ńňđ. 2 |

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

excellent basis for decision making, because it enables the decision maker to view

a continuum of riskâ€“return tradeoffs rather than a single-point estimate.

International Risk Considerations

Although the basic techniques of capital budgeting are the same for multinational

companies (MNCs) as for purely domestic firms, firms that operate in several

countries face risks that are unique to the international arena. Two types of risk

are particularly important: exchange rate risk and political risk.

Exchange rate risk reflects the danger that an unexpected change in the

exchange rate risk

The danger that an unexpected exchange rate between the dollar and the currency in which a projectâ€™s cash flows

change in the exchange rate are denominated will reduce the market value of that projectâ€™s cash flow. The

between the dollar and the

dollar value of future cash inflows can be dramatically altered if the local cur-

currency in which a projectâ€™s

rency depreciates against the dollar. In the short term, specific cash flows can be

cash flows are denominated will

hedged by using financial instruments such as currency futures and options.

reduce the market value of that

projectâ€™s cash flow. Long-term exchange rate risk can best be minimized by financing the project, in

whole or in part, in local currency.

Political risk is much harder to protect against. Once a foreign project is

accepted, the foreign government can block the return of profits, seize the firmâ€™s

assets, or otherwise interfere with a projectâ€™s operation. The inability to manage

political risk after the fact makes it even more important that managers account

for political risks before making an investment. They can do so either by adjusting

a projectâ€™s expected cash inflows to account for the probability of political inter-

ference or by using risk-adjusted discount rates (discussed later in this chapter) in

capital budgeting formulas. In general, it is much better to adjust individual proj-

ect cash flows for political risk subjectively than to use a blanket adjustment for

all projects.

In addition to unique risks that MNCs must face, several other special issues

are relevant only for international capital budgeting. One of these special issues is

taxes. Because only after-tax cash flows are relevant for capital budgeting, finan-

cial managers must carefully account for taxes paid to foreign governments on

profits earned within their borders. They must also assess the impact of these tax

payments on the parent companyâ€™s U.S. tax liability.

Another special issue in international capital budgeting is transfer pricing.

Much of the international trade involving MNCs is, in reality, simply the shipment

of goods and services from one of a parent companyâ€™s subsidiaries to another sub-

sidiary located abroad. The parent company therefore has great discretion in set-

ting transfer prices, the prices that subsidiaries charge each other for the goods and

transfer prices

Prices that subsidiaries charge services traded between them. The widespread use of transfer pricing in interna-

each other for the goods and tional trade makes capital budgeting in MNCs very difficult unless the transfer

services traded between them.

prices that are used accurately reflect actual costs and incremental cash flows.

Finally, MNCs often must approach international capital projects from a

strategic point of view, rather than from a strictly financial perspective. For exam-

ple, an MNC may feel compelled to invest in a country to ensure continued access,

even if the project itself may not have a positive net present value. This motivation

was important for Japanese automakers who set up assembly plants in the United

States in the early 1980s. For much the same reason, U.S. investment in Europe

surged during the years before the market integration of the European Community

364 PART 3 Long-Term Investment Decisions

In Practice

FOCUS ON PRACTICE Bestfoodsâ€™ Recipe for Risk

With future volume growth in ect analyses. These risks included like Bestfoods, the company

North America and Western exchange rate and political risks, adapted the capital asset pricing

Europe limited to 3 percent at as well as tax and legal considera- model (CAPM). The model factors

most, executives at Bestfoods tions and strategic issues. First, it in elements of economic and politi-

(now a unit of the Anglo-Dutch increased its familiarity with the cal risk to obtain the countryâ€™s risk

conglomerate Unilever) decided to foreign market by partnering with premium and develops betas for

look for more promising markets. other companies whenever possi- each country on the basis of the

Whereas other food manufactur- ble and by developing local man- local marketâ€™s volatility and its cor-

ers were hesitant to take the inter- agement and experience. From relation to the U.S. market. For

national plunge, Bestfoods took its this knowledge base, Bestfoods example, the high volatility of

popular brands, such as Hell- was willing to take calculated Brazilâ€™s market has a low correla-

manâ€™s/Best Foods, Knorr, Mazola, risks. Working with consultants, tion to the U.S. market, so the

and Skippy, where the growth the company created its own ana- country beta was .81. With the

wasâ€”emerging markets like Latin lytical model to set discount rates risk-free rates and country betas,

America, where the company for different markets. Bestfoods could calculate local

could grow at a rate of 15 percent Some companies attempt to and global costs of capital. This

a year. At the time it was acquired quantify the risk of foreign projects more sophisticated approach gave

by Unilever, Bestfoods derived by arbitrarily assigning a premium Bestfoods the confidence to pur-

about 22 percent of its revenues to the discount rate they use for sue an aggressive international

outside the United States and domestic projects. Executives who strategy that increased share-

Western Europe, producing may- rely on this subjective method may holder value and resulted in

onnaise, soups, and other foods for overestimate the costs of doing Unilever offering a substantial pre-

110 different markets at 130 manu- business overseas and rule out mium to acquire the company.

facturing plants worldwide. good projects. Unlike these com-

Bestfoodsâ€™ international panies, Bestfoods took the time to Sources: Adapted from Andrew Osterland,

expansion succeeded because the develop specific costs of capital â€śLowering the Bar,â€ť CFO (August 1, 2002),

downloaded from www.cfo.com; Stanley

company developed methods to for international markets. To incor-

Reed, â€śUnilever Restocks,â€ť Business Week

incorporate the risks and rewards porate the benefits of diversifica- International (August 6, 2001), downloaded

of its foreign investments into proj- tion for a multinational company from Electric Library, ask.elibrary.com

in 1992. MNCs often invest in production facilities in the home country of major

rivals to deny these competitors an uncontested home market. MNCs also may

feel compelled to invest in certain industries or countries to achieve a broad corpo-

rate objective such as completing a product line or diversifying raw material

sources, even when the projectâ€™s cash flows may not be sufficiently profitable.

Review Questions

9â€“11 Define risk in terms of the cash inflows from a capital budgeting project.

Briefly describe and compare the following behavioral approaches,

explaining how each can be used to deal with project risk: (a) sensitivity

analysis; (b) scenario analysis; (c) decision trees; and (d) simulation.

9â€“12 Briefly explain how each of the following considerations affects the capi-

tal budgeting decisions of multinational companies: (a) exchange rate risk;

(b) political risk; (c) tax law differences; (d) transfer pricing; and (e) a

strategic rather than strictly financial viewpoint.

