Chapter 12: The Capital Budgeting Decision
12–17. Solution:
Hudson Corporation
a. Net Present Value
Year Cash Flow × 8% PVIF Present Value
12–17. (Continued)
We divide the investment by the assumed annuity value.
IFA
$24,000 2.400 PV
10,000
=
Using Appendix D for n = 3, the first approximation appears
to fall between 12 percent and 14 percent. Since the heavy
inflows are in the early years, we will try 14 percent.
Chapter 12: The Capital Budgeting Decision
Year Cash Flow × 14% PVIF Present Value
1 $13,000 .877 $ 11,401
Chapter 12: The Capital Budgeting Decision
The correct answer falls between 14 percent and 15 percent.
We interpolate.
Calculator Solution:
(a)
Press the following keys: 2nd, CF, 2nd, and Clear.
Calculator displays CFo, 24,000 +|– key, press Enter.
Press down arrow, enter 13,000, and press Enter.
Press down arrow, enter 2, and press Enter.
Press down arrow, enter 4,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 8 and press Enter.
Press down arrow; calculator shows NPV = 0.00
Press CPT; calculator shows NPV = 2,357.77, which is the net present value of the project.
(b)
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 24,000 +|– key, press Enter.
Press down arrow, enter 13,000 and press Enter.
Press down arrow, enter 2, and press Enter.
Press down arrow, enter 4,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press IRR; calculator shows IRR = 0.00.
Press CPT; calculator shows IRR = 14.29.
Answer: IRR = 14.29%
18. Net present value and internal rate of return methods (LO12-4) The Pan American
Bottling Co. is considering the purchase of a new machine that would increase the speed of
Chapter 12: The Capital Budgeting Decision
bottling and save money. The net cost of this machine is $60,000. The annual cash flows
have the following projections:
Cash Flow
$23,000
26,000
29,000
15,000
8,000
a. If the cost of capital is 13 percent, what is the net present value of selecting a new
machine?
b. What is the internal rate of return?
c. Should the project be accepted? Why?
12–18. Solution:
Pan American Bottling Co.
a. Net Present Value
12-18. (Continued)
b. Internal Rate of Return
We will average the inflows to arrive at an assumed annuity.
Chapter 12: The Capital Budgeting Decision
Year Cash Flow × 25% PVIF Present Value
1 $23,000 .800 $18,400
12-18. (Continued)
The correct answer must fall between 20 and 25 percent. We
interpolate.
$64,440 ……….. PV @ 20% $64,440…………. PV @ 20%
Calculator Solution:
Find the NPV using a financial calculator:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 60,000 +|– key, press Enter.
Press down arrow, enter 23,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 26,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 29,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 15,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Chapter 12: The Capital Budgeting Decision
Present value of inflows
Profitability index ( ) Pr esent value of outflows
$46,459 1.16
$40,000
Y=
==
You should select Project X because it has the higher
profitability index. This is true in spite of the fact that it has a
lower net present value. The profitability index may be
appropriate when you have different size investments.
Calculator Solution:
(a)
Find NPV using a financial calculator:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 20,000 +|– key, press the Enter key.
Press down arrow, enter 10,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 8,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 9,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 8,600, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; the calculator shows I = 0; enter 14 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Press CPT; calculator shows NPV = 6,094.30, which is the net present value of Project X.
Profitability index using a financial calculator:
Profitability Index = Present Value of Inflows / Present Value of Outflows
Present Value of Inflows = NPV + Outflows
= 6,094.30 + 40,000 = $26,094.30
Profitability Index = 26,094.30/40,000 = 1.30
(b)
Find NPV using a financial calculator:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 40,000 +|– key, press the Enter key.
Press down arrow, enter 20,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 13,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 14,000, and press Enter.
Chapter 12: The Capital Budgeting Decision
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 16,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 14 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Press CPT; calculator shows NPV = 8,771.93, which is the net present value of Project Y.
Profitability Index Using Financial Calculator:
Profitability Index = Present Value of Inflows / Present Value of Outflows
Present Value of Inflows = NPV + Outflows
= 8,771.93 + 40,000 = $46,469.82
Profitability Index = $46,469.82/40,000 = 1.16
20. Reinvestment rate assumption in capital budgeting (LO12-4) Turner Video will invest
$58,500 in a project. The firm’s cost of capital is 12 percent. The investment will provide
the following inflows:
Year
Inflow
1 ……………..
$15,000
2 ……………..
17,000
3 ……………..
21,000
4 ……………..
25,000
5 ……………..
29,000
The internal rate of return is 11 percent.
a. If the reinvestment assumption of the net present value method is used, what will be
the total value of the inflows after five years? (Assume the inflows come at the end of
12–20. Solution:
Turner Video
a. Reinvestment assumption of NPV
No. of Future
Year Inflows Rate Periods Value Factor Value
Chapter 12: The Capital Budgeting Decision
b. Reinvestment assumption of IRR
No. of Future
Year Inflows Rate Periods Value Factor Value
1 $15,000 11% 4 1.518 $ 22,770
(a)
Calculator Solution:
Find PV of cash inflow using a financial calculator at 12 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 0, press the Enter key.
