Problem 11-12B (15 minutes)
Item
Year(s)
Amount
of Cash
Flows
19%
Factor
Present
Value of
Cash
Flows
Cost of equipment required ……
Now
$(800,000)
1.000
$(800,000)
Working capital required ……….
Now
$(225,000)
1.000
(225,000)
Annual net cash receipts ……….
1-11
$305,000
4.486
1,368,230
Cost of road repairs ……………..
10
$(66,000)
0.176
(11,616)
Salvage value of equipment ……
11
$200,000
0.148
29,600
Working capital released ……….
11
$225,000
0.148
33,300
Net present value ………………..
$394,514)
Yes, the project should not be accepted; it has a positive net present value.
This means that the rate of return on the investment is greater than the
company’s required rate of return of 19%.
Problem 11-13B (30 minutes)
1. The formula for the project profitability index is:
Net present value
The index for the projects under consideration would be:
Project 1: $86,080 ÷ $500,000 = 0.172
Project 2: $72,000 ÷ $450,000 = 0.160
Project 3: $46,400 ÷ $220,000 = 0.211
Project 4: $146,650 ÷ $470,000 = 0.312
2. a., b., and c.
Net Present
Value
Internal Rate
of Return
First preference ……..
4
4
Second preference ….
1
3
Third preference …….
2
1
Fourth preference …..
3
2
3. Which ranking is best will depend on the company’s opportunities for
reinvesting funds as they are released from a project. The internal rate
of return method assumes that any released funds are reinvested at the
internal rate of return. This means that funds released from project #4
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Solutions Manual Alternate Problems, Chapter 11 11-3
amount of cash inflow generated for each dollar of investment (as
shown by the project profitability index).
Problem 11-14B (30 minutes)
1. The formula for the project profitability index is:
Net present value
The project profitability index for each project is:
Project A:
$434,360 ÷ $880,000 = 0.49
Project B:
$371,170 ÷ $685,000 = 0.54
Project C:
$223,220 ÷ $580,000 = 0.38
Project D:
$165,060 ÷ $780,000 = 0.21
2. a., b., and c.
Net Present
Value
Project
Profitability
Index
Internal Rate
of Return
First preference ……….
A
B
A
Second preference ……
B
A
D
Third preference ………
C
C
C
Fourth preference …….
D
D
B
3. Which ranking is best depends on the company’s opportunities for
reinvesting funds as they are released from a project. The internal rate
of return method assumes that released funds are reinvested at the
internal rate of return. For example, funds released from project D
required.
Problem 11-15B (30 minutes)
1. The income statement would be:
Sales revenue (70,000 loaves × $1.30 per loaf) …
$91,000
Less cost of ingredients ($91,000 × 40%)…………
36,400
Contribution margin ……………………………………..
54,600
Selling and administrative expenses:
Utilities ……………………………………………………
$ 9,000
Salaries …………………………………………………..
19,000
Insurance ………………………………………………..
4,000
Depreciation* …………………………………………..
10,848
Total selling and administrative expenses ………….
42,848
Net operating income …………………………………..
$11,752
*
$180,800 × 90% = $162,720
$162,720 ÷ 15 years = $10,848 per year.
2. The formula for the simple rate of return is:
Simple rate of return
=
Annual incremental net
operating income
Initial investment
=
$11,752
= 6%
$180,800
Yes, the oven and equipment would be purchased because their return
exceeds the owner’s 5% requirement.
Problem 11-15B (continued)
3. The formula for the payback period is:
Payback period
=
Initial investment
Net annual cash inflow
=
$180,800
= 8 years
$22,600 per year*
*
Net operating income + Depreciation = Annual net cash inflow
$11,752 + $10,848 = $22,600
Yes, the oven and equipment would be purchased. The payback period
is less than the 9-year period required.
Problem 11-16B (20 minutes)
1. The annual net cash inflows would be:
Reduction in annual operating costs:
Operating costs, present hand method …..
$35,000
Operating costs, new machine ……………..
15,000
Annual savings in operating costs …………
20,000
Increased annual contribution margin:
4,000 packages × $0.80 per package …….
