SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE 12-1
$450,000 ÷ $50,000 = 9 years
BRIEF EXERCISE 12-2
Present Value
Net annual cash flows – $40,000 X 5.65
Capital investment
Net present value
$226,000
215,000
$ 11,000
The investment should be made because the net present value is positive.
BRIEF EXERCISE 12-3
Cash
10% Discount
Present
Flows X
Factor
= Value
Present value of net annual cash flows
Present value of salvage value
$25,000 X
65,000 X
3.79079
.62092
Capital investment
Net present value
= $ 94,770
= 40,360
135,130
136,000
$
(870)
Since the net present value is negative, the project is unacceptable.
BRIEF EXERCISE 12-4
Cash
9% Discount
Present
Flows X
Factor
= Value
Present value of net annual cash flows
Present value of salvage value
$34,000 X
0X
5.53482
.50187
Capital investment
Net present value
= ($188,184)
=(
0)
( 188,184)
( 200,000)
($ (11,816)
The reduction in downtime would have to have a present value of at least
$11,816 in order for the project to be acceptable.
12-6
Copyright © 2012 John Wiley & Sons, Inc.
Weygandt, Managerial Accounting, 6/e, Solutions Manual
(For Instructor Use Only)
BRIEF EXERCISE 12-5
Project A
Cash
Flows
Present value of net annual cash flows
Present value of salvage value
9% Discount Present
X
Factor
= Value
$70,000 X
0 X
6.41766
.42241
Capital investment
Net present value
= $449,236
=
0
449,236
400,000
$ 49,236
Profitability index = $449,236/$400,000 = 1.12
Project B
Cash
Flows
Present value of net annual cash flows
Present value of salvage value
9% Discount Present
X
Factor
= Value
$50,000 X
0 X
6.41766
.42241
Capital investment
Net present value
= $320,883
=
0
320,883
280,000
$ 40,883
Profitability index = $320,883/$280,000 = 1.15
Project B has a lower net present value than Project A, but because of its
lower capital investment, it has a higher profitability index. Based on its
profitability index, Project B should be accepted.
BRIEF EXERCISE 12-6
Original estimate
Cash
10% Discount Present
Flows X
Factor
= Value
Present value of net annual cash flows
Present value of salvage value
$46,000 X
0 X
5.75902
.42410
Capital investment
Net present value
Copyright © 2012 John Wiley & Sons, Inc.
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= $264,915
=
0
264,915
250,000
$ 14,915
(For Instructor Use Only)
12-7
BRIEF EXERCISE 12-6 (Continued)
Revised estimate
Cash
10% Discount
Present
Flows X
Factor
= Value
Present value of net annual cash flows
Present value of salvage value
$39,000 X
0X
6.49506
.35049
Capital investment
Net present value
= ($253,307)
=(
0)
( 253,307)
( 260,000)
($ (6,693)
The original net present value was projected to be a positive $14,915;
however, the revised estimate is a negative $6,693. The project is not a
success.
BRIEF EXERCISE 12-7
When net annual cash flows are expected to be equal, the internal rate of
return can be approximated by dividing the capital investment by the net
annual cash flows to determine the discount factor, and then locating this
discount factor on the present value of an annuity table.
$176,000/$33,740 = 5.21636
By tracing across on the 7-year row we see that the discount factor for 8% is
5.20637. Thus, the internal rate of return on this project is approximately 8%.
BRIEF EXERCISE 12-8
When net annual cash flows are expected to be equal, the internal rate of
return can be approximated by dividing the capital investment by the net
annual cash flows to determine the discount factor, and then locating this
discount factor on the present value of an annuity table. Since this exercise
has a salvage value, not all cash flows are equal. In this case, the internal
rate of return can be approximated by identifying the discount rate that will
result in a net present value of zero. By experimenting with various rates,
we determined that the net present value is approximately zero when a
discount rate of approximately 9% is used.
12-8
Copyright © 2012 John Wiley & Sons, Inc.
