GitmanAWE IM Ch08

7/24/2019 GitmanAWE IM Ch08

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Chapter 4 Time Value of Money

71

Principles of Managerial FinanceArab World Edition

Gitman, Zutter, Elali, Al-Roubaie

Part 3Long-Term Inestment!ecisions

Chapters in this Part

Chapter 8 Capital Budgeting Techniques

Chapter 9 Capital Budgeting Cash Flows

Chapter 10 Risk and Refinements in Capital Budgeting


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"#apter $"apital %u&geting Tec#ni'ues

Instructors Resources

Overview

This chapter continues the discussion of capital budgeting begun in the preceding chapter (Chapter 7),

which established the basic principles of determining relevant cash flows. Both the sophisticated [net

present value (NPV) and the internal rate of return (IRR)] and unsophisticated (average rate of return andpayback period) capital budgeting techniques are presented. Discussion centers on the calculation and

evaluation of the NPV and IRR in investment decisions, with and without a capital rationing constraint.

Several illustrations exist explaining why capital budgeting techniques will be useful to students in their

professional and personal life.

Answers to Review Questions

8-1 What is the financial managers goal in selecting investment projects for the firm? Define the

capital budgeting process and explain how it helps managers achieve their goal.

Once the relevant cash flows have been developed, they must be analyzed to determine whether the

projects are acceptable or to rank the projects in terms of acceptability in meeting the firms goal.

Managers reach their goal of maximizing shareholder wealth when they undertake all investments

wherein the present value of the cash inflows exceeds the present value of cash outflows.

8-2 What is the payback period? How is it calculated?

Thepayback periodis the exact amount of time required to recover the firms initial investment in aproject. In the case of a mixed stream, the cash inflows are added until their sum equals the initial

investment in the project. In the case of an annuity, the payback is calculated by dividing the initial

investment by the annual cash inflow.

8-3 What weaknesses are commonly associated with the use of the payback period to evaluate a

proposed investment?


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Gitman Principles of Managerial Finance,Arab WorldEdition

The weaknesses of using the payback period are (1) no explicit consideration of shareholders

wealth; (2) failure to take fully into account the time value of money; and (3) failure to consider

returns beyond the payback period and, hence, overall profitability of projects. [Note: If you discount

each cash flow at the time value of money and subtract that from the original expenditure, you end up

with a revised payback period, usually called the discounted payback period. However, this technique

still does not consider all of the cash flows.]

8-4 How is the net present value (NPV) calculated for a project with a conventional cash flow

pattern?

NPVcomputes the present value of all relevant cash flows associated with a project. For

conventional cash flow, NPV takes the present value of all cash inflows over years 1 through n and

subtracts from that sum the initial investment at time zero. The formula for the NPV of a project

with conventional cash flows is:

NPV =present value of cash inflows initial investment

8-5 What are the acceptance criteria for NPV? How are they related to the firms market value?

Acceptance criterion for the NPV method is if NPV > 0, accept; if NPV < 0, reject. If the firm

undertakes projects with a positive NPV, the market value of the firm should increase by the amount

of the NPV.

8-6 Explain the similarities and differences between NPV, PI, and EVA.

NPV, PI, and EVA are all based on the same underlying idea, that investments should earn a rate of

return high enough to meet investors expectations. The PI differs from NPV in that it is expressed asa rate of return. That is, it measures the present value of an investments cash inflows relative to the

up-front cash outflow. EVA calculates a cost of capital charge which is deducted each year from a

projects cash flows. To calculate the overall project EVA, you take the annual EVA figures and

discount them at the cost of capital. In general, NPV, PI, and EVA will always agree on whether a

project is worth investing in or not.

8-7 What is the internal rate of return (IRR) on an investment? How is it determined?

TheIRR on an investment is the discount rate that would cause the investment to have a NPV of

zero. It is found by solving the NPV equation given below for the value of k that equates the presentvalue of cash inflows with the initial investment.

0

1

NPV(1 )

nt

t

t

CFI

r=

= +


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8-8 What are the acceptance criteria for IRR? How are they related to the firms market value?

If a projects IRR is greater than the firms cost of capital, the project should be accepted; otherwise,

the project should be rejected. If the project has an acceptable IRR, the value of the firm should

increase. Unlike the NPV, the amount of the expected value increase is not known.