3,200
Total annual net cash inflows …………………
$23,200
2.
Item
Year(s)
Amount
of Cash
Flows
14%
Factor
Present
Value of
Cash
Flows
Cost of the machine …
Now
$(85,000)
1.000
$(85,000)
Overhaul required ……
14
$(5,000)
0.160
(800)
Annual net cash
inflows ………………..
1-17
$23,200
6.373
147,854
Salvage value ………….
17
$3,500
0.108
378
Net present value …….
$ 62,432
Problem 11-17B (30 minutes)
1. The present value of cash flows would be:
Item
Year(s)
Amount
of Cash
Flows
10%
Factor
Present
Value of
Cash
Flows
Purchase alternative:
Purchase cost of the plane ….
Now
$(780,000)
1.000
$(780,000)
Annual cost of servicing, etc. .
1-5
$(8,000)
3.791
(30,328)
Repairs:
First three years ……………..
1-3
$(3,000)
2.487
(7,461)
Fourth year ……………………
4
$(5,000)
0.683
(3,415)
Fifth year ………………………
5
$(10,000)
0.621
(6,210)
Resale value of the plane ……
5
$390,000
0.621
242,190
Present value of cash flows …
$(585,224)
Lease alternative:
Damage deposit ……………….
Now
$ (55,000)
1.000
$ (55,000)
Annual lease payments ………
1-5
$(130,000)
3.791
(492,830)
Refund of deposit ……………..
5
$55,000
0.621
34,155
Present value of cash flows …
$(513,675)
Net present value in favor of
leasing the plane ………………
$ 71,549
2. The company should accept the leasing alternative. Even though the
total cash flows for leasing exceed the total cash flows for purchasing,
the leasing alternative is attractive because of the company’s high
Problem 11-18B (60 minutes)
1.
a.
Sales revenue ………………………………………
$310,000
Variable production expenses (@ 16%) ……..
49,600
Contribution margin …………………………..….
260,400
Fixed expenses:
Advertising ………………………………………..
$ 39,000
Salaries …………………………………………….
106,000
Utilities …………………………………………….
4,900
Insurance ………………………………………….
600
Depreciation* …………………………………….
30,600
Total fixed expenses ………………………………
181,100
Net operating income …………………………….
$ 79,300
*
[$408,000 – (10% × $408,000)] ÷ 12 years = $30,600 per year
b. The formula for the simple rate of return is:
Simple rate of return
=
Annual incremental net operating income
Initial investment
=
$79,300
= 19.4 %
$408,000
c. The formula for the payback period is:
The formula for the payback period is:
Payback period
=
Investment required
Net annual cash inflow
=
$408,000
= 3.7 years
$109,900*
*
Net annual cash inflow = Net operating income + Depreciation
$79,300 + $30,600 = $109,900
Problem 11-18B (continued)
2. a. A cost reduction project is involved here, so the formula for the
simple rate of return would be:
3. According to the company’s criteria, machine A should not be purchased
Cost savings – Depreciation
Simple rate of return = Initial Salvage from
–
investment old equipment
Problem 11-19B (30 minutes)
1. The income statement is:
Sales revenue …………………………….
¥207,000
Commissions (43% × ¥207,000) …….
89,010
Contribution margin ……………………..
117,990
Fixed expenses:
Maintenance …………………………….
¥44,000
Insurance ………………………………..
8,200
Depreciation* …………………………..
33,400
Total fixed expenses …………………….
85,600
Net operating income …………………..
¥ 32,390
*¥167,000 ÷ 5 years = ¥33,400 per year
2. The initial investment in the simple rate of return calculations is net of
the salvage value of the old equipment as shown below:
Simple rate of return
=
Annual incremental net operating income
Initial investment
=
¥32,390
=
¥32,390
=
22.18%
¥167,000 – ¥21,000
¥146,000
Yes, the games would be purchased. The return exceeds the 11%
threshold set by the company.
