Capital Budgeting Solutions Manual Ch10

CHAPTER 10

The Fundamentals of Capital Budgeting

Before You Go On Questions and Answers

Section 10.1

1. Why are capital investments considered the most important decisions made by a firm’s

management?

Capital investments are the most important decisions made by a firm’s management,

because they usually involve large cash outflows and once made are not easily reversed.

These are usually long-term projects that will define the firm’s line of business and

significantly contribute to the total revenue figure for years to come.

2. What are the differences between capital projects that are independent, mutually

exclusive, and contingent?

A project is independent if the decision to accept or reject it does not affect the decision

to accept or reject another project. On the other hand, projects are mutually exclusive if

the acceptance of one implies rejection of the other. Contingent projects are those in

which the acceptance of one project is dependent on another project.

Section 10.2

1. What is the NPV of a project?

NPV is simply the difference between the present value of a project’s expected future

cash flows and its cost. It is the recommended technique used to value capital

investments, as it takes into account both the timing of the cash flows and their risk.

2. If a firm accepts a project with a $10,000 NPV, what is the effect on the value of the

firm?

If a firm accepts a project with a $10,000 NPV, it will increase its value by $10,000.

3. What are the five steps used in NPV analysis?

The five-step process used in the NPV analysis can be listed as follows:

(1) Determine the cost of the project.

(2) Estimate the project’s future cash flows over its expected life.

(3) Determine the riskiness of a project and the appropriate cost of capital.

(4) Compute the project’s NPV.

(5) Make a decision.

Section 10.3

1. What is the payback period?

The payback period is defined as the number of years it takes to recover the project’s

initial investment. All other things being equal, the project with the shortest payback

period is usually the optimal investment.

2. Why does the payback period provide a measure of a project’s liquidity risk?

The payback period determines how quickly you recover your investment in a project.

Thus, it serves as a good measure of the project’s liquidity.

3. What are the main shortcomings of the payback method?

The payback method does not account for time value of money, nor does it distinguish

between high- and low-risk projects. In addition, there is no rationale behind choosing the

cutoff criteria. For all these reasons, the payback method is not the ideal capital decision

rule.

Section 10.4

1. What are the major shortcomings of using the ARR method as a capital budgeting

method?

The biggest shortcoming of using ARR as a capital budgeting tool is that it uses

historical, or book value data rather than cash flows and thus disregards the time value of

money principle. In addition, as in the payback method, it fails to establish a rationale

behind picking the appropriate hurdle rate.

Section 10.5

1. What is the IRR method?

The IRR, or the internal rate of return, is the discount rate that makes the net present

value of the project’s future cash flows zero. The IRR determines whether the project’s

return rate is higher or lower than the required rate of return, which is the firm’s cost of

capital. As a rule, a project should be accepted if the IRR exceeds the firm’s cost of

capital; otherwise the project should be rejected.

2. In capital budgeting, what is a conventional cash flow pattern?

A conventional project cash flow in capital budgeting is one in which an initial cash

outflow is followed by one or more future cash inflows.

3. Why should the NPV method be the primary decision tool used in making capital

investment decisions?

Given all the different methods to evaluate capital investment decisions, the NPV method

is the preferred valuation tool as it accounts for both time value of money and the

project’s risk. Furthermore, NPV is not sensitive to nonconventional projects, and

therefore it is superior to the IRR technique and it gives a measure of the value

increase/decrease to the firm by undertaking the project.

Section 10.6

1. What changes have taken place in the capital budgeting techniques used by U.S.

companies?

Over the years, there has been a shift from using payback and ARR as the primary capital

budgeting tools to using NPV and IRR instead. Managers today understand the

importance of the time value of money and discounting and thus regard ARR as an

inaccurate and obsolete decision tool.

Self-Study Problems

10.1 Premium Manufacturing Company is evaluating two forklift systems to use in its plant that

produces the towers for a windmill power farm. The costs and the cash flows from these

systems are shown below. If the company uses a 12 percent discount rate for all projects,

determine which forklift system should be purchased using the net present value (NPV)

approach.

Year 0 Year 1 Year 2 Year 3

Otis Forklifts −$3,123,450 $979,225 $1,358,886 $2,111,497

Craigmore Forklifts −$4,137,410 $875,236 $1,765,225 $2,865,110

Solution:

NPV for Otis Forklifts:

075,337$922,502,1$296,083,1$308,874$450,123,3$

)12.1(497,111,2$

)12.1(886,358,1$

)12.01(225,979$450,123,3$

)k1(CFNPV

321

n

0tt

t

=+++−=

+++

+−=

+= ∑

=

NPV for Craigmore Forklifts:

606,90$227,039,2$229,407,1$461,781$410,137,4$

)12.1(110,865,2$

)12.1(225,765,1$

)12.01(236,875$410,137,4$

)k1(CFNPV

321

n

0tt

t

=+++−=

+++

+−=

+= ∑

=

Premium should purchase the Otis forklift since it has a larger NPV.

10.2 Rutledge, Inc., has invested $100,000 in a project that will produce cash flows of

$45,000, $37,500, and $42,950 over the next three years. Find the payback period for the

project.

Solution:

Payback period for Rutledge project:

Year

CF

Cumulative

Cash Flow

0 (100,000) (100,000)

1 45,000 (55,000)

2 37,500 (17,500)

3 42,950 25,450

Remaining cost to recoverPayback period = Years before cost recovery + Cash flow during the year

$17,500= 2$42,950 per year

2.41years

+

=

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year)

= 2 + ($17,500 / $42,950)

= 2.41 years

10.3 Perryman Crafts Corp. is evaluating two independent capital projects that together will

cost the company $250,000. The two projects will provide the following cash flows:

Year Project A Project B

1 $80,750 $32,450

2 $93,450 $76,125

3 $40,325 $153,250

4 $145,655 $96,110

Which project will be chosen if the company’s payback criterion is three years? What if the

company accepts all projects as long as the payback period is less than five years?

Solution:

Payback periods for Perryman projects A and B:

Project A

Year

Cash Flow

Cumulative

Cash Flows

0 $(250,000) $(250,000)

1 80,750 (169,250)

2 93,450 (75,800)

3 40,235 (35,565)

4 145,655 110,090

Project B

Year

Cash Flow

Cumulative

Cash Flows

0 $(250,000) $(250,000)

1 32,450 (217,550)

2 76,125 (141,425)

3 153,250 11,825

4 96,110 107,935

Payback period for Project A:


$35,565= 3$145,655 per year

3.24 years

+

=

Payback period for Project B:


$141,425= 2$153,250 per year

2.92 years

+

=

If the payback period is three years, only project B will be chosen. If the payback criterion is

five years, both A and B will be chosen.

10.4 Terrell Corp. is looking into purchasing a machine for its business that will cost $117,250

and will be depreciated on a straight-line basis over a five-year period. The sales and

expenses (excluding depreciation) for the next five years are shown in the following table.

The company’s tax rate is 34 percent.

The company w all pr ovi cou of re ) of at least 45 percent. Sill accept ojects that pr de an ac nting rate turn (ARR Year 1 Year 2 Year 3 Year 4 Year 5

Sales $123,450 $176,875 $242,455 $255,440 $267,125

Expenses $137,410 $126,488 $141,289 $143,112 $133,556

h

The company will accept all projects that provide an accounting rate of return (ARR) of at

least 45 percent. Should the company accept the project?

Solution:

Year 1 Year 2 Year 3 Year 4 Year 5

Sales $123,450 $176,875 $242,455 $255,440 $267,125

Expenses 137,410 126,488 141,289 143,112 133,556

Depreciation 23,450 23,450 23,450 23,450 23,450

EBIT $ (37,410) $ 26,937 $ 77,716 $ 88,878 $110,119

Taxes (34%) 12,719 9,159 26,423 30,219 37,440

Net Income $ (24,691) $ 17,778 $ 51,293 $ 58,659 $ 72,679

Beginning Book Value 117,250 93,800 70,350 46,900 23,450

Less: Depreciation (23,450) (23,450) (23,450) (23,450) (23,450)

Ending Book Value $ 93,800 $ 70,350 $ 46,900 $ 23,450 $ 0

Average net income = (–$24,691 + $17,778 + $51,293 + $58,659 + $72,679) / 5 = $35,143.60 Average book value = (1$117,250 + $93,800 + $70,350 + $46,900 + $23,450 + $02)/6

= $58,625 Accounting rate of return = $35,143.6 / $58,625 = 0.599 or 59.9%

The company should accept the project.

10.5 Refer to Problem 10.1. Compute the IRR for each of the two systems. Is the investment

decision different from the one determined by NPV?

Solution:

IRR for two forklift systems:

Otis Forklifts:

First compute the IRR by the trial-and-error approach:

NPV (Otis) = $337,075 > 0

Use a higher discount rate to get NPV = 0!

At k = 15%,

Otis 1 2$979,225 $1,358,886 $2,111,497NPV $3,123,450(1 0.15) (1.15) (1.15)

$3,123,450 $851,500 $1,027,513 $1,388,344$143,907.

= − + + ++

= − + + +=

3

Try a higher rate. At k = 17%,

OtisNPV $3,123,450 $836,944 $992,685 $1,318,357$24,536.

= − + + +=

Try a higher rate. At k = 17.5%,

OtisNPV $3,123,450 $833,383 $984,254 $1,301,598$4,215

= − + + += −

Thus the IRR for Otis is less than 17.5 percent. Using a financial calculator, you can find

that the exact rate to be 17.43 percent.

Craigmore Forklifts:

First compute the IRR by the trial-and-error approach:

NPV (Craigmore) = $90,606 > 0

Use a higher discount rate to get NPV = 0! At k = 15%,

Craigmore 1 2$875,236 $1,765,225 $2,865,110NPV $4,137,410

(1.15) (1.12) (1.12)$4,137,410 $761,075 $1,334,764 $1,883,856$157,715

= − + + +

= − + + += −

3

Try a lower rate. At k = 13%,

CraigmoreNPV $4,137,410 $774,545 $1,382,430 $1,985,665

$5,230

= − + + +

=

Try a higher rate. At k = 13.1%,

CraigmoreNPV $4,137,410 $773,860 $1,379,987 $1,980,403

$3,161

= − + + +

= −

Thus the IRR for Craigmore is less than 13.1 percent. The exact rate is 13.06 percent.

