CAPITAL BUDGETING PROBLEMS: CHAPTER 10

REVIEW QUESTION
10–1 What is the financial manager’s goal in selecting investment projects for
the firm? Define the capital budgeting process and explain how it helps
managers achieve their goal.

1. Step 1 of 3

Financial manager’s goal in selecting investment projects is as same as firm’s goal i.e. to
maximize owner’s wealth by selecting those projects which must be profitable for the firm in
terms of efficiency and profitability.

2. Step 2 of 3

Capital budgeting is the process of evaluating and selecting a company’s potential investments
proposals and deciding the acceptance criteria on the basis of its profitability. It involves the
decision related to acquiring long term investment proposals which are expected to provide
returns after more than one year.

3. Step 3 of 3

First managers will determine the cost and benefits associated with different proposals in
terms of cash flows arising during the whole span of time whether inflows or outflows and
then they evaluate and compare in terms of profitability arising out of these proposals to select
the best option for the firm.

10–2 What is the payback period? How is it calculated?

1. Step 1 of 3

Payback period: The payback period is defined as the total amount of time required to
recover the original investment of a project.

2. Step 2 of 3

Calculation of Payback period:

In case of annuity cash inflow the payback period can be computed using the following
equation:

3. Step 3 of 3

In case of mixed stream of cash flows payback period can be computed using the following
equation:
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

10–3 What weaknesses are commonly associated with the use of the payback
period to evaluate a proposed investment?

Following are the weaknesses that are associated with the use of payback period to
evaluate the proposed investments:

• It does not consider the wealth maximization of the stockholders as does not involve
discounting cash flows to calculate the value addition to the firm.

• The payback method always ignores cash flows beyond the payback period.

• This technique does not consider the time value of money.

10–4 How is the net present value (NPV) calculated for a project with a
conventional cash flow pattern?

10–5 What are the acceptance criteria for NPV? How are they related to the
firm’s market value?
1. Step 1 of 2

Acceptance Criteria for NPV (Net Present Value):

The project will be accepted if its NPV is positive i.e. NPV is greater than zero and rejected if
NPV is negative i.e. NPV is less than zero. In case of ranking mutually exclusive proposals, the
project with highest positive NPV is given the top priority over the lower positive NPV
projects.

2. Step 2 of 2

When NPV is Positive the firm’s rate of return will be greater than its cost of capital. This
action must rise the firm’s market value.

10–6 Explain the similarities and differences between NPV, PI, and EVA.
1. Step 1 of 4

Similarities between NPV, PI and EVA : These all are the capital budgeting techniques to
evaluate the investment proposals in terms of future profitability.

Difference between NPV, PI and EVA : There is slightly difference between all the techniques
in terms of calculations and decision criteria.

2. Step 2 of 4

The Net Present Value of a proposal is the total present values of all cash inflows discounted
at the discount rate equal to its cost of capital less the total present values all the cash outflows
arising with the proposal. The equation for the NPV is as follows:
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

3. Step 3 of 4

Profitability Index: The PI technique involves discounting the future cash flows at a discount
rate equals to cost of capital and comparing the present value of the future cash inflows with
the present value of the future cash outflows. It is calculated as follows:

Here CFt represents the expected future cash flows, and CF0 represents the initial cost.

4. Step 4 of 4

Economic Value Added: It is another method of evaluating capital budgeting decision. It

evaluates the project’s pure economic profit which is the excess return over the competitive
expected return in a business run.

10–7 What is the internal rate of return (IRR) on an investment? How is it

determined?
1. Step 1 of 3

Internal rate of return (IRR): The IRR of the proposal is defined as the discount rate which
produces a zero NPV i.e., the IRR is the discount rate which will equate the present value of
cash flows with the present value of cash outflows.

2. Step 2 of 3

From the following equation IRR can be arrived:

 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

3. Step 3 of 3
If the IRR is more than the minimum rate i.e. the cut-off rate then the project will be accepted
otherwise rejected. In case of ranking mutually exclusive proposals, the project with highest IRR
is given the top priority over the lower IRR projects.

10–8 What are the acceptance criteria for IRR? How are they related to the
firm’s market value?
Step 1 of 1

Acceptance criteria: For Independent projects, the project will be accepted if its IRR is more than its
cost of capital otherwise rejected. In case of ranking mutually exclusive proposals, the project with
highest IRR is given the top priority over the lower IRR projects.