3. The payback period is:
Payback period
=
Investment required
Net annual cash inflow
¥167,000 – ¥21,000
=
¥146,000
=
2.2 years
¥65,790*
¥65,790
Problem 11-20B (30 minutes)
1. The total-cost approach:
Year(s)
Amount
of Cash
Flows
7%
Factor
Present
Value of
Cash
Flows
Purchase the new generator:
Cost of the new generator …….
Now
$(21,000)
1.000
$(21,000)
Salvage of the old generator ….
Now
$3,000
1.000
3,000
Annual cash operating costs ….
1-5
$(6,000)
4.100
(24,600)
Salvage of the new generator ..
5
$4,000
0.713
2,852
Present value of the net cash
outflows ………………………….
$(39,748)
Keep the old generator:
Overhaul needed now …………..
Now
$(7,000)
1.000
$ (7,000)
Annual cash operating costs …..
1-5
$(11,000)
4.100
(45,100)
Salvage of the old generator …..
5
$2,000
0.713
1,426
Present value of the net cash
outflows ………………………….
$(50,674)
Net present value in favor of
purchasing the new generator ..
$ 10,926
The hospital should purchase the new generator because it has the
lowest present value of total cost.
Problem 11-20B (continued)
2.
The incremental-cost approach:
Year(s)
Amount
of Cash
Flows
16%
Factor
Present
Value of
Cash
Flows
Incremental investment—new
generator* ………………………..
Now
$(14,000)
1.000
$(14,000)
Salvage of the old generator ……
Now
$3,000
1.000
3,000
Savings in annual cash operating
costs ………………………………..
1-5
$5,000
4.100
20,500
Difference in salvage value in 8
years ………………………………..
5
$2,000
0.713
1,426
Net present value in favor of
purchasing the new generator .
$ 10,926
*$21,000 – $7,000 = $14,000.
Problem 11-21B (60 minutes)
1. The net cash inflow from sales of the detectors for each year would be:
Year
1
2
3
4-12
Sales in units ………………
2,000
5,000
8,000
10,000
Sales in dollars
(@ $45 each) ……………
$ 90,000
$ 225,000
$ 360,000
$450,000
Less variable expenses
(@ $25 each) ……………
50,000
125,000
200,000
250,000
Contribution margin ………
40,000
100,000
160,000
200,000
Less fixed expenses:
Advertising ……………….
74,000
74,000
53,000
43,000
Other fixed expenses* ..
117,625
117,625
117,625
117,625
Total fixed expenses ……..
191,625
191,625
170,625
160,625
Net cash inflow (outflow) .
$(151,625)
$ (91,625)
$ (10,625)
$ 39,375
*
Depreciation is not a cash outflow and therefore must be
eliminated when determining the net cash flow. The analysis is:
Cost of the equipment …………
$140,000
Less salvage value (10%) …….
14,000
Net depreciable cost ……………
$126,000
$126,000 ÷ 16 years = $7,875 per year depreciation
$125,500 – $7,875 depreciation = $117,625 cash fixed expenses
Problem 11-21B (continued)
2. The net present value of the proposed investment would be:
Item
Year(s)
Amount of
Cash
Flows
7%
Factor
Present
Value of
Cash
Flows
Investment in equipment …
Now
$(140,000)
1.000
$(140,000)
Working capital investment
Now
$(44,000)
1.000
(44,000)
Yearly cash flows ……………
1
$(151,625)
0.935
(141,769)
” ” ” …………….
2
$(91,625)
0.873
(79,989)
” ” ” …………….
3
$(10,625)
0.816
(8,670)
” ” ” …………….
4-12
$39,375
6.823
*
268,656
Salvage value of
equipment ………………….
12
$14,000
0.339
4,746
Release of working capital .
12
$44,000
0.339
14,916
Net present value …………..
$(126,110)
*
Present value factor for 12 periods ………………….
9.447
Present value factor for 3 periods ……………………
2.624
Present value factor for 9 periods, starting 4
periods in the future ………………………………….
6.823
Since the net present value is negative, the company should not accept
the smoke detector as a new product.
Problem 11-22B (30 minutes)
1. Average weekly use of the washers and dryers would be:
Washers:
$3,565
= 2,300 uses
$1.55 per use
Dryers:
$2,080
= 2,600 uses
$0.80 per use
The expected annual net cash receipts would be:
Washer cash receipts ($3,565 × 52) ……..
