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Capital Budgeting Decisions
Learning Objectives
1. Evaluate the acceptability of an investment project using
the net present value method.
2. Evaluate the acceptability of an investment project using the internal
rate of return method.
3. Evaluate an investment project that has uncertain future cash flows..
4. Rank investment projects in order of preference.
5. Determine the payback period for an investment.
6. (Appendix 14A) Understand the concept of present value and make present
value computations with and without the present value tables.
Lecture Notes
A. The Concept of Present Value (Appendix
14A Money has a time value. A dollar today is worth more
than a dollar in the future for the simple reason that a
dollar can be invested today to yield more than a dollar in
the future. When an investment involves cash flows over many
years, this time value of money becomes important and should
be taken into account in investment decisions. Simply adding
together cash flows from different periods is like adding
apples and oranges; dollars in different periods have
different values.
NOTE: As an example would you prefer to
receive a gift of $100 today or a year from now? Almost
everyone will respond they would prefer $100 today. Why is this? Some will say that the value of the dollar could
decline due to inflation. Some will say that they would like
to spend the money now. What if there is no inflation and
the money can't be spent until the end of the year even if
it is received now? Repeat the question in the first sentence. Hopefully,
you will respond that it is always possible to put $100
in the bank today and wind up with more than $100 in a year.
Therefore, the opportunity to take the money now is clearly
attractive. This is the reasoning underlying present value;
the value today of a dollar a year from now should depend
upon the rate of return during the year.
1. The mathematics of interest.
a. The relation between an amount P,
which is invested at the interest rate r, and the
value of the investment after n periods, Fn, is given
by:
Fn = P(1+r) n (n referring to
the nth power).
This formula assumes that the interest is
compounded at the end of each period. For simplicity,
we assume throughout the text and problem materials
that interest is compounded annually.
b. The difference between the present value,
P, and the future value at any point in time, Fn, is
the interest earned on the investment through time n.
Exhibit 14A-1 in the text illustrates the relation
between present value and future values and how future
values grow over time.
2. Present value factors.
a. Rather than making decisions based
on future values, it is conventional to express the
values of future cash flows in terms of present
values. This can be done by rearranging the compound
interest formula as follows:
P = Fn / (1 + r)n = Fn (1 /
(1+r)n)
To find the present value of the amount Fn to be
received n periods in the future, we just apply the
formula using the appropriate interest rate r ( you
may also see k or i designated for interest).
b. The process of finding the present value
of a future cash flow is called discounting. The
interest figure that is used to find the present value
is called the discount rate.
c. The quantity in brackets in the above
formula is called a "present value factor PVIF)."
PVIF = ( 1 / (1 + r )n)
Table 14C-3 provides present value factors for a
wide range of values of r and n. The present value
factors can also be easily computed using the power
key on calculators.
NOTE: It is worthwhile to go over
the present value table, emphasizing some important
points. Suggest to students that they think in terms
of making a deposit in a bank. Ask them why the
present value factors decrease as the interest rate
gets larger. The answer is that as the interest rate
gets larger, you can get the same future value with a
smaller deposit today. Ask them why the present value
factors get smaller as the number of periods
increases. The answer is that if there are more
periods for compounding to work, a smaller deposit
today will yield the same amount in the
future.
3. Present value of a series of cash
flows. Some investments involve a simple annuity,
which is a series of identical cash flows that begin at
the end of the first period and continue for a total of n
periods into the future. The present value of such an
annuity can be computed as the sum of individual present
value factors, through the use of annuity tables, or
using a formula.
NOTE:
Table 14C-4 in Appendix 14C was derived by simply adding
the present value factors down each column from Table
14C-3. You should understand that the annuity table
is valid only for a particular type of annuity - one that
starts at the end of the first period and involves
exactly the same cash flows every period until it
ends.
B. Capital budgeting. The term capital
budgeting is used to describe actions relating to planning
and financing capital outlays for purposes such as purchase
of new machines, introduction of new products, and
modernization of facilities. Capital budgeting involves a
commitment of funds now in order to receive cash flows in
the future.