8-9 Do the net present value (NPV) and internal rate of return (IRR) always agree with respect to

acceptreject decisions? With respect to ranking decisions? Explain.

The NPV and IRR always provide consistent accept/reject decisions. These measures, however, may

not agree with respect to ranking the projects. The NPV may conflict with the IRR due to different

cash flow characteristics of the projects. The greater the difference between timing and magnitude

of cash inflows, the more likely it is that rankings will conflict.

8-10 How is a net present value profile used to compare projects? What causes conflicts in the

ranking of projects via net present value and internal rate of return?

ANPVis a graphic representation of the NPV of a project at various discount rates. The NPV profile

may be used when conflicting rankings of projects exist by depicting each project as a line on the

profile and determining the point of intersection. If the intersection occurs at a positive discount rate,

any discount rate below the intersection will cause conflicting rankings, whereas any discount rates

above the intersection will provide consistent rankings. Conflicts in project rankings using NPV and

IRR result from differences in the magnitude and timing of cash flows. Projects with similar-sized

investments having low early-year cash inflows tend to be preferred at lower discount rates. At high

discount rates, projects with the higher early-year cash inflows are favored, as later-year cash inflows

tend to be severely penalized in present value terms.

8-11 Does the assumption concerning the reinvestment of intermediate cash inflow tend to favor

NPV or IRR? In practice, which technique is preferred and why?

The reinvestment rate assumptionrefers to the rate at which reinvestment of intermediate cash

flows theoretically may be achieved under the NPV or the IRR methods. The NPV method assumes

the intermediate cash flows are reinvested at the discount rate, whereas the IRR method assumes

intermediate cash flows are reinvested at the IRR. On a purely theoretical basis, the NPVs

reinvestment rate assumption is superior because it provides a more realistic rate, the firms cost

of capital, for reinvestment. The cost of capital is generally a reasonable estimate of the rate atwhich a firm could reinvest these cash inflows. The IRR, especially one well exceeding the cost of

capital, may assume a reinvestment rate the firm cannot achieve. In practice, the IRR is preferred

due to the general disposition of business people toward rates of return rather than pure dollar

returns.


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Suggested Answer toFocus on PracticeBox:

Limits on Payback Analysis

In your view, if the payback period method is used in conjunction with theNPVmethod, should it be

used before or after theNPVevaluation?

While the payback method is simple to use and can be used to initially screen projects, the majordisadvantage is that a very rewarding project may be overlooked if it does not meet the arbitrary paybackperiod. For example, if all projects that do not make a specified payback periodsay, 3 yearsarerejected, the company might forgo a very rewarding project whose payback is justified at, say, 3.5 years.

The projects most likely rejected by the payback analysis that could be acceptable using the NPV method

are those that are slow to provide a return cash flow in early years, but that provide a significant cash flow

in outlying years. However, the farther out the cash flows are, the more uncertain they become.

Therefore, if there is an abundance of projects to evaluate, it may make sense to use a simple method suchas the payback period analysis to winnow down the projects before applying a more sophisticated method,

such as the NPV method, to the survivors. If there is not an abundance of projects or if time allows, itmakes sense to apply more than one method of analysis to allof the projects before making a finaldecision.

Another variation is to extend the payback period an extra year on the initial screen so that those projectsjust beyond the preferred payback horizon are given a second chance.

Suggested Answer toFocus on EthicsBox:

Nonfinancial Considerations in Project Selection

What are the potential risks to a company of unethical behaviors by employees? What are potential

risks to the public and to stakeholders?

The consequences to the company may include prosecution, fines, and other penalties for the improper

conduct of its employees. Legal sanctions bring unwanted publicity that can result in loss of business or

damage to the companys good name, trade and customer relations, and even future business opportunities.

Consequences for the employee can include prosecution, fines, and imprisonment. Other penalties for

improper conduct can include loss of incentive pay and annual increases and other forms of disciplinary

action as determined by the company. Serious unethical behavior will almost certainly lead to termination

of employment, not to mention damage to the employees personal reputation.

Consequences for the public, depending upon the types of products the firm produces, may range from

compromised product safety, an increased environmental risk, and a loss of faith in the company.

Consequences for investors may be a reduced investment value.


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Answers to Warm-Up Exercises

E8-1. Payback period

Answer: The payback period for Project Hydrogen is 4.29 years. The payback period for Project

Helium is 5.75 years. Both projects are acceptable because their payback periods are less thanElyas Fields maximum payback period criterion of 6 years.