With the acceptable IRR the value of the firm will increase. Firm can earn minimum its required rate of
return. But amount by which value increases is not possible to judge.

10–9 Do the net present value (NPV) and internal rate of return (IRR) always
agree with respect to accept–reject decisions? With respect to ranking
decisions? Explain.

For independent projects the NPV profile shows that the IRR criteria and NPV criteria leads to the
same accept or reject decision. Now, if we assume that both the franchises are mutually exclusive.
In this case, there are chances of conflicts. The conflict in the ranking of mutually exclusive
proposals as per the NPV and the IRR techniques arises as a result of different reinvestment rate
assumptions of the two techniques acting in different ways on the proposals having time disparity
of cash inflows.

The reasons and conditions, under which different rankings may occur, can be summarized as
follows:

i) Scale or size disparity among different alternative proposals: The cost or scale of one
proposal may be different from that of others. A conflict in ranking can arise because of size
difference of different proposals. The ranking of NPV technique, which deals with absolute net
benefits, will be affected by the size of proposals. Higher the cash outflow larger would be the
expected returns in absolute terms and hence higher ranking would be. On the other hand, the
IRR deals with relative returns (i.e. in percentage form) and hence ignores the size of the
proposal.

ii) Different timing or Time Disparity among alternative proposals: The ranking of mutually
exclusive proposals as per NPV and the IRR technique may be different even when they involve
the same or almost the same outlay. The different ranking may then occur as a result of different
timing of the cash flows of different proposals.

iii) Life disparity or proposals with unequal lives also raise conflicts between NPV and IRR.

10–10 How is a net present value profile used to compare projects? What
causes conflicts in the ranking of projects via net present value and
internal rate of return?
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

10–11 Does the assumption concerning the reinvestment of intermediate cash

inflow tend to favor NPV or IRR? In practice, which technique is preferred
and why?
1. Step 1 of 2

The reinvestment rate assumption is the assumption regarding the rate of compounding and
discounting the intermediate cash flows. This reinvestment rate is built into the present value
factors which are used to find out the NPV and IRR by adjusting the future cash flows for time
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

value of money. It is assumed that when the cash flows are received, they are immediately
reinvested in another project or asset.

2. Step 2 of 2

With NPV Technique it is assumed that discounted cash flows are reinvested at the cost of
capital which represents the value of proposal are calculated at an accuracy as the cash flows
are discounted have time value of money is taken into account.

With IRR Technique it is assumed that cash flows are reinvested at IRR rate but it may not be
always possible to reinvest at the IRR rate because it more than the cost of capital.

Thus, NPV technique is preferred.

CAPITAL BUDGETING PROBLEMS: CHAPTER 10
CAPITAL BUDGETING PROBLEMS: CHAPTER 10
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Answers to Warm-Up Exercise

E10-1. Payback period

Answer: The payback period for Project Hydrogen is 4.29 years. The payback period for Project
Helium is 5.75 years. Both projects are acceptable because their payback periods are less than
Elysian Fields’ maximum payback period criterion of 6 years.
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

E10-2. NPV
Answer:

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.
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

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.
E10-4: IRR
Answer: You may use a financial calculator to determine the IRR of each project. Choose the project
with the higher IRR.

Project T-Shirt
PV 15,000, N 4, PMT 8,000
Solve for I
IRR 39.08%
Project Board Shorts
PV 25,000, N 5, PMT 12,000
Solve for I
IRR 38.62%
Based on IRR analysis, Billabong Tech should choose project T-Shirt.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

E10-5: NPV
Answer:
Note: The IRR for Project Terra is 10.68% while that of Project Firma is 10.21%.
Furthermore, when the discount rate is zero, the sum of Project Terra’s cash flows exceed that
of Project Firma. Hence, at any discount rate that produces a positive NPV, Project Terra
provides the higher net present value.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

◼ Solutions to Problems

P10-1. Payback period

LG 2; Basic
a. $42,000 $7,000 6 years
b. The company should accept the project, since 6 8.