Based on the IRR, we would still pick Otis over Craigmore forklift systems. The decision

is the same as that indicated by NPV

Critical Thinking Questions

10.1 Explain why the cost of capital is referred to as the “hurdle” rate in capital budgeting.

The cost of capital is the minimum required return on any new investment that allows a

firm to break even. Since we are using the cost of capital as a benchmark or “hurdle” to

compare the return earned by any project, it is sometimes referred to as the hurdle rate.

10.2 a. A company is building a new plant on the outskirts of Smallesville. The town has

offered to donate the land, and as part of the agreement, the company will have to

build an access road from the main highway to the plant. How will the project of

building the road be classified in capital budgeting analysis?

b. Sykes, Inc., is considering two projects: a plant expansion and a new computer

system for the firm’s production department. Classify these projects as independent,

mutually exclusive, or contingent projects and explain your reasoning.

c. Your firm is currently considering the upgrading of the operating systems of all the

firm’s computers. The firm can choose the Linux operating system that a local

computer services firm has offered to install and maintain. Microsoft has also put in a

bid to install the new Windows operating system for businesses. What type of project

is this?

a. This is a contingent project. Acceptance of the road-building project is contingent

on the new plant being a financially viable project. If the new plant will not have

a positive value, then the firm will not even consider this project. However, this

project’s cost will have to be considered along with the cost of building the new

plant in the capital budgeting analysis.

b. These two projects are independent projects. Accepting or rejecting one will not

influence the decision on the other project. The cash flows of the two projects are

unrelated.

c. These are two mutually exclusive projects. The company’s computers need only

one operating system. Either the Linux or the Windows operating system needs to

be installed, not both. Hence, the selection of one will eliminate the other from

consideration.

10.3 In the context of capital budgeting, what is “capital rationing”?

Capital rationing implies that a firm does not have the resources necessary to fund all of

the available projects. In other words, funding needs exceed funding resources. Thus, the

available capital will be allocated to the projects that will benefit the firm and its

shareholders the most. Projects that create the largest increase in shareholder wealth will

be accepted until all the available resources have been allocated.

10.4 Provide two conditions under which a set of projects might be characterized as mutually

exclusive.

When projects are mutually exclusive, acceptance of one project precludes the acceptance

of others. Typically, mutually exclusive projects perform the same function and so only

one of them needs to be accepted. A funding or resource constraint can also cause

projects to be mutually exclusive.

10.5 a. A firm invests in a project that would earn a return of 12 percent. If the appropriate

cost of capital is also 12 percent, did the firm make the right decision. Explain.

b. What is the impact on the firm if it accepts a project with a negative NPV?

a. We would normally argue that a firm should only accept projects in which the

project’s return exceeds the cost of capital. In other words, only if the net present

value exceeds zero should a project be accepted. But in reality, projects with a

zero NPV should also be accepted because the project earns a return that equals

the cost of capital. For some firms like the one above, this could be the situation

because they may not have projects that provide a return greater than the cost of

capital for the firm.

b. When a firm takes on positive NPV projects, the value of the firm increases. By

the same token, when a project undertaken has a negative NPV, the value of the

firm will decrease by the amount of the net present value.

10.6 Identify the weaknesses of the payback period method.

There are several critical weaknesses in the payback period approach of evaluating

capital projects.

The payback period ignores the time value of money by not discounting future

cash flows.

When comparing projects, it ignores risk differences between the projects.

A firm may establish payback criteria with no economic basis for that decision

and thereby run the risk of losing out on good projects.

The method ignores cash flows beyond the payback period, thus leading to non-

selection of projects that may produce cash flows well beyond the payback period

or more cash flows than accepted projects. This leads to a bias against longer-term

projects.

10.7 What are the strengths and weaknesses of the accounting rate of return (ARR) approach?

The biggest advantage of ARR is that it is easy to compute since accounting data is

readily available, whereas estimating cash flows is more difficult. However, the

disadvantages outweigh this specific advantage. Similar to the payback, it does not

discount cash flows, but merely averages net income over time. No economic rationale is

used in establishing an ARR cutoff rate. Finally, the ARR uses net income to evaluate the

project and not cash flows or market data. This is a serious flaw in this approach.

10.8 Under what circumstances might the IRR and NPV approaches have conflicting results?

IRR and the NPV methods of evaluating capital investment projects might produce

dissimilar results under two circumstances. First, if the project’s cash flows are not

conventional—that is, if the sign of the cash flow changes more than once during the life

of a project—then multiple IRRs can be obtained as solutions. We would be unable to

identify the correct IRR for decision making. (See Learning by Doing Application 10.3.)

The second situation occurs when two or more projects are mutually exclusive. The

project with the highest IRR may not necessarily be the one with the highest NPV and

thereby be the right choice. There is an important reason for this. IRR assumes that all

cash flows received during the life of a project are reinvested at the IRR, whereas the

NPV method assumes that they are reinvested at the cost of capital. Since the cost of

capital is the better proxy for opportunity cost, NPV uses the better proxy, while the IRR

may use an unrealistically higher rate as proxy.

10.9 The modified IRR (MIRR) alleviates two concerns with using the IRR method for

evaluating capital investments. What are they?

IRR assumes that the cash flows from a project are reinvested at the project’s IRR, while

the NPV assumes that they are invested at the firm’s cost of capital. The NPV

assumption is correct more often than not. The MIRR assumes that each operating cash

flow is reinvested at the firm’s cost of capital.

The second appeal of MIRR is that under this method all of the compounded operating

cash flow values are summed up to get the project’s terminal value. Since most projects

generate positive total net operating cash flows, MIRR does not suffer from issues

associated with unconventional cash flows.

10.10 Elkridge Construction Company has an overall (composite) cost of capital of 12 percent. This

cost of capital reflects the cost of capital for an Elkridge Construction project with average

risk. However, the firm takes on projects of various risk levels. The company experience

suggests that low-risk projects have a cost of capital of 10 percent and high-risk projects have

a cost of capital of 15 percent. Which of the following projects should the company select to

maximize shareholder wealth?

Project Expected Return Risk

1. Single-family homes 13% Low

2. Multifamily residential 12 Average

3. Commercial 18 High

4. Single-family homes 9 Low

5. Commercial 13 High

Project Risk Required

Return

Expected

Return Decision

1. Single-family homes Low 10% 13% Accept

2. Multifamily residential Average 12 12 Accept / Indifferent

3. Commercial High 15 18 Accept

4. Single-family homes Low 10 9 Reject

5. Commercial High 15 13 Reject

Questions and Problems

BASIC

10.1 Net present value: Riggs Corp. management is planning to spend $650,000 on a new

marketing campaign. They believe that this action will result in additional cash flows of

$325,000 over the next three years. If the discount rate is 17.5 percent, what is the NPV

on this project?

LO 2

Solution:

Initial investment = $650,000

Annual cash flows = $325,000

Length of project = n = 3 years

Required rate of return = k = 17.5%

Net present value = NPV

$62,337=+++−=

+++−=+

= ∑=

341,200$401,235$596,276000,650$)175.1(

000,325$)175.1(

000,325$)175.1(

000,325$000,650$)k1(

NCFNPV 321

n

0tt

t

10.2 Net present value: Kingston, Inc. management is considering purchasing a new machine

at a cost of $4,133,250. They expect this equipment to produce cash flows of $814,322,

$863,275, $937,250, $1,017,112, $1,212,960, and $1,225,000 over the next six years. If

the appropriate discount rate is 15 percent, what is the NPV of this investment?

LO 2

Solution:

Cost of new machine = $4,133,250


Required rate of return = k = 15%

441,933$−=++++++−=

++++++−=

+= ∑

=

601,529$055,603$537,581$616257$760,652$$106,708250,133,4$)15.1(000,225,1$

)15.1(960,212,1$

)15.1(112,017,1$

)15.1(250,937$

)15.1(275,863$

)15.1(322,814$250,133,4$

)k1(NCFNPV

654321

n

0tt

t

10.3 Net present value: Crescent Industries management is planning to replace some existing

machinery in its plant. The cost of the new equipment and the resulting cash flows are

shown in the accompanying table. If the firm uses an 18 percent discount rate, should

management go ahead with the project?

Year Cash Flow

0 −$3,300,000

1 $875,123

2 $966,222

3 $1,145,000

4 $1,250,399

5 $1,504,445

LO 2

Solution:

Initial investment = $3,300,000



$134,986=+++++−=

+++++−=

+= ∑

=

607,657$942,644$882,696$926,693$630,741$000,300,3$)18.1(455,504,1$

)18.1(399,250,1$

)18.1(000,145,1$

)18.1(222,966$

)18.1(123,875$000,300,3$

)k1(NCFNPV

54321

n

0tt

t

Since the NPV is positive, the firm should accept the project.

10.4 Net present value: Franklin Mints, a confectioner, is considering purchasing a new

jellybean-making machine at a cost of $312,500. The company’s management projects

that the cash flows from this investment will be $121,450 for the next seven years. If the

appropriate discount rate is 14 percent, what is the NPV for the project?

LO 2

Solution:





$208,315=+++++++−=

++

+++++−=

+= ∑

=

536,48$331,55$077,63$908,71$975,81$452,93$535,106$500,312$)14.1(

450,121$)14.1(

450,121$)14.1(

450,121$)14.1(

450,121$)14.1(

450,121$)14.1(

450,121$)14.1(

450,121$500,312$

)k1(NCFNPV

76

54321

n

0tt

t

10.5 Net present value: Blanda Incorporated management is considering investing in two

alternative production systems. The systems are mutually exclusive, and the cost of the

new equipment and the resulting cash flows are shown in the accompanying table. If the

firm uses a 9 percent discount rate for their production systems, in which system should

the firm invest?