E8-2. NPV

Answer:

Year Cash Inflow Present Value

1 $400,000 $ 377,358.49

2 375,000 333,748.67

3 300,000 251,885.78

4 350,000 277,232.78

5 200,000 149,451.63

Total $1,389,677.35

NPV =$1,389,677.35 $1,250,000 =$139,677.35

Nada Foods should acquire the new wrapping machine.

E8-3: NPV comparison of two projects

Answer:

Project K

Present value of expenses $45,000

Present value of cash inflows 51,542 (PMT =$20,000,N=3, I =8, PV=?)

NPV $ 6,542

Project T

Present value of expenses $275,000

Present value of cash inflows 277,373 (PMT =$60,000,N=6, I =8, PV=?)

NPV $ 2,373

Based on NPV analysis, Axis Corporation should choose an overhaul of the existing system.

E8-4: IRR

Answer: You may use a financial calculator to determine the IRR of each project. Choose the project

with the higher IRR.

Project T-Shirt

PV=15,000

N=4

PMT =8,000


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Solve forI IRR =39.08%

Project Board Shorts

PV=25,000

N=5

PMT =12,000

Solve forI IRR =38.62%

Based on IRR analysis, Billabong Tech should choose project T-Shirt.

E8-5: NPV

Answer:

Note:The IRR for Project Terra is 10.68% while that of Project Firma is 10.21%. Furthermore,

when the discount rate is zero, the sum of Project Terras cash flows exceed that of Project

Firma. Hence, at any discount rate that produces a positive NPV, Project Terra provides the

higher net present value.


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Solutions to Problems

Note to instructor:In most problems involving the IRR calculation, a financial calculator has been used.

P8-1. Payback period

a. $42,000 $7,000 =6 years

b. The company should accept the project, since 6


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P8-4. NPV for varying cost of capital

PVn=PMT (PVIFAk%,8 yrs.)

a. 10%

PVn=$5,000 (5.335)

PVn=$26,675

NPV =PVnInitial investment

NPV =$26,675 $24,000

NPV =$2,675

Calculator solution: $2,674.63

Accept; positive NPV

b. 12%

PVn=$5,000 (4.968)

PVn=$24,840


NPV =$24,840 $24,000

NPV =$840

Calculator solution: $838.20

Accept; positive NPV

c. 14%

PVn=$5,000 (4.639)

PVn=$23,195


NPV =$23,195 $24,000NPV =$805


Reject; negative NPV

P8-5. NPVindependent projects

Project A

N = 10, I = 14%, PMT = $4,000Solve for PV = $20,864.46

NPV = $20,864.46 $26,000

NPV = $5,135.54

Reject

Project BPV of Cash Inflows

CF0 = -$500,000; CF1 = $100,000; CF2 = $120,000; CF3 = $140,000; CF4 = $160,000;

CF5 = $180,000; CF6 = $200,000

Set I = 14%

Solve for NPV = $53,887.93

Accept


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Project CPV of Cash Inflows

CF0 = -$170,000; CF1 = $20,000; CF2 = $19,000; CF3 = $18,000; CF4 = $17,000;

CF5 = $16,000; CF6 = $15,000; CF7 = $14,000; CF8 = $13,000; CF9 = $12,000; CF10 =

$11,000,

Set I = 14%Solve for NPV = -$83,668.24

Reject

Project D

N = 8, I = 14%, PMT = $230,000

Solve for PV = $1,066,939

NPV = PVn Initial investment

NPV = $1,066,939 $950,000

NPV = $116,939

Accept

Project EPV of Cash Inflows

CF0 = -$80,000; CF1 = $0; CF2 = $0; CF3 = $0; CF4 = $20,000; CF5 = $30,000; CF6 = $0;

CF7 = $50,000; CF8 = $60,000; CF9 = $70,000

Set I = 14%

Solve for NPV = $9,963.63

Accept

P8-6. NPV

a. N = 5, I = 9%, PMT = $385,000Solve for PV = $1,497,515.74

The ie!ia"e #ae" of $1,500,000 i& o" #referre! 'e(a)&e i" ha& a hi*her #re&e" val)e"ha !oe& "he a)i".