P10-2. Payback comparisons

LG 2; Intermediate
a. Machine 1: $14,000 $3,000 4 years, 8 months
Machine 2: $21,000 $4,000 5 years, 3 months
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

b. Only Machine 1 has a payback faster than 5 years and is acceptable.

c. The firm will accept the first machine because the payback period of 4 years, 8 months is
less than the 5-year maximum payback required by Nova Products.
d. Machine 2 has returns that last 20 years while Machine 1 has only 7 years of returns.
Payback cannot consider this difference; it ignores all cash inflows beyond the payback
period. In this case, the total cash flow from Machine 1 is $59,000 ($80,000 $21,000) less
than Machine 2.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-3. Choosing between two projects with acceptable payback periods

LG 2; Intermediate

a.

Project A Project B
Cash Investment Cash Investment
Year Inflows Balance Year Inflows Balance
0 $100,000 0 $100,000
1 $10,000 90,000 1 40,000 60,000
2 20,000 70,000 2 30,000 30,000
3 30,000 40,000 3 20,000 10,000
4 40,000 0 4 10,000 0
5 20,000 5 20,000

Both Project A and Project B have payback periods of exactly 4 years.

b. Based on the minimum payback acceptance criteria of 4 years set by John Shell, both
projects should be accepted. However, since they are mutually exclusive projects, John
should accept Project B.
c. Project B is preferred over A because the larger cash flows are in the early years of the
project. The quicker cash inflows occur, the greater their value.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-4. Personal finance: Long-term investment decisions, payback period

LG 4

a. and b.

Project A Project B
Annual Cumulative Annual Cumulative
Year Cash Flow Cash Flow Cash Flow Cash Flow
0 $(9,000) $(9,000) $(9,000) $(9,000)
1 2,200 (6,800) 1,500 (7,500)
2 2,500 (4,300) 1,500 (6,000)
3 2,500 (1,800) 1,500 (4,500)
4 2,000 3,500 (1,000)
5 1,800 4,000
Total Cash Flow 11,000 12,000
Payback Period 3 1,800/2,000 3.9 years 4 1,000/4,000 4.25 years

c. The payback method would select Project A since its payback of 3.9 years is lower than
Project B’s payback of 4.25 years.

d. One weakness of the payback method is that it disregards expected future cash flows as in
the case of Project B.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-5. NPV
LG 3; Basic
NPV PVn Initial investment
a. N 20, I 14%, PMT $2,000
Solve for PV $13,246.26
NPV $13,246.26 $10,000
NPV $3,246.26
Accept project
b. N 20, I 14%, PMT $3,000
Solve for PV 19,869.39
NPV $19,869.39 $25,000
NPV $5,130.61
Reject
c. N 20, I 14%, PMT $5,000
Solve for PV $33,115.65
NPV $33,115.65 $30,000
NPV $33,115.65
NPV $3,115
Accept
CAPITAL BUDGETING PROBLEMS: CHAPTER 10
CAPITAL BUDGETING PROBLEMS: CHAPTER 10
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-6. NPV for varying cost of capital

LG 3; Basic
a. 10%
N 8, I 10%, PMT $5000
Solve for PV $26,674.63
NPV PVn Initial investment
NPV $26,674.63 $24,000
NPV $2,674.63
Accept; positive NPV
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

b. 12%
N 8, I 12%, PMT $5,000
Solve for PV $24,838.20
NPV PVn Initial investment
NPV $24,838.20 $24,000
NPV $838.20
Accept; positive NPV
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

c. 14%
N 8, I 14%, PMT $5,000
Solve for PV $23,194.32
NPV PVn Initial investment
NPV $23,194.32 $24,000
NPV -$805.68
Reject; negative NPV
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-7. NPV—independent projects