365

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

Risk-Adjusted Discount Rates

LG6

The approaches for dealing with risk that have been presented so far enable the

financial manager to get a â€śfeelâ€ť for project risk. Unfortunately, they do not

explicitly recognize project risk. We will now illustrate the most popular risk-

adjustment technique that employs the net present value (NPV) decision

method.7 The NPV decision rule of accepting only those projects with NPVs $0

will continue to hold. Close examination of the basic equation for NPV, Equa-

tion 9.1, should make it clear that because the initial investment (CF0) is known

with certainty, a projectâ€™s risk is embodied in the present value of its cash inflows:

n

CFt

k)t

1 (1

t

Two opportunities to adjust the present value of cash inflows for risk exist:

(1) The cash inflows (CFt) can be adjusted, or (2) the discount rate (k) can be

adjusted. Adjusting the cash inflows is highly subjective, so here we describe the

more popular process of adjusting the discount rate. In addition, we consider the

practical aspects of risk-adjusted discount rates.

Determining Risk-Adjusted Discount Rates (RADRs)

A popular approach for risk adjustment involves the use of risk-adjusted discount

rates (RADRs). This approach uses Equation 9.1 but employs a risk-adjusted dis-

count rate, as noted in the following expression:

n

CFt

NPV CF0 (9.4)

RADR)t

(1

t1

The risk-adjusted discount rate (RADR) is the rate of return that must be

risk-adjusted discount rate

(RADR) earned on a given project to compensate the firmâ€™s owners adequatelyâ€”that is, to

The rate of return that must be maintain or improve the firmâ€™s share price. The higher the risk of a project, the

earned on a given project to

higher the RADR, and therefore the lower the net present value for a given stream

compensate the firmâ€™s owners

of cash inflows. The logic underlying the use of RADRs is closely linked to the cap-

adequatelyâ€”that is, to maintain

ital asset pricing model (CAPM) developed in Chapter 5. Because the CAPM is

or improve the firmâ€™s share price.

based on an assumed efficient market, which does not exist for real corporate

(nonfinancial) assets such as plant and equipment, the CAPM is not directly

applicable in making capital budgeting decisions. Financial managers therefore

assess the total risk of a project and use it to determine the risk-adjusted discount

rate (RADR), which can be used in Equation 9.4 to find the NPV.

In order not to damage its market value, the firm must use the correct dis-

count rate to evaluate a project. If a firm discounts a risky projectâ€™s cash inflows

at too low a rate and accepts the project, the firmâ€™s market price may drop as

investors recognize that the firm itself has become more risky. On the other hand,

if the firm discounts a projectâ€™s cash inflows at too high a rate, it will reject

acceptable projects. Eventually the firmâ€™s market price may drop, because

7. The IRR could just as well have been used, but because NPV is theoretically preferable, it is used instead.

366 PART 3 Long-Term Investment Decisions

investors who believe that the firm is being overly conservative will sell their

stock, putting downward pressure on the firmâ€™s market value.

Unfortunately, there is no formal mechanism for linking total project risk to

the level of required return. As a result, most firms subjectively determine the

RADR by adjusting their existing required return. They adjust it up or down

depending on whether the proposed project is more or less risky, respectively, than

the average risk of the firm. This CAPM-type of approach provides a â€śrough esti-

mateâ€ť of the project risk and required return because both the project risk measure

and the linkage between risk and required return are estimates.

Bennett Company wishes to use the risk-adjusted discount rate approach to

EXAMPLE

determine, according to NPV, whether to implement project A or project B. In

addition to the data presented earlier, Bennettâ€™s management after much analysis

assigned a â€śrisk indexâ€ť of 1.6 to project A and of 1.0 to project B. The risk index

is merely a numerical scale used to classify project risk: Higher index values are

assigned to higher-risk projects, and vice versa. The CAPM-type relationship

used by the firm to link risk (measured by the risk index) and the required return

(RADR) is shown in the following table.

Risk index Required return (RADR)

0.0 6% (risk-free rate, RF)

0.2 7

0.4 8

0.6 9

0.8 10

Project B â†’ 1.0 11

1.2 12

1.4 13

Project A â†’ 1.6 14

1.8 16

2.0 18

Because project A is riskier than project B, its RADR of 14% is greater than

project Bâ€™s 11%. The net present value of each project, calculated using its

RADR, is found as shown on the time lines in Figure 9.8. The results clearly

show that project B in preferable, because its risk-adjusted NPV of $9,798 is

greater than the $6,063 risk-adjusted NPV for project A. As reflected by the

NPVs in Figure 9.2, if the discount rates were not adjusted for risk, project A

would be preferred to project B.

Calculator Use We can again use the preprogrammed NPV function in a finan-

cial calculator to simplify the NPV calculation. The keystrokes for project Aâ€”

the annuityâ€”typically are as shown at the top of the next page. The keystrokes

for project Bâ€”the mixed streamâ€”are also shown at the top of the next page.

The calculated NPVs for projects A and B of $6,063 and $9,798, respectively,

agree with those shown in Figure 9.8.

367

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

Project A Project B

Input Function Input Function

42000 45000

CF0 CF0

14000 CF1 28000 CF1

CF2

5 N 12000

I CF3

14 10000

NPV N

3

11 I

Solution

6063.13 NPV

Solution

9798.43

FIGURE 9.8 Calculation of NPVs for Bennett Companyâ€™s Capital Expenditure Alternatives

using RADRs

Time lines depicting the cash flows and NPV calculations using RADRs for projects A and B

Project A End of Year

0 1 2 3 4 5

$42,000 $14,000 $14,000 $14,000 $14,000 $14,000

k = 14%

48,063

NPVA = $ 6,063

Project B End of Year

0 1 2 3 4 5

$45,000 $28,000 $12,000 $10,000 $10,000 $10,000

k = 11%

25,225

k = 11%

9,739

k = 11%

7,312

$54,798

k = 11%

6,587

k = 11%

5,935

NPVB = $ 9,798

Note: When we use the risk indexes of 1.6 and 1.0 for projects A and B, respectively, along with the table in the middle of the preceding page, a

risk-adjusted discount rate (RADR) of 14% results for project A and a RADR of 11% results for project B.

