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Problem 11-13A (continued)
2. The simple rate of return is computed as follows:
Annual incremental net operating income
Simple rate of return = Initial investment
$400,000
= = 11.4%
$3,500,000
3. The company would want Casey to invest in the project because it has a
positive net present value of $101,400. However, Casey might be
Problem 11-14A (20 minutes)
The net present value is computed as follows:
Now
1
2
3
4
Purchase of equipment ..........
$(130,000)
Working capital investment ...
(60,000)
Sales ....................................
$250,000
$250,000
$250,000
$250,000
Variable expenses .................
(120,000)
(120,000)
(120,000)
(120,000)
Fixed out-of-pocket costs ......
(70,000)
(70,000)
(70,000)
(70,000)
Overhaul of equipment ..........
(8,000)
Working capital released .......
60,000
Salvage value of equipment ...
__________
________
_______
_______
12,000
Total cash flows (a) ..............
$(190,000)
$60,000
$52,000
$60,000
$132,000
Discount factor (15%) (b) .....
1.000
0.870
0.756
0.658
0.572
Present value (a)×(b) ...........
$(190,000)
$52,200
$39,312
$39,480
$75,504
Net present value .................
$16,496
Problem 11-15A (30 minutes)
1. The income statement would be:
Sales ........................................................
$300,000
Variable expenses:
Cost of ingredients (20% × $300,000) .....
$60,000
Commissions (12.5% × $300,000) ...........
37,500
97,500
Contribution margin ...................................
202,500
Fixed expenses:
Salaries ..................................................
70,000
Rent ($3,500 × 12) .................................
42,000
Depreciation* .........................................
16,800
Insurance ...............................................
3,500
Utilities ...................................................
27,000
159,300
Net operating income ................................
$ 43,200
*
$270,000 – $18,000 = $252,000
$252,000 ÷ 15 years = $16,800 per year.
2. The formula for the simple rate of return is:
Annual incremental net operating income
Simple rate of return = Initial investment
$43,200
= = 16.0%
$270,000
Yes, the franchise would be acquired because it promises a rate of
return in excess of 12%.
Problem 11-15A (continued)
3. The formula for the payback period is:
Investment required
Payback period = Annual net cash inflow
$270,000
= = 4.5 years
$60,000*
Problem 11-16A (30 minutes)
1. The annual net cost savings would be:
Reduction in labor costs .........................................
$108,000
Reduction in material waste ...................................
6,500
Total .....................................................................
114,500
Less increased maintenance costs ($3,000 × 12) ....
36,000
Annual net cost savings .........................................
$ 78,500
2. Using this cost savings figure, and other data from the text, the net present value analysis would be:
Now
1
2
3
4
5
6
Cost of machine ................
$(250,000)
Software and installation ...
(80,000)
Salvage value of old
equipment ........................
12,000
Annual net cost savings .....
$78,500
$78,500
$78,500
$78,500
$78,500
$78,500
Replacement of parts ........
(45,000)
Salvage value of new
machine ...........................
_______
______
______
______
______
______
20,000
Total cash flows (a) ..........
$(318,000)
$78,500
$78,500
$33,500
$78,500
$78,500
$98,500
Discount factor (16%) (b) .
1.000
0.862
0.743
0.641
0.552
0.476
0.410
Present value (a)×(b) .......
$(318,000)
$67,667
$58,326
$21,474
$43,332
$37,366
$40,385
Net present value .............
$(49,450)
Problem 11-17A (30 minutes)
1. The formula for the project profitability index is:
Net present value of the project
The indexes for the projects under consideration would be:
Project 1:
$66,140 ÷ $270,000 = 0.24
Project 2:
$72,970 ÷ $450,000 = 0.16
Project 3:
$73,400 ÷ $360,000 = 0.20
Project 4:
$87,270 ÷ $480,000 = 0.18
2. a., b., and c.
Net Present
Value
Project
Profitability
Index
Internal Rate
of Return
First preference ........