LO 2

Year System 1 System 2 0 ‐15,000 ‐45,000 1 15,000 32,000 2 15,000 32,000 3 15,000 32,000

Solution

The NPV of System 1 is $22,969.42 and the NPV of System 2 is $36,001.43. Since the

NPV of the System 2 is larger than the NPV for System 1, and the investments are

mutually exclusive, the firm should take System 2.

10.6 Payback: Refer to problem 10.5. What are the payback periods for production systems

1 and 2? If the systems are mutually exclusive and the firm always chooses projects with

the lowest payback period, in which system should the firm invest?

LO 3

Solution

System 1 has a payback of exactly one year. System 2 has a payback of 1.41 years.

Given the shorter payback period for system 1, the investment should be made in System

1 based on the payback criteria.

10.7 Payback: Quebec, Inc., is purchasing machinery at a cost of $3,768,966. The company’s

management expects the machinery to produce cash flows of $979,225, $1,158,886, and

$1,881,497 over the next three years, respectively. What is the payback period?

LO 3

Solution:

Year

CF

Cumulative

Cash Flow

0 $(3,768,966) $(3,768,966)

1 979,225 (2,789,741)

2 1,158,886 (1,630,855)

3 1,881,497 250,642


= 2 + ($1,630,855 / $1,881,497) = 2.87 years

10.8 Payback: Northern Specialties just purchased inventory-management computer software

at a cost of $1,645,276. Cost savings from the investment over the next six years will be

reflected in the following cash flow stream: $212,455, $292,333, $387,479, $516,345,

$645,766, and $618,325. What is the payback period on this investment?

LO 3

Solution:

Year

CF

Cumulative

Cash Flow

0 $(1,645,276) $(1,645,276)

1 212,455 (1,432,821)

2 292,333 (1,140,488)

3 387,479 (753,009)

4 516,345 (236,664)

5 645,766 409,102

6 618,325 1,027,427


= 4 + ($236,664 / $645,766)

= 4.37 years

10.9 Payback: Nakamichi Bancorp has made an investment in banking software at a cost of

$1,875,000. Management expects productivity gains and cost savings over the next

several years. If the firm is expected to generate cash flows of $586,212, $713,277,

$431,199, and $318,697 over the next four years, what is the investment’s payback

period?

LO 3

Solution:

Year

CF

Cumulative

Cash Flow

0 $(1,875,000) $(1,875,000

1 586,212 (1,288,788)

2 713,277 (575,511)

3 431,199 (144,312)

4 318,697 174,385


= 3 + ($144,312 / $318,697)

= 3.45 years

10.10 Average accounting rate of return (ARR): Capitol Corp. is expecting a project to

generate after-tax income of $63,435 over each of the next three years. The average book

value of its equipment over that period will be $212,500. If the firm’s acceptance

decision on any project is based on an ARR of 37.5 percent, should this project be

accepted?

LO 4

Solution:

Annual after-tax income = $63,435

Average after-tax income = ($63,435 +$63,435 + $63,435) / 3 = $63,435

Average book value of equipment = $212,500

29.9%==

=

500,212$435,63$

book value Averageincometax -after Average return of rate Accounting

Since the project’s ARR is below the acceptance rate of 37.5 percent, the project should be

rejected.

10.11 Internal rate of return: Refer to Problem 10.4. What is the IRR that Franklin Mints

management can expect on this project?

LO 5

Solution:





To determine the IRR, a trial-and-error approach can be used. Set NPV = 0.

Since the project had a positive NPV of $134,986, try IRR > k.

Try IRR = 25%.

420,71$920,383$500,312$

25.0)25.1(

11450,121$500,312$0

)IRR1(FCF0NPV

7

n

0tt

t

≠+−≠

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

Try a higher rate, IRR = 34%.

339,1$161,311$500,312$

34.0)34.1(

11450,121$500,312$0

)IRR1(FCF0NPV

7

n

0tt

t

−≠+−≠

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

Try a lower rate, IRR = 33.8%.

015$515,312$500,312$

338.0)338.1(

11450,121$500,312$0

)IRR1(FCF0NPV

7

n

0tt

t

≅=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

The IRR of the project is 33.8 percent. Using a financial calculator, we find that the IRR

is 33.8 percent.

10.12 Internal rate of return: Hathaway, Inc., a resort company, is refurbishing one of its

hotels at a cost of $7.8 million. The firm expects that this will lead to additional cash

flows of $1.8 million for the next six years. What is the IRR of this project? If the

appropriate cost of capital is 12 percent, should Hathaway go ahead with this project?

LO 5

Solution:


Annual cash flows = $1,800,000



To determine the IRR, a trial-and-error approach can be used. Set NPV = 0.

Try IRR = 12%.

467,399$533,400,7$000,800,7$

12.0)12.1(

11000,800,1$000,800,7$0

)IRR1(FCF0NPV

6

n

0tt

t

−≠+−≠

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

Since NPV < 0, try a lower rate, IRR = 10%.

469,39$469,839,7$000,800,7$

10.0)10.1(

11000,800,1$000,800,7$0

)IRR1(FCF0NPV

6

n

0tt

t

≠+−≠

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

Try IRR = 10.2%.

265,6$735,793,7$000,800,7$

102.0)102.1(

11000,800,1$000,800,7$0

)IRR1(FCF0NPV

6

n

0tt

t

−≠+−≠

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

Try IRR = 10.15%.

129,5$129,805,7$000,800,7$

1015.0)1015.1(

11000,800,1$000,800,7$0

)IRR1(FCF0NPV

6

n

0tt

t

≠+−≠

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

The IRR of the project is between 10.15 and 10.2 percent. Using a financial calculator,

we find that the IRR is 10.1725 percent. Since IRR < k, reject the project.

INTERMEDIATE 10.13 Net present value: Champlain Corp. is investigating two computer systems. The Alpha

8300 costs $3,122,300 and will generate annual cost savings of $1,345,500 over the next

five years. The Beta 2100 system costs $3,750,000 and will produce cost savings of

$1,125,000 in the first three years and then $2 million for the next two years. If the

company’s discount rate for similar projects is 14 percent, what is the NPV for the two

systems? Which one should be chosen based on the NPV?

LO 2

Solution:

Cost of Alpha 8300 = $3,122,300

Annual cost savings = $1,345,500



$1,496,910=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

210,619,4$300,122,3$

14.0)14.1(

11500,345,1$300,122,3$

)k1(FCFNPV

5n

0tt

t

Cost of Beta 2100 = $3,750,000



$1,084,734=+++−=

++

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

737,038,1161,184,1$836,611,2$000,750,3$

)14.1(000,000,2$

)14.1(000,000,2$

14.0)14.1(

11500,125,1$000,750,3$

)k1(FCFNPV 54

3n

0tt

t

Based on the NPV, the Alpha 8300 system should be chosen.

10.14 Net present value: Briarcrest Condiments is a spice-making firm. Recently, it developed

a new process for producing spices. This process requires new machinery that would cost

$1,968,450, have a life of five years and would produce cash flows as shown in the table.

What is the NPV if the firm uses a discount rate of 15.9 percent?

Year Cash Flow

1 $512,496

2 $(242,637)

3 $814,558

4 $887,225

5 $712,642

LO 2

Solution:

Cost of equipment = $1,968,450



$351,223−=+++−+−=

+++−+−=

+= ∑

=

764,340700,491205,523$630,180$188,442$450,968,1$)159.1(

642,712$)159.1(

225,887$)159.1(

558,814$)159.1(

637,242$)159.1(

496,512$450,968,1$

)k1(FCFNPV

54321

n

0tt

t

10.15 Net present value: Cranjet Industries is expanding its product line and its production

capacity. The costs and expected cash flows of the two independent projects are given in

the following table. The firm typically uses a discount rate of 16.4 percent.

a. What are the NPVs of the two projects?

b Should both projects be accepted? Or either? Or neither? Explain your reasoning.

Year

Product Line

Expansion

Production Capacity

Expansion

0 $(2,575,000) $(8,137,250)

1 $600,000 $2,500,000

2 $875,000 $2,500,000

3 $875,000 $2,500,000

4 $875,000 $3,250,000

5 $875,000 $3,250,000

LO 2

Solution:

a. Required rate of return = 16.4%

Product Line Expansion:

Cost of product line expansion = $2,575,000

$27,222

0

=+++−+−=

+++−+−=

+= ∑

=

490,409646,476816,554$806,645$464,515$000,575,2$)164.1(

000,875$)164.1(

000,875$)164.1(

000,875$)164.1(

000,875$)164.1(

000,600$00,575,2$

)k1(FCFNPV

54321

n

0tt

t

Production Capacity Expansion:

Cost of production capacity expansion = $8,137,250

$732,228=+++−=

++

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

962,520,1$400,770,1$116,578,5$250,137,8$

)164.1(000,250,3$

)164.1(000,250,3$

164.0)164.1(

11000,500,2$250,137,8$

)k1(FCFNPV

54

3

n

0tt

t

b. Since they are independent, and both have NPV > 0, both projects should be

accepted.

10.16 Net present value: Emporia Mills is evaluating two alternative heating systems. Costs

and projected energy savings are given in the following table. The firm uses 11.5 percent

to discount such project cash flows. Which system should be chosen?

Year System 100 System 200

0 $(1,750,000) $(1,735,000)

1 $275,223 $750,000

2 $512,445 $612,500

3 $648,997 $550,112

4 $875,000 $384,226

LO 2

Solution:

Required rate of return = 11.5%

System 100:


$56,667−=++−+−=

++−+−=+

= ∑=

120,566186,468$190,412$837,246$000,750,1$)115.1(

000,875$)115.1(

997,648$)115.1(

445,512$)115.1(

223,275$000,750,1$)k1(

FCFNPV 4321

n

0tt

t

System 200:


$75,758=++−+−=

++−+−=+

= ∑=

592,248850,396$670,492$446,672$000,735,1$)115.1(

226,384$)115.1(

112,550$)115.1(

500,612$)115.1(

000,750$000,735,1$)k1(

FCFNPV 4321

n

0tt

t

Since System 200 has a positive NPV, select that system. Reject System 100 as it has

negative NPV.