368 PART 3 Long-Term Investment Decisions

Spreadsheet Use Analysis of projects using risk-adjusted discount rates

(RADRs) also can be calculated as shown on the following Excel spreadsheet.

The usefulness of risk-adjusted discount rates should now be clear. The real

difficulty lies in estimating project risk and linking it to the required return

(RADR).

RADRs in Practice

In spite of the appeal of total risk, RADRs are often used in practice. Their popu-

larity stems from two facts: (1) They are consistent with the general disposition of

financial decision makers toward rates of return, and (2) they are easily estimated

and applied. The first reason is clearly a matter of personal preference, but the

second is based on the computational convenience and well-developed proce-

dures involved in the use of RADRs.

In practice, firms often establish a number of risk classes, with an RADR

assigned to each. Each project is then subjectively placed in the appropriate risk

class, and the corresponding RADR is used to evaluate it. This is sometimes done

on a division-by-division basis, in which case each division has its own set of risk

classes and associated RADRs, similar to those for Bennett Company in Table

9.9. The use of divisional costs of capital and associated risk classes enables a

large multidivisional firm to incorporate differing levels of divisional risk into the

capital budgeting process and still recognize differences in the levels of individual

project risk.

369

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

TABLE 9.9 Bennett Companyâ€™s Risk Classes and RADRs

Risk-adjusted

discount rate,

Risk class Description RADR

I Below-average risk: Projects with low risk. Typically involve 8%

routine replacement without renewal of existing activities.

10%a

II Average risk: Projects similar to those currently implemented.

Typically involve replacement or renewal of existing activities.

III Above-average risk: Projects with higher than normal, but 14%

not excessive, risk. Typically involve expansion of existing or

similar activities.

IV Highest risk: Projects with very high risk. Typically involve 20%

expansion into new or unfamiliar activities.

aThis RADR is actually the firmâ€™s cost of capital, which is discussed in detail in Chapter 10. It represents

the firmâ€™s required return on its existing portfolio of projects, which is assumed to be unchanged with

acceptance of the â€śaverage riskâ€ť project.

Assume that the management of Bennett Company decided to use risk classes to

EXAMPLE

analyze projects and so placed each project in one of four risk classes according

to its perceived risk. The classes ranged from I for the lowest-risk projects to IV

for the highest-risk projects. Associated with each class was an RADR appropri-

ate to the level of risk of projects in the class, as given in Table 9.9. Bennett clas-

sified as lower-risk those projects that tend to involve routine replacement or

renewal activities; higher-risk projects involve expansion, often into new or unfa-

miliar activities.

The financial manager of Bennett has assigned project A to class III and proj-

ect B to class II. The cash flows for project A would be evaluated using a 14%

RADR, and project Bâ€™s would be evaluated using a 10% RADR.8 The NPV of

project A at 14% was calculated in Figure 9.8 to be $6,063, and the NPV for proj-

ect B at a 10% RADR was shown in Figure 9.2 to be $10,924. Clearly, with

RADRs based on the use of risk classes, project B is preferred over project A. As

noted earlier, this result is contrary to the preference shown in Figure 9.2, where

differing risks of projects A and B were not taken into account.

Review Questions

9â€“13 Describe the logic involved in using risk-adjusted discount rates (RADRs).

How is this approach related to the capital asset pricing model (CAPM)?

Explain.

9â€“14 How are risk classes often used to apply RADRs?

8. Note that the 10% RADR for project B using the risk classes in Table 9.9 differs from the 11% RADR used in the

preceding example for project B. This difference is attributable to the less precise nature of the use of risk classes.

370 PART 3 Long-Term Investment Decisions

SUMMARY

FOCUS ON VALUE

After estimating the relevant cash flows, the financial manager must apply appropriate

decision techniques to assess whether the project creates value for shareholders. Net

present value (NPV) and internal rate of return (IRR) are the generally preferred capital

budgeting techniques. Both use the cost of capital as the required return needed to compen-

sate shareholders for undertaking projects with the same risk as that of the firm. Both

indicate whether a proposed investment creates or destroys shareholder value. NPV is the

theoretically preferred approach, but IRR is preferred in practice because of its intuitive

appeal.

Procedures for explicitly recognizing real options embedded in capital projects and

procedures for selecting projects under capital rationing enable the financial manager to

refine the capital budgeting process further. Not all capital budgeting projects have the

same level of risk as the firmâ€™s existing portfolio of projects. The financial manager must

therefore adjust projects for differences in risk when evaluating their acceptability. Risk-

adjusted discount rates (RADRs) provide a mechanism for adjusting the discount rate in a

manner consistent with the riskâ€“return preferences of market participants and thereby

accepting only value-creating projects. These techniques should enable the financial man-

ager to make capital budgeting decisions that are consistent with the firmâ€™s goal of maxi-

mizing stock price.

REVIEW OF LEARNING GOALS

Calculate, interpret, and evaluate the payback Apply net present value (NPV) and internal rate

LG1 LG2

period. The payback period measures the of return (IRR) to relevant cash flows to choose

exact amount of time required for the firm to acceptable capital expenditures. Sophisticated capi-

recover its initial investment from cash inflows. tal budgeting techniques use the cost of capital to

The formula and decision criterion for the pay- consider the time factor in the value of money. Two

back period are summarized in Table 9.10. Shorter such techniques are net present value (NPV) and in-

payback periods are preferred. In addition to its ternal rate of return (IRR). The key formulas and

ease of calculation and simple intuitive appeal, the decision criteria for these techniques are summa-

advantages of the payback period lie in its con- rized in Table 9.10. Both NPV and IRR provide the

sideration of cash inflows, the implicit considera- same acceptâ€“reject decisions but often provide con-

tion given to timing, and its ability to measure risk flicting ranks.

exposure. Its weaknesses include its lack of linkage

to the wealth maximization goal, failure to explic- Use net present value profiles to compare the

LG3

itly consider time value, and the fact that it NPV and IRR techniques in light of conflicting

ignores cash flows that occur after the payback rankings. Net present value profiles are useful in

period. comparing projects, especially when conflicting

371

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

TABLE 9.10 Summary of Key Formulas/Definitions and Decision Criteria

for Capital Budgeting Techniques

Technique Formula/definition Decision criteria

Payback perioda For annuity: Accept if maximum acceptable payback

period.

Initial investment

Reject if maximum acceptable payback

Annual cash inflow

period.

For mixed stream: Calculate cumulative cash

inflows on year-to-year basis until the initial

investment is recovered.

