CHAPTER 10
LG 3
415
Herky Foods is considering acquisition of a new wrapping machine. The initial
investment is estimated at $1.25 million, and the machine will have a 5-year life
with no salvage value. Using a 6% discount rate, determine the net present value
(NPV) of the machine given its expected operating cash inflows shown in the
following table. Based on the project’s NPV, should Herky make this investment?
Year
Cash inflow
1
$400,000
2
375,000
3
4
300,000
350,000
5
200,000
E10–3
Axis Corp. is considering investment in the best of two mutually exclusive projects.
Project Kelvin involves an overhaul of the existing system; it will cost $45,000 and
generate cash inflows of $20,000 per year for the next 3 years. Project Thompson
involves replacement of the existing system; it will cost $275,000 and generate cash
inflows of $60,000 per year for 6 years. Using an 8% cost of capital, calculate each
project’s NPV, and make a recommendation based on your findings.
LG 4
E10–4
Billabong Tech uses the internal rate of return (IRR) to select projects. Calculate
the IRR for each of the following projects and recommend the best project based on
this measure. Project T-Shirt requires an initial investment of $15,000 and generates
cash inflows of $8,000 per year for 4 years. Project Board Shorts requires an initial
investment of $25,000 and produces cash inflows of $12,000 per year for 5 years.
LG 5
E10–5
Cooper Electronics uses NPV profiles to visually evaluate competing projects. Key
data for the two projects under consideration are given in the following table. Using
these data, graph, on the same set of axes, the NPV profiles for each project using
discount rates of 0%, 8%, and the IRR.
LG 3
LG 4
E10–2
Capital Budgeting Techniques
Initial investment
Year
Problems
LG 2
All problems are available in
P10–1
Terra
Firma
$30,000
$25,000
Operating cash inflows
1
$ 7,000
$6,000
2
10,000
9,000
3
4
12,000
10,000
9,000
8,000
.
Payback period Jordan Enterprises is considering a capital expenditure that requires
an initial investment of $42,000 and returns after-tax cash inflows of $7,000 per year
for 10 years. The firm has a maximum acceptable payback period of 8 years.
a. Determine the payback period for this project.
b. Should the company accept the project? Why or why not?
416
PART 5
Long-Term Investment Decisions
LG 2
P10–2
Payback comparisons Nova Products has a 5-year maximum acceptable payback
period. The firm is considering the purchase of a new machine and must choose
between two alternative ones. The first machine requires an initial investment of
$14,000 and generates annual after-tax cash inflows of $3,000 for each of the next
7 years. The second machine requires an initial investment of $21,000 and provides
an annual cash inflow after taxes of $4,000 for 20 years.
a. Determine the payback period for each machine.
b. Comment on the acceptability of the machines, assuming that they are independent projects.
c. Which machine should the firm accept? Why?
d. Do the machines in this problem illustrate any of the weaknesses of using payback? Discuss.
LG 2
P10–3
Choosing between two projects with acceptable payback periods Shell Camping
Gear, Inc., is considering two mutually exclusive projects. Each requires an initial
investment of $100,000. John Shell, president of the company, has set a maximum
payback period of 4 years. The after-tax cash inflows associated with each project
are shown in the following table:
Cash inflows (CFt)
Year
Project A
Project B
1
$10,000
$40,000
2
3
20,000
30,000
30,000
20,000
4
40,000
10,000
5
20,000
20,000
a. Determine the payback period of each project.
b. Because they are mutually exclusive, Shell must choose one. Which should the
company invest in?
c. Explain why one of the projects is a better choice than the other.
Personal Finance Problem
LG 2
P10–4
Long-term investment decision, payback method Bill Williams has the opportunity
to invest in project A that costs $9,000 today and promises to pay annual end-ofyear payments of $2,200, $2,500, $2,500, $2,000, and $1,800 over the next 5 years.
Or, Bill can invest $9,000 in project B that promises to pay annual end-of-year payments of $1,500, $1,500, $1,500, $3,500, and $4,000 over the next 5 years.
a. How long will it take for Bill to recoup his initial investment in project A?
b. How long will it take for Bill to recoup his initial investment in project B?
c. Using the payback period, which project should Bill choose?
d. Do you see any problems with his choice?
LG 3
P10–5
NPV Calculate the net present value (NPV) for the following 20-year projects.
Comment on the acceptability of each. Assume that the firm has an opportunity cost
of 14%.
a. Initial investment is $10,000; cash inflows are $2,000 per year.
b. Initial investment is $25,000; cash inflows are $3,000 per year.
c. Initial investment is $30,000; cash inflows are $5,000 per year.