'. N = 5, I = 9%, PV = $1,500,000Solve for PMT = $385,638.69

(. Pre&e" val)e+)i" )e = PVor!iar a)i" -1 + !i&(o)" ra"e

$1,497,515.74 -1.09 = $1,632,292Calculator solution: $1,632,292

Changing the annuity to a beginning-of-the-period annuity due would cause Salim

Innovations to prefer the $1,500,000 one-time payment since the PVof the annuity due is

greater than the lump sum.d. No, the cash flows from the project will not influence the decision on how to fund the project.

The investment and financing decisions are separate.

P8-7-9. NPV and maximum return

a. N = 4, I = 10%, PMT = $4,000

Solve for PV = $12,679.46

NPV = PV Ii"ial ive&"e"

NPV = $12,679.46 $13,000NPV =/$320.54


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ee(" "hi& #roe(" !)e "o i"& e*a"ive NPV.'. N = 4, PV= $13,000, PMT = $4,000

Solve for I = 8.86%

8.86% is the maximum required return that the firm could have for the project to be

acceptable. Since the firms required return is 10% the cost of capital is greater than the

expected return and the project is rejected.

P8-8. NPVmutually exclusive projects

a. and b.

Press A

0 = $85,000 1 = $18,000 1 = 8Se" I = 15%

Solve for NPV = $4,228.21Reject

Press B

0 = $60,000 1 = $12,000 2 = $14,000 3 = $16,000 4 = $18,000

5 = $20,000 6 = $25,000Se" I = 15%

Solve for NPV = $2,584.34+((e#"

Press C

0 = $130,000 1 = $50,000 2 = $30,000 3 = $20,000 4 = $20,000

5 = $20,000 6 = $30,000 7 = $40,000 8 = $50,000

Se" I = 15%Solve for NPV = $15,043.89

Accept

c. Rankingusing NPV as criterion

Rank Press NPV

1 C $15,043.89

2 B 2,584.34

3 A 4,228.21

P8-9. Payback and NPV

a. Project Payback Period

A $40,000 $13,000 = 3.08 years

B 3 +($10,000 $16,000) =3.63 yearsC 2 +($5,000 $13,000) =2.38 years

Project C, with the shortest payback period, is preferred.

b. Project

A PVn= $13,000 3.274

PVn= $42,562

PV= $42,562 $40,000

NPV = $2,562


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B

Year CF PVIF16%,n PV

1 $7,000 0.862 $ 6,034

2 10,000 0.743 7,4303 13,000 0.641 8,333

4 16,000 0.552 8,832

5 19,000 0.476 9,044

$39,673

NPV = $39,673 $40,000

NPV = $327


C


1 $19,000 0.862 $16,378

2 16,000 0.743 11,888

3 13,000 0.641 8,333

4 10,000 0.552 5,520

5 7,000 0.476 3,332

$45,451

NPV =$45,451 $40,000

NPV =$5,451


Project C is preferred using the NPV as a decision criterion.

c. At a cost of 16%, Project Chas the highest NPV. Because of Project Cs cash flow

characteristics, high early-year cash inflows, it has the lowest payback period and the

highest NPV.

P8-10. Internal rate of return

IRR is found by solving:

1

$0 initial investment

(1 IRR)

nt

t

t

CF

=

=

+

It can be computed to the nearest whole percent by the estimation method as shown for Project A

below or by using a financial calculator. (Subsequent IRR problems have been solved with a

financial calculator and rounded to the nearest whole percent.)

Project A

Average annuity = ($20,000 +$25,000 +30,000 +$35,000 +$40,000) 5

Average annuity = $150,000 5

Average annuity = $30,000


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PVIFAk%,5yrs. = $90,000 $30,000 = 3.000

PVIFA19%,5 yrs.= 3.0576

PVlFA20%,5 yrs.= 2.991

However, try 17% and 18% since cash flows are greater in later years.

PV@17%

PV@18%CFt PVIF17%,t [(1) (2)] PVIF18%,t [(1) (4)]

Yeart (1) (2) (3) (4) (5)

1 $20,000 0.855 $17,100 0.847 $16,940

2 25,000 0.731 18,275 0.718 17,950

3 30,000 0.624 18,720 0.609 18,270

4 35,000 0.534 18,690 0.516 18,060

5 40,000 0.456 18,240 0.437 17,480

$91,025 $88,700

Initial investment 90,000 90,000

NPV $ 1,025 $ 1,300

NPV at 17% is closer to $0, so IRR is 17%. If the firms cost of capital is below 17%, the project

would be acceptable.