Net present value (NPV)b Present value of cash inflows Initial Accept if $0.

investment. Reject if $0.

Internal rate of return (IRR)b The discount rate that causes NPV $0 Accept if the cost of capital.

(present value of cash inflows equals the Reject if the cost of capital.

initial investment).

aUnsophisticated technique, because it does not give explicit consideration to the time value of money.

bSophisticated technique, because it gives explicit consideration to the time value of money.

rankings exist between NPV and IRR. On a purely Capital rationing commonly occurs in practice.

theoretical basis, NPV is preferred over IRR, be- Its objective is to select from all acceptable projects

cause NPV assumes reinvestment of intermediate the group that provides the highest overall net pre-

cash inflows at the cost of capital and is not subject sent value but does not require more dollars than are

to the mathematical problems that often arise when budgeted. Of the two basic approaches for choosing

one is calculating IRRs for nonconventional cash projects under capital rationing, the NPV approach

flows. In practice, the IRR is more commonly used better achieves the objective of using the budget to

because it is consistent with the general preference generate the highest present value of cash inflows.

toward rates of return.

Recognize sensitivity analysis and scenario

LG5

Discuss two additional considerations in capital analysis, decision trees, and simulation as be-

LG4

budgetingâ€”recognizing real options and choos- havioral approaches for dealing with project risk,

ing projects under capital rationing. By explicitly and the unique risks that multinational companies

recognizing real optionsâ€”opportunities that are face. Risk in capital budgeting is concerned with

embedded in capital projects and that allow man- either the chance that a project will prove unac-

agers to alter their cash flow and risk in a way that ceptable or, more formally, the degree of variability

effects project acceptability (NPV)â€”the financial of cash flows. Sensitivity analysis and scenario

manager can find a projectâ€™s strategic NPV. Some of analysis are two behavioral approaches for dealing

the more common types of real options are aban- with project risk to capture the variability of cash

donment, flexibility, growth, and timing options. inflows and NPVs. A decision tree is a behavioral

The strategic NPV explicitly recognizes the value of approach for dealing with risk that relies on esti-

real options and thereby improves the quality of mates of probabilities associated with the outcomes

the capital budgeting decision. of competing courses of action to determine the

372 PART 3 Long-Term Investment Decisions

expected values used to select a preferred action. Understand the calculation and practical as-

LG6

Simulation is a statistics-based behavioral approach pects of risk-adjusted discount rates (RADRs).

that results in a probability distribution of project The risk adjusted discount rate (RADR) technique

returns. It usually requires a computer and allows involves a market-based adjustment of the discount

the decision maker to understand the riskâ€“return rate used to calculate NPV. The RADR is closely

tradeoffs involved in a proposed investment. linked to the CAPM, but because real corporate as-

Although the basic capital budgeting techniques sets are generally not traded in an efficient market,

are the same for multinational and purely domestic the CAPM cannot be applied directly to capital

companies, firms that operate in several countries budgeting. RADRs are commonly used in practice

must also deal with both exchange rate and political because decision makers prefer rates of return and

risks, tax law differences, transfer pricing, and find them easy to estimate and apply.

strategic rather than strictly financial considerations.

SELF-TEST PROBLEMS (Solutions in Appendix B)

ST 9â€“1 All techniques with NPV profileâ€”Mutually exclusive projects Fitch Industries

LG1 LG2 LG3

is in the process of choosing the better of two equal-risk, mutually exclusive cap-

ital expenditure projectsâ€”M and N. The relevant cash flows for each project are

shown in the following table. The firmâ€™s cost of capital is 14%.

Project M Project N

Initial investment (CF0) $28,500 $27,000

Year (t) Cash inflows (CFt)

1 $10,000 $11,000

2 10,000 10,000

3 10,000 9,000

4 10,000 8,000

a. Calculate each projectâ€™s payback period.

b. Calculate the net present value (NPV) for each project.

c. Calculate the internal rate of return (IRR) for each project.

d. Summarize the preferences dictated by each measure you calculated,

and indicate which project you would recommend. Explain

why.

e. Draw the net present value profiles for these projects on the same set of

axes, and explain the circumstances under which a conflict in rankings

might exist.

ST 9â€“2 Risk-adjusted discount rates CBA Company is considering two mutually

LG6

exclusive projects, A and B. The following table shows the CAPM-type relation-

ship between a risk index and the required return (RADR) applicable to CBA

Company.

373

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

Risk index Required return (RADR)

0.0 7.0% (risk-free rate, RF)

0.2 8.0

0.4 9.0

0.6 10.0

0.8 11.0

1.0 12.0

1.2 13.0

1.4 14.0

1.6 15.0

1.8 16.0

2.0 17.0

Project data are shown as follows:

Project A Project B

Initial investment (CF0) $15,000 $20,000

Project life 3 years 3 years

Annual cash inflow (CF) $7,000 $10,000

Risk index 0.4 1.8

a. Ignoring any differences in risk and assuming that the firmâ€™s cost of capital is

10%, calculate the net present value (NPV) of each project.

b. Use NPV to evaluate the projects, using risk-adjusted discount rates (RADRs)

to account for risk.

c. Compare, contrast, and explain your findings in parts a and b.

PROBLEMS

9â€“1 Payback period Lee Corporation is considering a capital expenditure that

LG1

requires an initial investment of $42,000 and returns after-tax cash inflows of

$7,000 per year for 10 years. The firm has a maximum acceptable payback

period of 8 years.

a. Determine the payback period for this project.

b. Should the company accept the project? Why or why not?

9â€“2 Payback comparisons Dallas Tool has a 5-year maximum acceptable payback

LG1

period. The firm is considering the purchase of a new machine and must choose

between two alternative ones. The first machine requires an initial investment of

$14,000 and generates annual after-tax cash inflows of $3,000 for each of the

next 7 years. The second machine requires an initial investment of $21,000 and

provides an annual cash inflow after taxes of $4,000 for 20 years.

a. Determine the payback period for each machine.

374 PART 3 Long-Term Investment Decisions

b. Comment on the acceptability of the machines, assuming that they are inde-

pendent projects.

c. Which machine should the firm accept? Why?

d. Do the machines in this problem illustrate any of the weaknesses of using

payback? Discuss.

9â€“3 NPV Calculate the net present value (NPV) for the following 20-year projects.