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BRIEF EXERCISE 12-8 (Continued)
Net annual cash flows = $400,000 – $150,000 = $250,000
Cash
9% Discount
Flows X
Factor
=
Present value of net annual cash flows
Present value of salvage value
$250,000 X
716,000 X
7.16073
.35554
Capital investment
Net present value
Present
Value
= $1,790,183
=
254,567
2,044,750
2,045,000
$
(250)
The 9% internal rate of return exceeds the company’s 7% required rate of
return; thus, the project should be accepted.
BRIEF EXERCISE 12-9
The annual rate of return is calculated by dividing expected annual income
by the average investment. The company’s expected annual income is:
$130,000 – $70,000 = $60,000
Its average investment is:
$470,000 + $10,000
= $240,000
2
Therefore, its annual rate of return is:
$60,000/$240,000 = 25%
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12-9
SOLUTIONS FOR DO IT! REVIEW EXERCISES
DO IT! 12-1
Estimated annual cash inflows.......................................
Estimated annual cash outflows ....................................
Net annual cash flow ..........................................................
$80,000
40,000
$40,000
Cash payback period = $120,000/$40,000 = 3 years.
DO IT! 12-2
Estimated annual cash inflows.......................................
Estimated annual cash outflows ....................................
Net annual cash flow ..........................................................
Present value of net annual cash
flows
Capital investment
Net present value
a
Table 4, Appendix A.
$80,000
40,000
$40,000
Cash
Flow
12% Discount
Factor
Present
Value
$40,000
3.03735 a
$121,494
120,000
$ 1,494
Since the net present value is positive, the project should be accepted
DO IT! 12-3
Estimated annual cash inflows.......................................
Estimated annual cash outflows ....................................
Net annual cash flow ..........................................................
$80,000
40,000
$40,000
$120,000/$40,000 = 3.00. Using Table 4 of Appendix A and the factors that
correspond with the four-period row, 3.00 is between the factors for 12%
and 15%.
Since the project has an internal rate that is more than 12%, the company’s
required rate of return, the project should be accepted.
12-10
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Weygandt, Managerial Accounting, 6/e, Solutions Manual
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DO IT! 12-4
Revenues ................................................................................
Less:
Expenses (excluding depreciation) ........................
Depreciation ($120,000/4 years) ...............................
Annual net income...............................................................
$80,000
$40,000
30,000
70,000
$ 10,000
Average investment = ($120,000 + 0)/2 = $60,000.
Annual rate of return = $10,000/$60,000 = 16.7%.
Since the annual rate of return, 16.7%, is greater than Wallowa’s required
rate of return, 12%, the proposed project is acceptable.
Copyright © 2012 John Wiley & Sons, Inc.
Weygandt, Managerial Accounting, 6/e, Solutions Manual
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12-11
SOLUTIONS TO EXERCISES
EXERCISE 12-1
(a) The cash payback period is:
$56,000 ÷ $7,500 = 7.5 years
The net present value is:
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
8%
Cash
Discount
Present
Flows X Factor = Value
$ 7,500 X 5.74664 = $43,100
27,000 X .54027 = 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
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 12-2
(a)
Year
1
2
3
AA
Net Annual Cash Flow
$ 7,000
9,000
12,000
Cumulative Net Cash Flow
$ 7,000
16,000
28,000
Cash payback period 2.50 years
$22,000 – $16,000 = $6,000
$6,000 ÷ $12,000 = .50
12-12
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EXERCISE 12-2 (Continued)
BB
22,000 ÷ 10,000 = 2.2 years
Year
1
2
3
CC
Net Annual Cash Flow
$13,000
12,000
11,000
Cumulative Net Cash Flow
$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
payback period. As indicated, only CC is acceptable because its cash
payback is 1.75 years.
(b)
AA
Year
Discount
Factor
Cash
Flow
1
.89286
$ 7,000
2
.79719
9,000
3
.71178
12,000
Total present value
Investment
Net present value
Present
Value
BB
Cash
Present
Flow
Value
$ 6,250 $10,000
7,175
10,000
10,000
8,541
21,966
(22,000 )
$
(34 )
CC
Cash
Flow
$ 8,929
$13,000
7,972
12,000
11,000
7,118
24,019 (1)
(22,000 )
$ 2,019
Present
Value
$11,607
9,566
7,830
29,003
(22,000 )
$ 7,003
(1) This total may also be obtained from Table 4: $10,000 X 2.40183 = $24,018.
