Exercise 24-1
Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages
over the company’s current truck (not the least of which is that it runs). The new truck would cost
$56,000. Because of the increased capacity, reduced maintenance costs, and increased fuel economy,
the new truck is expected to generate cost savings of $8,000. At the end of 8 years the company will
sell the truck for an estimated $27,000. Traditionally the company has used a rule of thumb that a
proposal should not be accepted unless it has a payback period that is less than 50% of the asset’s
estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely
solely on the payback approach, but should also employ the net present value method when
evaluating new projects. The company’s cost of capital is 8%.
(a)
Compute the cash payback period and net present value of the proposed investment.
Cash
payback
period
Net present
value
7
years
4,560
$
The cash payback period is:
$56,000 ÷ $8,000 = 7 years
The net present value is:
Cash
Flows
×
8% Discount
Factor
Present value of net annual
cash flows
$8,000
×
5.74664
=
$45,973
Present value of salvage value
27,000
×
0.54027
=
14,587
=
Present
Value
1496
5
60,560
Less: Capital investment
56,000
Net present value
$4,560
(b)
Does the project meet the company’s cash payback criteria? N
Does it meet the net present value criteria for acceptance? Y
In order to meet the cash payback criteria, the project would have to have a cash payback period of
less than 4 years (8 ÷ 2). It does not meet this criteria. The net present value is positive, however,
suggesting the project should be accepted. The reason for the difference is that the project’s high
estimated salvage value increases the present value of the project. The net present value is a better
indicator of the project’s worth.
Exercise 24-6
BSU Inc. wants to purchase a new machine for $29,300, excluding $1,500 of installation costs. The old
machine was bought five years ago and had an expected economic life of 10 years without salvage
value. This old machine now has a book value of $2,000, and BSU Inc. expects to sell it for that
amount. The new machine would decrease operating costs by $7,000 each year of its economic life.
The straight-line depreciation method would be used for the new machine, for a six-year period with no
salvage value.
(a)
Determine the cash payback period.
Cash payback period
4.1
years
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Total net investment = $29,300 + $1,500 - $2,000 = $28,800
Annual net cash flow = $7,000
Payback period = $28,800 ÷ $7,000 = 4.1years
(b)
Determine the approximate internal rate of return.
12%
Internal rate of return
Net present value approximates zero when discount rate is 12%.
Item
Amount
Net annual cash flows
$7,000
Years
1-6
PV
Factor
4.11141
Less: Capital investment
Presen
t
Value
$28,780
(28,800)
Net present value
$-20
(c)
Assuming the company has a required rate of return of 10%, determine whether the new machine
should be purchased.
The investment should be accepted.
Because the approximate internal rate of return of 12% exceeds the required rate of return of 10%, the
investment should be accepted.
Problem 24-1A (Part Level Submission)
U3 Company is considering three long-term capital investment proposals. Each investment has a
useful life of 5 years. Relevant data on each project are as follows.
Project Bono
Project Edge
Project Clayton
$160,000
$175,000
$200,000
Year 1
14,000
18,000
27,000
2
14,000
17,000
23,000
3
14,000
16,000
21,000
4
14,000
12,000
13,000
5
14,000
9,000
12,000
Total
$70,000
$72,000
$96,000
Capital investment
Annual net income:
Depreciation is computed by the straight-line method with no salvage value. The company’s cost of
capital is 15%. (Assume that cash flows occur evenly throughout the year.)
(a)
Compute the cash payback period for each project.
Project Bono
3.48
years
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Project Edge
3.40
years
Project Clayton
3.17
years
Project Bono $160,000 ÷ ($14,000 + $32,000) = 3.48 years
Project Edge
Cumulative Cash
Flow
Year
Cash Flow
1
$53,000 ($18,000 + $35,000)
$53,000
2
$52,000 ($17,000 + $35,000)
$105,000
3
$51,000 ($16,000 + $35,000)
$156,000
4
$47,000 ($12,000 + $35,000)
$203,000
5
$44,000 ($9,000 + $35,000)
$247,000
Cash payback period 3.40 years
$175,000 - $156,000 = $19,000
$19,000 ÷ $47,000 = 0.40
Project Clayton
Year
Cash Flow
Cumulative Cash Flow
1
$67,000 ($27,000 + $40,000)
$67,000
2
$63,000 ($23,000 + $40,000)
$130,000
3
$61,000 ($21,000 + $40,000)
$191,000
4
$53,000 ($13,000 + $40,000)
$244,000
5
$52,000 ($12,000 + $40,000)
$296,000
Cash payback period 3.17 years
$200,000 - $191,000 = $9,000
$9,000 ÷ $53,000 = 0.17
(b)
Compute the net present value for each project.