LG 3; Intermediate Project A
N 10, I 14%, PMT $4,000
Solve for PV $20,864.46
NPV $20,864.46 $26,000
NPV $5,135.54
Reject
Project B—PV of Cash Inflows
CF0 -$500,000; CF1 $100,000; CF2 $120,000; CF3 $140,000; CF4 $160,000;
CF5 $180,000; CF6 $200,000
Set I 14%
Solve for NPV $53,887.93
Accept
Project C—PV of Cash Inflows
CF0 -$170,000; CF1 $20,000; CF2 $19,000; CF3 $18,000; CF4 $17,000;
CF5 $16,000; CF6 $15,000; CF7 $14,000; CF8 $13,000; CF9 $12,000; CF10
$11,000,
Set I 14%
Solve for NPV -$83,668.24
Reject
Project D
N 8, I 14%, PMT $230,000
Solve for PV $1,066,939
NPV PVn Initial investment
NPV $1,066,939 $950,000
NPV $116,939
Accept
Project E—PV of Cash Inflows
CF0 -$80,000; CF1 $0; CF2 $0; CF3 $0; CF4 $20,000; CF5 $30,000; CF6 $0;
CF7 $50,000; CF8 $60,000; CF9 $70,000
Set I 14%
Solve for NPV $9,963.63
Accept
CAPITAL BUDGETING PROBLEMS: CHAPTER 10
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-8. NPV
LG 3; Challenge
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

a. N 5, I 9%, PMT $385,000

Solve for PV $1,497,515.74
The immediate payment of $1,500,000 is not preferred because it has a higher present value
than does the annuity.

b. N 5, I 9%, PV $1,500,000
Solve for PMT $385,638.69
c. Present valueAnnuity Due PVordinary annuity (1 discount rate)
$1,497,515.74 (1.09) $1,632,292
Calculator solution: $1,632,292
Changing the annuity to a beginning-of-the-period annuity due would cause Simes Innovations
to prefer to make a $1,500,000 one-time payment because the present value of the annuity
due is greater than the $1,500,000 lump-sum option.

d. No, the cash flows from the project will not influence the decision on how to fund the
project. The investment and financing decisions are separate.

P10-9. NPV and maximum return

LG 3; Challenge
a. N 4, I 10%, PMT $4,000
Solve for PV $12,679.46
NPV PV Initial investment
NPV $12,679.46 $13,000
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

NPV –$320.54
Reject this project due to its negative NPV.
b. N 4, PV -$13,000, PMT $4,000
Solve for I 8.86%
8.86% is the maximum required return that the firm could have for the project to be acceptable.
Since the firm’s required return is 10% the cost of capital is greater than the expected return
and the project is rejected.

P10-10. NPV—mutually exclusive projects

LG 3; Intermediate
a. and b.
Press A
CF0 -$85,000; CF1 $18,000; F1 8
Set I 15%
Solve for NPV -$4,228.21
Reject
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Press B
CF0 -$60,000; CF1 $12,000; CF2 $14,000; CF3 $16,000; CF4 $18,000;
CF5 $20,000; CF6 $25,000
Set I 15%
Solve for NPV $2,584.34
Accept
Press C
CF0 -$130,000; CF1 $50,000; CF2 $30,000; CF3 $20,000; CF4 $20,000;
CF5 $20,000; CF6 $30,000; CF7 $40,000; CF8 $50,000
Set I 15%
Solve for NPV $15,043.89
Accept
c. Ranking—using NPV as criterion

Rank Press NPV

1 C $15,043.89
2 B 2,584.34
3 A 4,228.21

d. Profitability Indexes
Profitability Index Present Value Cash Inflows Investment
Press A: $80,771 $85,000 0.95
Press B: $62,588 $60,000 1.04
Press C: $145,070 $130,000 1.12
e. The profitability index measure indicates that Press C is the best, then Press B, then Press A
(which is unacceptable). This is the same ranking as was generated by the NPV rule.

P10-11. Personal finance: Long-term investment decisions, NPV method

LG 3
Key information:
Cost of MBA program $100,000
Annual incremental benefit $ 20,000
Time frame (years) 40
Opportunity cost 6.0%
Calculator Worksheet Keystrokes:
CF0 100,000
CF1 20,000
F1 40
Set I 6%
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Solve for NPV $200,926

The financial benefits outweigh the cost of the MBA program.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-12. Payback and NPV

LG 2, 3; Intermediate

a.
Project Payback Period
A $40,000 $13,000 3.08 years
B 3 ($10,000 $16,000) 3.63 years
C 2 ($5,000 $13,000) 2.38 years

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

b. Worksheet keystrokes

Year Project A Project B Project C

0 $40,000 $40,000 $40,000
1 13,000 7,000 19,000
2 13,000 10,000 16,000
3 13,000 13,000 13,000
4 13,000 16,000 10,000
5 13,000 19,000 7,000

Solve for $2,565.82 $322.53 $5,454.17

NPV
Accept Reject Accept

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

c. At a cost of 16%, Project C has the highest NPV. Because of Project C’s cash flow
characteristics, high early-year cash inflows, it has the lowest payback period and the
highest NPV.