Calculator solution: 17.43%

Project B

PVn = PMT (PVIFAk%,4 yrs.)

$490,000 = $150,000 (PVIFAk%,4 yrs.)

$490,000 $150,000 = (PVIFAk%,4 yrs.)

3.27 =PVIFAk%,4

8% < IRR


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P8-11. IRR, investment life, and cash inflows

a. PVn= PMT (PVIFAk%,n)

$61,450 = $10,000 (PVIFA k%,10 yrs.)

$61,450 $10,000 =PVIFAk%,10 yrs.

6.145 = PVIFAk%,10 yrs.

k= IRR =10% (calculator solution: 10.0%)The IRR


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Reject

NPVB=$35,000(PVIF15%,1) +$50,000(PVIFA15%,2)(PVIF15%,1) $100,000

NPVB=$35,000(0.870) +$50,000(1.626)(0.870) $100,000

NPVB=$30,450 +$70,731$100,000 =$1,181

Calculator solution: $1,117.78Accept

NPVC=$20,000(PVIF15%,1) +$40,000(PVIF15%,2) +$60,000(PVIF15%,3) $80,000

NPVC=$20,000(0.870) +$40,000(0.756) +$60,000(0.658) $80,000

NPVC=$17,400 +$30,240 +39,480 $80,000 =$7,120


Accept

NPVD=$100,000(PVIF15%,1) +$80,000(PVIF15%,2) +$60,000(PVIF15%,3)

$180,000

NPVD=$100,000(0.870) +$80,000(0.756) +$60,000(0.658) $180,000NPVD=$87,000 +$60,480 +39,480 $180,000 =$6,960


Accept

b.

Rank Press NPV

1 C $7,1202 D 6,9603 B 1,181

c. Using the calculator the IRRs of the projects are:

Project IRR

A 9.70%B 15.63%C 19.44%D 17.51%

Since the lowest IRR is 9.7% all of the projects would be acceptable if the cost of capital

was 9.7%.

NOTE:Since Project A was the only reject project from the four projects, all that was

needed to find the minimum acceptable cost of capital was to find the IRR of A.

P8-14. All techniques, conflicting rankings


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a.

Project A Project B

Year

Cash

Inflows

Investment

Balance Year

Cash

Inflows

Investment

Balance

0

$150,000 0

$150,0001 $45,000 105,000 1 $75,000 75,000

2 45,000 60,000 2 60,000 15,000

3 45,000 15,000 3 30,000 +15,000

4 45,000 +30,000 4 30,000 0

5 45,000 30,000

6 45,000 30,000

$150,000Payback 3.33 years 3 years 4 months

$45,000A

= = =

$15,000Payback 2 years years 2.5 years 2 years 6 months$30,000

B = + = =

b. NPVA=$45,000(PVIFA0%,6) $150,000

NPVA=$45,000(6) $150,000

NPVA=$270,000 $150,000 =$120,000

Calculator solution: $120,000

NPVB=$75,000(PVIF0%,1) +$60,000(PVIF0%,2) +$30,000(PVIFA0%,4)(PVIF0%,2)

$150,000

NPVB=$75,000 +$60,000 +$30,000(4) $150,000

NPVB=$75,000 +$60,000 +$120,000 $150,000 =$105,000

Calculator solution: $105,000

c. NPVA=$45,000(PVIFA9%,6) $150,000

NPVA=$45,000(4.486) $150,000

NPVA=$201,870 $150,000 =$51,870


NPVB=$75,000(PVIF9%,1) +$60,000(PVIF9%,2) +$30,000(PVIFA9%,4)(PVIF9%,2)

$150,000

NPVB=$75,000(0.917) +$60,000(0.842) +$30,000(3.24)(0.842) $150,000

NPVB=$68,775 +$50,520 +$81,842 $150,000 =$51,137


d. Using a financial calculator:

IRRA=19.91%

IRRB=22.71%


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e.

Rank

Project Payback NPV IRR

A 2 1 2

B 1 2 1

The project that should be selected is A. The conflict between NPV and IRR is due partially

to the reinvestment rate assumption. The assumed reinvestment rate of Project B is 22.71%,

the projects IRR. The reinvestment rate assumption of A is 9%, the firms cost of capital. On

a practical level Project B will probably be selected due to managements preference for

making decisions based on percentage returns, and their desire to receive a return of cash

quickly.