CHAPTER 10
417
Capital Budgeting Techniques
LG 3
P10–6
NPV for varying costs of capital Dane Cosmetics is evaluating a new fragrancemixing machine. The machine requires an initial investment of $24,000 and will
generate after-tax cash inflows of $5,000 per year for 8 years. For each of the costs
of capital listed, (1) calculate the net present value (NPV), (2) indicate whether to
accept or reject the machine, and (3) explain your decision.
a. The cost of capital is 10%.
b. The cost of capital is 12%.
c. The cost of capital is 14%.
LG 3
P10–7
Net present value—Independent projects Using a 14% cost of capital, calculate the
net present value for each of the independent projects shown in the following table,
and indicate whether each is acceptable.
Initial investment (CF0)
Project A
Project B
Project C
Project D
Project E
$26,000
$500,000
$170,000
$950,000
$80,000
$
Year (t)
Cash inflows (CFt)
1
$4,000
$100,000
$20,000
$230,000
2
3
4,000
4,000
120,000
140,000
19,000
18,000
230,000
230,000
0
0
0
4
4,000
160,000
17,000
230,000
20,000
5
4,000
180,000
16,000
230,000
30,000
6
7
4,000
4,000
200,000
15,000
14,000
230,000
230,000
0
50,000
8
4,000
13,000
230,000
60,000
9
4,000
12,000
10
4,000
11,000
70,000
LG 3
P10–8
NPV Simes Innovations, Inc., is negotiating to purchase exclusive rights to manufacture and market a solar-powered toy car. The car’s inventor has offered Simes the
choice of either a one-time payment of $1,500,000 today or a series of five year-end
payments of $385,000.
a. If Simes has a cost of capital of 9%, which form of payment should it choose?
b. What yearly payment would make the two offers identical in value at a cost of
capital of 9%?
c. Would your answer to part a of this problem be different if the yearly payments
were made at the beginning of each year? Show what difference, if any, that
change in timing would make to the present value calculation.
d. The after-tax cash inflows associated with this purchase are projected to amount
to $250,000 per year for 15 years. Will this factor change the firm’s decision
about how to fund the initial investment?
LG 3
P10–9
NPV and maximum return A firm can purchase a fixed asset for a $13,000 initial
investment. The asset generates an annual after-tax cash inflow of $4,000 for 4 years.
a. Determine the net present value (NPV) of the asset, assuming that the firm has a
10% cost of capital. Is the project acceptable?
b. Determine the maximum required rate of return (closest whole-percentage rate)
that the firm can have and still accept the asset. Discuss this finding in light of
your response in part a.
418
PART 5
LG 3
Long-Term Investment Decisions
P10–10
NPV—Mutually exclusive projects Hook Industries is considering the replacement
of one of its old drill presses. Three alternative replacement presses are under consideration. The relevant cash flows associated with each are shown in the following
table. The firm’s cost of capital is 15%.
Initial investment (CF0)
Press A
Press B
Press C
$85,000
$60,000
$130,000
Year (t)
a.
b.
c.
d.
e.
Cash inflows (CFt)
1
$18,000
$12,000
$50,000
2
18,000
14,000
30,000
3
18,000
16,000
20,000
4
5
18,000
18,000
18,000
20,000
20,000
20,000
6
18,000
25,000
30,000
7
18,000
—
40,000
8
18,000
—
50,000
Calculate the net present value (NPV) of each press.
Using NPV, evaluate the acceptability of each press.
Rank the presses from best to worst using NPV.
Calculate the profitability index (PI) for each press.
Rank the presses from best to worst using PI.
Personal Finance Problem
LG 2
LG 3
P10–11
Long-term investment decision, NPV method Jenny Jenks has researched the financial pros and cons of entering into an elite MBA program at her state university.
The tuition and needed books for a master’s program will have an upfront cost of
$100,000. On average, a person with an MBA degree earns an extra $20,000 per
year over a business career of 40 years. Jenny feels that her opportunity cost of capital is 6%. Given her estimates, find the net present value (NPV) of entering this
MBA program. Are the benefits of further education worth the associated costs?
LG 3
P10–12
Payback and NPV Neil Corporation has three projects under consideration. The
cash flows for each project are shown in the following table. The firm has a 16%
cost of capital.
Initial investment (CF0)
Project A
Project B
Project C
$40,000
$40,000
$40,000
Year (t)
Cash inflows (CFt)
1
$13,000
$ 7,000
$19,000
2
3
13,000
13,000
10,000
13,000
16,000
13,000
4
13,000
16,000
10,000
5
13,000
19,000
7,000
CHAPTER 10
Capital Budgeting Techniques
419
a. Calculate each project’s payback period. Which project is preferred according to
this method?
b. Calculate each project’s net present value (NPV). Which project is preferred
according to this method?
c. Comment on your findings in parts a and b, and recommend the best project.