10.17 Payback: Creative Solutions, Inc., has just invested $4,615,300 in equipment. The firm

uses payback period criteria of not accepting any project that takes more than four years

to recover its costs. The company anticipates cash flows of $644,386, $812,178,

$943,279, $1,364,997, $2,616,300, and $2,225,375 over the next six years. Does this

investment meet the firm’s payback criteria?

LO 3

Solution:

Year

CF

Cumulative

Cash Flow

0 $(4,615,300) $(4,615,300)

1 644,386 (3,970,914)

2 812,178 (3,158,736)

3 943,279 (2,215,457)

4 1,364,997 (850,460)

5 2,616,300 1,765,840

6 2,225,375 3,991,215


$850,460= 4$2,616,300

4.33 years

+

=

Since the project payback period exceeds the firm’s target of four years, it should not

have been accepted.

10.18 Discounted payback: Timeline Manufacturing Co. is evaluating two projects. It uses

payback criteria of three years or less. Project A has a cost of $912,855, and project B’s

cost is $1,175,000. Cash flows from both projects are given in the following table. What

are their discounted payback periods, and which will be accepted with a discount rate of 8

percent?

Year Project A Project B

1 $ 86,212 $586,212

2 $313,562 $413,277

3 $427,594 $231,199

4 $285,552

LO 3

Solution:

Project A

Year

CF

Cumulative

CF

PVCF

Cumulative

PVCF

0 $(912,855) $(912,855) $(912,855) $(912,855)

1 86,212 (826,643) 79,826 (833,029)

2 313,562 (513,081) 268,829 (564,200)

3 427,594 (85,487) 339,438 (224,762)

4 285,552 200,065 209,889 (14,873)

The payback period exceeds four years.

Project B

Year

CF

Cumulative

CF

PVCF

Cumulative

PVCF

0 $(1,175,000) $(1,175,000) $(1,175,000) $(1,175,000)

1 586,212 (588,788) 542,789 (632,211)

2 413,277 (175,511) 354,318 (277,893)

3 231,199 55,688 183,533 (94,359)


= 3 + years

Since the firm’s acceptance criteria is three years, neither project will be accepted.

10.19 Payback: Regent Corp. is evaluating three competing pieces of equipment. Costs and

cash flow projections for all three are given in the following table. Which would be the

best choice based on payback period?

Year Type 1 Type 2 Type 3

0 $(1,311,450) $(1,415,888) $(1,612,856)

1 $212,566 $586,212 $786,212

2 $269,825 $413,277 $175,000

3 $455,112 $331,199 $175,000

4 $285,552 $141,442 $175,000

5 $121,396 $175,000

6 $175,000

LO 3

Solution:

Type 1 Type 2 Type 3

Year

CF

Cumulative

CF

CF

Cumulative

CF

CF

Cumulative

CF

0 $(1,311,450) $(1,311,450) $(1,415,888) $(1,415,888) $(1,612,856) ($1,612,856)

1 212,566 (1,098,884) 586,212 (829,676) 786,212 (826,644)

2 269,825 (829,059) 413,277 (416,399) 175,000 (651,644)

3 455,112 (373,947) 331,199 (85,200) 175,000 (476,644)

4 285,552 (88,395) 141,442 56,242 175,000 (301,644)

5 121,396 33,001 175,000 (126,644)

6 175,000 48.356

Type 1:


$88,395= 4$121,396

4.73 years

+

=

Type 2:


$85,200= 3$141,442

3.6 years

+

=

Type 3:


$126,644= 5$175,000

5.72 years

+

=

Select Type 2 because it has the lowest payback period.

10.20 Discounted payback: Nugent Communication Corp. is investing $9,365,000 in new

technologies. The company expects significant benefits in the first three years after

installation (as can be seen by the cash flows), and smaller constant benefits in each of

the next four years. What is the discounted payback period for the project assuming a

discount rate of 10 percent?

Years

1 2 3 4 – 7

Cash flows $2,265,433 $4,558,721 $3,378,911 $1,250,000

LO 3

Solution:

Discount rate = k = 10%

Year

CF

Cumulative

CF

PVCF

Cumulative

PVCF

0 $(9,365,000) $(9,365,000) $(9,365,000) $(9,365,000)

1 2,265,433 (7,099,567) 2,059,485 (7,305,515)

2 4,588,721 (2,540,846) 3,767,538 (3,537,977)

3 3,378,911 838,065 2,538,626 (999,352)

4 1,250,000 2,088,065 853,767 (145,585)

5 1,250,000 3,338,065 776,152 630,567

6 1,250,000 4,588,065 705,592 1,336,159

7 1,250,000 5,838,065 641,448 1,977,607


= 4 + ($145,585 / $1,250,000)

= 4.19 years

10.21 Modified internal rate of return (MIRR): Morningside Bakeries has recently purchased

equipment at a cost of $650,000. The firm expects to generate cash flows of $275,000 in each

of the next four years. The cost of capital is 14 percent. What is the MIRR for this project?

LO 5

Solution:

PV of costs = $650,000


Cost of capital = k = 14%

Annual cash flows = CFt = $275,000

315,353,1$000,275$500,313$390,357$425,407$)14.1(000,275$)14.1(000,275$)14.1(000,275$)14.1(000,275$

)1(CF)1(CF)1(CFTV0123

n21

=+++=+++=

++++++= −−− nn2n1n kkk LL

Now we can solve for the MIRR using Equation 10.5.

20.1%====+

==+

+=

+=

2012.0MIRR2012.1)5962.3()MIRR1(

0820.2000,650$315,353,1$)MIRR1(

)MIRR1(315,353,1$000,650$

)1(TVPV

41

4

4

tCosts MIRR

10.22 Modified internal rate of return (MIRR): Sycamore Home Furnishings is considering

acquiring a new machine that can create customized window treatments. The equipment will

cost $263,400 and will generate cash flows of $85,000 over each of the next six years. If the

cost of capital is 12 percent, what is the MIRR on this project?

LO 5

Solution:

PV of costs = $263,400


Cost of capital = k = 12%

Annual cash flows = CFt = $85,000

791,689$000,85$200,95$624,106$419,119$749,133$799,149$

)12.1(000,85$)12.1(000,85$)12.1(000,85$)12.1(000,85$)12.1(000,85$)12.1(000,85$

)1(CF)1(CF)1(CFTV

01

2345n21

=+++++=

++

+++=

++++++= −−− nn2n1n kkk LL

Now we can solve for the MIRR using Equation 10.5.

16

Costs t

6

6

TVPV(1 MIRR)

$689,791$263,400(1 MIRR)$689,791(1 MIRR) 2.6188$263,400

(1 MIRR) (2.6188) 1.1740MIRR 0.1740 17.4%

=+

=+

+ = =

+ = == =

10.23 Internal rate of return: Great Flights, Inc., an aviation firm, is considering purchasing

three aircraft for a total cost of $161 million. The company would lease the aircraft to an

airline. Cash flows from the proposed leases are shown in the following table. What is the

IRR of this project?

Years Cash Flow

1–4 $23,500,000

5–7 $72,000,000

8–10 $80,000,000

LO 5

Solution:




Years Cash Flow

1–4 $23,500,000

5–7 $72,000,000

8–10 $80,000,000

To determine the IRR, the trial-and-error approach can be used. Set NPV=0.

Try a higher rate than k = 15%; try IRR = 22%.

131,589,4$233,614,40$346,374,66$552,600,58$000,000,161$

)22.1(1

22.0)22.1(

11000,000,80$

)22.1(1

22.0)22.1(

11000,000,72$

22.0)22.1(

11000,500,23$000,000,161$0

)IRR1(FCF0NPV

7

3

4

34

n

0tt

t

≠+++−≠

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

Try IRR = 23%.

871,415,2$708,778,37$035,271,63$386,534,57$000,000,161$

)23.1(1

23.0)23.1(

11000,000,80$

)23.1(1

23.0)23.1(

11000,000,72$

23.0)23.1(

11000,500,23$000,000,161$0

)IRR1(FCF0NPV

7

3

4

34

n

0tt

t

−≠+++−≠

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

Try IRR = 22.7%.

307,360$355,605,38$552,183,64$786,850,57$000,000,161$

)227.1(1

227.0)227.1(

11000,000,80$

)227.1(1

227.0)227.1(

11000,000,72$

227.0)227.1(

11000,500,23$000,000,161$0

)IRR1(FCF0NPV

7

3

4

34

n

0tt

t

−≠+++−≠

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−≠

+== ∑

=

The IRR of the project is between 22 and 23 percent. Using a financial calculator, we find

that the IRR is 22.65 percent.

10.24 Internal rate of return: Refer to problem 10.5. Compute the IRR for both

production system 1 and production system 2. Which has the higher IRR? Which

production system has the highest NVP? Explain why the IRR and NPV rankings

of systems 1 and 2 are different?

LO 5

Solution

The IRR of system 1 is 83.93 percent and the IRR of system 2 is 50.07%. The NPV of

system 1 is $22,969.42 and the NPV of system 2 is $36,001.43. System 1 delivers a

higher IRR because it requires a lower initial investment and the cost is recovered the

first year. Thus, even with lower cash inflows in the years after startup, system 1is able

to deliver a higher return on the initial investment. System 2 has a higher initial

investment but delivers a higher net cash flow for the firm.

