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Exercise 24-5 (20 minutes)
a.
Payback period = = = 2.21 years
where
Annual after-tax income ................................................................
$150,000
Plus depreciation* ...........................................................................
85,000
Annual net cash flow ......................................................................
$235,000
*Annual depreciation = = $85,000
b.
Payback period = = = 3.62 years
where
Annual after-tax income ................................................................
$ 60,000
Plus depreciation* ...........................................................................
45,000
Annual net cash flow ......................................................................
$105,000
*Annual depreciation = = $45,000
Exercise 24-6 (20 minutes)
a.
Net present value of investment*
Present value of six $235,000** cash inflows ($235,000 x 4.3553) ...........
$1,023,496
Present value of $10,000 at end of six years ($10,000 x 0.5645) ..............
5,645
Present value of cash inflows ................................................................
1,029,411
Less immediate cash outflow ................................................................
520,000
Net present value .........................................................................................
$ 509,141
*Present value factors from tables at the end of Appendix B:
4.3553 = Present value of an annuity of 1, where n = 6, i = 10% (from Table B.3)
0.5645 = Present value of 1, where n = 6, i = 10% (from Table B.1)
Cost of investment
Annual net cash flow
$520,000
$235,000
$520,000 - $10,000
6
Cost of investment
Annual net cash flow
$380,000
$105,000
$380,000 - $20,000
8
Exercise 24-6 (continued)
b.
Net present value of investment*
Present value of eight $105,000** cash inflows ($105,000 x 5.3349) ........
$560,165
Present value of $20,000 at end of eight years ($20,000 x 0.4665) ..........
9,330
Present value of cash inflows ................................................................
569,495
Less immediate cash outflow ................................................................
380,000
Net present value .........................................................................................
$189,495
*Present value factors from tables at the end of Appendix B:
5.3349 = Present value of an annuity of 1, where n = 8, i = 10% (from Table B.3)
0.4665 = Present value of 1, where n = 8, i = 10% (from Table B.1)
Exercise 24-7 (15 minutes)
$700,000 + $100,000
Exercise 24-8 (20 minutes)
COMPUTING NET CASH FLOWS FROM NET INCOME
Net income
Cash flows
Sales ................................................................................
$225,000
$225,000
Materials, labor & overhead ..........................................
120,000
120,000
Depreciation ................................................................
30,000
Selling and administrative ............................................
22,500
22,500
Pretax income ................................................................
52,500
Income taxes (30%)........................................................
15,750
15,750
Net income ................................................................
$ 36,750
Net cash flows ................................................................
$ 66,750
1. Payback period = = 5.39 years
2. Accounting rate of return = = 20.42%
$360,000
$66,750
$36,750
$180,000*
Exercise 24-10 (20 minutes)
PROJECT A
Net Cash
Flows
Present
Value of
1 at 10%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 40,000
0.9091
$ 36,364
Year 2 ................................................................
56,000
0.8264
46,278
Year 3 ................................................................
80,295
0.7513
60,326
Year 4 ................................................................
90,400
0.6830
61,743
Year 5 ................................................................
65,000
0.6209
40,359
Totals ................................................................
$331,695
245,070
Amount invested ..................................................
(160,000)
Net present value .................................................
$ 85,070
PROJECT B
Net Cash
Flows
Present
Value of
1 at 10%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 32,000
0.9091
$ 29,091
Year 2 ................................................................
50,000
0.8264
41,320
Year 3 ................................................................
66,000
0.7513
49,586
Year 4 ................................................................
72,000
0.6830
49,176
Year 5 ................................................................
24,000
0.6209
14,902
Totals ................................................................
$244,000
184,075
Amount invested ..................................................
(105,000)
Net present value .................................................
$ 79,075
Project A’s profitability index = $245,070 / $160,000 = 1.53
Project B’s profitability index = $184,075 / $105,000 = 1.75
Both projects have positive net present values. However, if the company
can choose only one project, it should select project B, since it has a
higher profitability index.
Exercise 24-11 (25 minutes)
a.
Project X1
Net Cash
Flows
Present
Value of
1 at 4%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 25,000
0.9615
$ 24,038
Year 2 ................................................................
35,500
0.9246
32,823
Year 3 ................................................................
60,500
0.8890
53,785
Totals ................................................................
$121,000
$110,646
Amount invested ..................................................
(80,000)
Net present value .................................................
$ 30,646
Project X2
Net Cash
Flows
Present
Value of
1 at 4%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 60,000
0.9615
$ 57,690
Year 2 ................................................................
50,000
0.9246
46,230
Year 3 ................................................................
40,000
0.8890
35,560
Totals ................................................................
$150,000
$139,480
Amount invested ..................................................
(120,000)
Net present value .................................................
$ 19,480
b.
Profitability index, Project X1 = $110,646 / $80,000 = 1.38
Profitability index, Project X2 = $139,480 / $120,000 = 1.16
If the company can only choose one of these projects it would select
Project X1, as it has a higher profitability index.