Project
Bono
Project
Clayton
Project Edge
Net
present
value
$
$
-5,801
$
-7,312
2,163
Project Bono
Item
Net annual cash flows
Amoun
t
Years
$46,000
1-5
PV
Factor
3.35216
Present
Value
$154,199
Less: Capital investment
160,000
Negative net present
value
$(5,801)
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Project Edge
Project Clayton
Discount
Year
Factor
Cash
Flow
1
.86957
$53,000
$46,087
$67,000
$58,261
2
.75614
52,000
39,319
63,000
47,637
3
.65752
51,000
33,534
61,000
40,109
4
.57175
47,000
26,872
53,000
30,303
5
.49718
44,000
21,876
52,000
25,853
$247,000
167,688
$296,000
202,163
Total
Cash
Flow
PV
PV
Less: Capital investment
(175,000)
(200,000)
Positive (negative)
net present value
$(7,312)
$2,163
(c)
Compute the annual rate of return for each project. (Hint: Use average annual net income in your
computation.)
Project
Bono
Annual
rate of
return
Project
Edge
Project
Clayton
17.5
16.46
19.2
%
%
%
Project Bono
= $14,000 ÷ [($160,000 + $0) ÷ 2]
= 17.5%
Project Edge
= $14,400 ÷ [($175,000 + $0) ÷ 2]
= 16.46%
Project Clayton
= $19,200 ÷ [($200,000 + $0) ÷ 2]
= 19.2%
(d)
Rank the projects on each of the foregoing bases. Which project do you recommend?
Project
Cash
Payback
Net
Present
Value
Annual
Rate of
Return
Bono
3
2
2
Edge
2
3
3
Clayton
1
1
1
The best project is Clayton.
Brief Exercise G-23
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Sophie Corp. purchased a new blending machine for $3,150.15. It paid $500 down and financed the
remaining $2,650.15. It is required to pay 10 annual payments at the end of each year at an annual
rate of interest of 11%.
What is the amount of the annual payment? (Round answer to 2 decimal places, e.g. 15.25.)
Amount of the annual payment
Amount of the annual
payment
$450
PV of an annuity=
$2,650.15=
p × Present value of an annuity factor
p × 5.88923
p=
$2,650.15 ÷ 5.88923
p=
$450
(Annuity = PV of an annuity ÷ PV of an annuity factor)
Brief Exercise G-8
For each of the following cases, indicate (a) what interest rate columns and
(b) what number of periods you would refer to in looking up the discount
rate.
(1) In Table 3 (Present Value of 1):
Number of
Years
Involved
Annual
Rate
Discounts
per Year
Case A
12%
7
Annually
Case B
8%
11
Annually
Case C
10%
8
Semiannually
(a)
Case A
12
Case B
8
Case C
5
(b)
%
%
%
7
periods
11
periods
16
periods
(2) In Table 4 (Present Value of an Annuity of 1):
Annual
Rate
Number
of
Number
of
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Frequency
of
Years
Involved
Payments
Involved
Payments
Case A
10%
20
20
Annually
Case B
10%
7
7
Annually
Case C
6%
5
10
Semiannually
(a)
Case A
10%
Case B
Case C
(b)
10%
3%
20 periods
7 periods
10 periods
Brief Exercise G-13
Kaehler Enterprises earns 5% on an investment that pays back $80,000 at the end of each of the next
6 years.
What is the amount Kaehler Enterprises invested to earn the 5% rate of return?
Kaehler Enterprises invested
$406,055.2
Discount rate from Table 4 is 5.07569. Present value of 6 payments of $80,000 each discounted at 5%
is therefore $406,055.2 ($80,000 × 5.07569). Kaehler Enterprises invested $406,055.2 to earn
$80,000 per year for 6 years.
(PV of an annuity = Annuity × PV of an annuity factor)
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