Explain your recommendation.
LG 3
P10–13
NPV and EVA A project costs $2.5 million up front and will generate cash flows in
perpetuity of $240,000. The firm’s cost of capital is 9%.
a. Calculate the project’s NPV.
b. Calculate the annual EVA in a typical year.
c. Calculate the overall project EVA and compare to your answer in part a.
LG 4
P10–14
Internal rate of return For each of the projects shown in the following table, calculate the internal rate of return (IRR). Then indicate, for each project, the maximum
cost of capital that the firm could have and still find the IRR acceptable.
Initial investment (CF0)
Project A
Project B
Project C
Project D
$90,000
$490,000
$20,000
$240,000
Year (t)
LG 4
P10–15
Cash inflows (CFt)
1
$20,000
$150,000
$7,500
$120,000
2
25,000
150,000
7,500
100,000
3
30,000
150,000
7,500
80,000
4
5
35,000
40,000
150,000
—
7,500
7,500
60,000
—
IRR—Mutually exclusive projects Bell Manufacturing is attempting to choose
the better of two mutually exclusive projects for expanding the firm’s warehouse
capacity. The relevant cash flows for the projects are shown in the following table.
The firm’s cost of capital is 15%.
Initial investment (CF0)
Year (t)
Project X
Project Y
$500,000
$325,000
Cash inflows (CFt)
1
$100,000
$140,000
2
3
120,000
150,000
120,000
95,000
4
190,000
70,000
5
250,000
50,000
a. Calculate the IRR to the nearest whole percent for each of the projects.
b. Assess the acceptability of each project on the basis of the IRRs found in part a.
c. Which project, on this basis, is preferred?
420
PART 5
Long-Term Investment Decisions
Personal Finance Problem
LG 4
P10–16
Long-term investment decision, IRR method Billy and Mandy Jones have $25,000
to invest. On average, they do not make any investment that will not return at least
7.5% per year. They have been approached with an investment opportunity that
requires $25,000 upfront and has a payout of $6,000 at the end of each of the next
5 years. Using the internal rate of return (IRR) method and their requirements,
determine whether Billy and Mandy should undertake the investment.
LG 4
P10–17
IRR, investment life, and cash inflows Oak Enterprises accepts projects earning
more than the firm’s 15% cost of capital. Oak is currently considering a 10-year
project that provides annual cash inflows of $10,000 and requires an initial investment of $61,450. (Note: All amounts are after taxes.)
a. Determine the IRR of this project. Is it acceptable?
b. Assuming that the cash inflows continue to be $10,000 per year, how many
additional years would the flows have to continue to make the project acceptable
(that is, to make it have an IRR of 15%)?
c. With the given life, initial investment, and cost of capital, what is the minimum
annual cash inflow that the firm should accept?
LG 3
LG 4
P10–18
NPV and IRR Benson Designs has prepared the following estimates for a longterm project it is considering. The initial investment is $18,250, and the project is
expected to yield after-tax cash inflows of $4,000 per year for 7 years. The firm has
a 10% cost of capital.
a. Determine the net present value (NPV) for the project.
b. Determine the internal rate of return (IRR) for the project.
c. Would you recommend that the firm accept or reject the project? Explain your
answer.
LG 3
LG 4
P10–19
NPV, with rankings Botany Bay, Inc., a maker of casual clothing, is considering
four projects. Because of past financial difficulties, the company has a high cost of
capital at 15%. Which of these projects would be acceptable under those cost
circumstances?
Initial investment (CF0)
Project A
Project B
Project C
Project D
$50,000
$100,000
$80,000
$180,000
Year (t)
Cash inflows (CFt)
1
$20,000
$35,000
$20,000
$100,000
2
20,000
50,000
40,000
80,000
3
20,000
50,000
60,000
60,000
a. Calculate the NPV of each project, using a cost of capital of 15%.
b. Rank acceptable projects by NPV.
c. Calculate the IRR of each project, and use it to determine the highest cost of
capital at which all of the projects would be acceptable.
CHAPTER 10
LG 2
LG 3
P10–20
LG 4
Capital Budgeting Techniques
421
All techniques, conflicting rankings Nicholson Roofing Materials, Inc., is considering two mutually exclusive projects, each with an initial investment of $150,000.
The company’s board of directors has set a maximum 4-year payback requirement
and has set its cost of capital at 9%. The cash inflows associated with the two
projects are shown in the following table.
