DO IT! 12-4
Revenues ………………………………………………………….. $80,000
Less:
Since the annual rate of return, 16.7%, is greater than Wallowa’s required
rate of return, 12%, the proposed project is acceptable.
SOLUTIONS TO EXERCISES
EXERCISE 12-1
(a) The cash payback period is:
$56,000 ÷ $7,500 = 7.5 years
The net present value is:
Cash
Flows
X
8%
Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
$ 7,500
27,000
X
X
5.74664
.54027
=
=
$43,100
14,587
57,687
56,000
$ 1,687
(b) 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
EXERCISE 12-2
(a)
AA
Year
Net Annual Cash Flow
Cumulative Net Cash Flow
1
2
3
$ 7,000
9,000
12,000
$ 7,000
16,000
28,000
Cash payback period 2.50 years
$22,000 – $16,000 = $6,000
$6,000 ÷ $12,000 = .50
EXERCISE 12-2 (Continued)
BB
22,000 ÷ 10,000 = 2.2 years
CC
Year
Net Annual Cash Flow
Cumulative Net Cash Flow
1
2
3
$13,000
12,000
11,000
$13,000
25,000
36,000
Cash payback period 1.75 years
$22,000 – 13,000 = $9,000
$9,000 ÷ $12,000 = .75
The most desirable project is CC because it has the shortest payback
period. The least desirable project is AA because it has the longest
(b)
AA
BB
CC
Year
Discount
Factor
Cash
Flow
Present
Value
Cash
Flow
Present
Value
Cash
Flow
Present
Value
1
2
3
.89286
.79719
.71178
$ 7,000
9,000
12,000
$ 6,250
7,175
8,541
$10,000
10,000
10,000
$ 8,929
7,972
7,118
$13,000
12,000
11,000
$11,607
9,566
7,830
Total present value
Investment
Net present value
21,966
(22,000
$ (34
)
)
24,019
(22,000
$ 2,019
(1)
)
29,003
(22,000
$ 7,003
)
Project CC is still the most desirable project. Also, on the basis of net
EXERCISE 12–3
Investment in new equipment …………. $2,450,000
Calculation of net present value:
Year
Discount
Factor, 9%
Amount
Present
Value
Cash flows 1 0.91743 $ 390,000 $ 357,798
2 0.84168 400,000 336,672
3 0.77218 411,000 317,366
some of the non-quantitative factors involved.
EXERCISE 12-4
Machine A
Cash
Flows
X
9% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
$15,000
0
X
X
5.53482
.50187
=
=
$83,022
0
83,022
75,500
$ 7,522
Profitability index = $83,022/$75,500 = 1.10
Machine B
Cash
Flows
X
9% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
$30,000
0
X
X
5.53482
.50187
=
=
($166,045)
( 0)
( 166,045)
( 180,000)
($ (13,955)
Profitability index = $166,045/$180,000 = .92
EXERCISE 12-5
When net annual cash flows are expected to be equal, the internal rate of
By tracing across on the 6-year row, we see that the discount factor for
11% is 4.23054. Thus, the internal rate of return on this project is
EXERCISE 12-6
Item
Amount
Years
PV Factor
Present
Value
EXERCISE 12-7
(a)
Project
Capital
Investment
÷
Net Annual Cash
Flows*
=
Internal
Rate of
Return
Factor
Closest
Discount
Factor
Internal
Rate of
Return
22A
23A
24A
$240,000
$270,000
$280,000
÷
÷
÷
($16,700 + $40,000)
($20,600 + $30,000)
($17,500 + $40,000)
=
=
=
4.233
5.336
4.870
4.23054
5.32825
4.86842
11%
12%
10%
*(Annual income + Depreciation expense)
EXERCISE 12-8
$70,000 – $41,500 = $28,500
Its average investment is:
$300,000 + $80,000
=
$190,000
2
Therefore, its annual rate of return is:
$28,500 ÷ $190,000 = 15%
EXERCISE 12-9
(a) Cost of hoist: $35,000 + $3,300 + $700 = $39,000.
Net annual cash flows:
Number of extra mufflers 5 X 52 weeks (a) 260
(b) Average investment: ($39,000 + $3,000) ÷ 2 = $21,000.
EXERCISE 12-10
(a) 1. Cash payback period: $190,000 ÷ $50,000 = 3.8 years.
2. Annual rate of return: $12,000 ÷ [($190,000 + $0) ÷ 2] = 12.63%.
(b)
Item
Amount
Years
PV Factor
Present Value
Net annual cash flows
Capital investment
Net present value
$ 50,000
1–5
3.60478
$180,239))
(190,000)
$ (9,761)))
EXERCISE 12-11
(a)
Year
Net Annual Cash Flow
Cumulative Net Cash Flow
1
2
3
$45,000
40,000
35,000
$ 45,000
85,000
120,000
(b) Average annual net income = ($10,000 + $12,000 + $14,000 + $16,000 +
$18,000) ÷ 5 = $14,000
(c) Discount Present
Year Factor, 12% Amount Value
Net cash flows 1 0.89286 $45,000 $ 40,179
2 0.79719 40,000 31,888
Present value of cash
in flows 130,231
SOLUTIONS TO PROBLEMS
PROBLEM 12-1A
(a) Project Kilo $150,000 ÷ ($14,000 + $30,000) = 3.41 years
Project Lima
Year
Cash Flow
Cumulative Cash Flow
1
2
3
4
5
$51,000 ($18,000 + $33,000)
$50,000 ($17,000 + $33,000)
$49,000 ($16,000 + $33,000)
$45,000 ($12,000 + $33,000)
$42,000 ($ 9,000 + $33,000)
$ 51,000
$101,000
$150,000
$195,000
$237,000
Cash payback period 3.33 years
$165,000 – $150,000 = $15,000
$15,000 ÷ $45,000 = .33
Project Oscar
Year
Cash Flow
Cumulative Cash Flow
1
2
3
4
5
$67,000 ($27,000 + $40,000)
$63,000 ($23,000 + $40,000)
$61,000 ($21,000 + $40,000)
$53,000 ($13,000 + $40,000)
$52,000 ($12,000 + $40,000)
$ 67,000
$130,000
$191,000
$244,000
$296,000
Cash payback period 3.17 years
$200,000 – $191,000 = $9,000
$9,000 ÷ $53,000 = .17
PROBLEM 12-1A (Continued)
(b) Project Kilo
Item
Amount
Years
PV Factor
Present
Value
Net annual cash flows
Capital investment
Negative net present
value
$44,000
1–5
3.35216
$147,495
(150,000)
$ (2,505)
Project Lima
Project Oscar
Year
Discount
Factor
Cash
Flow
PV
Cash
Flow
PV
1
2
3
4
5
Total
.86957
.75614
.65752
.57175
.49718
$ 51,000
50,000
49,000
45,000
42,000
$237,000
$ 44,348
37,807
32,218
25,729
20,882
160,984
(165,000)
$ (4,016)
$ 67,000
63,000
61,000
53,000
52,000
$296,000
$ 58,261
47,637
40,109
30,303
25,853
202,163
(200,000)
$ 2,163
Capital investment
Positive (negative)
net present value
(c) Project Kilo = $14,000 ÷ [($150,000 + $0) ÷ 2] = 18.67%.
(d)
Project
Cash Payback
Net
Present Value
Annual
Rate of Return
Kilo
Lima
Oscar
3
2
1
2
3
1
2
3
1
The best project is Oscar.