P10-13. NPV and EVA

LG 3; Intermediate
a. NPV $2,500,000 $240,000 0.09 $166,667
b. Annual EVA $240,000 – ($2,500,000 x 0.09) $15,000
c. Overall EVA $15,000 0.09 $166,667
In this case, NPV and EVA give exactly the same answer.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-14. IRR—Mutually exclusive projects

LG 4; Intermediate
IRR is found by solving:

$0 initial investment
(1 IRR)t
Most financial calculators have an ―IRR‖ key, allowing easy computation of the internal rate of
return. The numerical inputs are described below for each project.
Project A
CF0 $90,000; CF1 $20,000; CF2 $25,000; CF3 $30,000; CF4 $35,000; CF5 $40,000
Solve for IRR 17.43%
If the firm’s cost of capital is below 17%, the project would be acceptable.
Project B
CF0 $490,000; CF1 $150,000; CF2 $150,000; CF3 $150,000; CF4 $150,000
[or, CF0 $490,000; CF1 $150,000, F1 4]
Solve for IRR 8.62%
The firm’s maximum cost of capital for project acceptability would be 8.62%.
Project C
CF0 $20,000; CF1 $7500; CF2 $7500; CF3 $7500; CF4 $7500; CF5 $7500
[or, CF0 $20,000; CF1 $7500; F1 5]
Solve for IRR 25.41%
The firm’s maximum cost of capital for project acceptability would be 25.41%.
Project D
CF0 $240,000; CF1 $120,000; CF2 $100,000; CF3 $80,000; CF4 $60,000
Solve for IRR 21.16%
The firm’s maximum cost of capital for project acceptability would be 21% (21.16%).
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-15. IRR—Mutually exclusive projects

LG 4; Intermediate
a. and b.
Project X
$100,000 $120,000 $150,000 $190,000 $250,000
$0 $500,000
(1 IRR)1 (1 IRR)2 (1 IRR)3 (1 IRR)4 (1 IRR)5
CF0 -$500,000; CF1 $100,000; CF2 $120,000; CF3 $150,000; CF4 $190,000
CF5 $250,000
Solve for IRR 15.67; since IRR cost of capital, accept.

Project Y
$140,000 $120,000 $95,000 $70,000 $50,000
$0 $325,000
(1 IRR)1 (1 IRR)2 (1 IRR)3 (1 IRR)4 (1 IRR)5
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-16. Personal Finance: Long-term investment decisions, IRR method

LG 4; Intermediate

IRR is the rate of return at which NPV equals zero

Computer inputs and output:

N 5, PV $25,000, PMT $6,000
Solve for IRR 6.40%

Required rate of return: 7.5%

Decision: Reject investment opportunity

P10-17. IRR, investment life, and cash inflows

LG 4; Challenge
a. N 10, PV -$61,450, PMT $10,000
Solve for I 10.0%
The IRR cost of capital; reject the project.
b. I 15%, PV $61,450, PMT $10,000
Solve for N 18.23 years
The project would have to run a little over 8 more years to make the project acceptable with
the 15% cost of capital.
c. N 10, I 15%, PV $61,450
Solve for PMT $12,244.04
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-18. NPV and IRR

LG 3, 4; Intermediate
a. N 7, I 10%, PMT $4,000
Solve for PV $19,473.68
NPV PV Initial investment
NPV $19,472 $18,250
NPV $1,223.68
b. N 7, PV $18,250, PMT $4,000
Solve for I 12.01%
c. The project should be accepted since the NPV 0 and the IRR the cost of capital.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-19. NPV, with rankings

LG 3, 4; Intermediate
a. NPVA $45,665.50 (N 3, I 15, PMT $20,000) $50,000
NPVA -$4,335.50
Or, using NPV keystrokes
CF0 $50,000; CF1 $20,000; CF2 $20,000; CF3 $20,000
Set I 15%
NPVA $4,335.50
Reject
NPVB Key strokes
CF0 $100,000; CF1 $35,000; CF2 $50,000; CF3 $50,000
Set I 15%
Solve for NPV $1,117.78
Accept
NPVC Key strokes
CF0 $80,000; CF1 $20,000; CF2 $40,000; CF3 $60,000
Set I 15%
Solve for NPV $7,088.02
Accept
NPVD Key strokes
CF0 $180,000; CF1 $100,000; CF2 $80,000; CF3 $60,000
Set I 15%
Solve for NPV $6,898.99
Accept
b.

