i)"-l]A(l + ^')"

Formulas Dealing With Series of Equal, Periodic Values, Beginning 1 Year

Hence

6. Present value of a perpetual series:

v„ = v/ii + iy-i

7. Future value of a terminable series:

v„=v[(i + i)'>-i]/ii + iy-i

8. Present value of a terminable series:

Fo = F[(l + 0'*"-l]/[(l + 0*-l](l + 0'*

where

i = the Annual rate of interest expressed as a decimal

n = the number of years over which a value is discounted or compounded, or the number of years in a terminable series

F = an annually or periodically recurring value

t = the number of years between periodic recurrences of V

Vo = the present or initial value at year zero

Vn = the future or end value after n years

A COMPUTER PROGRAM FOR RATE OF RETURN

COMPUTATION

The program published by Row (1963) was written to compute, simultaneously, rates of return for up to six investment alternatives, each with

separate physical output data, under a common set of price and cost assumptions. Internal rate of return is given by the interest rate that most nearly

equates future costs and returns with the capital investment necessary to

obtain them. Copies of Row's paper are available.

The program is suitable for computing return rates for many stand improvement and regeneration projects. However, it has been altered to allow

analysis of alternatives which extend beyond 99 years and which include

20
more numerous costs and returns. Another change permits the analyst to

choose the range and interval of interest rates to be used in computing

present worths. It is possible, for example, to use rates lower than 3 percent

or greater than 30 percent and to set the interest rate increment as small as

0.1 percent.

A printout of the revised program and instructions for preparing data

input cards follow. The program is written in Fortran IV language and

can be used with any IBM^ 700/7000 series computer.

^ Use of commercial names is for identification only and does not imply endorsement.

» LABEL

GHARTY

C INVeSTHHNT ANALYSIS PROGRAM SOUTHERN FOREST EXPERIMENT STATION

C ICLARK ROW 62

DIMENSION AISiC(10)9CANC(10)«NC{6,200)«PECa(6,200)«Nl(6o2QO)«YL01(6,

1200},QUAL1(69 200),N2(6»200)»QUAL2(6,200),N3(6«200)«YL03(6 9200)*QUA

2L3(6,200)tPR(3,20),CPR(,3,20UFVALC25l,RATE(200),RTLOG(2CO)iVALIN(

36,20O),LY(6)»KCX(6),KlX(6)9K2X(6)«K3X(6)9A(26),LIC6)9YL02(6,200l

DIMENSION RINT(3)

OISCiX)= RTLOI«»X

142 READ(5»17000)(RINT(npI«l,3)

17000 FORMAT Í3F4.3)

RATE(1)=RINT(1)

DO 17001 1=2,200

IF(RATEII-1)-RINTC3)) 17002,17003,17003

17002 RATE(I)=RATE(I-l)*RINT(2)

GO TO 17001

17003 LENGTH=I-1

IF(M0D(L£NGTH,2)) 17004, ITO^OS» 17004

17004 LLNGTH=*CLENGTH+l)/2

GO TO 137

17005 LLNGTH=LENGTH/2

CO TO 137

17001 CONTINUE

137 DO 138 1=1,LENGTH

138 RTLOG(n = l.+RATE(n

KEAD(5,ll)N0,LZ,LX,(LI(L),L=l,6),(LY(L}fL=l,6),KX,KCXX,

l(KCX(L)9L=l,6),KIXX,<KlX(L),L=l,6),K2XX,(K2XCLi,L=

21f6),K3XX»IK3,X(L),L=l,6), JXsMX.NZ.NX

11 . FORMAT t3I2,1213,12/2113/713,412)

READ(5,15nA(I),1=1,14)

15 FORMAT C14A5)

READ(5,15)(At(I),1 = 15926)

HRITEf6,20 )

20 FORMAT (91H1 INVESTMENT ANALYSIS PROGR'AM

1- SOUTHERN FOREST EXPERIMENT STATIONI

WRITEC6,21)N0,CA{I),I=1,14)

21 FOftMAT (14H0 PROBLEM NO , I4,r IH , 16A5Í

144 IF{LZ-2)145,146,147

145 WRITEI6,23 )

23 FORMAT (73H0 ROTATX

ION LENGTH IN YEARS)

GO TO 149

146 MRITE(6,24 )

24 FORMAT t70H0 SIT

XE INDEX IN FEET)

GO TO 149

147 MRITE(6,25 )

25 FORMAT (69H0 PPPB

IDUCTION SYSTEM)

149 WRITE(69 26) (LI(L), L»1,LX)

26 FORMAT (111,5120)

IF (KCXX) 160,160,152

152 SíRITE<6,27 )

27 FORMAT {17H0 PERIODIC COSTS,/115H YEAR COST YEAR C

lOST YEAR COST YEAR COST YEAR COST

2 YEAR COST)

DO 155 KC=lirKCXX

HEAD(5,13)(NC(L,KC),P£C0CL,KC),L=1,6)

