CHAPTER 9

NET PRESENT VALUE AND OTHER INVESTMENT

CRITERIA

Answers to Concepts Review and Critical Thinking Questions

1. A payback period less than the project’s life means that the NPV is positive for a zero discount rate,

but nothing more definitive can be said. For discount rates greater than zero, the payback period will

still be less than the project’s life, but the NPV may be positive, zero, or negative, depending on

whether the discount rate is less than, equal to, or greater than the IRR. The discounted payback

includes the effect of the relevant discount rate. If a project’s discounted payback period is less than

the project’s life, it must be the case that NPV is positive.

2. If a project has a positive NPV for a certain discount rate, then it will also have a positive NPV for a

zero discount rate; thus, the payback period must be less than the project life. Since discounted

payback is calculated at the same discount rate as is NPV, if NPV is positive, the discounted payback

period must be less than the project’s life. If NPV is positive, then the present value of future cash

inflows is greater than the initial investment cost; thus PI must be greater than 1. If NPV is positive

for a certain discount rate R, then it will be zero for some larger discount rate R*; thus the IRR must

be greater than the required return.

3. a. Payback period is simply the accounting break-even point of a series of cash flows. To actually

compute the payback period, it is assumed that any cash flow occurring during a given period is

realized continuously throughout the period, and not at a single point in time. The payback is

then the point in time for the series of cash flows when the initial cash outlays are fully

recovered. Given some predetermined cutoff for the payback period, the decision rule is to

accept projects that payback before this cutoff, and reject projects that take longer to payback.

b. The worst problem associated with payback period is that it ignores the time value of money. In

addition, the selection of a hurdle point for payback period is an arbitrary exercise that lacks any

steadfast rule or method. The payback period is biased towards short-term projects; it fully

ignores any cash flows that occur after the cutoff point.

c.Despite its shortcomings, payback is often used because (1) the analysis is straightforward and

simple and (2) accounting numbers and estimates are readily available. Materiality consider-

ations often warrant a payback analysis as sufficient; maintenance projects are another example

where the detailed analysis of other methods is often not needed. Since payback is biased

towards liquidity, it may be a useful and appropriate analysis method for short-term projects

where cash management is most important.

4. a. The discounted payback is calculated the same as is regular payback, with the exception that

each cash flow in the series is first converted to its present value. Thus discounted payback

provides a measure of financial/economic break-even because of this discounting; just as regular

payback provides a measure of accounting break-even because it does not discount the cash

flows. Given some predetermined cutoff for the discounted payback period, the decision rule is

to accept projects that whose discounted cash flows payback before this cutoff period, and to

reject all other projects.

b. The primary disadvantage to using the discounted payback method is that it ignores all cash

flows that occur after the cutoff date, thus biasing this criterion towards short-term projects. As

a result, the method may reject projects that in fact have positive NPVs, or it may accept

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projects with large future cash outlays resulting in negative NPVs. In addition, the selection of a

cutoff point is again an arbitrary exercise.

c.Discounted payback is an improvement on regular payback because it takes into account the

time value of money. For conventional cash flows and strictly positive discount rates, the

discounted payback will always be greater than the regular payback period.

5. a. The average accounting return is interpreted as an average measure of the accounting

performance of a project over time, computed as some average profit measure attributable to the

project divided by some average balance sheet value for the project. This text computes AAR as

average net income with respect to average (total) book value. Given some predetermined cutoff

for AAR, the decision rule is to accept projects with an AAR in excess of the target measure,

and reject all other projects.

b. AAR is not a measure of cash flows and market value, but a measure of financial statement

accounts that often bear little resemblance to the relevant value of a project. In addition, the

selection of a cutoff is arbitrary, and the time value of money is ignored. For a financial

manager, both the reliance on accounting numbers rather than relevant market data and the

exclusion of time value of money considerations are troubling. Despite these problems, AAR

continues to be used in practice because (1) the accounting information is usually available, (2)

analysts often use accounting ratios to analyze firm performance, and (3) managerial

compensation is often tied to the attainment of certain target accounting ratio goals.

