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Problem 8-24 (continued)
4. The formula for the internal rate of return is:
Investment required
Factor of the internal=
rate of return Annual net cash inflow
$94,500
= = 4.500
$21,000
Looking in Exhibit 8B-2, and reading along the 12-period line, a factor of
42 Managerial Accounting for Managers, 4th Edition
Problem 8-25 (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)
Lease Alternative:
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
lowest present value of total costs.
Problem 8-26 (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
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 8-27 (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
Solutions Manual, Chapter 8 45
Problem 8-27 (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)
46 Managerial Accounting for Managers, 4th Edition
Problem 8-28 (20 minutes)
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)
Purchase the new truck:
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)
that alternative.
Solutions Manual, Chapter 8 47
Problem 8-29 (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)
Bonds:
Now
1
2
3
Purchase of the bonds..
$(50,000)
Annual interest income .
$6,000
$6,000
$6,000
Sales of the bonds .......
________
______
______
52,700
Total cash flows (a) .....
$(50,000)
$6,000
$6,000
$58,700
Discount factor (b) .......
1.000
0.862
0.743
0.641
Present value (a)×(b) ..
$(50,000)
$5,172
$4,458
$37,627
Net present value ........
$(2,743)
preferred stock or the bonds.
48 Managerial Accounting for Managers, 4th Edition
Problem 8-29 (continued)
2. Considering all three investments together, Linda did not earn a 16%
rate of return. The computation is:
Net
Present
Value
Common stock .........................
$ 7,560
Preferred stock .........................
(8,650)
Bonds ......................................
(2,743)
Overall net present value ..........
$(3,833)
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.
Investment required
Factor of the internal =
rate of return Annual net cash inflow
Substituting the $239,700 investment and the factor for 14% for 12
periods into this formula, we get:
=
$239,700 5.660
Annual cash inflow
Therefore, the required annual net cash inflow is: $239,700 ÷ 5.660 =
$42,350.
Solutions Manual, Chapter 8 49
Problem 8-30 (60 minutes)
1. Computation of the annual net cost savings:
Savings in labor costs (25,000 hours × $16 per hour) .
$400,000
Savings in inventory carrying costs .............................
210,000
Total .........................................................................
610,000
Less increased power and maintenance cost
($2,500 per month × 12 months) ............................
30,000
Annual net cost savings .............................................
$580,000
2. The net present value is computed as follows:
Now
1
2
3
4
5
Cost of the robot .......
$(1,600,000)
Installation &
software ....................
(450,000)
Annual net cost
savings......................
$580,000
$580,000
$580,000
$580,000
$580,000
Inventory reduction ...
400,000
Salvage value (old) ....
_________
_______
_______
_______
_______
70,000
Total cash flows (a) ...
$(2,050,000)
$980,000
$580,000
$580,000
$580,000
$650,000
Discount factor (b) .....
1.000
0.833
0.694
0.579
0.482
0.402
Present value
(a)×(b) .....................
$(2,050,000)
$816,340
$402,520
$335,820
$279,560
$261,300
Present value .............
$45,540
50 Managerial Accounting for Managers, 4th Edition
Problem 8-30 (continued)
3. Recomputation of the annual net cost savings:
Savings in labor costs (22,500 hours × $16 per hour)
$360,000
Savings in inventory carrying costs ...........................
210,000
Total .......................................................................
570,000
Less increased power and maintenance cost
($2,500 per month × 12 months) ..........................
30,000
Annual net cost savings ...........................................
$540,000
The revised present value computations are follows:
Now
1
2
3
4
5
Cost of the robot .........
$(1,600,000)
Installation &
software ......................
(525,000)
Annual net cost
savings........................
$540,000
$540,000
$540,000
$540,000
$540,000
Inventory reduction .....
400,000
Salvage value (old) ......
_________
_______
_______
_______
_______
70,000
Total cash flows (a) .....
$(2,125,000)
$940,000
$540,000
$540,000
$540,000
$610,000
Discount factor (b) .......
1.000
0.833
0.694
0.579
0.482
0.402
Present value
(a)×(b) .......................
$(2,125,000)
$783,020
$374,760
$312,660
$260,280
$245,220
Present value ...............
$(149,060)