10.25 Internal rate of return: Ancala Corporation is considering investments in two new golf

apparel lines for next season: golf hats and belts. Due to a funding constraint, these lines

are mutually exclusive. A summary of each project’s estimated cash flows over its three -

year life, as well as the IRRs and NPVs of each are outlined below. The CFO of the firm

has decided to manufacture the belts; however, the CEO of Ancala is questioning this

decision given that the IRR is higher for manufacturing hats. Explain to the CEO why the

IRRs and NPVs of the belt and hat projects disagree? Is the CFO’s decision the correct .

Year Golf Belts Golf Hats 0 -$1,000 -$500 1 1,000 500 2 500 300 3 500 300

NPV $697.97 $427.87 IRR 54% 61%

LO 5

Solution

The IRRs and NPVs of the belt and hat lines disagree because of the differences in the

scale of the project. Hats deliver a higher IRR because they require a lower initial

investment. Thus, even with lower cash inflows in the years after startup, the hat project

is able to deliver a higher return on the initial investment. While the golf belts project

does cost more, it delivers a higher net cash flow for Ancala investors. This NPV factors

in the initial cost of the project, and reflects the total net cash flow for the firm’s

shareholders.

The CFO’s decision to choose the golf belts project is the right choice because it yields

the higher net cash flows for Ancala’s investors.

10.26 Internal rate of return: Compute the IRR on the following cash flow streams:

a. An initial investment of $25,000 followed by a single cash flow of $37,450 in

year 6.

b. An initial investment of $1 million followed by a single cash flow of $1,650,000

in year 4.

c. An initial investment of $2 million followed by cash flows of $1,650,000 and

$1,250,000 in years 2 and 4, respectively.

LO 5

Solution:

a. Try IRR = 7%.

45$955,24$000,25$)07.1(

450,37$000,25$0

)IRR1(FCF0NPV

6

n

0tt

t

−≠+−≠

+−≠

+== ∑

=

Try IRR = 6.97%.

3$997,24$000,25$)0697.1(

450,37$000,25$0

)IRR1(FCF0NPV

6

n

0tt

t

−≠+−≠

+−≠

+== ∑

=

The IRR of the project is approximately 6.97 percent. Using a financial calculator,

we find that the IRR is 6.968 percent.

b. Try IRR = 12%.

605,48$605,048,1$000,000,1$)12.1(000,650,1$000,000,1$0

)IRR1(FCF0NPV

4

n

0tt

t

≠+−≠

+−≠

+== ∑

=

Try IRR = 13%.

976,11$976,011,1$000,000,1$)13.1(000,650,1$000,000,1$0

)IRR1(FCF0NPV

4

n

0tt

t

≠+−≠

+−≠

+== ∑

=

Try IRR = 13.3%.

300,1$300,001,1,1$000,000,1$)133.1(000,650,1$000,000,1$0

)IRR1(FCF0NPV

4

n

0tt

t

≠+−≠

+−≠

+== ∑

=



c. Try IRR = 15%.

671,37$692,714$637,247,1$000,000,2$)15.1(000,250,1$

)15.1(000,650,1$000,000,2$0

)IRR1(FCF0NPV

42

n

0tt

t

−≠++−≠

++−≠

+== ∑

=

Try IRR = 14%.

721,9$100,740$621,269,1$000,000,2$)14.1(000,250,1$

)14.1(000,650,1$000,000,2$0

)IRR1(FCF0NPV

42

n

0tt

t

≠++−≠

++−≠

+== ∑

=

The IRR of the project is between 14 and 15 percent. Using a financial calculator,


10.27 Internal rate of return: Compute the IRR for the following project cash flows.

a. An initial outlay of $3,125,000 followed by annual cash flows of $565,325 for the

next eight years

b. An initial investment of $33,750 followed by annual cash flows of $9,430 for the

next five years

c. An initial outlay of $10,000 followed by annual cash flows of $2,500 for the next

seven years

LO 5

Solution:

a. Initial investment = $3,125,000


Length of investment = n = 8 years

Try IRR = 8%.

$124,006=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

006,249,3$000,125,3$

08.0)08.1(

11325,565$000,125,3$

)k1(FCFNPV

8n

0tt

t

Try a higher rate, IRR = 9%.

$4,248=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

248,129,3$000,125,3$

09.0)09.1(

11325,565$000,125,3$

)k1(FCFNPV

8n

0tt

t

The IRR of the project is approximately 9 percent. Using a financial calculator,


b. Initial investment = $33,750



Try IRR = 12%.

$243=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

993,33$750,33$

12.0)12.1(

11430,9$750,33$

)k1(FCFNPV

5n

0tt

t

Try IRR = 12.3%.

0$8 ≅−=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

33742$750,33$

123.0)123.1(

11430,9$750,33$

)k1(FCFNPV

5n

0tt

t



c. Initial investment = $10,000



Try IRR = 16%.

$96=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

096,10$000,10$

16.0)16.1(

11500,2$000,10$

)k1(FCFNPV

7n

0tt

t

Try IRR = 16.3%.

0$8 ≅=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

008,10$000,10$

163.0)163.1(

11500,2$000,10$

)k1(FCFNPV

7n

0tt

t



ADVANCED

10.28 Draconian Measures, Inc., is evaluating two independent projects. The company uses a

13.8 percent discount rate for such projects. The cost and cash flows are shown in the

following table. What are the NPVs of the two projects?

Year Project 1 Project 2

0 $(8,425,375) $(11,368,000)

1 $3,225,997 $2,112,589

2 $1,775,882 $3,787,552

3 $1,375,112 $3,125,650

4 $1,176,558 $4,115,899

5 $1,212,645 $4,556,424

6 $1,582,156

7 $1,365,882

LO 2

Solution:

Project 1:

Cost of Project 1 = $8,425,375



$668,283−=+

++++++−=

++

+++++−=

+= ∑

=

608,552$443,728$364,635$527,701064,933$291,371,1$795,834,2$375,425,8$

)138.1(882,365,1$

)138.1(156,582,1$

)138.1(645,212,1$

)138.1(558,176,1$

)138.1(112,375,1$

)138.1(882,775,1$

)138.1(997,225,3$375,425,8$

)k1(FCFNPV

76

54321

n

0tt

t

Since Project 1 NPV is negative, we reject this project.

Project 2:

Cost of Project 2 = $11,368,000



$375,375=+++++−=

+++++−=

+= ∑

=

332,387,2$119,454,2$868,120,2$651,924,2$405,856,1$000,368,11$)138.1(424,556,4$

)138.1(889,115,4$

)138.1(650,125,3$

)138.1(552,787,3$

)138.1(589,112,2$000,368,11$

)k1(FCFNPV

54321

n

0tt

t

Since Project 2 NPV is positive, we accept this project.

10.29 Refer to Problem 10.28.

a. What are the IRRs for the projects?

b. Does the IRR criterion indicate a different decision than the NPV criterion?

c. Explain how you would expect the management of Draconian Measures to decide.

LO 5

Solution:

a. Project 1:

At the required rate of return of 13.8 percent, Project 1 has a NPV of $(668,283).

To find the IRR, try lower rates.

Try IRR = 11%.

$73,801−=++

+++++−=

++

+++++−=

+= ∑

=

$657,889 $845,885 $719,646 $775,035$1,005,470$1,441,346$2,906,304 375,425,8$

)11.1(882,365,1$

)11.1(156,582,1$

)11.1(645,212,1$

)11.1(558,176,1$

)11.1(112,375,1$

)11.1(882,775,1$

)11.1(997,225,3$375,425,8$

)k1(FCFNPV

76

54321

n

0tt

t

Try a lower rate, IRR=10.7%.

$5,235−=++

+++++−=

++

+++++−=

+= ∑

=

$1,365,882$1,582,156 $1,212,645$1,176,558$1,375,112$1,775,8823,225,997$375,425,8$

)107.1(882,365,1$

)107.1(156,582,1$

)107.1(645,212,1$

)107.1(558,176,1$

)107.1(112,375,1$

)107.1(882,775,1$

)107.1(997,225,3$375,425,8$

)k1(FCFNPV

76

54321

n

0tt

t



Project 2:

At the required rate of return of 13.8 percent, Project 1 has a NPV of $ 375,375.

To find the IRR, try higher rates.

Try IRR = 15%.

$6,760=+++++−=

+++++−=

+== ∑

=

348,265,2$279,353,2$166,055,2$933,863,2$034,837,1$ 000,368,11$)15.1(424,556,4$

)15.1(889,115,4$

)15.1(650,125,3$

)15.1(552,787,3$

)15.1(589,112,2$000,368,11$0

)IRR1(FCF0NPV

54321

n

0tt

t

Try IRR = 15.1%.

$23,154−=+++++−=

+++++−=

+== ∑

=

524,255,2$111,345,2$814,049,2$959,858,2$438,835,1$ 000,368,11$)151.1(424,556,4$

)151.1(889,115,4$

)151.1(650,125,3$

)151.1(552,787,3$

)151.1(589,112,2$000,368,11$0

)IRR1(FCF0NPV

54321

n

0tt

t

The IRR of the project is between 15 and 15.1 percent. Using a financial

calculator, we find that the IRR is 15.023 percent.

b. Based on the IRR, Project 1 will be rejected and Project 2 will be accepted. These

decisions are identical to those based on NPV. (Given that Project 1 had a

negative NPV, the IRR will always be less than the required rate of return 0.

c. Management would use the decision spelled out by NPV, although in this case the

IRR has come up with the same decision.

10.30 Dravid, Inc., is currently evaluating three projects that are independent. The cost of funds

can be either 13.6 percent or 14.8 percent depending on their financing plan. All three

projects cost the same at $500,000. Expected cash flow streams are shown in the

following table. Which projects would be accepted at a discount rate of 14.8 percent?

What if the discount rate was 13.6 percent?