(The difference of $1 is due to rounding)
Project CC is still the most desirable project. Also, on the basis of net
present values, project BB is also acceptable. Project AA is not
desirable.
Copyright © 2012 John Wiley & Sons, Inc.
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12-13
EXERCISE 12-3
Investment in new equipment ................
Disposal of old equipment ......................
Additional training required....................
Net initial investment required...............
$2,450,000
(260,000)
85,000
$2,275,000
Calculation of net present value:
Cash flows
Maintenance
Net cash flows from
operations:
Terminal salvage
Present value of
cash inflows
Initial investment
Net present value
Year
1
2
3
4
5
6
7
Discount
Factor, 9%
0.91743
0.84168
0.77218
0.70843
0.64993
0.59627
0.54703
5
0.64993
7
0.54703
Amount
$ 390,000
400,000
411,000
426,000
434,000
435,000
436,000
(100,000)
350,000
Present
Value
$ 357,798
336,672
317,366
301,791
282,070
259,377
238,505
(64,993)
2,028,586
191,461
2,220,047
(2,275,000)
$ (54,953)
Based on the net present calculation alone, the sewing machine should not
be purchased. However, the internal rate of return would be only slightly
lower than the 9% minimum required, so the company may want to look at
some of the non-quantitative factors involved.
12-14
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Weygandt, Managerial Accounting, 6/e, Solutions Manual
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EXERCISE 12-4
Machine A
Cash
9% Discount
Present
Flows X
Factor
= Value
Present value of net annual cash flows
Present value of salvage value
$15,000 X
0 X
5.53482
.50187
= $83,022
=
0
83,022
75,500
$ 7,522
Capital investment
Net present value
Profitability index = $83,022/$75,500 = 1.10
Machine B
Cash
9% Discount
Flows X
Factor
=
Present value of net annual cash flows
Present value of salvage value
$30,000 X
0 X
5.53482
.50187
Capital investment
Net present value
Present
Value
= ($166,045)
= (
0)
( 166,045)
( 180,000)
($ (13,955)
Profitability index = $166,045/$180,000 = .92
Machine B has a negative net present value, and also a lower profitability
index. Machine B should be rejected and Machine A should be purchased.
EXERCISE 12-5
When net annual cash flows are expected to be equal, the internal rate of
return can be approximated by dividing the capital investment by the net
annual cash flows to determine the discount factor, and then locating this
discount factor on the present value of an annuity table.
$430,000/$101,000 = 4.25743
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
approximately 11%. Since this is above the company’s required rate of
return, the project should be accepted.
Copyright © 2012 John Wiley & Sons, Inc.
Weygandt, Managerial Accounting, 6/e, Solutions Manual
(For Instructor Use Only)
12-15
EXERCISE 12-6
(a)
Total net investment = $29,300 + $1,500 – $2,000 = $28,800
Annual net cash flow = $7,000
Payback period = $28,800 ÷ $7,000 = 4.1 years
(b)
Net present value approximates zero when discount rate is 12%.
Item
Net annual cash flows
Capital investment
Net present value
(c)
Amount
$7,000
Years
1–6
Present
Value
$28,780
(28,800)
$
(20)
PV Factor
4.11141
Because the approximate internal rate of return of 12% exceeds the
required rate of return of 10%, the investment should be accepted.
EXERCISE 12-7
(a)
Project
22A
23A
24A
Capital
Investment ÷
$240,000
$270,000
$280,000
÷
÷
÷
Net Annual Cash
Flows*
($16,700 + $40,000)
($20,600 + $30,000)
($17,500 + $40,000)
Internal
Rate of
Return
= Factor
=
=
=
4.233
5.336
4.870
Closest
Discount
Factor
Internal
Rate of
Return
4.23054
5.32825
4.86842
11%
12%
10%
*(Annual income + Depreciation expense)
(b) The acceptable projects are 22A and 23A because their rates of return
are equal to or greater than the 11% required rate of return.