Cash inflows (CFt)
a.
b.
c.
d.
e.
LG 2
LG 3
P10–21
LG 4
Year
Project A
Project B
1
$45,000
$75,000
2
3
45,000
45,000
60,000
30,000
4
45,000
30,000
5
45,000
30,000
6
45,000
30,000
Calculate the payback period for each project.
Calculate the NPV of each project at 0%.
Calculate the NPV of each project at 9%.
Derive the IRR of each project.
Rank the projects by each of the techniques used. Make and justify a recommendation.
Payback, NPV, and IRR Rieger International is attempting to evaluate the feasibility of investing $95,000 in a piece of equipment that has a 5-year life. The firm
has estimated the cash inflows associated with the proposal as shown in the
following table. The firm has a 12% cost of capital.
Year (t)
Cash inflows (CFt)
1
$20,000
2
3
25,000
30,000
4
35,000
5
40,000
a. Calculate the payback period for the proposed investment.
b. Calculate the net present value (NPV) for the proposed investment.
c. Calculate the internal rate of return (IRR), rounded to the nearest whole percent,
for the proposed investment.
d. Evaluate the acceptability of the proposed investment using NPV and IRR. What
recommendation would you make relative to implementation of the project?
Why?
LG 3
LG 4
LG 5
P10–22
NPV, IRR, and NPV profiles Thomas Company is considering two mutually exclusive projects. The firm, which has a 12% cost of capital, has estimated its cash flows
as shown in the following table.
422
PART 5
Long-Term Investment Decisions
Initial investment (CF0)
Year (t)
Project A
Project B
$130,000
$85,000
Cash inflows (CFt)
1
2
$25,000
35,000
$40,000
35,000
3
45,000
30,000
4
50,000
10,000
5
55,000
5,000
a.
b.
c.
d.
Calculate the NPV of each project, and assess its acceptability.
Calculate the IRR for each project, and assess its acceptability.
Draw the NPV profiles for both projects on the same set of axes.
Evaluate and discuss the rankings of the two projects on the basis of your findings in parts a, b, and c.
e. Explain your findings in part d in light of the pattern of cash inflows associated
with each project.
LG 2
LG 3
LG 4
LG 5
P10–23
LG 6
All techniques—Decision among mutually exclusive investments Pound Industries
is attempting to select the best of three mutually exclusive projects. The initial
investment and after-tax cash inflows associated with these projects are shown in the
following table.
Cash flows
Project A
Project B
Project C
Initial investment (CF0)
$60,000
$100,000
$110,000
Cash inflows (CFt), t = 1 to 5
$20,000
$ 31,500
$ 32,500
a. Calculate the payback period for each project.
b. Calculate the net present value (NPV) of each project, assuming that the firm has
a cost of capital equal to 13%.
c. Calculate the internal rate of return (IRR) for each project.
d. Draw the net present value profiles for both projects on the same set of axes, and
discuss any conflict in ranking that may exist between NPV and IRR.
e. Summarize the preferences dictated by each measure, and indicate which project
you would recommend. Explain why.
LG 2
LG 3
LG 4
LG 5
LG 6
P10–24
All techniques with NPV profile—Mutually exclusive projects Projects A and B, of
equal risk, are alternatives for expanding Rosa Company’s capacity. The firm’s cost
of capital is 13%. The cash flows for each project are shown in the following table.
a. Calculate each project’s payback period.
b. Calculate the net present value (NPV) for each project.
c. Calculate the internal rate of return (IRR) for each project.
d. Draw the net present value profiles for both projects on the same set of axes, and
discuss any conflict in ranking that may exist between NPV and IRR.
e. Summarize the preferences dictated by each measure, and indicate which project
you would recommend. Explain why.
CHAPTER 10
Initial investment (CF0)
Year (t)
LG 6
P10–25
Capital Budgeting Techniques
Project A
Project B
$80,000
$50,000
423
Cash inflows (CFt)
1
$15,000
$15,000
2
20,000
15,000
3
25,000
15,000
4
5
30,000
35,000
15,000
15,000
Integrative—Multiple IRRs Froogle Enterprises is evaluating an unusual investment project. What makes the project unusual is the stream of cash inflows and outflows shown in the following table:
Year
Cash flow
0
$ 200,000
1
- 920,000
2
3
1,582,000
- 1,205,200
4
343,200
a. Why is it difficult to calculate the payback period for this project?
b. Calculate the investment’s net present value at each of the following discount
rates: 0%, 5%, 10%, 15%, 20%, 25%, 30%, 35%.
c. What does your answer to part b tell you about this project’s IRR?
d. Should Froogle invest in this project if its cost of capital is 5%? What if the cost
of capital is 15%?
e. In general, when faced with a project like this, how should a firm decide whether
to invest in the project or reject it?
