Chapter 14 – Capital Investment Decisions
145. Fill in the lettered blanks in the following table:
Investment A
Investment B
Investment C
Amount of investment
$40,000
(A)
$20,000
Economic life in years
10
5
8
Annual cash flow
$ 5,000
(B)
$ 2,500
Payback period in years
(C)
4
(D)
Present value of cash flows
(E)
$33,000
(F)
Net present value
$ 5,500
$ 3,000
($1,000)
A.
$33,000 − $3,000 = $30,000
B.
$30,000 / 4 = $7,500
C.
$40,000 / $5,000 = 8
D.
$20,000 / $2,500 = 8
$40,000 + $5,500 = $45,500
$20,000 − $1,000 = $19,000
146. Barker Production Company is considering the purchase of a flexible manufacturing system. The annual cash
benefits/savings associated with the system are:
Decreased waste
$ 75,000
Increased quality
100,000
Decrease in operating costs
62,500
Increase in on-time deliveries
12,500
The system will cost $750,000 and will last ten years. The company’s cost of capital is 10%.
Required:
A.
What is the payback period for the flexible manufacturing system?
B.
What is the NPV for the flexible manufacturing system?
A.
$750,000 / $250,000 = 3 years
B.
6.145 × $250,000 − $750,000 = $786,250
(PVAF n = 10, 10%)
Figure 14-10.
Present value of $1
Periods
4%
6%
8%
10%
12%
14%
1
0.962
0.943
0.926
0.909
0.893
0.877
2
0.925
0.890
0.857
0.826
0.797
0.769
3
0.889
0.840
0.794
0.751
0.712
0.675
4
0.855
0.792
0.735
0.683
0.636
0.592
5
0.822
0.747
0.681
0.621
0.567
0.519
6
0.790
0.705
0.630
0.564
0.507
0.456
7
0.760
0.665
0.583
0.513
0.452
0.400
8
0.731
0.627
0.540
0.467
0.404
0.351
9
0.703
0.592
0.500
0.424
0.361
0.308
10
0.676
0.558
0.463
0.386
0.322
0.270
Present value of an Annuity of $1
Periods
4%
6%
8%
10%
12%
14%
Chapter 14 – Capital Investment Decisions
1
0.962
0.943
0.926
0.909
0.893
0.877
2
1.886
1.833
1.783
1.736
1.690
1.647
3
2.775
2.673
2.577
2.487
2.402
2.322
4
3.630
3.465
3.312
3.170
3.037
2.914
5
4.452
4.212
3.993
3.791
3.605
3.433
6
5.242
4.917
4.623
4.355
4.111
3.889
7
6.002
5.582
5.206
4.868
4.564
4.288
8
6.733
6.210
5.747
5.335
4.968
4.639
9
7.435
6.802
6.247
5.759
5.328
4.946
10
8.111
7.360
6.710
6.145
5.650
5.216
147. Refer to Figure 14-10. Jimmy Reynolds is considering investing $12,000 in a project with the following cash
revenues and expenses:
Revenues
Expenses
Year 1
$20,000
$18,000
Year 2
$22,000
$19,000
Year 3
$22,000
$20,000
Year 4
$22,000
$17,000
Year 5
$25,000
$17,000
Jimmy requires a minimum rate of return of 8%.
A.
Calculate the net cash inflows in each of the 5 years.
B.
What is the payback period?
C.
What is the net present value of the investment?
A.
Year 1
Year 2
Year 3
Year 4
Year 5
B.
Payback period = ($2,000 + $3,000 + $2,000 + $5,000) = 4 years
$12,000 – $2,000 – $3,000 – $2,000 – $5,000 = $0
C.
Net present value = $15,134 − $12,000 = $3,134
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
148. Refer to Figure 14-10. Jasmine Company is considering an investment costing $20,000. The investment would return
$8,000 per year in each of three years. Jasmine requires a minimum rate of return of 6%.
A.
What is the payback period for the investment?
Chapter 14 – Capital Investment Decisions
B.
What is the net present value of the investment?
C.
The internal rate of return is greater than __________________% and less than
__________________%.
A.
Payback period = $20,000 / $8,000 = 2.5 years
B.
= ($8,000 × 0.943) + ($8,000 × 0.890) + ($8,000 × 0.840) −
= $1,384
OR
Net present value
= ($8,000 × 2.673) − $20,000 = $1,384
C.
Discount factor = $20,000 / $8,000 = 2.500
The internal rate of return for this discount factor lies between 8% and 10%
149. Refer to Figure 14-10. Geary Company is considering an investment costing $110,000. The investment would return
$40,000 per year in each of three years. Geary requires a minimum rate of return of 10%.