4
1
2
Second preference ....
3
3
1
Third preference .......
2
4
4
Fourth preference .....
1
2
3
Problem 11-17A (continued)
3. Which ranking is best will depend on Revco Products’ opportunities for
reinvesting funds as they are released from the 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
Problem 11-18A (20 minutes)
1. The annual net cash inflows would be:
Reduction in annual operating costs:
Operating costs, present hand method .....
$30,000
Operating costs, new machine .................
7,000
Annual savings in operating costs ............
23,000
Increased annual contribution margin:
6,000 boxes × $1.50 per box ...................
9,000
Total annual net cash inflows .....................
$32,000
2. The net present value is computed as follows:
Now
1
2
3
4
5
Purchase of machine ........
$(120,000)
Annual net cash inflows ....
$32,000
$32,000
$32,000
$32,000
$32,000
Replacement parts ...........
(9,000)
Salvage value of machine .
________
______
______
_______
______
7,500
Total cash flows (a) .........
$(120,000)
$32,000
$32,000
$23,000
$32,000
$39,500
Discount factor (20%) (b)
1.000
0.833
0.694
0.579
0.482
0.402
Present value (a)×(b) ......
$(120,000)
$26,656
$22,208
$13,317
$15,424
$15,879
Net present value ............
(26,516)
Problem 11-19A (45 minutes)
1. The payback periods for Products A and B are calculated using a two-
step process. First, the annual net cash inflows are calculated as
follows:
Product A
Product B
Sales revenues .....................................
$250,000
$350,000
Variable expenses ................................
(120,000)
(170,000)
Fixed out-of-pocket operating costs ......
(70,000)
(50,000)
Annual net cash inflows ........................
$ 60,000
$130,000
The second step is to compute each product’s payback period as
follows:
Product A
Product B
Investment required (a) ........................
$170,000
$380,000
Annual net cash inflow (b) ....................
$60,000
$130,000
Payback period (a) ÷ (b) ......................
2.83 years
2.92 years
Problem 11-19A (continued)
2. The net present values for Products A and B are computed as follows:
Product A:
Now
1
2
3
4
5
Purchase of equipment ......
$(170,000)
Sales ................................
$250,000
$250,000
$250,000
$250,000
$250,000
Variable expenses .............
(120,000)
(120,000)
(120,000)
(120,000)
(120,000)
Fixed out-of-pocket
costs ................................
(70,000)
(70,000)
(70,000)
(70,000)
(70,000)
Total cash flows (a) ..........
$(170,000)
$60,000
$60,000
$60,000
$60,000
$60,000
Discount factor (b) ............
1.000
0.862
0.743
0.641
0.552
0.476
Present value (a)×(b) .......
$(170,000)
$51,720
$44,580
$38,460
$33,120
$28,560
Net present value .............
$26,440
Now
1
2
3
4
5
Purchase of equipment ......
$(380,000)
Sales ................................
$350,000
$350,000
$350,000
$350,000
$350,000
Variable expenses .............
(170,000)
(170,000)
(170,000)
(170,000)
(170,000)
Fixed out-of-pocket
costs ................................
(50,000)
(50,000)
(50,000)
(50,000)
(50,000)
Total cash flows (a) ..........
$(380,000)
$130,000
$130,000
$130,000
$130,000
$130,000
Discount factor (b) ............
1.000
0.862
0.743
0.641
0.552
0.476
Present value (a)×(b) .......
$(380,000)
$112,060
$96,590
$83,330
$71,760
$61,880
Net present value .............
$45,620
Problem 11-19A (continued)
3. The project profitability index for each product is computed as follows:
Product A
Product B
Net present value (a) ....................................
$26,440
$45,620
Investment required (b) ................................
$170,000
$380,000
Project profitability index (a) ÷ (b) .................
0.16
0.12
4. The simple rate of return for each product is computed as follows:
Product A
Product B
Annual net cash inflow ..................................
$60,000
$130,000
Depreciation expense ....................................