Exercise 24-12 (25 minutes)
a.
Project X1
Net Cash
Flows
Present
Value of
1 at 12%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 25,000
0.8929
$ 22,323
Year 2 ................................................................
35,500
0.7972
28,301
Year 3 ................................................................
60,500
0.7118
43,064
Totals ................................................................
$121,000
$93,688
Amount invested ..................................................
(80,000)
Net present value .................................................
$13,688
Project X2
Net Cash
Flows
Present
Value of
1 at 4%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 60,000
0.8929
$ 53,574
Year 2 ................................................................
50,000
0.7972
39,860
Year 3 ................................................................
40,000
0.7118
28,472
Totals ................................................................
$150,000
$121,906
Amount invested ..................................................
(120,000)
Net present value .................................................
$ 1,906
b.
Profitability index, Project X1 = $93,688 / $80,000 = 1.17
Profitability index, Project X2 = $121,906 / $120,000 = 1.02
If the company can only choose one of these projects it would select
Project X1, as it has a higher profitability index.
Exercise 24-13 (20 minutes)
Using Excel, Project X1 (X2) has an internal rate of return of 20.34% (12.99%).
Project X1 Project X2
A
B
C
D
1
Initial investment
-80000
-120000
2
Annual cash flows,
end of period
3
1
25000
60000
4
2
35500
50000
5
3
60500
40000
8
Formula for IRR
=IRR(C1:C5)
=IRR(D1:D5)
Both of these IRR’s are above the company’s required rate of return of 4%,
thus both projects should be accepted.
Exercise 24-14 (35 minutes)
1.
PROJECT C1
Net Cash
Flows
Present
Value of
1 at 12%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 12,000
0.8929
$ 10,715
Year 2 ................................................................
108,000
0.7972
86,098
Year 3 ................................................................
168,000
0.7118
119,582
Totals ................................................................
$288,000
$216,395
Amount invested ..................................................
(228,000)
Net present value .................................................
$ (11,605)
Exercise 24-14 (continued)
PROJECT C2
Net Cash
Flows
Present
Value of
1 at 12%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$ 96,000
0.8929
$ 85,718
Year 2 ................................................................
96,000
0.7972
76,531
Year 3 ................................................................
96,000
0.7118
68,333
Totals ................................................................
$288,000
$230,582
Amount invested ..................................................
(228,000)
Net present value .................................................
$ 2,582
PROJECT C3
Net Cash
Flows
Present
Value of
1 at 12%
Present
Value of
Net Cash
Flows
Year 1 ................................................................
$180,000
0.8929
$160,722
Year 2 ................................................................
60,000
0.7972
47,832
Year 3 ................................................................
48,000
0.7118
34,166
Totals ................................................................
$288,000
$242,720
Amount invested ..................................................
(228,000)
Net present value .................................................
$ 14,720
Analysis and Interpretation: Both Project C2 and C3 yield a positive net
present value. Accordingly, both C2 and C3 are acceptable investments.
Project C1 has a negative net present value, so it should be rejected.
2. INTERNAL RATE OF RETURN VS. NET PRESENT VALUE FOR C2
Exercise 24-15A (20 minutes)
Using Excel, Project A (B) has an internal rate of return of 26.96 (35.00%).
Project A Project B
A
B
C
D
1
Initial investment
-160000
-105000
2
Annual cash flows,
end of period
3
1
40000
32000
4
2
56000
50000
5
3
80295
66000
6
4
90400
72000
7
5
65000
24000
8
Formula for IRR
=IRR(C1:C7)
=IRR(D1:D7)
Exercise 24-16 (15 minutes)
1. Recovery time computation
Payback Period
Break-Even Time
$90,000 / $35,000 = 2.57 years
3.2 years (see answer for QS 24-15)
2. The advantage of break-even time is that it considers the time value of
3. When (1) the interest rate is very low, 1% for example, and (2) the
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Financial and Managerial Accounting, 6th Edition
1404
PROBLEM SET A
Problem 24-1A (50 minutes)
Part 1
Annual straight-line depreciation = = $115,000
Part 2
Net
Net Cash
Income
Flow
Expected annual sales of new product ..................
$1,840,000
$1,840,000
Expected costs of new product
Direct materials ......................................................
(480,000)
(480,000)
Direct labor .............................................................
(672,000)
(672,000)
Overhead excluding depr. on new asset .............
(336,000)
(336,000)
Depreciation on new asset....................................
(115,000)
Selling and administrative expenses ...................
(160,000)
(160,000)
Income before taxes .................................................
77,000
Income taxes (30%)...................................................
(23,100)
(23,100)
Net income ................................................................
$ 53,900
Net cash flow* ...........................................................
$ 168,900
* Alternatively, annual net cash flow can be computed as
Net income + Depreciation = $53,900 + $115,000 = $168,900
Part 3
Payback Period = = 2.84 years
$480,000 - $20,000
4 years
$480,000
$168,900