1. Typical capital budgeting decisions.
Capital budgeting decisions tend to fall into two broad
categories-screening decisions and preference decisions.
a. Screening decisions relate to
whether a proposed project meets some preset standard
of acceptance. For example, does a particular
investment generate at least a minimum desired return
of, say, 20%? Screening involves grouping alternatives
into acceptable and not acceptable categories.
b. Preference decisions relate to selecting
from among several competing courses of action.
Preference decisions rank alternatives in order of
desirability.
2. Characteristics of business investments.
Most business investments involve depreciable assets that
have little or no resale value at the end of their useful
lives. Thus, the assets must generate sufficient cash to
provide a return on the investment and to provide a
return of the total amount of the original investment
itself. Furthermore, since a dollar today is worth more
than a dollar tomorrow, the future cash flows should be
discounted to the present.
C. Discounted Cash Flows-The Net Present Value
Method. The net present value of a project is the
difference between the present value of all cash inflows and
the present value of all cash outflows. If the net present
value is positive, the investment project is acceptable. If
the net present value is negative, the investment project is
unacceptable. Both of these statements assume, of course,
that there are no other important factors beyond the cash
flows.
1. Importance of the discount rate.
This discount rate is typically the minimum required rate
of return that a company sets on all investment projects
and is often the company's cost of capital. The cost of
capital is the overall cost to an organization of
obtaining investment funds, including the cost of both
debt and equity sources. A change in the discount rate
can dramatically affect the decision of whether to accept
or reject an investment project.
2. Emphasis on cash flows. When computing
the net present value of a project, cash flow-and not
accounting net income-is ordinarily discounted. However,
recent work by Ohlson and Feltham and others has shown
that under specific conditions, it is also appropriate to
discount carefully defined accounting net income.
Nevertheless, the conditions are fairly stringent, so we
only consider discounting cash flows in the text.
a. Typical cash outflows include the initial
investment, increased working capital requirements, repairs and maintenance,
and incremental operating costs.
b. Typical cash inflows include incremental revenues,
reductions in costs, salvage value, and release of working capital.
SUGGESTION: The role of working capital
in capital budgeting sometimes confuses people..
The initial investment in working
capital at the beginning of the project for items such
as inventories is recaptured at the end of the project
when the working capital is no longer required. Thus,
working capital is recognized as a cash outflow at the
beginning of the project and as a cash inflow at the
end of the project.
3. Recovery of the initial investment.
The net present value method automatically provides for a
return on the original investment in a project. This is
illustrated in the text in Example B.
4. Assumptions of the net present value
method. The net present value method assumes that all
cash flows are known with certainty and that all cash
flows generated by the project are immediately reinvested
at a rate of return equal to the discount rate.
5. Additional simplifying assumptions. We
make several additional assumptions that are not inherent
characteristics of the Net Present Value Method but which
simplify the material considerably.
a. We assume that all cash flows either
occur immediately or at the ends of periods. (Usually
the periods are years.) In reality, most cash flows
occur more or less uniformly throughout the period.
b. We assume that there is no inflation. As
discussed in Appendix 14B, inflation affects both the
discount rate that should be used and the estimates of
future cash flows. If there is inflation, then
managers must take care to be consistent in their use
of discount rates and cash flows. For simplicity, we
assume in both this chapter and in the subsequent
chapter that there is no inflation.
c. We assume that there are no income taxes
in Chapter 14. In appendix 14D, income
taxes are introduced. Income taxes affect both the cash flows and the
discount rate that should be used. If there are income
taxes, an after-tax discount rate should be used.
D. Discounted Cash Flows-The Internal
Rate of Return Method. The internal rate of return (IRR)
is the rate of return on an investment over its useful life.
The internal rate of return of a project is the discount
rate that will result in a zero net present value for the
project.