LG2

Comment on the acceptability of each. Assume that the firm has an opportunity

cost of 14%.

a. Initial investment is $10,000; cash inflows are $2,000 per year.

b. Initial investment is $25,000; cash inflows are $3,000 per year.

c. Initial investment is $30,000; cash inflows are $5,000 per year.

9â€“4 NPV for varying costs of capital Cherylâ€™s Beauty Aids is evaluating a new

LG2

fragrance-mixing machine. The machine requires an initial investment of

$24,000 and will generate after-tax cash inflows of $5,000 per year for 8

years. For each of the costs of capital listed, (1) calculate the net present value

(NPV), (2) indicate whether to accept or reject the machine, and (3) explain

your decision.

a. The cost of capital is 10%.

b. The cost of capital is 12%.

c. The cost of capital is 14%.

9â€“5 Net present valueâ€”Independent projects Using a 14% cost of capital, calculate

LG2

the net present value for each of the independent projects shown in the following

table, and indicate whether each is acceptable.

Project A Project B Project C Project D Project E

Initial investment (CF0) $26,000 $500,000 $170,000 $950,000 $80,000

Year (t) Cash inflows (CFt)

1 $4,000 $100,000 $20,000 $230,000 $ 0

2 4,000 120,000 19,000 230,000 0

3 4,000 140,000 18,000 230,000 0

4 4,000 160,000 17,000 230,000 20,000

5 4,000 180,000 16,000 230,000 30,000

6 4,000 200,000 15,000 230,000 0

7 4,000 14,000 230,000 50,000

8 4,000 13,000 230,000 60,000

9 4,000 12,000 70,000

10 4,000 11,000

9â€“6 NPV and maximum return A firm can purchase a fixed asset for a $13,000 ini-

LG2

tial investment. The asset generates an annual after-tax cash inflow of $4,000

for 4 years.

a. Determine the net present value (NPV) of the asset, assuming that the firm

has a 10% cost of capital. Is the project acceptable?

375

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

b. Determine the maximum required rate of return (closest whole-percentage

rate) that the firm can have and still accept the asset. Discuss this finding in

light of your response in part a.

9â€“7 NPVâ€”Mutually exclusive projects Jackson Enterprises is considering the

LG2

replacement of one of its old drill presses. Three alternative replacement presses

are under consideration. The relevant cash flows associated with each are shown

in the following table. The firmâ€™s cost of capital is 15%.

Press A Press B Press C

Initial investment (CF0) $85,000 $60,000 $130,000

Year (t) Cash inflows (CFt)

1 $18,000 $12,000 $50,000

2 18,000 14,000 30,000

3 18,000 16,000 20,000

4 18,000 18,000 20,000

5 18,000 20,000 20,000

6 18,000 25,000 30,000

7 18,000 â€” 40,000

8 18,000 â€” 50,000

a. Calculate the net present value (NPV) of each press.

b. Using NPV, evaluate the acceptability of each press.

c. Rank the presses from best to worst using NPV.

9â€“8 Payback and NPV McAllister Products has three projects under consideration.

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The cash flows for each of them are shown in the following table. The firm has a

16% cost of capital.

Project A Project B Project C

Initial investment (CF0) $40,000 $40,000 $40,000

Year (t) Cash inflows (CFt)

1 $13,000 $ 7,000 $19,000

2 13,000 10,000 16,000

3 13,000 13,000 13,000

4 13,000 16,000 10,000

5 13,000 19,000 7,000

a. Calculate each projectâ€™s payback period. Which project is preferred according

to this method?

b. Calculate each projectâ€™s net present value (NPV). Which project is preferred

according to this method?

376 PART 3 Long-Term Investment Decisions

c. Comment on your findings in parts a and b, and recommend the best project.

Explain your recommendation.

9â€“9 Internal rate of return For each of the projects shown in the following table, cal-

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culate the internal rate of return (IRR). Then indicate, for each project, the maxi-

mum cost of capital that the firm could have and still find the IRR acceptable.

Project A Project B Project C Project D

Initial investment (CF0) $90,000 $490,000 $20,000 $240,000

Year (t) Cash inflows (CFt)

1 $20,000 $150,000 $7,500 $120,000

2 25,000 150,000 7,500 100,000

3 30,000 150,000 7,500 80,000

4 35,000 150,000 7,500 60,000

5 40,000 â€” 7,500 â€”

9â€“10 IRRâ€”Mutually exclusive projects Paulus Corporation is attempting to choose

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the better of two mutually exclusive projects for expanding the firmâ€™s warehouse

capacity. The relevant cash flows for the projects are shown in the following

table. The firmâ€™s cost of capital is 15%.

Project X Project Y

Initial investment (CF0) $500,000 $325,000

Year (t) Cash inflows (CFt)

1 $100,000 $140,000

2 120,000 120,000

3 150,000 95,000

4 190,000 70,000

5 250,000 50,000

a. Calculate the IRR to the nearest whole percent for each of the projects.

b. Assess the acceptability of each project on the basis of the IRRs found in part a.

c. Which project, on this basis, is preferred?

9â€“11 IRR, investment life, and cash inflows Cincinnati Machine Tool (CMT) accepts

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projects earning more than the firmâ€™s 15% cost of capital. CMT is currently con-

sidering a 10-year project that provides annual cash inflows of $10,000 and

requires an initial investment of $61,450. (Note: All amounts are after taxes.)

a. Determine the IRR of this project. Is it acceptable?

b. Assuming that the cash inflows continue to be $10,000 per year, how many

additional years would the flows have to continue to make the project accept-

able (that is, to make it have an IRR of 15%)?

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CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

c. With the given life, initial investment, and cost of capital, what is the mini-

mum annual cash inflow that the firm should accept?

9â€“12 NPV and IRR Lilo Manufacturing has prepared the following estimates for a

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long-term project it is considering. The initial investment is $18,250, and the

project is expected to yield after-tax cash inflows of $4,000 per year for 7 years.

The firm has a 10% cost of capital.

a. Determine the net present value (NPV) for the project.

b. Determine the internal rate of return (IRR) for the project.

c. Would you recommend that the firm accept or reject the project? Explain

your answer.

9â€“13 Payback, NPV, and IRR Bruce Reed Enterprises is attempting to evaluate the

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LG1

feasibility of investing $95,000 in a piece of equipment that has a 5-year life.

The firm has estimated the cash inflows associated with the proposal as shown

in the following table. The firm has a 12% cost of capital.