13 F0RMAT(6<î3,F9-2) )

155 WRITEÍ6,29)(NC(L,KC), PEC0(L,KC),L=1,LX)

21
29 FORMAT (ló^f9.2,5(I 11,F9.2))

160 IF ÍKIXX) 1709170,162

162 WRITEf6, 30)CA(I)»I= 15,18)

30 FORMAT Í25H0 PERIODIC RETURNS FROM , 4A5)

WRITEC6,31 )

31 FORMAT Í118H YEAR YIELD QUAL YEAR YIELD QUAL YEAR YIELD

IQUAL YEAR YIELD QUAL YEAR YIELD QUAL YEAR YIELD QUALÎ

DO 165 Kl= IjKlXX

REA0C5,14HN1(L,K1),YLD1{L,K1),QUAL1(L,K1)»L = 1,6)

14 FORMAT (6CI3,F5.1,F4o2))

165 WRIT£(6, 32) (NKL, Kl ) ,YLD1 (L,K1 ) »QUALl (L,K1 ) ,

1L=1,LX)

32 FORMAT ÍÍ6, F6,l, F6«2, 5(18, F6.1, F6.2))

170 IF(K2XX) 180,180,172

172 WRITEf6,30)ÍAn),I=19,22)

WRIT£Í6,31 )

DO 175 K2=1,K2XX

READ(5,14ÍÍN2(L,K2),YL02ÍL,K2),QUAL2(L,K2),L=:1,6)

175 WRIT£I6»32)(N2ÍL,K2),YLD2(L,K2),QUAL2(L,K2),L=1,LX)

180 IF (K3XX) 190,190,182

182 WRITEC6,30)ÍA(I), 1=23,26)

WRITeí6,31 )

00 185 K3=:1,K3XX

READí5,14)CN3(L,K3),YLD3a,K3),QUAL3íL,K3),L=l,6)

185 WRITEÍ6#32)(N3(L,K3),YLD3(L,K3),QUAL3(L,K3),L=1,LX)

12 FORMAT (8F9«3)

190 READ<5,12)IANC(J), CANC(J),J=l,JX)

DO 191 M=1,MX

1200 F0RMAT(6F8.3)

191 READ(5,1200)(PR(K,M),CPR(K,M),K=1,KX)

192 ÍF(NZ-IU95,195,193

193 READf5,12Í (FVAHN) ,N=1» NX)

195 DO 390 J=«1,JX

DO 390 M=1,MX

198 DO 390 N=1,NX

WRÎTEÎ6, 34)ANC(J),CANC(J)

34 FORMAT {37H0 ANNUAL COST $, F7.2, 46H

1 CHANGE IN ANNUAL COST ,2PF11.2, 17H PERCENT PER

2YEAR)

WRITE(6,35)(A{4»K+li),A(4»K*12),

1A(4»K*13),A(4«K+14),PR(K,M),A<4«K+11),A(4»K+12),

2A14»K+13),A(4»K+14),CPR{K,M),K=1,KX)

35 FORMAT Í12H PRICE OF , 4A5, 5H $,0PF7.2, 26H CHANGE IN

IPRICE OF , 4A5,2PF11.2, 17H PERCENT PER YEAR)

IF(NZ-1)204,204,205

204 WRITEÍ6,36 )

36 FORMAT C30H PERPETUAL INVESTMENT SERIES)

GO TO 210

205 WRITEC6,37) FVAL(N)

37 FORMAT Í37H VALUE AT END OF ONE INVESTMENT $, F7.2)

210 DO 345 L=1,LX

KCXA=KCX(L)

KIXA^KIXÍL)

K2XA=K2XtL)

K3XAs=K3X(L)

XLY=FLOATCLY(L))

ASSIGN 220 TO NZERO

DO 340 1=1,LENGTH

GO TO NZERO,(22CU330)

220 DANC*0-0

DCANC=0a0

22
DKC=OoO

DKl^O.O

DK2=0.0

DK3=0.0

DFVAL=0,Û

. RTLOI=RTLOGÎÎ)

DISCO = RTLOG(n»»XLY

IF{ANC(J)) 225,2309225

225 DANC={ANC(JÎ«{DÏSCO-l.))/(ftAT6(n»0ÏSCO)

230 IF (CANCCJ)) 235,240,235

235 DCANC=CCANC(J)»ANC(J)»(DÍSC0-XLY»RATEíI)-U))/(RATECn»»2»DíSC0J

240 IF(KCXÂ) 250,250,241

241 DO 245 KC=l,KCXA

XNC=FLOAT{NC(L,KC))

245 OKC=OKC+PECO(L,KC)/DISC<XNC)

250 IF CKIXA) 260,260,251

251 DO 255 K1=1,K1XA

XN1=FL0ATCN1{L,K1))

255 DK1^0K1+CYL0HL,K1)»PRI1,M)«QUALUL,KU»(1.*CPR(1,MÎ

l»XNl))/DiSC(XNl)

260 IF (K2XAÎ270,270,261

261 DO 265 K2=1,K2XA

XN2=FL0ATCN2ÍL,K2))