Year Project 1 Project 2 Project 3

1 0 0 $245,125

2 $125,000 0 $212,336

3 $150,000 $500,000 $112,500

4 $375,000 $500,000 $74,000

LO 2

Solution:

Cost of projects = $500,000



Project 1:

$90,103

k

−=++++−=

++++−=+

= ∑=

906,215$144,99$848,94$0$ 000,500$)148.1(

000,375$)148.1(

000,150$)148.1(

000,125$)148.1(

0$000,500$)1(

FCFNPV 4321

n

0tt

t

Project 2:

$118,353

k

=++++−=

++++−=+

= ∑=

874,287$479,330$0$0$ 000,500$)148.1(

000,500$)148.1(

000,500$)148.1(

0$)148.1(

0$000,500$)1(

FCFNPV 4321

n

0tt

t

Project 3:

$8,397−=++++−=

++++−=+

= ∑=

605,42$358,74$116,161$13,5242$ 000,500$)148.1(

000,74$)148.1(

500,112$)148.1(

336,212$)148.1(

125,245$000,500$)k1(

FCFNPV 4321

n

0tt

t

At a discount rate of 14.8 percent, only project 2 will be accepted. At a discount rate of

13.6 percent, the NPVs of the three projects are -$75,645, $141,295, and $1,491

respectively. Both projects 2 and 3 have positive NPVs and will be accepted.

Year Project 1 PVCF Project 2 PVCF Project 3 PVCF

0 $(500,000) $(500,000) $(500,000) $(500,000) $(500,000) $(500,000)

1 − − − − 245,125 215,779

2 125,000 96,862 − − 212,336 164,538

3 150,000 102,319 500,000 341,063 112,500 76,739

4 375,000 225,175 500,000 300,232 74,000 44,434

NPV (75,645) 141,295 1,491

10.31 Intrepid, Inc., is looking to invest in two or three independent projects. The costs and the

cash flows are given in the following table. The appropriate cost of capital is 14.5

percent. Compute the IRRs and identify the projects that will be accepted.


0 $(275,000) $(312,500) $(500,000)

1 $63,000 $153,250 $212,000

2 $85,000 $167,500 $212,000

3 $85,000 $112,000 $212,000

4 $100,000 $212,000

LO 5

Solution:

Project 1:

Cost of Project 1 = $275,000



$40,338−=++++−=

++++−=

+= ∑

=

181,58$624,56$835,64$5,0225 000,275$)145.1(

000,100$)145.1(

000,85$)145.1(

000,85$)145.1(

000,63$000,275$

)k1(FCFNPV

4321

n

0tt

t

At the required rate of return of 14.5 percent, Project 1 has a NPV of $(40,338). To find

the IRR, try lower rates.

Try IRR = 7.6%.

0$200 ≅−=++++−=

++++−=

+== ∑

=

602,74$231,68$417,73$550,58000,275$)075.1(

000,100$)075.1(

000,85$)075.1(

000,85$)075.1(

000,63$000,275$0

)IRR1(FCF0NPV

4321

n

0tt

t

The IRR of the project is approximately 7.6 percent. Using a financial calculator, we find


Project 2:




$23,717=+++−=

+++−=+

= ∑=

611,74$763,127$33,8431 $500,312$)145.1(

000,112$)145.1(

500,167$)145.1(

250,153$500,312$)k1(

FCFNPV 321

n

0tt

t

At the required rate of return of 14.5 percent, Project 1 has a NPV of $23,717. To find the

IRR, try higher rates.

Try IRR =19%.

$1,027=+++−=

+++−=

+== ∑

=

463,66$283,118$782,128$500,312$)19.1(

000,112$)19.1(

500,167$)19.1(

250,153$500,312$0

)IRR1(FCF0NPV

321

n

0tt

t

Try IRR=19.2%.

0$80 ≅=+++−=

+++−=

+== ∑

=

129,66$886,117$565,128$500,312$)192.1(

000,112$)192.1(

500,167$)192.1(

250,153$500,312$0

)IRR1(FCF0NPV

321

n

0tt

t

The IRR of the project is approximately 19.2 percent. Using a financial calculator, we

find that the IRR is 19.22 percent.

Project 3:




$111,429=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

429,611$000,500$

145.0)145.1(

11000,212$000,500$

)k1(FCFNPV

4n

0tt

t

At the required rate of return of 14.5 percent, Project 1 has a NPV of $111,429. To find

the IRR, try higher rates.

Try IRR =25%.

$659≠+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

659,500$000,500$

25.0)25.1(

11000,212$000,500$0

)IRR1(FCF0NPV

4

n

0tt

t

Try IRR=25.1%.

0231$659,500$000,500$

251.0)251.1(

11000,212$000,500$0

)IRR1(FCF0NPV

4

n

0tt

t

≅−=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=



Only Projects 2 and 3 will be accepted as the IRRs exceed the required rate of return of

14.5 percent.

10.32 Jekyll & Hyde Corp. is evaluating two mutually exclusive projects. The cost of capital is

15 percent. Costs and cash flows are given in the following table. Which project should

be accepted?


0 $(1,250,000) $(1,250,000)

1 $250,000 $350,000

2 $350,000 $350,000

3 $450,000 $350,000

4 $500,000 $350,000

5 $750,000 $350,000

LO 5

Solution:

Project 1:

Cost of project = $1,250,000



$186,683=+++++−=

+++++−=

+= ∑

=

883,372$877,285$882,295$650,264$17,3912$ 000,250,1$)15.1(

000,750$)15.1(

000,500$)15.1(

000,450$)15.1(

000,350$)15.1(

000,250$000,250,1$

)k1(FCFNPV

54321

n

0tt

t

At the required rate of return of 15 percent, Project 1 has an NPV of $186,683.Based on

the positive NPV, Project 1 should be accepted.

To find the IRR, try higher rates.

Try IRR = 20%.

$4,340≠+++++−=

+++++−=

+== ∑

=

408,301$127,241$417,260$056,243$08,3332$ 000,250,1$)20.1(

000,750$)20.1(

000,500$)20.1(

000,450$)20.1(

000,350$)20.1(

000,250$000,250,1$0

)k1(FCF0NPV

54321

n

0tt

t

Try IRR = 20.1%.

0$1,057 ≅=+++++−=

+++++−=

+== ∑

=

155,300$324,240$767,259$651,242$08,1602$ 000,250,1$)201.1(

000,750$)201.1(

000,500$)201.1(

000,450$)201.1(

000,350$)201.1(

000,250$000,250,1$0

)IRR1(FCF0NPV

54321

n

0tt

t



Project 2:

Cost of project = $1,250,000



$76,746−=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

254,173,1$000,250,1$

15.0)15.1(

11000,350$000,250,1$

)k1(FCFNPV

5n

0tt

t

At the required rate of return of 15 percent, Project 1 has an NPV of $(76,746). Based on

the negative NPV, Project 2 should be rejected.

To find the IRR, try lower rates.

Try IRR = 12%.

$11,672=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

672,261,1$000,250,1$

12.0)12.1(

11000,350$000,250,1$0

)IRR1(FCF0NPV

5

n

0tt

t

Try IRR = 12.4%.

0$732 ≅−=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

269,249,1$000,250,1$

124.0)124.1(

11000,350$000,250,1$0

)IRR1(FCF0NPV

5

n

0tt

t



Given a required rate of return of 15 percent, Project 1 will be accepted as the IRR of

20.1 percent exceeds the required rate of return. Project 2 will be rejected.

10.33 Larsen Automotive, a manufacturer of auto parts, is considering investing in two projects.

The company typically compares project returns to a cost of funds of 17 percent.

Compute the IRRs based on the given cash flows, and state which projects will be

accepted.


0 $(475,000) $(500,000)

1 $300,000 $117,500

2 $110,000 $181,300

3 $125,000 $244,112

4 $140,000 $278,955

LO 5

Solution:

Project 1:

Cost of project = $475,000



$14,524=++++−=

++++−=

+= ∑

=

711,74$046,78$356,80$56,4102$ 000,475$)17.1(

000,140$)17.1(

000,125$)17.1(

000,110$)17.1(

000,300$000,475$

)k1(FCFNPV

4321

n

0tt

t

At the required rate of return of 17 percent, Project 1 has an NPV of $14,524. To find the


Try IRR = 19%.

$1,230−≠++++−=

++++−=

+= ∑

=

814,69$177,74$678,77$52,1012$ 000,475$)19.1(

000,140$)19.1(

000,125$)19.1(

000,110$)19.1(

000,300$000,475$

)k1(FCFNPV

4321

n

0tt

t

Try IRR = 18.8%.

0$302 ≅=++++−=

++++−=

+= ∑

=

285,70$552,74$940,77$52,5252$ 000,475$)188.1(

000,140$)188.1(

000,125$)188.1(

000,110$)188.1(

000,300$000,475$

)k1(FCFNPV

4321

n

0tt

t



Project 2:




$34,150=++++−=

++++−=

+= ∑

=

864,148$416,152$442,132$00,4271$ 000,475$)17.1(

955,278$)17.1(

312,244$)17.1(

300,181$)17.1(

500,117$000,500$

)k1(FCFNPV

4321

n

0tt

t

At the required rate of return of 17 percent, Project 1 has an NPV of $34,150. To find the


Try IRR = 20%.

0$385 ≅−=++++−=

++++−=

+== ∑

=

527,134$269,141$903,125$7,9179$ 000,475$)20.1(

955,278$)20.1(

312,244$)20.1(

300,181$)20.1(

500,117$000,500$0

)IRR1(FCF0NPV

4321

n

0tt

t

The IRR of the project is approximately 20 percent. Using a financial calculator, we find


Both projects can be accepted since their IRRs exceed the cost of capital of 17 percent.