Year (t) Cash inflows (CFt)

1 $20,000

2 25,000

3 30,000

4 35,000

5 40,000

a. Calculate the payback period for the proposed investment.

b. Calculate the net present value (NPV) for the proposed investment.

c. Calculate the internal rate of return (IRR), rounded to the nearest whole per-

cent, for the proposed investment.

d. Evaluate the acceptability of the proposed investment using NPV and IRR.

What recommendation would you make relative to implementation of the

project? Why?

9â€“14 NPV, IRR, and NPV profiles Candor Enterprises is considering two mutually

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exclusive projects. The firm, which has a 12% cost of capital, has estimated its

cash flows as shown in the following table.

Project A Project B

Initial investment (CF0) $130,000 $85,000

Year (t) Cash inflows (CFt)

1 $25,000 $40,000

2 35,000 35,000

3 45,000 30,000

4 50,000 10,000

5 55,000 5,000

378 PART 3 Long-Term Investment Decisions

a. Calculate the NPV of each project, and assess its acceptability.

b. Calculate the IRR for each project, and assess its acceptability.

c. Draw the NPV profiles for both projects on the same set of axes.

d. Evaluate and discuss the rankings of the two projects on the basis of your

findings in parts a, b, and c.

e. Explain your findings in part d in light of the pattern of cash inflows associ-

ated with each project.

9â€“15 All techniquesâ€”mutually exclusive investment decision Easi Chair Company

LG1 LG2 LG3

is attempting to select the best of three mutually exclusive projects. The initial

investment and after-tax cash inflows associated with these projects are shown

in the following table.

Cash flows Project A Project B Project C

Initial investment (CF0) $60,000 $100,000 $110,000

Cash inflows (CFt), t 1 to 5 $20,000 $ 31,500 $ 32,500

a. Calculate the payback period for each project.

b. Calculate the net present value (NPV) of each project, assuming that the firm

has a cost of capital equal to 13%.

c. Calculate the internal rate of return (IRR) for each project.

d. Draw the net present value profiles for these projects on the same set of axes,

and discuss any conflict in ranking that may exist between NPV and IRR.

e. Summarize the preferences dictated by each measure, and indicate which

project you would recommend. Explain why.

9â€“16 All techniques with NPV profileâ€”Mutually exclusive projects Projects A and

LG1 LG2 LG3

B, of equal risk, are alternatives for expanding the Rosa Companyâ€™s capacity.

The firmâ€™s cost of capital is 13%. The cash flows for each project are shown in

the following table.

Project A Project B

Initial investment (CF0) $80,000 $50,000

Year (t) Cash inflows (CFt)

1 $15,000 $15,000

2 20,000 15,000

3 25,000 15,000

4 30,000 15,000

5 35,000 15,000

a. Calculate each projectâ€™s payback period.

b. Calculate the net present value (NPV) for each project.

c. Calculate the internal rate of return (IRR) for each project.

d. Draw the net present value profiles for these projects on the same set of axes,

and discuss any conflict in ranking that may exist between NPV and IRR.

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CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

e. Summarize the preferences dictated by each measure, and indicate which

project you would recommend. Explain why.

9â€“17 Integrativeâ€”Complete investment decision Hot Springs Press is considering

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LG1

the purchase of a new printing press. The total installed cost of the press is $2.2

million. This outlay would be partially offset by the sale of an existing press.

The old press has zero book value, cost $1 million 10 years ago, and can be

sold currently for $1.2 million before taxes. As a result of acquisition of the

new press, sales in each of the next 5 years are expected to increase by $1.6 mil-

lion, but product costs (excluding depreciation) will represent 50% of sales. The

new press will not affect the firmâ€™s net working capital requirements. The new

press will be depreciated under MACRS using a 5-year recovery period (see

Table 3.2 on page 89). The firm is subject to a 40% tax rate on both ordinary

income and capital gains. Hot Spring Pressâ€™s cost of capital is 11%. (Note:

Assume that both the old and the new press will have terminal values of $0 at

the end of year 6.)

a. Determine the initial investment required by the new press.

b. Determine the operating cash inflows attributable to the new press. (Note: Be

sure to consider the depreciation in year 6.)

c. Determine the payback period.

d. Determine the net present value (NPV) and the internal rate of return (IRR)

related to the proposed new press.

e. Make a recommendation to accept or reject the new press, and justify your

answer.

9â€“18 Integrativeâ€”Investment decision Holliday Manufacturing is considering the

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replacement of an existing machine. The new machine costs $1.2 million and

requires installation costs of $150,000. The existing machine can be sold cur-

rently for $185,000 before taxes. It is 2 years old, cost $800,000 new, and has a

$384,000 book value and a remaining useful life of 5 years. It was being depreci-

ated under MACRS using a 5-year recovery period (see Table 3.2 on page 89)

and therefore has the final 4 years of depreciation remaining. If it is held until

the end of 5 years, the machineâ€™s market value will be $0. Over its 5-year life,

the new machine should reduce operating costs by $350,000 per year. The new

machine will be depreciated under MACRS using a 5-year recovery period (see

Table 3.2 on page 89). The new machine can be sold for $200,000 net of

removal and clean up costs at the end of 5 years. An increased investment in net

working capital of $25,000 will be needed to support operations if the new

machine is acquired. Assume that the firm has adequate operating income

against which to deduct any loss experienced on the sale of the existing machine.

The firm has a 9% cost of capital and is subject to a 40% tax rate on both ordi-

nary income and capital gains.

a. Develop the relevant cash flows needed to analyze the proposed

replacement.

b. Determine the net present value (NPV) of the proposal.

c. Determine the internal rate of return (IRR) of the proposal.

d. Make a recommendation to accept or reject the replacement proposal, and

justify your answer.

e. What is the highest cost of capital that the firm could have and still accept the

proposal? Explain.

380 PART 3 Long-Term Investment Decisions

9â€“19 Real options and the strategic NPV Jenny Rene, the CFO of Asor Products,

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Inc., has just completed an evaluation of a proposed capital expenditure for

equipment that would expand the firmâ€™s manufacturing capacity. Using the tra-

ditional NPV methodology, she found the project unacceptable because

NPVtraditional $1,700 $0

Before recommending rejection of the proposed project, she has decided to assess

whether there might be real options embedded in the firmâ€™s cash flows. Her eval-

uation uncovered the following three options.

