罗斯公司理财第六版习题答案第6章

Chapter 6: Some Alternative Investment Rules

Concept Questions - Chapter 6

6.2 ? List the problems of the payback period rule.

1. It does not take into account the time value of money. 2. It ignores payments after the payback period. 3. The cutoff period is arbitrary. ? What are some advantages?

1. It is simple to implement.

2. It may help in controlling and evaluating managers. 6.4 ? What are the three steps in calculating AAR?

1. Determine average net income. 2. Determine average investment

3. Divide average net income by average investment. ? What are some flaws with the AAR approach?

1. It uses accounting figures. 2. It takes no account of timing. 3. The cutoff period is arbitrary.

6.5 ? How does one calculate the IRR of a project?

Using either trial-and-error or a financial calculator, one finds the discount rate that produces an NPV of zero.

6.6 ? What is the difference between independent projects and mutually exclusive projects?

An independent project is one whose acceptance does not affect the acceptance of another. A mutually exclusive project, on the other hand is one whose acceptance precludes the acceptance of another.

? What are two problems with the IRR approach that apply to both

independent and mutually exclusive projects?

1. The decision rule depends on whether one is investing of financing. 2. Multiple rates of return are possible.

? What are two additional problems applying only to mutually exclusive

projects?

1. The IRR approach ignores issues of scale.

2. The IRR approach does not accommodate the timing of the cash flows

properly.

6.7 ? How does one calculate a project's profitability index?

Divide the present value of the cash flows subsequent to the initial investment by the initial investment.

? How is the profitability index applied to independent projects, mutually

exclusive projects, and situations of capital rationing?

1. With independent projects, accept the project if the PI is greater than 1.0 and

reject if less than 1.0.

2. With mutually exclusive projects, use incremental analysis, subtracting the

cash flows of project 2 from project 1. Find the PI. If the PI is greater than 1.0, accept project 1. If less than 1.0, accept project 2.

Answers to End-of-Chapter Problems B-65

3. In capital rationing, the firm should simply rank the projects according to their

respective PIs and accept the projects with the highest PIs, subject to the budget constrain.

Answers to End-of-Chapter Problems

QUESTIONS AND PROBLEMS The Payback Period Rule

6.1 Fuji Software, Inc., has the following projects. Year Project A Project B 0 _$7,500 _$5,000 1 4,000 2,500 2 3,500 1,200 3 1,500 3,000

a. Suppose Fuji’s cutoff payback period is two years. Which of these two projects should be chosen? b. Suppose Fuji uses the NPV rule to rank these two projects. If the appropriate discount rate is 15 percent, which project should be chosen?

6.1

a. b. Payback period of Project A = 1 + ($7,500 - $4,000) / $3,500 = 2 years

Payback period of Project B = 2 + ($5,000 - $2,500 -$1,200) / $3,000 = 2.43 years Project A should be chosen.

NPVA = -$7,500 + $4,000 / 1.15 + $3,500 / 1.152 + $1,500 / 1.153 = -$388.96 NPVB = -$5,000 + $2,500 / 1.15 + $1,200 / 1.152 + $3,000 / 1.153 = $53.83 Project B should be chosen.

6.2 Suppose Peach Paving Company invests $1 million today on a new construction project. The project will generate annual cash flows of $150,000 in perpetuity. The appropriate annual discount rate for the project is 10 percent.

a. What is the payback period for the project? If the Peach Paving Company desires to have a 10-year payback period, should the project be adopted?

b. What is the discounted payback period for the project? c. What is the NPV of the project?

6.2 a. b. c. Payback period = 6 + {$1,000,000 - ($150,000 ? 6)} / $150,000 = 6.67 years Yes, the project should be adopted. $150,000 ?110.10 = $974,259

The discounted payback period = 11 + ($1,000,000 - $974,259) / ($150,000 / 1.112)

= 11.54 years

NPV = -$1,000,000 + $150,000 / 0.10 = $500,000

The Average Accounting Return

6.3 The annual, end-of-year, book-investment accounts for the machine whose purchase your firm is considering are shown below. Purchase Year Year Year Year Date 1 2 3 4

Gross investment $16,000 $16,000 $16,000 $16,000 $16,000 Less: accumulated

depreciation ______0_ ___4_,0_0_0_ ___8_,0_0_0_ __1_2_,0_0_0_ _1_6_,_0_0_0 Net investment $16,000 $12,000 $ 8,000 $ 4,000 $ 0

If your firm purchases this machine, you can expect it to generate, on average, $4,500 per year in additional net income.

a. What is the average accounting return for this machine? b. What three flaws are inherent in this decision rule?