10.34 Compute the IRR for each of the following projects:


0 $(10,000) $(10,000) $(10,000)

1 $4,750 $1,650 $800

2 $3,300 $3,890 $1,200

3 $3,600 $5,100 $2,875

4 $2,100 $2,750 $3,400

5 $800 $6,600

LO 5

Solution:

Project 1:



0$13 ≅=++++−=

++++−=

+== ∑

=

160,1$306,2$452,2$,0954$ 000,10$)16.1(

100,2$)16.1(

600,3$)16.1(

300,3$)16.1(

750,4$000,10$0

)IRR1(FCF0NPV

4321

n

0tt

t

The IRR of the project is approximately 16 percent. Using a financial calculator, we find


Project 2:



0$4 ≅−=+++++−=

+++++−=

+== ∑

=

421$545,1$470,3$009,3$,4511$ 000,10$)137.1(

800$)137.1(

750,2$)137.1(

100,5$)137.1(

890,3$)137.1(

650,1$000,10$0

)IRR1(FCF0NPV

54321

n

0tt

t



Project 3:



0$13 ≅−=+++++−=

+++++−=

+== ∑

=

934,3$248,2$108,2$976$217$ 000,10$)109.1(

600,6$)109.1(

400,3$)109.1(

875,2$)109.1(

200,1$)109.1(

800$000,10$0

)IRR1(FCF0NPV

54321

n

0tt

t



10.35 Primus Corp. is planning to convert an existing warehouse into a new plant that will

increase its production capacity by 45 percent. The cost of this project will be

$7,125,000. It will result in additional cash flows of $1,875,000 for the next eight years.

The company uses a discount rate of 12 percent.

a. What is the payback period?

b. What is the NPV for this project?

c. What is the IRR?

LO 2, LO 3, LO 5

Solution:

a.

Year Project 1 Cumulative CF

0 $(7,125,000) $(7,125,000)

1 1,875,000 (5,250,000)

2 1,875,000 (3,375,000)

3 1,875,000 (1,500,000)

4 1,875,000 375,000

5 1,875,000 2,250,000

6 1,875,000 4,125,000

7 1,875,000 6,000,000

8 1,875,000 7,875,000

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the

year)

= 3 + ($1,500,000 / $1,875,000) = 3.80 years

b. Cost of this project = $7,125,000

Required rate of return = 12%


$2,189,325=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

325,314,9$000,125,7$

12.0)12.1(

11000,875,1$000,1250,7$

)k1(FCFNPV

8

n

0tt

t

c. To compute the IRR, try rates higher than 12 percent.

Try IRR = 20%.

$69,675=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

675,194,7$000,125,7$

20.0)20.1(

11000,875,1$000,1250,7$0

)k1(FCF0NPV

8

n

0tt

t

Try IRR = 20.3%.

$5,832=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

832,130,7$000,125,7$

203.0)203.1(

11000,875,1$000,1250,7$0

)k1(FCF0NPV

8

n

0tt

t



10.36 Quasar Tech Co. is investing $6 million in new machinery that will produce the next-

generation routers. Sales to its customers will amount to $1,750,000 for the next three

years and then increase to $2.4 million for three more years. The project is expected to

last six years and cost, excluding depreciation will be $898,620 annually. The machinery

will be depreciated to a salvage value of 0 over 6 years using the straight-line method.

The company’s tax rate is 30 percent, and the cost of capital is 16 percent.

a. What is the payback period?

b. What is the average accounting return (ARR)?

c. Calculate the project NPV.

d. What is the IRR for the project?

LO 2, LO 3, LO 5

Solution:

a.

Year

Net Income

Depreciation

Project 1

Cash Flows

Cumulative

CF

0 $(6,000,000) $(6,000,000)

1 $(104,034) $1,000,000 895,966 (5,104,034)

2 $(104,034) $1,000,000 895,966 (4,208,068)

3 $(104,034) $1,000,000 895,966 (3,312,102)

4 350,966 $1,000,000 1,350,966 (1,961,136)

5 350,966 $1,000,000 1,350,966 (610,170)

6 350,966 $1,000,000 1,350,966 740,796

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the

year)

= 5 + ($610,170 / $1,350,966) = 5.45 years

b.

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Sales $ 1,750,000 $ 1,750,000 $ 1,750,000 $ 2,400,000 $ 2,400,000 $ 2,400,000

Expenses 898,620 898,620 898,620 898,620 898,620 898,620

Depreciation 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000

EBIT $(1,48,620) $(1,48,620) $(1,48,620) $ 501,380 $ 501,380 $ 501,380

Taxes (30%) 44,586 44,586 44,586 (150,414) (150,414) (150,414)

Net income $ (104,034) $ (104,034) $ (104,034) $ 350,966 $ 350,966 $ 350,966

Beginning BV 6,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000

Less:

Depreciation

1,000,000 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000

Ending BV $ 5,000,000 $ 4,000,000 $ 3,000,000 $ 2,000,000 $ 1,000,000 $ 0

Average after-tax income = $123,466

Average book value of equipment = $3,000,000

4.1%==

=

000,000,3$466,123$


c. Cost of this project = $6,000,000



$2,043,927−=++−=

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

833,943,1$241,012,2$000,000,6$

)16.1(1

16.0)16.1(

11966,350,1$

16.0)16.1(

11966,895$000,000.6$

)k1(FCFNPV

3

33

n

0tt

t

d. To compute the IRR, try rates lower than 16 percent.

Try IRR = 3%.

$31,424=++−=

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

084,497,3$340,534,2$000,000,6$

)03.1(1

03.0)03.1(

11966,350,1$

03.0)03.1(

11966,895$000,000.6$0

)IRR1(FCF0NPV

3

33

n

0tt

t

Try IRR = 3.1%.

$9,700=++−=

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+−= ∑

=

225,480,3$475,529,2$000,000,6$

)031.1(1

031.0)031.1(

11966,350,1$

031.0)031.1(

11966,895$000,000.6$0

)IRR1(FCF0NPV

3

33

n

0tt

t

The IRR of the project is approximately 3.1 percent. Using a financial calculator, we find


10.37 Skywards, Inc., an airline caterer, is purchasing refrigerated trucks at a total cost of $3.25

million. After-tax net income from this investment is expected to be $750,000 for the

next five years. Annual depreciation expense will be $650,000. The cost of capital is 17

percent.

a. What is the discounted payback period?

b. Compute the ARR.

c. What is the NPV on this investment?

d. Calculate the IRR.

LO 2, LO 3, LO 4, LO 5

Solution:

a.

Year

Project 1

Cumulative CF

PVCF

Cumulative PVCF

0 $(3,250,000) $(3,250,000) $(3,250,000) $(3,250,000)1 1,400,000 (1,850,000) 1,196,581 (2,053,419)2 1,400,000 (450,000) 1,022,719 (1,030,700)3 1,400,000 950,000 874,119 (156,581)4 1,400,000 2,350,000 747,110 590,5295 1,400,000 3,750,000 638,556 1,229,085

Discount payback period = Years before recovery + (Remaining cost / Next year’s CF)

= 3 + ($156,581 / $747,110) = 3.21 years

b.

Year 1 Year 2 Year 3 Year 4 Year 5Net income $ 750,000 $ 750,000 $ 750,000 $ 750,000 $ 750,000Beginning BV 3,250,000 2,600,000 1,950,000 1,300,000 650,000Less: Depreciation

650,000 650,000 650,000 650,000 650,000

Ending BV $2,600,000 $1,950,000 $1,300,000 $ 650,000 $ 0


Average book value of equipment = $1,625,000

%2.46000,625,1$

000,750$book value Average

incometax -after Average return of rate Accounting

==

=

c. Cost of this project = $3,250,000



$1,229,085=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

085,479,4$000,250,3$

17.0)17.1(

11000,400,1$000,250,3$

)k1(FCFNPV

5n

0tt

t

d. To compute the IRR, try rates much higher than 17 percent.

Try IRR = 30%.

$159,798=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

798,409,3$000,250,3$

30.0)30.1(

11000,400,1$000,250,3$0

)IRR1(FCF0NPV

5

n

0tt

t

Try IRR = 32.5%.

0$2,904 ≅=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

904,252,3$000,250,3$

325.0)325.1(

11000,400,1$000,250,3$0

)IRR1(FCF0NPV

5

n

0tt

t



10.38 Trident Corp. is evaluating two independent projects. The costs and expected cash flows

are given in the following table. The company’s cost of capital is 10 percent.

Year A B

0 $(312,500) $(395,000)

1 $121,450 $153,552

2 $121,450 $158,711

3 $121,450 $166,220

4 $121,450 $132,000

5 $121,450 $122,000

a. Calculate the projects’ NPV.

b. Calculate the projects’ IRR.

c. Which project should be chosen based on NPV? Based on IRR? Is there a

conflict?

d. If you are the decision maker for the firm, which project or projects will be

accepted? Explain your reasoning.

LO 2, LO 5

Solution:

a. Project A:

Cost of this project = $312,500




$147,891=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

391,4605000,312$

10.0)10.1(

11450,121$500,312

)k1(FCFNPV

5n

0tt

t

Project B:




$166,553=+++++−=

+++++−=

+= ∑

=

752,75158,90884,124$166,131$553,139$000,395)10.1(

000,122$)10.1(

000,132$)10.1(

220,166$)10.1(

711,158$)10.1(

552,153$000,395$

)k1(FCFNPV

54321

n

0tt

t

b. Project A:

Since NPV > 0, to compute the IRR, try rates higher than 10 percent.

Try IRR = 27%.

$1,166≠+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

666,3135000,312$

27.0)27.1(

11450,121$500,3120

)IRR1(FCF0NPV

5

n

0tt

t

Try IRR = 27.2%,

0$82 ≅−=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

666,3135000,312$

272.0)272.1(

11450,121$500,3120

)IRR1(FCF0NPV

5

n

0tt

t

The IRR of Project A is approximately 27.2 percent. Using a financial calculator,


Project B:

Since NPV > 0, to compute the IRR, try rates higher than 10 percent.

Try IRR = 26%.

$717≠+++++−=

+++++−=

+== ∑

=

416,38371,52094,83$969,99$867,121$000,395)26.1(

000,122$)26.1(

000,132$)26.1(

220,166$)26.1(

711,158$)26.1(

552,153$000,395$0

)IRR1(FCF0NPV

54321

n

0tt

t

Try IRR = 26.1%.