Rank Press NPV

1 C $7,088.02
2 D 6,898.99
3 B 1,117.78
4 A 4335.50

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

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

Since the lowest IRR is 9.7%, all of the projects would be acceptable if the cost of capital
was 9.7%.
Note: Since Project A was the only rejected project from the four projects, all that was
needed to find the minimum acceptable cost of capital was to find the IRR of A.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-20. All techniques, conflicting rankings

LG 2, 3, 4: Intermediate
a.

Project A Project B
Cash Investment Cash Investment
Year Inflows Balance Year Inflows Balance
0 $150,000 0 $150,000
1 $45,000 105,000 1 $75,000 75,000
2 45,000 60,000 2 60,000 15,000
3 45,000 15,000 3 30,000 15,000
4 45,000 30,000 4 30,000 0
5 45,000 30,000
6 45,000 30,000

$150,000
Payback A 3.33 years 3 years 4 months
$45,000

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

b. At a discount rate of zero, dollars have the same value through time and all that is needed is a
summation of the cash flows across time.
NPVA ($45,000 6) - $150,000 $270,000 $150,000 $120,000
NPVB $75,000 $60,000 $120,000 $150,000 $105,000
c. NPVA:
CF0 $150,000; CF1 $45,000; F1 6
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Set I 9%
Solve for NPVA $51,886.34
NPVB:
CF0 $150,000; CF1 $75,000; CF2 $60,000; CF3 $120,000
Set I 9%
Solve for NPV $51,112.36
Accept
d. IRRA:
CF0 $150,000; CF1 $45,000; F1 6
Solve for IRR 19.91%
IRRB:
CF0 $150,000; CF1 $75,000; CF2 $60,000; CF3 $120,000
Solve for IRR 22.71%

e.

Rank
Project Payback NPV IRR
A 2 1 2
B 1 2 1

The project that should be selected is A. The conflict between NPV and IRR is due partially
to the reinvestment rate assumption. The assumed reinvestment rate of Project B is 22.71%,
the project’s IRR. The reinvestment rate assumption of A is 9%, the firm’s cost of capital. On
a practical level Project B may be selected due to management’s preference for making
decisions based on percentage returns and their desire to receive a return of cash quickly.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-21. Payback, NPV, and IRR

LG 2, 3, 4; Intermediate
a. Payback period
Balance after 3 years: $95,000 $20,000 $25,000 $30,000 $20,000
3 ($20,000 $35,000) 3.57 years
b. NPV computation
CF0 $95,000; CF1 $20,000; CF2 $25,000; CF3 $30,000; CF4 $35,000
CF5 $40,000
Set I 12%
Solve for NPV $9,080.60
$20,000 $25,000 $30,000 $35,000 $40,000
c. $0 $95,000
(1 IRR)1 (1 IRR)2 (1 IRR)3 (1 IRR)4 (1 IRR)5
CF0 $95,000; CF1 $20,000; CF2 $25,000; CF3 $30,000; CF4 $35,000
CF5 $40,000
Solve for IRR 15.36%
d. NPV $9,080; since NPV 0; accept
IRR 15%; since IRR 12% cost of capital; accept
The project should be implemented since it meets the decision criteria for both NPV and
IRR.
 CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-22. NPV, IRR, and NPV profiles

LG 3, 4, 5; Challenge
a. and b.
Project A
CF0 $130,000; CF1 $25,000; CF2 $35,000; CF3 $45,000
CF4 $50,000; CF5 $55,000
Set I 12%
NPVA $15,237.71
Based on the NPV the project is acceptable since the NPV is greater than zero.
Solve for IRRA 16.06%

Based on the IRR the project is acceptable since the IRR of 16% is greater than the 12% cost of capital.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Project B
CF0 $85,000; CF1 $40,000; CF2 $35,000; CF3 $30,000
CF4 $10,000; CF5 $5,000
Set I 12%
NPVB $9,161.79
Based on the NPV the project is acceptable since the NPV is greater than zero.
Solve for IRRB 17.75%
Based on the IRR the project is acceptable since the IRR of 17.75% is greater than the 12%
cost of capital.

c.