6.3 a. Average Investment:

($16,000 + $12,000 + $8,000 + $4,000 + 0) / 5 = $8,000 Average accounting return:

$4,500 / $8,000 = 0.5625 = 56.25%

B-66 Answers to End-of-Chapter Problems

b. 1. 2. 3. AAR does not consider the timing of the cash flows, hence it does not consider the time value of money.

AAR uses an arbitrary firm standard as the decision rule. AAR uses accounting data rather than net cash flows.

6.4 Western Printing Co. has an opportunity to purchase a $2 million new printing machine. It has an economic life of five years and will be worthless after that time. This new investment is expected to generate an annual net income of $100,000 one year from today and the income stream will grow at 7

percent per year subsequently. The company adopts a straight-line depreciation method (i.e., equal amounts of depreciation in each year). What is the average accounting return of the investment? Supposing Western Printing’s AAR cutoff is 20 percent, should the machine be purchased?

6.4 Average Investment = ($2,000,000 + 0) / 2 = $1,000,000 Average net income = [$100,000 {(1 + g)5 - 1} / g] / 5 = {$100,000A (1.075 - 1} / 0.07} / 5 = $115,014.78

AAR = $115,014.78 / $1,000,000 = 11.50%

No, since the machine’s AAR is less than the firm’s cutoff AAR.

6.5 Nokia Group has invested $8,000 in a high-tech project. This cost is depreciated on an accelerated basis that yields $4,000, $2,500, $1,500 of depreciation, respectively, during its three-year economic life. The project is expected to produce income before tax of $2,000 each year during its economic life. If the tax rate is 25%, what is the project’s average accounting return (AAR)? a. 44.44% b. 50.23% c. 66.67% d. 70.00% e. 82.21%

The Internal Rate of Return

6.5 a

6.6 Compute the internal rate of return on projects with the following cash flows. Cash Flows ($)

Year Project A Project B 0 _3,000 _6,000 1 2,500 5,000 2 1,000 2,000

6.6

PI = $40,000 ?70.15 / $160,000 = 1.04

Since the PI exceeds one accept the project.

6.7 CPC, Inc., has a project with the following cash flows. Year Cash Flows ($) 0 _8,000 1 4,000 2 3,000 3 2,000

a. Compute the internal rate of return on the project.

b. Suppose the appropriate discount rate is 8 percent. Should the project be adopted by CPC?

6.7 The IRR is the discount rate at which the NPV = 0. -$3,000 + $2,500 / (1 + IRRA) + $1,000 / (1 + IRRA)2 = 0 By trial and error, IRRA = 12.87% Since project B’s cash flows are two times of those of project A, the IRRB = IRRA =

12.87%

6.8 Compute the internal rate of return for the cash flows of the following two projects. Cash Flows ($) Time A B

0 _2,000 _1,500 1 2,000 500

Answers to End-of-Chapter Problems B-67

2 8,000 1,000 3 _8,000 1,500

6.8 a. b. Solve x by trial and error:

-$4,000 + $2,000 / (1 + x) + $1,500 / (1 + x)2 + $1,000 / (1 + x)3 = 0 x = 6.93%

No, since the IRR (6.93%) is less than the discount rate of 8%.

6.9 Suppose you are offered $5,000 today and obligated to make scheduled payments as follows: Year Cash Flows ($) 0 5,000 1 _2,500 2 _2,000 3 _1,000 4 _1,000

a. What is the IRRs of this offer?

b. If the appropriate discount rate is 10 percent, should you accept this offer? c. If the appropriate discount rate is 20 percent, should you accept this offer? Chapter 6 Some Alternative Investment Rules 165

d. What is the corresponding NPV of the project if the appropriate discount rates are 10 percent and 20 percent, respectively? Are the choices under the NPV rule consistent with those of the IRR rule?

6.9 Find the IRRs of project A analytically. Since the IRR is the discount rate that makes the NPV

equal to zero, the following equation must hold.