P8-15. NPV, IRR, and NPV profiles

a. and b.

Project APVof cash inflows:


1 $25,000 0.893 $ 22,325

2 35,000 0.797 27,895

3 45,000 0.712 32,040

4 50,000 0.636 31,800

5 55,000 0.567 31,185

$145,245

NPV = PVof cash inflows initial investmentNPV = $145,245 $130,000

NPV = $15,245


Based on the NPV the project is acceptable since the NPV is greater than zero.

1 2 3 4 5

$25,000 $35,000 $45,000 $50,000 $55,000$0 $130,000

(1 IRR) (1 IRR) (1 IRR) (1 IRR) (1 IRR)= + + + +

+ + + + +

IRR = 16%


Based on the IRR the project is acceptable since the IRR of 16% is greater than the 12% costof capital.

Project B

PVof cash inflows:


1 $40,000 0.893 $35,720

2 35,000 0.797 27,895

3 30,000 0.712 21,360


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4 10,000 0.636 6,360

5 5,000 0.567 2,835

$94,170

NPV = $94,170 $85,000

NPV = $9,170


Based on the NPV the project is acceptable since the NPV is greater than zero.

1 2 3 4 5

$40,000 $35,000 $30,000 $10,000 $5,000$0 $85,000


+ + + + +

IRR = 18%


Based on the IRR the project is acceptable since the IRR of 16% is greater than the 12% cost

of capital.

c.

Data for NPV Profiles

NPV

Discount Rate A B

0% $80,000 $35,000

12% $15,245

15% $ 9,170

16% 0

18% 0


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d. The net present value profile indicates that there are conflicting rankings at a discount rate

less than the intersection point of the two profiles (approximately 15%). The conflict in

rankings is caused by the relative cash flow pattern of the two projects. At discount rates

above approximately 15%, Project B is preferable; below approximately 15%, Project A is

better. Based on Candor Enterprises 12% cost of capital, Project A should be chosen.

e. Project A has an increasing cash flow from Year 1 through Year 5, whereas Project B has a

decreasing cash flow from Year 1 through Year 5. Cash flows moving in opposite directionsoften cause conflicting rankings. TheIRRmethod reinvests Project Bs larger early cash

flows at the higher IRR rate, not the 12% cost of capital.

P8-16. All techniquesdecision among mutually exclusive investments

Project

A B C

Cash inflows (years 15) $20,000

$ 31,500 $ 32,500

a. Payback * 3 years 3.2 years 3.4 years

b. NPV

*

$10,340 $ 10,786 $ 4,303

c. IRR* 20% 17% 15%

*Supporting calculations shown below:

a. Payback Period: Project A: $60,000 $20,000 =3 years

Project B: $100,000 $31,500 =3.2 years

Project C: $110,000 $32,500 =3.4 years

b. NPV

Project A

PVn= PMT (PVIFA13%,5 yrs.)PVn= $20,000 3.517

PVn= 70,340

NPV = $70,340 $60,000

NPV = $10,340


Project B

PVn= $31,500.00 3.517

PVn= $110,785.50

NPV = $110,785.50 $100,000NPV = $10,785.50


Project C

PVn= $32,500.00 3.517

PVn= $114,302.50

NPV =$114,302.50 $110,000

NPV =$4,302.50


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c. IRR

Project, A

NPV at 19% =$1,152.70

NPV at 20% =$187.76

Since NPV is closer to zero at 20%, IRR =20%


Project B

NPV at 17% = $779.40

NPV at 18% = $1,494.11



Project C

NPV at 14% = $1,575.13

NPV at 15% = $1,054.96



d.


NPV

Discount Rate A B C

0% $40,00

0

$57,500 $52,500

13% $10,34

0

10,786 4,303


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15% 0

17% 0

20% 0

The difference in the magnitude of the cash flow for each project causes the NPV to compare

favorably or unfavorably, depending on the discount rate.

e. Even though A ranks higher in Payback and IRR, financial theorists would argue that B is

superior since it has the highest NPV. Adopting B adds $445.50 more to the value of the firm

than does A.