Press down arrow, enter 15,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 17,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 21,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 25,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 29,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Chapter 12: The Capital Budgeting Decision
Press NPV; calculator shows I = 0; enter 12 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Press CPT; calculator shows NPV = 74,235.87, which is the present value of the inflow.
Next, find the FV of the 74,235.87 as of year 5 at a 12 percent annual rate.
N
I/Y
PV
PMT
FV
5
12
74,235.87
0
CPT FV – 130,828.97
Answer: $130,828.97
Calculator Solution:
Find PV of cash inflow using a financial calculator at 11 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 0, press the Enter key.
Press down arrow, enter 15,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 17,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 21,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 25,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 29,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 11 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Press CPT; calculator shows NPV = 76,344.48, which is the present value of the inflow.
Next, find the FV of the 76,344.48 as of year 5 at an 11 percent annual rate.
N
I/Y
PV
PMT
FV
5
11
76,344.48
0
CPT FV – 128,644.88
Answer: $128,644.88
21. Modified internal rate of return (LO12-4) The Caffeine Coffee Company uses the
modified internal rate of return. The firm has a cost of capital of 11 percent. The project
being analyzed is as follows ($26,000 investment):
Year
Cash Flow
1 …………
$12,000
2 …………
11,000
3 …………
9,000
Chapter 12: The Capital Budgeting Decision
a. What is the modified internal rate of return? An approximation from Appendix B is
adequate. (You do not need to interpolate.)
b. Assume the traditional internal rate of return on the investment is 17.5 percent.
Explain why your answer in part a would be lower.
12–21. Solution:
Caffeine Coffee Company
Terminal Value (end of year 3)
a. FV Factor
Period of (11%) Future
Growth (Appendix A) Value
Year 1 $12,000 2 1.232 $14,784
Calculator Solution:
Chapter 12: The Capital Budgeting Decision
Using a financial calculator:
Find the PV of cash inflow using a financial calculator at 11 percent:
Press the following keys: 2nd, CF, 2nd, Clear.
Calculator displays CFo, 0, press the Enter key.
Press down arrow, enter 12,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 11,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 9,000, and press Enter.
Press down arrow, enter 1, and press Enter.
Press NPV; calculator shows I = 0; enter 11 and press Enter.
Press down arrow; calculator shows NPV = 0.00.
Press CPT; calculator shows NPV = 26,319.38, which is the present value of the inflow.
Next find the FV of the 26,319.38 as of year 3 at an 11 percent annual rate.
(a)
N
I/Y
PV
PMT
FV
3
11
26,319.38
0
CPT FV 35,995.20
Answer: $35,995.20
Next, find the discount rate that produces a PV of 26,000.
N
I/Y
PV
PMT
FV
3
CPT I I/Y 11.45
26,000
0
–35,995.20
Answer: MIRR = 11.45
22. Capital rationing and mutually exclusive investments (LO12-4) The Suboptimal Glass
Company uses a process of capital rationing in its decision making. The firm’s cost of
capital is 10 percent. It will only invest $77,000 this year. It has determined the internal
rate of return for each of the following projects.
Project
Project Size
Internal Rate of
Return
A …………………
$10,500
21%
B …………………
30,500
22
C …………………
25,500
18
D …………………
10,500
13
E …………………
10,500
20
F ………………….
20,500
11
G …………………
10,500
16
a. Select the projects that the firm should accept.
Chapter 12: The Capital Budgeting Decision
b. If Projects A and B are mutually exclusive, how would that affect your overall
answer? That is, which projects would you accept in spending the $77,000?
12-22. Solution:
Suboptimal Glass Company
You should rank the investments in terms of IRR.
Project IRR Project Size Total Budget
B 22% $30,500 $ 30,500
23. Net present value profile (LO12-4) Keller Construction is considering two new
investments. Project E calls for the purchase of earthmoving equipment. Project H
represents an investment in a hydraulic lift. Keller wishes to use a net present value profile
in comparing the projects. The investment and cash flow patterns are as follows:
Chapter 12: The Capital Budgeting Decision
Project E
($20,000 Investment)
Project H
($20,000 Investment)
Year
Cash Flow
Year
Cash Flow
1 ………………………
$ 5,000
1 …………………………….
$16,000
2 ………………………
6,000
2 …………………………….
5,000
3 ………………………
7.000
3 …………………………….
4,000
4 ………………………
10,000
a. Determine the net present value of the projects based on a zero discount rate.
b. Determine the net present value of the projects based on a 9 percent discount rate.
c. The internal rate of return on Project E is 13.25 percent, and the internal rate of return
on Project H is 16.30 percent. Graph a net present value profile for the two
investments similar to Figure 12-3. (Use a scale up to $8,000 on the vertical axis, with
$2,000 increments. Use a scale up to 20 percent on the horizontal axis, with
5 percent increments.)
d. If the two projects are not mutually exclusive, what would your acceptance or
rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net
present value profile for your decision; no actual numbers are necessary.)
e. If the two projects are mutually exclusive (the selection of one precludes the selection
of the other), what would be your decision if the cost of capital is (1) 6 percent,
(2) 13 percent, and (3) 18 percent? Once again, use the net present value profile for
your answer.
12-23. Solution:
Keller Construction Company
a. Zero discount rate
Project E
Inflows Outflow