34,000
76,000
Annual incremental net operating income .......
$26,000
$54,000
Product A
Product B
Annual incremental net operating income (a)..
$26,000
$54,000
Initial investment (b) .....................................
$170,000
$380,000
Simple rate of return (a) ÷ (b) .......................
15.3%
14.2%
5. The net present value calculations suggest that Product B is preferable
to Product A. However, the project profitability index reveals that
Problem 11-20A (45 minutes)
1.
Present cost of transient workers ..........................
$40,000
Less out-of-pocket costs to operate the cherry picker:
Cost of an operator and assistant .......................
$14,000
Insurance ..........................................................
200
Fuel ..................................................................
1,800
Maintenance contract .........................................
3,000
19,000
Annual savings in cash operating costs ..................
$21,000
2. The first step is to determine the annual incremental net operating
income:
Annual savings in cash operating costs .............
$21,000
Less annual depreciation ($90,000 ÷ 12 years) .
7,500
Annual incremental net operating income .........
$13,500
3. The formula for the payback period is:
Investment required
Payback period = Annual net cash inflow
$94,500
= = 4.5 years
$21,000*
*
In this case, the cash inflow is measured by the annual savings
in cash operating costs.
Yes, the cherry picker would be purchased. The payback period is less
than 5 years. Note that this answer conflicts with the answer in Part 2.
Problem 11-21A (30 minutes)
1. The present value of each alternative’s cash flows is computed as
follows:
Purchase Alternative:
Now
1
2
3
Purchase of cars ..........
$(170,000)
Annual servicing costs ..
$(3,000)
$(3,000)
$(3,000)
Repairs........................
(1,500)
(4,000)
(6,000)
Resale value of cars .....
________
______
______
85,000
Total cash flows (a) .....
$(170,000)
$(4,500)
$(7,000)
$76,000
Discount factor (b) .......
1.000
0.847
0.718
0.609
Present value (a)×(b) ..
$(170,000)
$(3,812)
$(5,026)
$46,284
Present value ...............
$(132,554)
Now
1
2
3
Security deposit ................
$(10,000)
Annual lease payments .....
$(55,000)
$(55,000)
$(55,000)
Refund of deposit .............
_______
_______
_______
10,000
Total cash flows (a) ..........
$(10,000)
$(55,000)
$(55,000)
$(45,000)
Discount factor (b) ............
1.000
0.847
0.718
0.609
Present value (a)×(b) .......
$(10,000)
$(46,585)
$(39,490)
$(27,405)
Net present value .............
$(123,480)
2. The company should lease the cars because this alternative has the
Problem 11-22A (30 minutes)
1. The annual incremental net operating income can be determined as
follows:
Ticket revenue (50,000 × $3.60) ................
$180,000
Selling and administrative expenses:
Salaries ..................................................
$85,000
Insurance ...............................................
4,200
Utilities ...................................................
13,000
Depreciation* .........................................
27,500
Maintenance ...........................................
9,800
Total selling and administrative expenses ....
139,500
Net operating income ................................
$ 40,500
*$330,000 ÷ 12 years = $27,500 per year.
2. The simple rate of return is:
Annual incremental net operating income
Simple rate=
of return Initial investment (net of salvage from old equipment)
$40,500 $40,500
= = = 15%
$330,000 - $60,000 $270,000
Yes, the water slide would be constructed. Its return is greater than the
specified hurdle rate of 14%.
3. The payback period is:
Investment required (net of salvage from old equipment)
Payback =
period Annual net cash inflow
$330,000 - $60,000 $270,000
= = = 3.97 years (rounded)
$68,000* $68,000*
*Net operating income + Depreciation = Annual net cash flow
$40,500 + $27,500 = $68,000.
Yes, the water slide would be constructed. The payback period is within
the 5 year payback required by Mr. Sharkey.
Problem 11-23A (30 minutes)
1. Average weekly use of the auto wash and the vacuum will be:
$1,350
Auto wash: = 675 uses
$2.00
Vacuum: 675 × 60% = 405 uses
The expected annual net cash flow from operations would be:
Auto wash cash receipts ($1,350 × 52) ...........
