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Chapter 12: The Capital Budgeting Decision
12-11
12. Internal rate of return (LO4) King’s Department Store is contemplating the purchase of a
new machine at a cost of $13,869. The machine will provide $3,000 per year in cash flow
for six years. King’s has a cost of capital of 12 percent. Using the internal rate of return
method, evaluate this project and indicate whether it should be undertaken.
12-12. Solution:
King’s Department Store
Appendix D
13. Internal rate of return (LO4) Home Security Systems is analyzing the purchase of
manufacturing equipment that will cost $40,000. The annual cash inflows for the next three
years will be:
Year
Cash Flow
1 .........................
$20,000
2 .........................
18,000
3 .........................
13,000
a. Determine the internal rate of return using interpolation.
b. With a cost of capital of 12 percent, should the machine be purchased?
12-13. Solution:
Chapter 12: The Capital Budgeting Decision
Home Security Systems
a. Step 1 Average the inflows.
$20,000
18,000
13,000
$51,000 3 $17,000=
Step 2 Divide the inflows by the assumed annuity in Step 1.
Investment $40,000 2.353
Annuity 17,000
==
Step 3 Go to Appendix D for the 1st approximation.
12-13. (Continued)
Year Cash Flow PVIF at 14% Present Value
1 $20,000 .877 $17,540
Chapter 12: The Capital Budgeting Decision
12-13
Year Cash Flow PVIF at 15% Present Value
1 $20,000 .870 $17,400
Because the NPV is now below $40,000, we know the IRR
is between 14% and 15%. We will interpolate.
$40,157 .......... PV @ 14% $40,157 ............ PV @ 14%
14% + ($157/$595) (1%) = .264
Year Cash Flow PVIF at 16% Present Value
1 $20,000 .862 $ 17,240
Chapter 12: The Capital Budgeting Decision
12-14
12-13. (Continued)
$40,157 .......... PV @ 14% $40,157 ............ PV @ 14%
14. Net present value method (LO4) Altman Hydraulic Corporation will invest $160,000 in a
project that will produce the cash flow shown below. The cost of capital is 11 percent.
Should the project be undertaken? Use the net present value method. (Note that the third
year’s cash flow is negative.)
Year
Cash Flow
1 ...........
$54,000
2 ...........
66,000
3 ...........
(60,000)
4 ...........
57,000
5 ...........
120,000
12-14. Solution:
Altman Hydraulic Corporation
Chapter 12: The Capital Budgeting Decision
12-15
Year Cash Flow PVIF at 11% Present Value
1 $54,000 .901 $ 48,654
2 $66,000 .812 $ 53,592
Present value of inflows $167,109
15. Net present value method (LO4) Hamilton Control Systems will invest $90,000 in a
temporary project that will generate the following cash inflows for the next three years.
Year
Cash Flow
1...........
$23,000
2...........
38,000
3...........
60,000
The firm will be required to spend $15,000 to close down the project at the end of the three
years. If the cost of capital is 10 percent, should the investment be undertaken? Use the net
present value method.
12-15. Solution:
Hamilton Control Systems
Present Value of inflows
Chapter 12: The Capital Budgeting Decision
12-16
Year Cash Flow × PVIF at 10% Present Value
1 $23,000 .909 $ 20,907
Present Value of outflows
0 $90,000 1.000 $ 90,000
16. Net present value method (LO4) Cellular Labs will invest $150,000 in a project that will
not begin to produce returns until after the third year. From the end of the 3rd year until the
end of the 12th year (10 periods), the annual cash flow will be $40,000. If the cost of
capital is 12 percent, should this project be undertaken?
12-16. Solution:
Cellular Labs
Present Value of Inflows
Find the Present Value of a Deferred Annuity
Discount from Beginning of the third period (end of second
period to present):
Chapter 12: The Capital Budgeting Decision
12-17
FV = $226,000, n = 2, i = 12%
undertaken.
17. Net present value and internal rate of return methods (LO4) The Hudson Corporation
makes an investment of $14,400 that provides the following cash flow:
Year
Cash Flow
1................
$ 7,000
2................
7,000
3................
4,000
a. What is the net present value at an 11 percent discount rate?
b. What is the internal rate of return? Use the interpolation procedure shown in this
chapter.
c. In this problem would you make the same decision under both parts a and b?
12-17. Solution:
Hudson Corporation
Chapter 12: The Capital Budgeting Decision
12-18
a. Net Present Value
Year Cash Flow × 11% PVIF Present Value
1 $7,000 .901 $ 6,307
b. Internal Rate of Return
We will average the inflows to arrive at an assumed annuity
value.
$7,000
12-17. (Continued)
We divide the investment by the assumed annuity value.
IFA
$14,400 2.4 PV
6,000 =
Year Cash Flow × 13% PVIF Present Value
1 $7,000 .885 $ 6,195
Chapter 12: The Capital Budgeting Decision
12-19
2 7,000 .783 5,481
Year Cash Flow × 15%PVIF Present Value
1 $7,000 .870 $ 6,090
The correct answer must fall between 13% and 15%. We
interpolate.
12-17. (Continued)
$48
13% (2%) 13% .11 (2%) 13% .22% 13.22%
$434
+ = + = + =
As an alternative answer, students who use 14% as the second
trial and error rate will show to following:
Year Cash Flow × 14%PVIF Present Value
1 $7,000 .877 $ 6,139
Chapter 12: The Capital Budgeting Decision
The correct answer falls between 13% and 14%. We
interpolate.
$14,448 PV @ 13% $14,448 PV @ 13%