Data for NPV Profiles

NPV
Discount Rate A B
0% $80,000 $35,000
12% $15,238 $9,161
15% — $ 4,177
16% 0 —
18% — 0

d. The net present value profile indicates that there are conflicting rankings at a discount rate
less than the intersection point of the two profiles (approximately 15%). The conflict in
rankings is caused by the relative cash flow pattern of the two projects. At discount rates
above approximately 15%, Project B is preferable; below approximately 15%, Project A is
better. Based on Thomas Company’s 12% cost of capital, Project A should be chosen.
e. Project A has an increasing cash flow from Year 1 through Year 5, whereas Project B has a
decreasing cash flow from Year 1 through Year 5. Cash flows moving in opposite directions
often cause conflicting rankings. The IRR method reinvests Project B’s larger early cash
flows at the higher IRR rate, not the 12% cost of capital.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-23. All techniques—decision among mutually exclusive investments

LG 2, 3, 4, 5, 6; Challenge

Project
A B C
Cash inflows (years 1 5) $20,000 $ 31,500 $ 32,500
a. Payback* 3 years 3.2 years 3.4 years
b. NPV* $10,345 $ 10,793 $ 4,310
c. IRR* 19.86% 17.33% 14.59%
*
Supporting calculations shown below:
a. Payback Period: Project A: $60,000 $20,000 3 years
Project B: $100,000 $31,500 3.2 years
Project C: $110,000 $32,500 3.4 years
b. NPV
Project A
CF0 $60,000; CF1 $20,000; F1 5
Set I 13%
Solve for NPVA $10,344.63
Project B
CF0 $100,000; CF1 $31,500; F1 5
Set I 13%
Solve for NPVB $10,792.78
Project C
CF0 $110,000; CF1 $32,500; F1 5
Set I 13%
Solve for NPVC $4,310.02
c. IRR
Project A
CF0 $60,000; CF1 $20,000; F1 5
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Solve for IRRA 19.86%

Project B
CF0 $100,000; CF1 $31,500; F1 5
Solve for IRRB 17.34%
Project C
CF0 $110,000; CF1 $32,500; F1 5
Solve for IRRC 14.59%

d.

Data for NPV Profiles

NPV
Discount Rate A B C
0% $40,000 $57,500 $52,500
13% $10,340 10,793 4,310
15% — — 0
17% — 0 —
20% 0 — —

The difference in the magnitude of the cash flow for each project causes the NPV to compare
favorably or unfavorably, depending on the discount rate.
e. Even though A ranks higher in Payback and IRR, financial theorists would argue that B is
superior since it has the highest NPV. Adopting B adds $448.15 more to the value of the firm
than does adopting A.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-24. All techniques with NPV profile—mutually exclusive projects

LG 2, 3, 4, 5, 6; Challenge
a. Project A
Payback period
Year 1 Year 2 Year 3 $60,000
Year 4 $20,000
Initial investment $80,000
Payback 3 years ($20,000 30,000)
Payback 3.67 years
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Project B
Payback period
$50,000 $15,000 3.33 years
b. Project A
CF0 $80,000; CF1 $15,000; CF2 $20,000; CF3 $25,000; CF4 $30,000;
CF5 $35,000
Set I 13%
Solve for NPVA $3,659.68
Project B
CF0 $50,000; CF1 $15,000; F1 5
Set I 13%
Solve for NPVB $2,758.47
c. Project A
CF0 $80,000; CF1 $15,000; CF2 $20,000; CF3 $25,000; CF4 $30,000;
CF5 $35,000
Solve for IRRA 14.61%
Project B
CF0 $50,000; CF1 $15,000; F1 5
Solve for IRRB 15.24%
d.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Data for NPV Profiles

NPV
Discount Rate A B
0% $45,000 $25,000
13% $3,655 2,755
14.6% 0 —
15.2% — 0

Intersection—approximately 14%
If cost of capital is above 14%, conflicting rankings occur.
The calculator solution is 13.87%.
e. Both projects are acceptable. Both have similar payback periods, positive NPVs, and
equivalent IRRs that are greater than the cost of capital. Although Project B has a slightly
higher IRR, the rates are very close. Since Project A has a higher NPV, accept Project A.