Option 1: Abandonmentâ€”The project could be abandoned at the end of 3

years, resulting in an addition to NPV of $1,200.

Option 2: Expansionâ€”If the projected outcomes occurred, an opportunity to

expand the firmâ€™s product offerings further would occur at the end of 4 years.

Exercise of this option is estimated to add $3,000 to the projectâ€™s NPV.

Option 3: Delayâ€”Certain phases of the proposed project could be delayed if

market and competitive conditions caused the firmâ€™s forecast revenues to

develop more slowly than planned. Such a delay in implementation at that

point has a NPV of $10,000.

Rene estimated that there was a 25% chance that the abandonment option

would need to be exercised, a 30% chance the expansion option would be exer-

cised, and only a 10% chance that the implementation of certain phases of the

project would have to be delayed.

a. Use the information provided to calculate the strategic NPV, NPVstrategic, for

Asor Productsâ€™ proposed equipment expenditure.

b. Judging on the basis of your findings in part a, what action should Rene

recommend to management with regard to the proposed equipment

expenditures?

c. In general, how does this problem demonstrate the importance of considering

real options when making capital budgeting decisions?

9â€“20 Capital rationingâ€”IRR and NPV approaches Bromley and Sons is attempting

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to select the best of a group of independent projects competing for the firmâ€™s fixed

capital budget of $4.5 million. The firm recognizes that any unused portion of this

budget will earn less than its 15% cost of capital, thereby resulting in a present

value of inflows that is less than the initial investment. The firm has summarized

the key data to be used in selecting the best group of projects in the following table.

Present value of

Project Initial investment IRR inflows at 15%

A $5,000,000 17% $5,400,000

B 800,000 18 1,100,000

C 2,000,000 19 2,300,000

D 1,500,000 16 1,600,000

E 800,000 22 900,000

F 2,500,000 23 3,000,000

G 1,200,000 20 1,300,000

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CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

a. Use the internal rate of return (IRR) approach to select the best group of

projects.

b. Use the net present value (NPV) approach to select the best group of

projects.

c. Compare, contrast, and discuss your findings in parts a and b.

d. Which projects should the firm implement? Why?

9â€“21 Capital rationingâ€”NPV approach A firm with a 13% cost of capital must

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select the optimal group of projects from those shown in the following table,

given its capital budget of $1 million.

NPV at 13%

Project Initial investment cost of capital

A $300,000 $ 84,000

B 200,000 10,000

C 100,000 25,000

D 900,000 90,000

E 500,000 70,000

F 100,000 50,000

G 800,000 160,000

a. Calculate the present value of cash inflows associated with each

project.

b. Select the optimal group of projects, keeping in mind that unused funds are

costly.

9â€“22 Basic sensitivity analysis Renaissance Pharmaceutical is in the process of evalu-

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ating two mutually exclusive additions to its processing capacity. The firmâ€™s

financial analysts have developed pessimistic, most likely, and optimistic esti-

mates of the annual cash inflows associated with each project. These estimates

are shown in the following table.

Project A Project B

Initial investment (CF0) $8,000 $8,000

Outcome Annual cash inflows (CF)

Pessimistic $ 200 $ 900

Most likely 1,000 1,000

Optimistic 1,800 1,100

a. Determine the range of annual cash inflows for each of the two projects.

b. Assume that the firmâ€™ s cost of capital is 10% and that both projects have 20-

year lives. Construct a table similar to this for the NPVs for each project.

Include the range of NPVs for each project.

c. Do parts a and b provide consistent views of the two projects? Explain.

d. Which project do you recommend? Why?

382 PART 3 Long-Term Investment Decisions

9â€“23 Sensitivity analysis James Secretarial Services is considering the purchase of

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one of two new personal computers, P and Q. Both are expected to provide ben-

efits over a 10-year period, and each has a required investment of $3,000. The

firm has a 10% cost of capital. Management has constructed the following table

of estimates of annual cash inflows for pessimistic, most likely, and optimistic

results.

Computer P Computer Q

Initial investment (CF0) $3,000 $3,000

Outcome Annual cash inflows (CF)

Pessimistic $ 500 $ 400

Most likely 750 750

Optimistic 1,000 1,200

a. Determine the range of annual cash inflows for each of the two computers.

b. Construct a table similar to this for the NPVs associated with each outcome

for both computers.

c. Find the range of NPVs, and subjectively compare the risks associated with

purchasing these computers.

9â€“24 Decision trees The Ouija Board-Games Company can bring out one of two

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new games this season. The Signs Away game has a higher initial cost but also a

higher expected return. Monopolistic Competition, the alternative, has a slightly

lower initial cost but also a lower expected return. The present values and prob-

abilities associated with each game are listed in the table.

Initial Present value

Game investment of cash inflows Probabilities

Signs Away $140,000 1.00

$320,000 .30

220,000 .50

80,000 .20

Monopolistic Competition $120,000 1.00

$260,000 .20

200,000 .45

50,000 .35

a. Construct a decision tree to analyze the games.

b. Which game do you recommend (following a decision-tree analysis)?

c. Has your analysis captured the differences in the risks associated with these

games? Explain.

9â€“25 Simulation Wales Castings has compiled the following information on a capi-

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tal expenditure proposal:

(1) The projected cash inflows are normally distributed with a mean of $36,000

and a standard deviation of $9,000.

383

CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

(2) The projected cash outflows are normally distributed with a mean of

$30,000 and a standard deviation of $6,000.

(3) The firm has an 11% cost of capital.

(4) The probability distributions of cash inflows and cash outflows are not

expected to change over the projectâ€™s 10-year life.

a. Describe how the foregoing data can be used to develop a simulation model

for finding the net present value of the project.

b. Discuss the advantages of using a simulation to evaluate the proposed

project.

9â€“26 Risk-adjusted discount ratesâ€”Basic Country Wallpapers is considering invest-

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ing in one of three mutually exclusive projects, E, F, and G. The firmâ€™s cost of

capital, k, is 15%, and the risk-free rate, RF, is 10%. The firm has gathered the

following basic cash flow and risk index data for each project.