12-16
Copyright © 2012 John Wiley & Sons, Inc.
Weygandt, Managerial Accounting, 6/e, Solutions Manual
(For Instructor Use Only)
EXERCISE 12-8
The annual rate of return is calculated by dividing expected annual income
by the average investment. The company’s expected annual income is:
$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
Contribution margin per muffler ($72 – $36 – $12)
Total net annual cash flows (a) X (b)
Cash payback period = $39,000 ÷ $6,240 = 6.25 years.
(a)
260
(b) X $24
$6,240
(b) Average investment: ($39,000 + $3,000) ÷ 2 = $21,000.
Annual depreciation: ($39,000 – $3,000) ÷ 8 = $4,500.
Annual net income: $6,240 – $4,500 = $1,740.
Annual rate of return = $1,740 ÷ $21,000 = 8.3% (rounded).
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12-17
EXERCISE 12-10
(a) 1.
2.
Cash payback period: $190,000 ÷ $50,000 = 3.8 years.
Annual rate of return: $12,000 ÷ [($190,000 + $0) ÷ 2] = 12.63%.
(b)
Item
Net annual cash flows
Capital investment
Net present value
Amount
Years
PV Factor
$ 50,000
1–5
3.60478
Present Value
$180,239))
(190,000)
$ (9,761)))
EXERCISE 12-11
(a)
Year
1
2
3
Net Annual Cash Flow
$45,000
40,000
35,000
Cumulative Net Cash Flow
$ 45,000
85,000
120,000
Cash payback period 2.57 years (2 + [($105,000 – $85,000) ÷ $35,000])
(b) Average annual net income = ($10,000 + $12,000 + $14,000 + $16,000 +
$18,000) ÷ 5 = $14,000
Average investment = ($105,000 + $0) ÷ 2 = $52,500
Annual rate of return = $14,000 ÷ $52,500 = 26.67%
(c)
Net cash flows
Year
1
2
3
4
5
Discount
Factor, 12%
0.89286
0.79719
0.71178
0.63552
0.56743
Amount
$45,000
40,000
35,000
30,000
25,000
Present value of cash
in flows
Initial investment
130,231
(105,000)
Net present value
12-18
Copyright © 2012 John Wiley & Sons, Inc.
Present
Value
$ 40,179
31,888
24,912
19,066
14,186
$ 25,231
Weygandt, Managerial Accounting, 6/e, Solutions Manual
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SOLUTIONS TO PROBLEMS
PROBLEM 12-1A
(a) Project Kilo $150,000 ÷ ($14,000 + $30,000) = 3.41 years
Year
1
2
3
4
5
Project Lima
Cash Flow
$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)
Cumulative Cash Flow
$ 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
Year
1
2
3
4
5
Project Oscar
Cash Flow
$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)
Cumulative Cash Flow
$ 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
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Weygandt, Managerial Accounting, 6/e, Solutions Manual
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12-19
PROBLEM 12-1A (Continued)
(b)
Project Kilo
Item
Net annual cash flows
Capital investment
Negative net present
value
Discount
Factor
.86957
.75614
.65752
.57175
.49718
Year
1
2
3
4
5
Total
Capital investment
Positive (negative)
net present value
Amount
$44,000
Years
1–5
PV Factor
3.35216
Present
Value
$147,495
(150,000)
$ (2,505)
Project Lima
Cash
Flow
PV
$ 44,348
$ 51,000
37,807
50,000
32,218
49,000
25,729
45,000
20,882
42,000
$237,000
160,984
(165,000)
Project Oscar
Cash
Flow
PV
$ 67,000
$ 58,261
63,000
47,637
40,109
61,000
30,303
53,000
25,853
52,000
202,163
$296,000
(200,000)
$
$ (4,016)
2,163
(c) Project Kilo = $14,000 ÷ [($150,000 + $0) ÷ 2] = 18.67%.