P8-17. All techniques with NPV profilemutually exclusive projects

a. Project A

Payback period

Year 1 +Year 2 +Year 3 = $60,000

Year 4 = $20,000

Initial investment = $80,000

Payback = 3 years +($20,000 30,000)

Payback = 3.67 years

Project B

Payback period

$50,000 $15,000 =3.33 years

b. Project A

PVof cash inflows


1 $15,000 0.885 $13,275

2 20,000 0.783 15,660

3 25,000 0.693 17,325

4 30,000 0.613 18,390

5 35,000 0.543 19,005

$83,655


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NPV = PVof cash inflows initial investment

NPV = $83,655 $80,000

NPV = $3,655


Project B

NPV = PVof cash inflows initial investmentPVn= PMT (PVIFA13%,n)

PVn= $15,000 3.517

PVn= $52,755

NPV = $52,755 $50,000

NPV = $2,755


c. Project A

1 2 3 4 5

$15,000 $20,000 $25,000 $30,000 $35,000$0 $80,000


+ + + + +

IRR = 15%


Project B

$0 = $15,000 (PVIFAk%,5) $50,000

IRR = 15%


d.


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NPV

Discount Rate A B

0% $45,000 $25,000

13% $3,655 2,755

14.6% 0 15.2% 0

Intersectionapproximately 14%

If cost of capital is above 14%, conflicting rankings occur.

The calculator solution is 13.87%.

e. Both projects are acceptable. Both have similar payback periods, positive NPVs, and

equivalent IRRs that are greater than the cost of capital. Although Project B has a slightly

higher IRR, the rates are very close. Since Project A has a higher NPV accept Project A.

P8-18 NPV and EVAa. NPV = $2,500,000 + $240,000 0.09 = $166,667

'. +)al V+ = $240,000 / -$2,500,000 0.09 = $15,000

(. verall V+= $15,000 0.09 = $166,667In this case, NPV and EVA give exactly the same answer.

P8-19 IntegrativeConflicting rankings

a. Plant Expansion0 = $3,500,000, 1 = 1,500,000, 2 = $2,000,000, 3 = $2,500,000, 4 =

$2,750,000Se" I = 20% Solve for NPV = $1,911,844.14

Solve for I = 43.70%1 = 1,500,000, 2 = $2,000,000, 3 = $2,500,000, 4 = $2,750,000

Se" I = 20% Solve for NPV = $5,411,844.14 -Thi& i& "he PV of "he (a&h iflo:&PI = $5,411,844.14 $3,500,000 = 1.55

Product Introduction0 = $500,000, 1 = 250,000, 2 = $350,000, 3 = $375,000, 4 =$425,000Se" I = 20% Solve for NPV = $373,360.34

Solve for I = 52.33%

1 = 250,000, 2 = $350,000, 3 = $375,000, 4 = $425,000

Se" I = 20% Solve for NPV = $873,360.34 -Thi& i& "he PV of "he (a&h iflo:&PI = $873,360.34 $500,000 = 1.75

'.Rank

Project NPV IRR PI

Pla" #a&io 1 2 2Pro!)(" I"ro!)("io 2 1 1

(. The NPV i& hi*her for "he #la" e#a&io, ')" 'o"h "he I a! "he PI are hi*her for "he#ro!)(" i"ro!)("io #roe(". The ra;i*& !o o" a*ree 'e(a)&e "he #la" e#a&io ha& a)(h lar*er &(ale. The NPV re(o*i


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#roe(" here. The I a! PI e"ho!& &i#l ea&)re "he ra"e of re")r o "he #roe(" a! o"i"& &(ale -a! "herefore o" ho: )(h oe i "o"al "he fir a;e& fro ea(h #roe(".

!. =e(a)&e "he NPV of "he #la" e#a&io #roe(" i& hi*her, "he fir>& &harehol!er& :o)l! 'e'e""er off if "he fir #)r&)e! "ha" #roe(", eve "ho)*h i" ha& a lo:er ra"e of re")r.

P8-20. Ethics problem

Expenses are almost sure to increase for Gap. The stock price would almost surely decline in theimmediate future, as cash expenses rise relative to cash revenues. In the long run, Gap may be

able to attract and retain better employees, new human rights and environmentally conscious

customers, and new investor demand from the burgeoning socially responsible investing mutual

funds. This long-run effect is not assured, and we are again reminded that its not merely

shareholder wealth maximization were afterbut maximizing shareholder wealth subject to

ethical constraints.

In fact, if Gap was unwilling to renegotiate worker conditions, Calvert Group (and others) might

sell Gap shares and thereby decrease shareholder wealth.