$185,380
Dryer cash receipts ($2,080 × 52) ………..
108,160
Total cash receipts …………………………….
293,540
Less cash disbursements:
Washer: Water and electricity
($0.075 × 2,300 × 52) ………………….
$ 8,970
Dryer: Gas and electricity
($0.09 × 2,600 × 52) ……………………
12,168
Rent ($5,600 × 12) …………………………
67,200
Cleaning ($2,900 × 12) ……………………
34,800
Maintenance and other ($2,015 × 12) …
24,180
147,318
Annual net cash receipts …………………….
$146,222
2.
Item
Year(s)
Amount of
Cash Flows
13%
Factor
Present
Value of
Cash Flows
Cost of equipment ………..
Now
$(155,000)
1.000
$(155,000)
Working capital invested ..
Now
$(8,000)
1.000
(8,000)
Annual net cash receipts ..
1-3
$146,222
2.361
345,230
Salvage of equipment ……
3
$17,050
0.693
11,816
Working capital released ..
3
$8,000
0.693
5,544
Net present value …………
$199,590
Problem 11-23B (45 minutes)
1. A net present value computation for each investment follows:
Item
Year(s)
Amount of
Cash Flows
12%
Factor
Present
Value of
Cash Flows
Common stock:
Purchase of the stock ……..
Now
$(75,000)
1.000
$(75,000)
Sale of the stock ……………
6
$170,000
0.507
86,190
Net present value …………..
$ 11,190
Preferred stock:
Purchase of the stock ……..
Now
$(47,000)
1.000
$(47,000)
Annual cash dividend
(8%)…………………………
1-6
$3,760
4.111
15,457
Sale of the stock ……………
6
$33,000
0.507
16,731
Net present value …………..
$(14,812)
Bonds:
Purchase of the bonds …….
Now
$(28,000)
1.000
$(28,000)
Semiannual interest
received …………………….
1-12*
$1,000
8.384**
8,384
Sale of the bonds …………..
12*
$35,000
0.497**
17,395
Net present value …………..
$ (2,221)
*
12 semiannual interest periods.
**
Factor for 12 periods at 11%.
She earned a 12% rate of return on the common stock, but not on the
preferred stock or the bonds.
Problem 11-23B (continued)
2. Considering all three investments together, she did not earn a 12% rate
of return. The computation is:
Net
Present
Value
Common stock ……………………
$ 11,190
Preferred stock ……………………
(14,812)
Bonds ……………………………….
(2,221)
Overall net present value ………
$ (5,843)
The defect in the broker’s computation is that it does not consider the
time value of money and therefore has overstated the rate of return
earned.
3.
Because the assumption is that the project will yield the same annual
cash inflow every year, the formula for the net present value of the
project is:
Substituting the $238,000 investment and the factor for 9% for 11
periods into this formula and requiring that the net present value be
positive, we get:
6.805 × Annual cash inflow – $238,000 > 0
Net present Present value Annual Investment
value of = factor for × cash – required
the project an annuity inflow
Problem 11-24B (45 minutes)
The annual net cash inflow from rental of the property would be:
Net operating income ……….
$43,900
Add back depreciation ………
19,600
Annual net cash inflow ……..
$63,500
Item
Year(s)
Amount
of Cash
Flows
12%
Factor
Present
Value of
Cash
Flows
Keep the property:
Annual loan payment ……
1-10
$(14,100)
5.650
$ (79,665)
Annual net cash inflow ….
1-16
$63,500
6.974
442,849
Resale value of the
property ………………….
16
$117,520
*
0.163
19,156
Present value of cash
flows ………………………
$382,340
Sell the property:
Payoff of mortgage ………
Now
$(91,000)
1.000
$ (91,000)
Down payment received ..
Now
$209,000
1.000
209,000
Annual payments
received ………………….
1-16
$30,000
6.974
209,220
Present value of cash
flows ………………………
$327,220
Net present value in favor
of keeping the property …
$ 55,120