$70,200
Vacuum cash receipts (405 × $1.00 × 52) ......
21,060
Total cash receipts ......................................
91,260
Less cash disbursements:
Water (675 × $0.20 × 52) ...........................
$ 7,020
Electricity (405 × $0.10 × 52) .....................
2,106
Rent ($1,700 × 12) .....................................
20,400
Cleaning ($450 × 12) ..................................
5,400
Insurance ($75 × 12) ..................................
900
Maintenance ($500 × 12) ............................
6,000
Total cash disbursements ...............................
41,826
Annual net cash flow from operations .............
$49,434
Problem 11-23A (continued)
2. The net present value is computed as follows:
Now
1
2
3
4
5
Purchase of equipment .
$(200,000)
Working capital ............
(2,000)
Annual net cash flows ..
$49,434
$49,434
$49,434
$49,434
$49,434
Working capital
released ......................
2,000
Salvage value ..............
________
______
______
______
______
20,000
Total cash flows (a) .....
$(202,000)
$49,434
$49,434
$49,434
$49,434
$71,434
Discount factor (b) .......
1.000
0.909
0.826
0.751
0.683
0.621
Present value (a)×(b) ..
$(202,000)
$44,936
$40,832
$37,125
$33,763
$44,361
Net present value ........
$(983)
No, Mr. Duncan should not open the auto wash. The negative net present value indicates that the rate
of return on this investment is slightly less than the 10% required rate of return.
Problem 11-24A (20 minutes)
The net present value of each alternative is computed as follows:
Keep the old truck:
Now
1
2
3
4
5
Overhaul needed now ..
$(7,000)
Annual operating costs .
(10,000)
(10,000)
(10,000)
(10,000)
(10,000)
Salvage value (old) ......
______
_______
_______
_______
_______
1,000
Total cash flows (a) .....
$(7,000)
$(10,000)
$(10,000)
$(10,000)
$(10,000)
$(9,000)
Discount factor (b) .......
1.000
0.862
0.743
0.641
0.552
0.476
Present value (a)×(b) ..
$(7,000)
$(8,620)
$(7,430)
$(6,410)
$(5,520)
$(4,284)
Present value ...............
$(39,264)
Now
1
2
3
4
5
Purchase new truck ......
$(30,000)
Salvage value (old) ......
9,000
Annual operating costs .
(6,500)
(6,500)
(6,500)
(6,500)
(6,500)
Salvage value (new) ....
_______
______
______
______
______
4,000
Total cash flows (a) .....
$(21,000)
$(6,500)
$(6,500)
$(6,500)
$(6,500)
$(2,500)
Discount factor (b) .......
1.000
0.862
0.743
0.641
0.552
0.476
Present value (a)×(b) ..
$(21,000)
$(5,603)
$(4,830)
$(4,167)
$(3,588)
$(1,190)
Present value ...............
$(40,378)
Problem 11-25A (45 minutes)
1. A net present value computation for each investment follows:
Common stock:
Now
1
2
3
Purchase of the stock ...
$(95,000)
Sales of the stock ........
________
______
______
160,000
Total cash flows (a) .....
$(95,000)
$0
$0
$160,000
Discount factor (b) .......
1.000
0.862
0.743
0.641
Present value (a)×(b) ..
$(95,000)
$0
$0
$102,560
Net present value ........
$7,560
Preferred stock:
Now
1
2
3
Purchase of the stock ...
$(30,000)
Annual cash dividend ...
$1,800
$1,800
$1,800
Sales of the stock ........
________
______
______
27,000
Total cash flows (a) .....
$(30,000)
$1,800
$1,800
$28,800
Discount factor (b) .......
1.000
0.862
0.743
0.641
Present value (a)×(b) ..
$(30,000)
$1,552
$1,337
$18,461
Net present value ........
$(8,650)