MyFinanceLab

Further chapter-relevant problems and assignments can be found at the books accompanying resource:

MyFinanceLab. Go towww.myfinancelab.com.
http://www.myfinancelab.com/http://www.myfinancelab.com/http://www.myfinancelab.com/


25/27


Case

Making Halwan Tools Lathe Investment Decision

The student is faced with a typical capital budgeting situation in Chapter 8s case. Halwan Tool must

select one of two lathes that have different initial investments and cash inflow patterns. After calculatingboth unsophisticated and sophisticated capital budgeting techniques, the student must reevaluate the

decision by taking into account the higher risk of one lathe.

a. Payback period

Lathe A:

Years 14 =$644,000

Payback = 4 years +($16,000 $450,000) =4.04 years

Lathe B:

Years 13 =$304,000

Payback = 3 years +($56,000 $86,000) =3.65 yearsLathe A will be rejected since the payback is longer than the 4-year maximum accepted, and Lathe B

is accepted because the project payback period is less than the 4-year payback cutoff.

b.

1) NPV

YearLathe A

Cash Flow PVIF13% PVLathe B

Cash Flow PVIF13%,t PV

1 $128,000 0.885 $113,28

0

$88,000 0.885 $

77,8802 182,000 0.783 142,506 120,000 0.783 93,960

3 166,000 0.693 115,038 96,000 0.693 66,528

4 168,000 0.613 102,984 86,000 0.613 52,718

5 450,000 0.543 244,350 207,000 0.543 112,401

PV= 718,158

PV= $403,487

NPVA= $718,158 $660,000 NPVB=$403,487 $360,000

=$58,158 =$43,487

Calculator solution: $58,132.88 Calculator solution: $43,483.24

2) IRR

Lathe A

1 2 3 4 5

$128, 000 $182, 000 $166, 000 $168, 000 $450, 000$0 $660,000


+ + + + +

IRR = 16%


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Lathe B

1 2 3 4 5

$88,000 $120,000 $96,000 $86,000 $207,000$0 $360,000


+ + + + +

IRR = 17%


Under the NPV rule both lathes are acceptable since the NPVs for A and B are greater than zero.

Lathe A ranks ahead of B since it has a larger NPV. The same accept decision applies to both

projects with the IRR, since both IRRs are greater than the 13% cost of capital. However, the

ranking reverses with the 17% IRR for B being greater than the 16% IRR for Lathe A.

c. Summary

Lathe A Lathe B

Payback period 4.04 years 3.65 years

NPV $58,158 $43,487

IRR 16% 17%

Both projects have positive NPVs and IRRs above the firms cost of capital. Lathe A, however,

exceeds the maximum payback period requirement. Because it is so close to the 4-year maximum

and this is an unsophisticated capital budgeting technique, Lathe A should not be eliminated from

consideration on this basis alone, particularly since it has a much higher NPV.

If the firm has unlimited funds, it should choose the project with the highest NPV, Lathe A, in order

to maximize shareholder value. If the firm is subject to capital rationing, Lathe B, with its shorter

payback period and higher IRR, should be chosen. The IRR considers the relative size of the

investment, which is important in a capital rationing situation.

d. To create an NPV profile it is best to have at least 3 NPV data points. To create the third point an 8%discount rate was arbitrarily chosen. With the 8% rate the NPV for Lathe A is $176,077 and the NPV

for Lathe B is $104,663


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Lathe B is preferred over Lathe A based on the IRR. However, as can be seen in the NPV profile, to

the left of the cross-over point of the two lines Lathe A is preferred. The underlying cause of this

conflict in rankings arises from the reinvestment assumption of NPV versus IRR. NPV assumes the

intermediate cash flows are reinvested at the cost of capital, while the IRR has cash flows being

reinvested at the IRR. The difference in these two rates and the timing of the cash flows will

determine the cross-over point.

e. On a theoretical basis Lathe A should be preferred because of its higher NPV and thus its known

impact on shareholder wealth. From a practical perspective Lathe B may be selected due to its higher

IRR and its faster payback. This difference results from managers preference for evaluating decisions

based on percent returns rather than dollar returns, and on the desire to get a return of cash flows as

quickly as possible.

Spreadsheet Exercise

The answer to Chapter 8s Drillago Company spreadsheet problem is located in MyFinanceLab:

www.myfinancelab.com

In Their Own Words

Harnessing the Power of the Sun

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Documents

GitmanAWE IM Ch08