1. The case of even cash flows.
When the cash flows associated with an investment are the
same every year, the net present value of the project can
be computed as follows:
Net present value = Investment required (show as
a negative number)
+ (Net annual cash flow times the PVIFA ). ( Present
value factor for an annuity)
The internal rate of return is the discount rate
that results in a zero net present value. Setting the net
present value equal to zero above and solving for the
"Present value factor for an annuity" (PVIFA) yields the
following formula:
Factor of the IRR = Investment required / Net
annual cash inflow
To find the internal rate of return, locate the factor
computed above in the present value table for an annuity
in the row corresponding to the useful life of the
project. In practice this often requires interpolation
since the factor is likely to fall between two values in
the present value table.
2. The problem of uneven cash flows. When cash
flows are uneven, the above formula cannot be used to
find the factor that results in a zero net present value.
Instead, it may be necessary to resort to trial and
error. Doing this by hand can be quite a chore, but is
fairly easy if the problem is set up on a computer
spreadsheet. Also, computer spreadsheets contain macros
(such as "solver" in Excel) that can automate the trial
and error process.
3. Using the internal rate of return. The
internal rate of return of any investment is compared to
whatever rate of return the organization requires on its
investment projects. If the internal rate of return is
equal to or greater than the required rate of return,
then the project is acceptable. If the internal rate of
return is less than the required rate of return, the
project is rejected. Of course, non-financial factors may
override these rules.
E. Cost of Capital as a Screening
Tool. The cost of capital can be used as a screening
tool in both discounted cash flow methods. When the internal
rate of return method is used, the cost of capital is the
hurdle rate that a project must clear for acceptance. When
the net present value method is used, the cost of capital is
the discount rate.
F. Net Present Value versus Internal Rate
of Return. The net present value method of making
capital budgeting decisions has several advantages over the
internal rate of return method.
1. The net present value method is
simpler to use. It does not require trial-and-error
methods.
2. The internal rate of return method
assumes that the cash flows can be reinvested at whatever
the internal rate of return turns out to be-even if the
internal rate of return is very high. The net present
value method assumes that cash flows can be reinvested at
the discount rate. The assumption made under the net
present value method is usually more realistic.
G. Expanding the Net Present Value
Approach. The net present value approach can be expanded
to include two alternatives and to integrate the concept of
relevant costs. Two approaches-the total-cost approach and
the incremental-cost approach-are used to compare competing
investment projects.
1. The Total-Cost Approach. In the
total-cost approach to net present value, all cash
inflows and all cash outflows are included in the
computation of net present value for each alternative.
The net present value figures for each of the two
alternatives are compared and the alternative with the
higher net present value is preferred.
2. The Incremental-Cost Approach. Under the incremental-cost
approach, only those costs and revenues that differ between the alternatives
are included in the discounted cash flow analysis. When only two alternatives
are being considered, the incremental-cost approach offers a simpler,
more direct route to a decision.
3. Evaluating an investment with uncertain cash flows. In practice,
of course, future cash flows are seldom known with certainty. In principle,
this complication can be incorporated into net present value analysis
in a number of ways. We approach the problem from the perspective
of using a sort of breakeven analysis. We ask how large would this
particulare cash flow have to be to change the decision? The decision
maker may not know exactly what the cash flow is going to be, but
may be fairly confident that it will be larger (or smaller) than this
critical value.
H. Investments in Automated
Equipment. Investments in automated equipment differ in
several ways from investments in other types of equipment.
These differences are discussed below.
1. Cost of automation. The cost involved
in automating a process is often much greater than the
cost of purchasing conventional equipment. Even more
important, the front-end investment in robots and other
hardware usually constitutes no more than half of the
total cost to automate. Costs of engineering, software,
and implementation can exceed the cost of the equipment
itself.
