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Exercise 13-3 (30 minutes)
1.
Annual savings in part-time help ............................
$3,800
Added contribution margin from expanded sales
(1,000 dozen × $1.20 per dozen) ........................
1,200
Annual cash inflows ...............................................
$5,000
2.
Investment required
Factor of the internal =
rate of return Annual cash inflow
$18,600
= = 3.720
$5,000
Looking in Exhibit 13B-2, a factor of 3.720 falls closest to the 16% rate of return.
3. The cash flows will not be even over the six-year life of the machine because of the extra $9,125
inflow in the sixth year. Therefore, the above approach cannot be used to compute the internal rate
of return in this situation. Using trial-and-error or some other method, the internal rate of is 22%:
Now
1
2
3
4
5
6
Purchase of machine .........
$(18,600)
Reduced part-time help .....
$3,800
$3,800
$3,800
$3,800
$3,800
$3,800
Added contribution margin
1,200
1,200
1,200
1,200
1,200
1,200
Salvage value of machine ..
_______
______
______
______
______
______
9,125
Total cash flows (a) ..........
$(18,600)
$5,000
$5,000
$5,000
$5,000
$5,000
$14,125
Discount factor (22%) (b) .
1.000
0.820
0.672
0.551
0.451
0.370
0.303
Present value (a)×(b) .......
$(18,600)
$4,100
$3,360
$2,755
$2,255
$1,850
$4,280
Net present value .............
$0
Exercise 13-5 (10 minutes)
1. The project profitability index for each proposal is:
Proposal
Number
Net Present
Value
(a)
Investment
Required
(b)
Project Profitability
Index
(a) (b)
A
$36,000
$90,000
0.40
B
$38,000
$100,000
0.38
C
$35,000
$70,000
0.50
D
$40,000
$120,000
0.33
2. The ranking is:
Proposal
Number
Project Profitability
Index
C
0.50
A
0.40
B
0.38
D
0.33
Note that proposal D has the highest net present value, but it ranks
lowest in terms of the project profitability index.
Exercise 13-6 (10 minutes)
This is a cost reduction project, so the simple rate of return would be
computed as follows:
Operating cost of old machine ....................
$ 30,000
Less operating cost of new machine ...........
12,000
Less annual depreciation on the new
machine ($120,000 ÷ 10 years) ...............
12,000
Annual incremental net operating income ...
$ 6,000
Cost of the new machine ...........................
$120,000
Scrap value of old machine ........................
40,000
Initial investment .......................................
$ 80,000
Annual incremental net operating income
Simple rate =
of return Initial investment
$6,000
= = 7.5%
$80,000
Exercise 13-7 (15 minutes)
Project A:
Now
1
2
3
4
5
6
Purchase of equipment .....
$(100,000)
Annual cash inflows .........
$21,000
$21,000
$21,000
$21,000
$21,000
$21,000
Salvage value ..................
_______
______
______
______
______
______
8,000
Total cash flows (a) .........
$(100,000)
$21,000
$21,000
$21,000
$21,000
$21,000
$29,000
Discount factor (14%) (b)
1.000
0.877
0.769
0.675
0.592
0.519
0.456
Present value (a)×(b) ......
$(100,000)
$18,417
$16,149
$14,175
$12,432
$10,899
$13,224
Net present value ............
$(14,704)
Now
1
2
3
4
5
6
Working capital invested ..
$(100,000)
Annual cash inflows .........
$16,000
$16,000
$16,000
$16,000
$16,000
$ 16,000
Working capital released ..
_______
______
______
______
______
______
100,000
Total cash flows (a) .........
$(100,000)
$16,000
$16,000
$16,000
$16,000
$16,000
$116,000
Discount factor (14%) (b)
1.000
0.877
0.769
0.675
0.592
0.519
0.456
Present value (a)×(b) ......
$(100,000)
$14,032
$12,304
$10,800
$9,472
$8,304
$52,896
Net present value ............
$7,808
The $100,000 should be invested in Project B rather than in Project A. Project B has a positive net
present value whereas Project A has a negative net present value.
Exercise 13-9 (20 minutes)
1. The net present value is computed as follows:
Now
1
2
3
4
5
Purchase of
equipment ................
$(3,000,000)
Sales ........................
$2,500,000
$2,500,000
$2,500,000
$2,500,000
$2,500,000
Variable expenses .....
(1,000,000)
(1,000,000)
(1,000,000)
(1,000,000)
(1,000,000)
Out-of-pocket costs ...
__________
(600,000)
(600,000)
(600,000)
(600,000)
(600,000)
Total cash flows (a) ..
$(3,000,000)
$ 900,000
$ 900,000
$ 900,000
$ 900,000
$ 900,000
Discount factor (b) ....
1.000
0.870
0.756
0.658
0.572
0.497
Present value
(a)×(b) ....................
$(3,000,000)
$783,000
$680,400
$592,200
$514,800
$447,300
Net present value .....
$17,700
2. The simple rate of return would be:
Annual incremental net income
Simple rate =
of return Initial investment
$300,000
= = 10.0%
$3,000,000
3. The company would want Derrick to pursue the investment opportunity because it has a positive net
Problem 13-11 (30 minutes)
1. The project profitability index is computed as follows:
Project
Net Present
Value
(a)
Investment
Required
(b)
Project
Profitability
Index
(a) ÷ (b)
A ............
$44,323
$160,000
0.28
B ............
$42,000
$135,000
0.31
C ............
$35,035
$100,000
0.35
D ............
$38,136
$175,000
0.22
2. a., b., and c.
Net Present
Value
Project
Profitability
Index
Internal Rate
of Return
First preference ........
A
C
D
Second preference ....
B
B
C
Third preference .......
D
A
A
Fourth preference .....
C
D
B