6. a. NPV is simply the present value of a project’s cash flows. NPV specifically measures, after

considering the time value of money, the net increase or decrease in firm wealth due to the

project. The decision rule is to accept projects that have a positive NPV, and reject projects with

a negative NPV.

b. NPV is superior to the other methods of analysis presented in the text because it has no serious

flaws. The method unambiguously ranks mutually exclusive projects, and can differentiate

between projects of different scale and time horizon. The only drawback to NPV is that it relies

on cash flow and discount rate values that are often estimates and not certain, but this is a

problem shared by the other performance criteria as well. A project with NPV = $2,500 implies

that the total shareholder wealth of the firm will increase by $2,500 if the project is accepted.

7. a. The IRR is the discount rate that causes the NPV of a series of cash flows to be identically zero.

IRR can thus be interpreted as a financial break-even rate of return; at the IRR discount rate, the

net value of the project is zero. The IRR decision rule is to accept projects with IRRs greater

than the discount rate, and to reject projects with IRRs less than the discount rate.

b. IRR is the interest rate that causes NPV for a series of cash flows to be zero. NPV is preferred in

all situations to IRR; IRR can lead to ambiguous results if there are non-conventional cash

flows, and also ambiguously ranks some mutually exclusive projects. However, for stand-alone

projects with conventional cash flows, IRR and NPV are interchangeable techniques.

c.IRR is frequently used because it is easier for many financial managers and analysts to rate

performance in relative terms, such as “12%”, than in absolute terms, such as “$46,000.” IRR

may be a preferred method to NPV in situations where an appropriate discount rate is unknown

are uncertain; in this situation, IRR would provide more information about the project than

would NPV.

8. a. The profitability index is the present value of cash inflows relative to the project cost. As such,

it is a benefit/cost ratio, providing a measure of the relative profitability of a project. The

profitability index decision rule is to accept projects with a PI greater than one, and to reject

projects with a PI less than one.

b. PI = (NPV + cost)/cost = 1 + (NPV/cost). If a firm has a basket of positive NPV projects and is

subject to capital rationing, PI may provide a good ranking measure of the projects, indicating

the “bang for the buck” of each particular project.

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9. PB = I / C ; – I + C / r = NPV, 0 = – I + C / IRR so IRR = C / I ; thus IRR = 1 / PB

For long-lived projects with relatively constant cash flows, the sooner the project pays back, the

greater is the IRR.

10. There are a number of reasons. Two of the most important have to do with transportation costs and

exchange rates. Manufacturing in the U.S. places the finished product much closer to the point of sale,

resulting in significant savings in transportation costs. It also reduces inventories because goods

spend less time in transit. Higher labor costs tend to offset these savings to some degree, at least

compared to other possible manufacturing locations. Of great importance is the fact that

manufacturing in the U.S. means that a much higher proportion of the costs are paid in dollars. Since

sales are in dollars, the net effect is to immunize profits to a large extent against fluctuations in

exchange rates. This issue is discussed in greater detail in the chapter on international finance.

11. The single biggest difficulty, by far, is coming up with reliable cash flow estimates. Determining an

appropriate discount rate is also not a simple task. These issues are discussed in greater depth in the

next several chapters. The payback approach is probably the simplest, followed by the AAR, but even

these require revenue and cost projections. The discounted cash flow measures (discounted payback,

NPV, IRR, and profitability index) are really only slightly more difficult in practice.

12. Yes, they are. Such entities generally need to allocate available capital efficiently, just as for-profits

do. However, it is frequently the case that the “revenues” from not-for-profit ventures are not

tangible. For example, charitable giving has real opportunity costs, but the benefits are generally hard

to measure. To the extent that benefits are measurable, the question of an appropriate required return

remains. Payback rules are commonly used in such cases. Finally, realistic cost/benefit analysis along

the lines indicated should definitely be used by governments and would go a long way toward

balancing the budget!

Solutions to Questions and Problems

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple

steps. Due to space and readability constraints, when these intermediate steps are included in this

solutions manual, rounding may appear to have occurred. However, the final answer for each problem is

found without rounding during any step in the problem.

Basic

1. To calculate the payback period, we need to find the time that the project has recovered its initial

investment. After two years, the project has created:

$1,200 + 2,500 = $3,700

in cash flows. The project still needs to create another:

$4,800 – 3,700 = $1,100

in cash flows. During the third year, the cash flows from the project will be $3,400. So, the payback

period will be 2 years, plus what we still need to make divided by what we will make during the third

year. The payback period is:

Payback = 2 + ($1,100 / $3,400) = 2.32 years

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