P10-25. Integrative—Multiple IRRs

LG 6; Basic
a. First the project does not have an initial cash outflow. It has an inflow, so the payback is
immediate. However, there are cash outflows in later years. After 2 years, the project’s
outflows are greater than its inflows, but that reverses in year 3. The oscillating cash flows
(positive-negative-positive-negative-positive) make it difficult to even think about how the
payback period should be defined.
b. CF0 $200,000, CF1 920,000, CF2 $1,592,000, CF3 $1,205,200, CF4 $343,200
Set I 0%; Solve for NPV $0.00
Set I 5%; Solve for NPV $15.43
Set I 10%; Solve for NPV $0.00
Set I 15%; Solve for NPV $6.43
Set I 20%; Solve for NPV $0.00
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

Set I 25%; Solve for NPV $7.68

Set I 30%; Solve for NPV $0.00
Set I 35%, Solve for NPV $39.51
c. There are multiple IRRs because there are several discount rates at which the NPV is zero.
d. It would be difficult to use the IRR approach to answer this question because it is not clear
which IRR should be compared to each cost of capital. For instance, at 5%, the NPV is
negative, so the project would be rejected. However, at a higher 15% discount rate the NPV
is positive and the project would be accepted.
e. It is best simply to use NPV in a case where there are multiple IRRs due to the changing
signs of the cash flows.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-26. Integrative—Conflicting Rankings

LG 3, 4, 5; Intermediate
a. Plant Expansion
CF0 $3,500,000, CF1 1,500,000, CF2 $2,000,000, CF3 $2,500,000, CF4 $2,750,000
Set I 20%; Solve for NPV $1,911,844.14
Solve for IRR 43.70%
CF1 1,500,000, CF2 $2,000,000, CF3 $2,500,000, CF4 $2,750,000
Set I 20%; Solve for NPV $5,411,844.14 (This is the PV of the cash inflows)
PI $5,411,844.14 $3,500,000 1.55
Product Introduction
CF0 $500,000, CF1 250,000, CF2 $350,000, CF3 $375,000, CF4 $425,000
Set I 20%; Solve for NPV $373,360.34
Solve for IRR 52.33%
CF1 250,000, CF2 $350,000, CF3 $375,000, CF4 $425,000
Set I 20%; Solve for NPV $873,360.34 (This is the PV of the cash inflows)
PI $873,360.34 $500,000 1.75
b.

Rank
Project NPV IRR PI
Plant Expansion 1 2 2
Product Introduction 2 1 1

c. The NPV is higher for the plant expansion, but both the IRR and the PI are higher for the
product introduction project. The rankings do not agree because the plant expansion has a
much larger scale. The NPV recognizes that it is better to accept a lower return on a larger
project here. The IRR and PI methods simply measure the rate of return on the project and
not its scale (and therefore not how much money in total the firm makes from each project).
d. Because the NPV of the plant expansion project is higher, the firm’s shareholders would be
better off if the firm pursued that project, even though it has a lower rate of return.
CAPITAL BUDGETING PROBLEMS: CHAPTER 10

P10-27. Ethics problem

LG 1, 6; Intermediate
Expenses are almost sure to increase for Gap. The stock price would almost surely decline in the
immediate future, as cash expenses rise relative to cash revenues. In the long run, Gap may be able
to attract and retain better employees (as does Chick-fil-A, interestingly enough, by being closed
on Sundays), new human rights and environmentally conscious customers, and new investor demand
from the burgeoning socially responsible investing mutual funds. This long-run effect is not
assured, and we are again reminded that it’s not merely shareholder wealth maximization we’re
after—but maximizing shareholder wealth subject to ethical constraints. In fact, if Gap was
unwilling to renegotiate worker conditions, Calvert Group (and others) might sell Gap shares and
thereby decrease shareholder wealth.