A.
What is the payback period for the investment?
B.
Using the Present Value of an Annuity of $1 table, calculate the net present value of the
investment.
C.
The internal rate of return is greater than __________________% and less than
__________________%.
D.
Now assume that the investment includes equipment that can be sold at the end of the
third year for $10,000. What is the present value of this investment?
A.
Payback period = $110,000 / $40,000 = 2.75 years
B.
Net present value = ($40,000 × 2.487) − $110,000 = $(10,520)
C.
Discount factor = $110,000 / $40,000 = 2.75
The internal rate of return for this discount factor lies between 4% and 5%.
D.
Net present value
= ($40,000 × 0.909) + ($40,000 × 0.826) + ($50,000 × 0.751) −
$110,000
= $(3,050)
150. Refer to Figure 14-10. Howard-Parr Company is considering an investment that will have an initial cost of $500,000
and yield annual net cash inflows of $130,000. Yearly depreciation will be $100,000. The equipment is expected to be
useful for five years, at which point it will be scrapped with no salvage value. Howard-Parr requires a minimum rate of
return of 10%.
A.
What is the accounting rate of return?
B.
What is the net present value? Is the investment acceptable?
C.
Now suppose that Howard-Parr believes it can sell the equipment at the end of 5 years for
$50,000. What is the net present value? Is the investment acceptable?
D.
What can you say about the IRR in the first case (no salvage value) versus the IRR in the
second case ($50,000 salvage value)?
Chapter 14 – Capital Investment Decisions
A.
ARR = ($130,000 − $100,000) / $500,000 = 0.06 or 6%
B.
NPV = ($130,000 × 3.791) − $500,000 = ($7,170)
The investment is not acceptable because the NPV is negative.
C.
NPV = ($130,000 × 3.791) + ($50,000 × 0.621) − $500,000 = $23,880
Now the investment is acceptable because the NPV is positive.
151. Refer to Figure 14-10. A company is considering two modifications to its current manufacturing process. The after-
tax cash flows associated with the two investments are:
Year
Project I
Project II
0
$(37,500)
$(150,000)
1
—
91,075
2
50,460
91,075
The company’s cost of capital is 12%.
A.
Compute the net present value for each investment.
B.
Computer the internal rate of return for each investment.
C.
Which project is better? Explain your reasoning.
A.
NPV Project I = ($50,460 × 0.797) − $37,500 = $2,717
NPV Project II = ($91,075 × 1.690) − $150,000 = $3,917
B.
corresponding to IRR = 16%*
corresponding to IRR = 14%
C.
Project II is better, even though it has a lower IRR, because its net present value is higher.
152. Refer to Figure 14-10. Ray Corporation is looking to invest in a new piece of equipment. Two manufacturers of this
type of equipment are being considered. After-tax inflows for the two competing projects are:
Year
Fallon Equipment Inc.
Toller Equipment Inc.
1
$275,000
$70,000
2
225,000
70,000
3
185,000
285,000
4
140,000
330,000
5
65,000
390,000
Both projects require an initial investment of $400,000. In both cases, assume that the equipment has a life of 5 years with
no salvage value.
Chapter 14 – Capital Investment Decisions
Required:
A. Assuming a discount rate of 8%, compute the net present value of each piece of equipment.
B. A third option is now available for a supplier outside of the country. The cost is also $400,000, but it will produce even
cash flows over its 5-year life. What must the annual cash flow be for this equipment to be selected over the other two?
Assume an 8% discount rate.
A.
Year
0
1
2
3
4
5
Year
0
1
2
3
4
5
153. Refer to Figure 14-10. Durrel Company is considering two different modifications to its current manufacturing
process. The after-tax cash flows associated with the two investments are as follows:
Year
Project A
Project B
0
$(220,000)
$(220,000)
1
–
88,500
2
–
88,500
3
285,000
88,500
Durrel’s cost of capital is 6%.
Required:
Chapter 14 – Capital Investment Decisions
A. Compute the NPV for each investment and state which project should be chosen based on the NPV.
B. Compute the IRR for each investment and state which project should be chosen based on the IRR.
A.
Project A
Year
Project B
Year
Project A should be chosen based on NPV
B.
Project A
Project B
$220,000 / $285,000 = 0.77193
$220,000 / $88,500 = 2.485
From the table above, IRR is close to 8%.
From the table above, IRR is close to 10%.
Project B should be chosen based on IRR.
Figure 14-11.