0$54 ≅−=+++++−=

+++++−=

+== ∑

=

263,38205,52897,82$811,99$770,121$000,395)261.1(

000,122$)261.1(

000,132$)261.1(

220,166$)261.1(

711,158$)261.1(

552,153$000,395$0

)IRR1(FCF0NPV

54321

n

0tt

t

The IRR of Project B is approximately 26.1 percent. Using a financial calculator, we find


c. Since both projects have positive NPVs and they are independent projects, both

should be accepted under the NPV decision criteria. Under the IRR decision

criteria, since both projects have IRRs greater than the cost of capital, both will be

accepted. Thus, there is no conflict between the NPV and IRR decisions.

d. Based on NPV, both projects will be accepted.

10.39 Tyler, Inc., is considering switching to a new production technology. The cost of

equipment will be $4 million. The discount rate is 12 percent. The cash flows that the

firm expects to generate are as follows.

Years CF

0 $(4,000,000)

1-2 0

3–5 $845,000

6–9 $1,450,000

a. Compute the payback and discounted payback period for the project.

b. What is the NPV for the project? Should the firm go ahead with the project?

c. What is the IRR, and what would be the decision under the IRR?

LO 2, LO 3, LO 5

Solution:

a.

Year

Cash Flows

PVCF

Cumulative

CF

Cumulative

PVCF

0 $(4,000,000) $(4,000,000) $(4,000,000) $(4,000,000)

1 -- -- $(4,000,000) $(4,000,000)

2 -- -- $(4,000,000) $(4,000,000)

3 845,000 601,454 (3,155,000) (3,398,546)

4 845,000 537,013 (2,310,000) (2,861,533)

5 845,000 479,476 (1,465,000) (2,382,057)

6 1,450,000 734,615 (15,000) (1,647,442)

7 1,450,000 655,906 1,435,000 (991,536)

8 1,450,000 585,631 2,885,000 (405,905)

9 1,450,000 522,885 4,335,000 116,979.48


$15,000= 6$1,450,000

6.01 years

+

=

Remaining cost to recoverDiscounted Payback period = Years before cost recovery + Cash flow during the year

$405,905= 8$522,885

8.8 years

+

=

b. Cost of this project = $4,000,000



$116,980=++++−=

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+++−=

+= ∑

=

037,499,2$943,617,1$00000,000,4$

)12.1(1

12.0)12.1(

11000,450,1$

)12.1(1

12.0)12.1(

11000,845$00000,000.4$

)k1(FCFNPV

5

4

2

3n

0tt

t

Since NPV > 0, the project should be accepted.

c. Given a positive NPV, to compute the IRR, one should try rates higher than 12

percent.

Try IRR = 12.5%.

$8,394=++++−=

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+

×

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+++−=

+= ∑

=

479,418,2$915,589,1$00000,000,4$

)125.1(1

125.0)125.1(

11000,450,1$

)125.1(1

125.0)125.1(

11000,845$00000,000.4$

)k1(FCFNPV

5

4

2

3n

0tt

t

The IRR is approximately 12.5 percent. Using the financial calculator, we find that the

IRR is 12.539 percent. Based on the IRR exceeding the cost of capital of 12 percent, the

project should be accepted.

CFA Problems

10.40. Given the following cash flows for a capital project, calculate the NPV and IRR. The

required rate of return is 8 percent.

Year

0 1 2 3 4 5

CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000

NPV IRR

a. $1,905 10.9%

b. $1,905 26.0%

c. $3,379 10.9%

d. $3,379 26.0%

LO 2

SOLUTION:

c is correct.

2 3 4

15,000 15,000 20,000 10,000 5,000NPV 50,0001.08 1.08 1.08 1.08 1.08

= − + + + + + 5

NPV = –50,000 + 13,888.89 + 12,860.08 + 15,876.64 + 7,350.30 + 3,402.92

NPV = –50,000 + 53,378.83 = $3,378.83

The IRR, found with a financial calculator, is 10.88 percent.

10.41. Given the following cash flows for a capital project, calculate its payback period and

discounted payback period. The required rate of return is 8 percent.

Year

0 1 2 3 4 5

CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000

The discounted payback period is

a. 0.16 years longer than the payback period.

b. 0.80 years longer than the payback period.

c. 1.01 years longer than the payback period.

d. 1.85 years longer than the payback period.

LO 3

SOLUTION:

c is correct.

YEAR 0 1 2 3 4 5

CASH FLOW –50,000 15,000 15,000 20,000 10,000 5,000

CUMULATIVE CASH

FLOW –50,000 –35,000 –20,000 0 10,000 15,000

DISCOUNTED CASH

FLOW –50,000 13,888.89 12,860.08 15,876.64 7,350.30 3,402.92

CUMULATIVE DCF –50,000 –36,111.11 –23,251.03 –7,374.38 –24.09 3,378.83

As the table shows, the cumulative cash flow offsets the initial investment in

exactly three years. The payback period is 3.00 years. The discounted payback

period is between four and five years. The discounted payback period is 4 years

plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The

discounted payback period is 4.01 – 3.00 = 1.01 years longer than the payback

period.

10.42. An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2,

and $120 in Year 3. The required rate of return is 20 percent. The net present value is

closest to

a. $42.22

b. $58.33

c. $68.52

d. $98.95

LO 2

SOLUTION:

b is correct.

= $58.33 3

2 30

CF 40 80 120NPV 100(1 ) 1.20 1.20 1.20

tt

t r=

= = − + + ++∑

10.43. An investment of $150,000 is expected to generate an after-tax cash flow of $100,000 in

one year and another $120,000 in two years. The cost of capital is 10 percent. What is the

internal rate of return?

a. 28.19 percent

b. 28.39 percent

c. 28.59 percent

d. 28.79 percent

LO 5

SOLUTION:

d is correct. The IRR can be found using a financial calculator or with trial and

error. Using trial and error, the total PV is equal to zero if the discount rate is

28.79 percent.

YEA

R CASH FLOW

PRESENT VALUE

28.19% 28.39% 28.59% 28.79%

0 –150,000 –150,000 –150,000 –150,000 –150,000

1 100,000 78,009 77,888 77,767 77,646

2 120,000 73,025 72,798 72,572 72,346

Total 1,034 686 338 –8

A more precise IRR of 28.7854 percent has a total PV closer to zero.

10.44. An investment requires an outlay of 100 and produces after-tax cash flows of $40

annually for four years. A project enhancement increases the outlay by $15 and the

annual after-tax cash flows by $5. How will the enhancement affect the NPV profile?

The vertical intercept of the NPV profile of the project shifts:

a. up and the horizontal intercept shifts left.

b. up and the horizontal intercept shifts right.

c. down and the horizontal intercept shifts left.

d. down and the horizontal intercept shifts right.

LO 2

SOLUTION:

a is correct. The vertical intercept changes from $60 to $65, and the horizontal intercept

changes from 21.86 percent to 20.68 percent.

Sample Test Problems

10.1 Net present value: Techno Corp. is considering developing new computer software. The

cost of development will be $675,000, and the company expects the revenue from the sale of

the software to be $195,000 for each of the next six years. If the company uses a discount rate

of 14 percent, what is the net present value of this project?

Solution:





$83,290=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

290,758$000,675$

14.0)14.1(

11000,195$000,675$

)k1(FCFNPV

6n

0tt

t

10.2 Payback method: Parker Office Supplies is considering replacing the company’s outdated

inventory-management software. The cost of the new software will be $168,000. Cost

savings is expected to be $43,500 for each of the first three years and then to drop off to

$36,875 for the following two years. What is the payback period for this project?

Solution:

Year

CF

Cumulative

CF

0 $(168,000) $(168,000)

1 43,500 (124,500)

2 43,500 (81,000)

3 43,500 (37,500)

4 36,875 (625)

5 36,875 36,250


= 4 + ($625 / $36,875) = 4.02 years

10.3 Accounting rate of return: Fresno, Inc., is expecting to generate after-tax income of

$156,435 in each of the next three years. The average book value of its equipment over

that period will be $322,500. If the firm’s acceptance decision on any project is based on

an ARR of 40 percent, should this project be accepted?

Solution:

Annual after-tax income = $156,435


Average book value of equipment = $322,500

%4 5.8500,322435,156$


==

=

Since the project’s ARR is above the acceptance rate of 40 percent, the project should be

accepted.

10.4 Internal rate of return: Refer to Sample Test Problem 10.1. What is the IRR on this

project?

Solution:





$83,290=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

290,758$000,675$

14.0)14.1(

11000,195$000,675$

)k1(FCFNPV

6n

0tt

t

Since NPV > 0, try IRR > k. Try IRR = 18%.

$7,033≠+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

033,682$000,675$

18.0)18.1(

11000,195$000,675$0

)IRR1(FCF0NPV

6n

0tt

t

Try IRR = 18.4%.

0$96 ≅=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+== ∑

=

096,675$000,675$

184.0)184.1(

11000,195$000,675$

)IRR1(FCF0NPV

6n

0tt

t

The IRR is approximately 18.4 percent. Using the financial calculator, we find that the

IRR is 18.406 percent.

10.5 Net present value: Raycom, Inc. needs a new overhead crane and two alternatives are

available. Crane T costs $1.35 million and will produce cost savings of $765,000 for the

next three years. Crane R will cost $1.675 million and will yield cost savings of $815,000

for the next three years. The required rate of return is 15 percent. Which of the two

options should Raycom choose based on NPV criteria and why?

Solution:

Crane T:

Cost of this project = $1,350,000




$396,667=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

667,746,1$000,350,1$

15.0)15.1(

11000,765$000,350,1$

)k1(FCFNPV

3n

0tt

t

Crane R:

Cost of this project = $1,675,000




$185,829=+−=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −×+−=

+= ∑

=

829,860,1$000,675,1$

15.0)15.1(

11000,815$000,675,1$

)k1(FCFNPV

3n

0tt

t

Raycom should choose Crane T since it has the higher NPV.

Documents

Capital Budgeting Solutions Manual Ch10