Project Lima = $14,400 ÷ [($165,000 + $0) ÷ 2] = 17.5%.
Project Oscar = $19,200 ÷ [($200,000 + $0) ÷ 2] = 19.2%.
(d)
Project
Kilo
Lima
Oscar
Cash Payback
3
2
1
Net
Present Value
2
3
1
Annual
Rate of Return
2
3
1
The best project is Oscar.
12-20
Copyright © 2012 John Wiley & Sons, Inc.
Weygandt, Managerial Accounting, 6/e, Solutions Manual
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PROBLEM 12-2A
(a)
Sales
Expenses
Drivers’ salaries
Out-of-pocket expenses
Depreciation
Total expenses
Net income
Cash inflow
(1)
Annual
Net Income
(2)
Annual
Cash Inflow
*$108,000*
$108,000
* 48,000*
* 30,000*
* 25,000*
* 103,000*
*$ 5,000*
48,000
30,000
0
78,000
$ 30,000
*5 vans X 10 trips X 6 students X 30 weeks X $12.00 = $108,000.
(b) 1.
Cash payback period = $75,000 ÷ $30,000* = 2.50 years.
*$5,000 + $25,000
2.
Annual rate of return = $5,000 ÷ ($75,000 + 0) = 13.33%.
2
(c) Present value of annual cash inflows ($30,000 X 2.28323*) = $68,497
Capital investment
= (75,000)
Net present value
= $ (6,503)
*3 years at 15%, PV of annuity of 1.
(d) The computations show that the commuter service is not a wise
investment for these reasons: (1) annual net income will only be
$5,000, (2) the annual rate of return (13.33%) is less than the cost of
capital (15%), (3) the cash payback period is 83% (2.5 ÷ 3) of the useful
life of the vans, and (4) net present value is negative.
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12-21
PROBLEM 12-3A
(a)
(1) Option A
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Cash
Flows
a
$40,000a
( (50,000)
(
0)
X
X
X
X
8% Discount
Factor
5.20637
.73503
.58349
Capital investment
Net present value
=
=
=
=
Present
Value
($208,255)
( (36,752)
(
0)
($171,503)
( (160,000)
($ 11,503)
a
Net annual cash flows = $70,000 – $30,000 = $40,000
(2) Profitability index = $171,503/$160,000 = 1.07
(3) The internal rate of return can be approximated by finding the discount
rate that results in a net present value of approximately zero. This is
accomplished with a 10% discount rate.
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Cash
Flows
a
$40,000a
( (50,000)
(
0)
X
X
X
X
10% Discount
Factor
4.86842
.68301
.51316
Present
=
Value
= ($194,737)
= ( (34,151)
= (
0)
($160,586)
(160,000)
($
586
8% Discount
Factor
5.20637
.73503
.58349
Present
=
Value
= $281,144
=
0
=
4,668
$285,812
(227,000)
$ 58,812
Capital investment
Net present value
a
Net annual cash flows = $70,000 – $30,000 = $40,000
(1) Option B
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Cash
Flows
b
$54,000b
0
8,000
X
X
X
X
Capital investment
Net present value
b
Net annual cash flows = $80,000 – $26,000 = $54,000
(2) Profitability index = $285,812/$227,000 = 1.26
12-22
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PROBLEM 12-3A (Continued)
(3) Internal rate of return on Option B is 15%, as calculated below:
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Cash
Flows
b
$54,000b
0
8,000
X
X
X
X
15% Discount
Factor
4.16042
.57175
.37594
Capital investment
Net present value
b
Present
= Value
= $224,663
=
0
=
3,008
$227,671
(227,000)
$
671
Net annual cash flows = $80,000 – $26,000 = $54,000
(b) Option A has a lower net present value than Option B, and also a lower
profitability index and internal rate of return. Therefore, Option B is the
preferred project.
Copyright © 2012 John Wiley & Sons, Inc.
Weygandt, Managerial Accounting, 6/e, Solutions Manual
(For Instructor Use Only)
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