LG 3
LG 4
LG 5
P10–26
Integrative—Conflicting Rankings The High-Flying Growth Company (HFGC) has
been growing very rapidly in recent years, making its shareholders rich in the process.
The average annual rate of return on the stock in the last few years has been 20%, and
HFGC managers believe that 20% is a reasonable figure for the firm’s cost of capital.
To sustain a high growth rate, the HFGC CEO argues that the company must continue to invest in projects that offer the highest rate of return possible. Two projects
are currently under review. The first is an expansion of the firm’s production capacity,
and the second project involves introducing one of the firm’s existing products into a
new market. Cash flows from each project appear in the following table.
a. Calculate the NPV, IRR, and PI for both projects.
b. Rank the projects based on their NPVs, IRRs, and PIs.
c. Do the rankings in part b agree or not? If not, why not?
d. The firm can only afford to undertake one of these investments, and the CEO
favors the product introduction because it offers a higher rate of return (that is, a
higher IRR) than the plant expansion. What do you think the firm should do?
Why?
424
LG 1
PART 5
LG 6
Long-Term Investment Decisions
P10–27
Year
Plant expansion
Product introduction
0
1
- $3,500,000
1,500,000
- $500,000
250,000
2
2,000,000
350,000
3
2,500,000
375,000
4
2,750,000
425,000
ETHICS PROBLEM Gap, Inc., is trying to incorporate human resource and supplier
considerations into its management decision making. Here is Gap’s report of findings from a recent Social Responsibility Report:
Because factory owners sometimes try to hide violations, Gap emphasizes training
for factory managers. However, due to regional differences, the training varies from
one site to another. The report notes that 10 to 25 percent of workers in China,
Taiwan, and Saipan have been harassed and humiliated. Less than half of the factories in sub-Saharan Africa have adequate worker safety regulations and infrastructure. In Mexico, Latin America, and the Caribbean, 25 to 50 percent of the suppliers
fail to pay even the minimum wage.
Calvert Group, Ltd., a mutual fund family that focuses on “socially responsible
investing,” had this to say about the impact of Gap’s report:
With revenues of $15.9 billion and over 300,000 employees worldwide, Gap leads
the U.S. apparel sector and has contracts with over 3,000 factories globally. Calvert
has been in dialogue with Gap for about five years, the last two as part of the
Working Group.
Gap’s supplier monitoring program focuses on remediation, because its suppliers produce for multiple apparel companies and would likely move their capacity
to different clients rather than adopt conditions deemed too demanding. About onethird of the factories Gap examined comfortably met Gap’s criteria, another third
had barely acceptable conditions, and the final third missed the minimum standards.
Gap terminated contracts with 136 factories where it found conditions to be beyond
remediation.
Increased transparency and disclosure are crucial in measuring a company’s
commitment to raising human rights standards and improving the lives of workers.
Gap’s report is an important first step in the direction of a model format that other
companies can adapt.8
If Gap were to aggressively pursue renegotiations with suppliers, based on this
report, what is the likely effect on Gap’s expenses in the next 5 years? In your
opinion, what would be the impact on its stock price in the immediate future? After
10 years?
8. www.calvert.com/news_newsArticle.asp?article=4612&image=cn.gif&keepleftnav=Calvert+News
CHAPTER 10
Capital Budgeting Techniques
425
Spreadsheet Exercise
The Drillago Company is involved in searching for locations in which to drill for oil.
The firm’s current project requires an initial investment of $15 million and has an
estimated life of 10 years. The expected future cash inflows for the project are as
shown in the following table:
Year
1
Cash inflows
$
600,000
2
1,000,000
3
4
1,000,000
2,000,000
5
3,000,000
6
3,500,000
7
8
4,000,000
6,000,000
9
8,000,000
10
12,000,000
The firm’s current cost of capital is 13%.
TO DO
Create a spreadsheet to answer the following:
a. Calculate the project’s net present value (NPV). Is the project acceptable under
the NPV technique? Explain.
b. Calculate the project’s internal rate of return (IRR). Is the project acceptable
under the IRR technique? Explain.
c. In this case, did the two methods produce the same results? Generally, is there a
preference between the NPV and IRR techniques? Explain.
d. Calculate the payback period for the project. If the firm usually accepts projects
that have payback periods between 1 and 7 years, is this project acceptable?
Visit www.myfinancelab.com for Chapter Case: Making Norwich Tool’s Lathe Investment Decision,
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