Project (j)

E F G

Initial investment (CF0) $15,000 $11,000 $19,000

Year (t) Cash inflows (CFt )

1 $ 6,000 $ 6,000 $ 4,000

2 6,000 4,000 6,000

3 6,000 5,000 8,000

4 6,000 2,000 12,000

Risk index (RIj) 1.80 1.00 0.60

a. Find the net present value (NPV) of each project using the firmâ€™s cost of capi-

tal. Which project is preferred in this situation?

b. The firm uses the following equation to determine the risk-adjusted discount

rate, RADRj, for each project j:

RADRj RF [RIj (k RF)]

where

RF risk-free rate of return

RIj risk index for project j

k cost of capital

Substitute each projectâ€™s risk index into this equation to determine its RADR.

c. Use the RADR for each project to determine its risk-adjusted NPV. Which

project is preferable in this situation?

d. Compare and discuss your findings in parts a and c. Which project do you

recommend that the firm accept?

9â€“27 Risk-adjusted discount ratesâ€”Tabular After a careful evaluation of investment

LG6

alternatives and opportunities, Joely Company has developed a CAPM-type rela-

tionship linking a risk index to the required return (RADR), as shown in the fol-

lowing table.

384 PART 3 Long-Term Investment Decisions

Risk index Required return (RADR)

0.0 7.0% (risk-free rate, RF)

0.2 8.0

0.4 9.0

0.6 10.0

0.8 11.0

1.0 12.0

1.2 13.0

1.4 14.0

1.6 15.0

1.8 16.0

2.0 17.0

The firm is considering two mutually exclusive projects, A and B. The following

are the data the firm has been able to gather about the projects.

Project A Project B

Initial investment (CF0) $20,000 $30,000

Project life 5 years 5 years

Annual cash inflow (CF) $7,000 $10,000

Risk index 0.2 1.4

All the firmâ€™s cash inflows have already been adjusted for taxes.

a. Evaluate the projects using risk-adjusted discount rates.

b. Discuss your findings in part a, and recommend the preferred project.

9â€“28 Risk classes and RADR Attila Industries is attempting to select the best of

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three mutually exclusive projects, X, Y, and Z. Though all the projects have 5-

year lives, they possess differing degrees of risk. Project X is in class V, the high-

est-risk class; project Y is in class II, the below-average-risk class; and project Z

is in class III, the average-risk class. The basic cash flow data for each project

and the risk classes and risk-adjusted discount rates (RADRs) used by the firm

are shown in the following tables.

Project X Project Y Project Z

Initial investment (CF0) $180,000 $235,000 $310,000

Year (t) Cash inflows (CFt)

1 $ 80,000 $ 50,000 $ 90,000

2 70,000 60,000 90,000

3 60,000 70,000 90,000

4 60,000 80,000 90,000

5 60,000 90,000 90,000

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CHAPTER 9 Capital Budgeting Techniques: Certainty and Risk

Risk Classes and RADRs

Risk-adjusted

Risk Class Description discount rate (RADR)

I Lowest risk 10%

II Below-average risk 13

III Average risk 15

IV Above-average risk 19

V Highest risk 22

a. Find the risk-adjusted NPV for each project.

b. Which project, if any, would you recommend that the firm

undertake?

CHAPTER 9 CASE Making Norwich Toolâ€™s Lathe Investment Decision

N orwich Tool, a large machine shop, is considering replacing one of its

lathes with either of two new lathesâ€”lathe A or lathe B. Lathe A is a

highly automated, computer-controlled lathe; lathe B is a less expensive lathe

that uses standard technology. To analyze these alternatives, Mario Jackson, a

financial analyst, prepared estimates of the initial investment and incremental

(relevant) cash inflows associated with each lathe. These are shown in the fol-

lowing table.

Lathe A Lathe B

Initial investment (CF0) $660,000 $360,000

Year (t) Cash inflows (CFt)

1 $128,000 $ 88,000

2 182,000 120,000

3 166,000 96,000

4 168,000 86,000

5 450,000 207,000

Note that Mario plans to analyze both lathes over a 5-year period. At the end of

that time, the lathes would be sold, thus accounting for the large fifth-year cash

inflows.

One of Marioâ€™s dilemmas centered on the risk of the two lathes. He believes

that although the two lathes are equally risky, lathe A has a much higher chance

of breakdown and repair because of its sophisticated and not fully proven solid-

state electronic technology. Mario is unable to quantify this possibility effec-

tively, so he decides to apply the firmâ€™s 13% cost of capital when analyzing the

lathes. Norwich Tool requires all projects to have a maximum payback period of

4.0 years.

386 PART 3 Long-Term Investment Decisions

Required

a. Use the payback period to assess the acceptability and relative ranking of

each lathe.

b. Assuming equal risk, use the following sophisticated capital budgeting tech-

niques to assess the acceptability and relative ranking of each lathe:

(1) Net present value (NPV).

(2) Internal rate of return (IRR).

c. Summarize the preferences indicated by the techniques used in parts a and b,

and indicate which lathe you recommend, if either, (1) if the firm has unlim-

ited funds and (2) if the firm has capital rationing.

d. Repeat part b assuming that Mario decides that because of its greater risk,

lathe Aâ€™s cash inflows should be evaluated by using a 15% cost of capital.

e. What effect, if any, does recognition of lathe Aâ€™s greater risk in part d have

on our recommendation in part c?

WEB EXERCISE Go to the Web site www.arachnoid.com/lutusp/finance_old.html. Page down to

WW the portion of this screen that contains the financial calculator.

W

1. To determine the internal rate of return (IRR) of a project whose initial

investment was $5,000 and whose cash inflows are $1,000 per year for the

next 10 years, perform the steps outlined below. By entering various interest

rates, you will eventually get a present value of $5,000. When this happens

you, have determined the IRR of the project.

To get started, into PV, enter 0; into FV, enter 0; into np, enter 1000;

into pmt, enter 10; and then into ir, enter 8. Click on Calculate PV. This

gives you a number much greater than $5,000. Now change ir to 20 and

then click on Calculate PV. Keeping changing the ir until PV $5,000, the

same as the initial investment.

2. Try another project. The initial investment is $10,000. The cash inflows are

$2,500 per year for the next 6 years. What is its IRR?

3. To calculate the IRR of an investment of $3,000 with a single cash inflow of

$4,800 to be received exactly 3 years after the investment, do the following:

Into FV, enter 4800; into np, enter 3; into pmt, enter 0; and then into ir,

enter 8. Then click on Calculate PV. As before, keep changing ir until the PV

is equal to the initial investment of $3,000. What is this investmentâ€™s IRR?

Remember to check the bookâ€™s Web site at

www.aw.com/gitman

for additional resources, including additional Web exercises.

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