2. Benefits from automation. There are
many benefits from automation including:
a. Reduced labor cost, although the
saving is seldom sufficient by itself to justify
automation.
b. Reduced inventory costs. Automated
equipment is more reliable, more consistent, and
faster than conventional equipment. As a result, work
in process and finished goods inventories can be
reduced.
c. Fewer defects and higher quality. Due to
greater reliability and consistency, defects are
commonly reduced under automation. This results in
less waste, scrap, rework, warranty work, and customer
returns.
d. Faster throughput time. The increased
reliability and faster processing speeds reduce
throughput time.
e. Increased manufacturing flexibility. Setup time
can be greatly reduced, making it much easier to
switch between products.
Some of these benefits are intangible and
difficult to estimate. One approach is to compute the
net present value for a project based on the costs and
benefits that can be easily estimated-omitting the
difficult-to-estimate intangible benefits. If the net
present value is positive with the intangible benefits
excluded, it would be even more positive if they were
included. If the net present value is negative, one
can then ask whether the intangible benefits are
likely to be big enough to turn the project into one
with a positive net present value.
I. Preference Decisions - The Ranking of
Investment Projects. When making capital budgeting
decisions, projects are first screened into acceptable and
unacceptable groups. Projects in the acceptable group are
then ranked in order of preference. Either the internal rate
of return method or the net present value method can be used
to make this ranking.
1. Internal Rate of Return Method. When
using the internal rate of return method to rank
competing investment projects, the preference rule is:
The higher the internal rate of return, the more
desirable the project.
2. Net Present Value Method. Every project with
a positive net present value is acceptable. However, if investment
funds are limited, there needs to be some method of ranking acceptable
projects in order of how well they utilize the available funds. If
projects are not equal in size and there are limited investment funds,
then it is necessary to compute each project's profitability index.
The formula for the profitability index (PI) is:
PI = Present value of cash inflows /
Investment required
This is actually an application of the idea from
Chapter 13 that the possible uses of a scarce resource
should be ranked in order of the contribution margin per
unit of the scarce resource. In this case, the
constrained resource is investment funds and the present
value of the cash inflows is analogous to the
contribution margin. When using the profitability index,
the preference rule is: the higher the profitability
index, the more desirable the project.
J. Other Approaches to Capital Budgeting
Decisions. One other approach to capital budgeting
decisions is widely used: the payback period method.
1. The Payback Period Method. The payback
period is defined as the length of time that it takes for
an investment project to recoup its initial cost out of
the cash inflows that it generates.
a. When the net annual cash inflow is
always the same, the payback period can be computed as
follows:
Payback period = Investment required / Net
annual cash inflow
b. When cash flows associated with an investment
project are erratic or uneven, the payback period is
computed by subtracting the net cash flow from the
unrecovered investment each year until the unrecovered
investment is zero.
c. The basic criticisms of the payback period
method are that it does not measure the profitability
of an investment and it does not consider the time
value of money. However, it does have value in
situations where the useful life of the project is
short and difficult to predict. Japanese firms,
particularly in consumer electronics, use the payback
method when evaluating new products since the product
life cycle can be quite short and a new product can be
made unexpectedly obsolete by changes in
technology.
NOTE: Imagine you have to choose
between two alternatives that each require an initial
investment of $4,000. Option A returns $1,000 at the
end of each of four years. Option B returns $4,000 at
the end of the fourth year. Under the payback method,
Option A and Option B are equally preferable. Note,
however, that Option A is really better since the cash
flows come earlier. Now add the information that in
Year 5, Option A will produce an additional cash
inflow of $500,000 but that Option B will never
generate another dollar after the fourth year. Repeat
the question of preference of Option A or Option B
using only the payback method. The payback method
ignores the time value of money and does not measure
profitability; it just measures the time required to
recapture the original investment.
K. Post-audit of Investment Projects. Post-audit of an investment project means a follow-up after
the project has been approved to see whether or not expected
results are being realized. In a post-audit, actual data
(rather than estimated data) are used in computing the net
present value. The net present value based upon actual data
is compared to the net present value based upon estimated
data as a way of gauging the accuracy of the estimated data.
Such a post-audit may help refine planning models and also
may help encourage managers to be forthright in their
estimates of future cash flows
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