-$200 + $200 / (1 + r) + $800 / (1 + r)2 - $800 / (1 + r)3 = 0 $200 [-1 + 1 / (1 + r)] - {$800 / (1 + r)2}[-1 + 1 / (1 + r)] = 0 [-1 + 1 / (1 + r)] [$200 - $800 / (1 + r)2] = 0

For this equation to hold, either [-1 + 1 / (1 + r)] = 0 or [$200 - $800 / (1 + r)2] = 0. Solve each of these factors for the r that would cause the factor to equal zero. The resulting rates are the two IRRs for project A. They are either r = 0% or r = 100%. Note: By inspection you should have known that one of the IRRs of project A is zero. Notice that the sum of the un-discounted cash flows for project A is zero. Thus, not discounting the cash flows would yield a zero NPV. The discount rate which is tantamount to not discounting is zero. Here are some of the interactions used to find the IRR by trial and error. Sophisticated calculators can compute this rate without all of the tedium involved in the trial-and-error method. NPV = -$150 + $50 / 1.3 + $100 / 1.32 + $150 / 1.33 = $15.91 NPV = -$150 + $50 / 1.4 + $100 / 1.42 + $150 / 1.43 = -$8.60 NPV = -$150 + $50 / 1.37 + $100 / 1.372 + $150 / 1.373 = -$1.89 NPV = -$150 + $50 / 1.36 + $100 / 1.36 2 + $150 / 1.363 = $0.46 NPV = -$150 + $50 / 1.36194 + $100 / 1.361942 + $150 / 1.361943 = $0.0010 NPV = -$150 + $50 / 1.36195 + $100 / 1.361952 + $150 / 1.361953 = -$0.0013 NPV = -$150 + $50 / 1.361944 + $100 / 1.3619442 + $150 / 1.3619443 = $0.0000906 Thus, the IRR is approximately 36.1944%.

6.10 As the Chief Financial Officer of the Orient Express, you are offered the following two mutually exclusive projects. Year Project A Project B 0 _$5,000 _$100,000 1 3,500 65,000 2 3,500 65,000

a. What are the IRRs of these two projects?

b. If you are told only the IRRs of the projects, which would you choose?

B-68 Answers to End-of-Chapter Problems

c. What did you ignore when you made your choice in part (b)? d. How can the problem be remedied?

e. Compute the incremental IRR for the projects.

f. Based on your answer to part (e), which project should you choose?

g. Suppose you have determined that the appropriate discount rate for these projects is 15 percent. According to the NPV rule, which of these two projects should be adopted?

6.10

a. b. c. d. Solve r in the equation:

$5,000 - $2,500 / (1 + r) - $2,000 / (1 + r)2 - $1,000 / (1 + r)3 - $1,000 / (1 + r)4 = 0 By trial and error, IRR = r = 13.99%

Since this problem is the case of financing, accept the project if the IRR is less than the required rate of return. IRR = 13.99% > 10% Reject the offer.

IRR = 13.99% < 20% Accept the offer. When r = 10%:

NPV = $5,000 - $2,500 / 1.1 - $2,000 / 1.12 - $1,000 / 1.13 - $1,000 / 1.14

= -$359.95 When r = 20%:

NPV = $5,000 - $2,500 / 1.2 - $2,000 / 1.22 - $1,000 / 1.23 - $1,000 / 1.24

= $466.82

Yes, they are consistent with the choices of the IRR rule since the signs of the cash flows change only once.

6.11 Consider two streams of cash flows, A and B. Cash flow A consists of $5,000 starting three years from today and growing at 4 percent in perpetuity. Cash flow B consists of _$6,000 starting two years from today and continuing in perpetuity. Assume the appropriate discount rate is 12 percent. a. What is the present value of each stream?

b. What is the IRR of a project C, which is a combination of projects A and B; that is, C _ A _ B? c. If it is assumed that the discount rate is always positive, what is the rule related to IRR for assessing project C that would correspond to the NPV rule?

6.11

a. b. c. d. e.

Project A:

NPV = -$5,000 + $3,500 / (1 + r) + $3,500 / (1 + r)2 = 0 IRR = r = 25.69% Project B:

NPV = -$100,000 + $65,000 / (1 + r) + $65,000 / (1 + r)2 = 0 IRR = r = 19.43%

Choose project A because it has a higher IRR. The difference in scale is ignored. Apply the incremental IRR method. C0 C1 C2 B - A -$95,000 $61,500 $61,500 NPV = -$95,000 + $61,500 / (1 + r) + $61,500 / (1 + r)2 = 0 Incremental IRR = r = 19.09%

If the discount rate is less than 19.09%, choose project B. Otherwise, choose project A.

NPVA = -$5,000 + $3,500 / 1.15 + $3,500 / 1.152 = $689.98

NPVB = -$100,000 + $65,000 / 1.15 + $65,000 / 1.152 = $5,671.08 Choose project B.

B-69

f. g.

Answers to End-of-Chapter Problems

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