Present value of an Annuity of $1 in Arrears
Periods
4%
6%
8%
10%
12%
14%
1
0.962
0.943
0.926
0.909
0.893
0.877
2
1.886
1.833
1.783
1.736
1.690
1.647
3
2.775
2.673
2.577
2.487
2.402
2.322
4
3.630
3.465
3.312
3.170
3.037
2.914
5
4.452
4.212
3.993
3.791
3.605
4.433
6
5.242
4.917
4.623
4.355
4.111
3.889
7
6.002
5.582
5.206
4.868
4.564
4.288
8
6.733
6.210
5.747
5.335
4.968
4.639
9
7.435
6.802
6.247
5.759
5.328
4.946
10
8.111
7.360
6.710
6.145
5.650
5.216
154. Refer to Figure 14-11. Aragon Company is considering an investment in equipment that will have an initial cost of
$560,290 and yield annual net cash inflows of $90,000. Yearly depreciation will be $56,000. The equipment is expected
to be useful for 10 years and then it will be scrapped. Aragon requires a minimum rate of return of 10%.
A.
What is the payback period?
B.
What is the accounting rate of return?
C.
What is the net present value?
Chapter 14 – Capital Investment Decisions
D.
What is the approximate internal rate of return?
A.
Payback period = $560,290 / $90,000 = 6.2 years
B.
ARR = ($90,000 − $56,000) / $560,290 = 0.06068 or 6.07%
C.
NPV = ($90,000 × 6.145) − $560,290 = ($7,240)
D.
Discount factor = $560,290 / $90,000 = 6.225
corresponding to an IRR of slightly below 10%
155. Refer to Figure 14-11. Cleves Company is considering two projects.
Project X
Project Y
Initial investment
$500,000
$100,000
Annual cash flows
$88,500
$34,320
Life of the project
10 years
4 years
Depreciation per year
$50,000
$25,000
Cleves requires a minimum rate of return of 8%.
A.
What is the accounting rate of return for each project?
B.
What is the net present value for each project?
C.
What is the internal rate of return for each project?
D.
Given that only one project can be selected, which project should be chosen? Explain
your reasoning.
A.
Project X, ARR = ($88,500 − $50,000) / $500,000 = 0.077 or 7.7%
Project Y, ARR = ($34,320 − $25,000) / $100,000 = 0.0932 or 9.32%
Project Y, NPV = ($34,320 × 3.312) − $100,000 = $13,668
C.
Project X, Discount factor = $500,000 / $88,500 = 5.650
corresponding to IRR of 12%
Project Y, Discount factor = $100,000 / $34,320 = 2.914
corresponding to IRR of 14%
dollar amount over the life of the project.
156. Refer to Figure 14-11. Lyster Company wants to buy a new machine that will be able to perform many of the steps in
the manufacturing process that they currently have to do manually. The hope is that it will reduce the amount of time it
takes to create one unit and reduce the number of defective units. The machine requires an investment of $750,000. The
machine will last six years with no expected salvage value. The expected after-tax cash flows associated with the project
are as follows:
Year
Cash revenues
Cash expenses
1
$825,000
$510,000
2
825,000
510,000
3
825,000
510,000
4
825,000
510,000
5
825,000
510,000
6
825,000
510,000
Chapter 14 – Capital Investment Decisions
Required:
A. Compute the payback period for the new machine.
B. Compute the new machine’s ARR.
C. Compute the investment’s NPV, assuming a required rate of return of 12%.
A.
B.
ARR = average annual income / investment
C.
157. What is a capital investment decision? Give an example.
158. Name two nondiscounting capital investment models. What is meant by nondiscounting?
159. What are some reasons why firms use the payback period model in capital investment decision making?
160. Which model of capital investment decision making is most widely used? Why?
161. What is a postaudit? What are the advantages and disadvantages of the postaudit?
Chapter 14 – Capital Investment Decisions
162. Which model is better for independent projects − net present value or internal rate of return? For mutually exclusive
projects? Explain your reasoning for each case.
You decide
163. Explain the relationship between current and future dollars.
Match each item with the correct statement below.
a.
Payback period
b.
Accounting rate of return
c.
Net present value
d.
Internal rate of return
e.
Discount rate
f.
Annuity
g.
Post-audit
h.
Compounding of interest
164. can be used as a rough measure of risk and liquidity
a
165. can be used to determine whether or not an investment will negatively affect key financial ratios
166. interest rate used to discount future cash flows
e
Chapter 14 – Capital Investment Decisions
167. assumes that all future cash inflows earn the required rate of return
168. assumes that all future cash inflows earn the same rate of return as the project itself
169. a series of equal future cash flows
170. comparison of actual benefits and costs of a project with the expected benefits and costs
171. is the best method discounting model to use for mutually exclusive competing projects
172. earning of interest on interest