265 DK2=DK2+(YLD2ÍL,K2í»PRt2,M)»CÍUAL2(L,K2)*íl.*CPR(2,M

lÍ»XN2n/0ISCÍXN2)

270 IFCK3XA)280,280,27l

271 DO 275 K3=1,K3XA

XN3s=FL0ÄT<N3(L,K3))

275 DK3=DK3*(YL03(L,K3)«PR(3,M)*QUAL3ÎL,K3)*Cl.*CPR(3,H)»XN3ll

1/DISCCXN3]

280 TDVAL=DK1+DK2+DK3-DANC-DCANC-DKC

IFIN1-1)290,290,295

290 VALINa,I)=T0VAL «( 1 .*l./( OISCO-1. ) Î

GO TO 340

295 DFVAL=FVAL«N)/D1$C0

VALINCL,n=TDVAL+DFVAL

IFÍVALINÍL,IÍ)330,340,340

330 VALIN(L,n=0.0

ASSIGN 330 TO NZERO

340 CONTINUE

345 CONTINUE

WRITE(6,38 )

38 FORMAT (70H PRESENT DISCOUNTED NET WORTH AT GIVEN ALTERNATIVE RA

ITES OF INTEREST)

WR1TE(6,40)(LYÍL),L=1,6),(LY(L),L-1,6)

40 FORMAT Í7H RATE, 19, 518, 12H RATEt 19, 518)

DO 365 I=1,LLNGTH

I13=I*LLNGTH

365 WRITEI6,41) RATE!I),(VALIN(L,I),

1L-1,6),RATEC113),{VALIN(L,I13),L=1,6)

41 FORMAT(2PF7.1,0PFll,2,0P5F8.2,2PF9.1,0PFll.2,0P5F8.2)

390 CONTINUEREA0(5,11) IÊND

IF(IEND-98)400,142,410

400 WRITE(6,42 )

42 FORMAT(23H0 ERROR IN INPUT CARDS)

410 CALL EXIT

END

Data Input Instructions—Row Interest Rate Program as Altered

Card Columns Item

Control—1 1-4 Minimum rate of interest

5-8 Interest rate increment

9-12 Maximum rate of interest

Field

.XXX

.XXX

.XXX

Control—2 1-2 Problem number XX

3-4 Alternative type 01, 02, or 03 XX

5-6 No. alternatives 01-06 XX

7-24 3-digit no. identifying each alternative XXX

25-42 Length in years of each alternative

(1-999) XXX

43-44 Max. no. different products (0-^3) XX

23
Card Columns hem Field

Control—3 1-3 Max. no. periodic costs XXX

4-21 No. periodic costs, each alternative XXX

22-24 Max. no. returns for product 1 XXX

25-42 No. returns for prod. 1 each alternative XXX

43-45 Max. no. returns prod. 2 XXX

46-63 No. returns for prod. 2, each alternative XXX

Control—4 l-nS Max. no. returns prod. 3 (0-50) XXX

4-21 No. returns for prod. 3, each alternative XXX

22-23 No. sets of annual costs (0-10) XX

24-25 No. sets of product prices (0-20)

Type of terminal cidculation 01 or

XX

26-27

02 XX

2a-29 No. of final values (0-25) XX

Problem Name 1-72 Name of problem

Product Names 1-20 Name of product 1

21-40 Name of product 2

41-60 Name of product 3

Periodic Cost--« 1-3 Year of ith cost for alt. 1 XXX

4-12 ¿th cost for alt. 1 XXXXXX.XX

13-15 Year of ith cost of alt. 2 XXX

16-25 ith cost for alt. 2 XXXXXX.XX

26-28 Year of ith cost for alt. 3 XXX

29-37 ith cost for alt. 3 XXXXXXJCX

3e-40 Year of ith cost for alt. 4 XXX

41-^ ith cost for alt. 4 XXXXXX.XX

4^51 Year of ith cost for alt. 5 XXX

52-60 ith cost for alt. 5 XXXXXX.XX

61-63 Year of ith cost for alt 6 XXX

64-72 ith cost for alt. 6 XXXXXX.XX

Product retums--;Ä 1-^ Year of the /th return for the kxk

product for alt. 1 XXX

4-8 Volume of the /th yield for the Ath

product for alt. 1 XXX.X

9-12 Quality index of the /th return for

the Ä:th product for alt. 1 X.XX

— and so forth for all six alternatives

Amiual costs—i 1-9 ith annual cost assumption XXXXX.XXX

10-18 ith change in annual cost assumption XXXXX.XXX

— and so forth for up to 10 sets —

Prices—Í 1-8 ith unit price assumption for product 1 XXXX.XXX

9-16 ith annual change in unit price

assiuned for prod. 1 XXXX.XXX

Final Values—i 1-9

and so forth for all 3 products—

(additional cards of other sets of

price assumptions to a maximum

of 20)

ith final value assumptions

and so forth for a maximum of 25.

XXXXX.XXX

Terminal Card 1-2 Terminal code (98 or 99) XX

l!^U. 8. GOVERNMENT PRINTING OFFICE: 1966 798-480

24