Chapter 11
Capital Budgeting Decisions
Solutions to Questions
11-1 A capital budgeting screening decision is
concerned with whether a proposed investment
11-2 The “time value of money” refers to the
fact that a dollar received today is more valuable
11-3 Discounting is the process of computing
the present value of a future cash flow.
times.
11-4 Accounting net income is based on
accruals rather than on cash flows. Both the net
11-5 Unlike other common capital budgeting
methods, discounted cash flow methods
11-6 Net present value is the present value of
cash inflows less the present value of the cash
11-7 One assumption is that all cash flows
11-8 No. The cost of capital is not simply the
interest paid on long-term debt. The cost of
value method, the cost of capital is used as the
discount rate. If the net present value of the
compared to a project’s internal rate of return. If
the project’s internal rate of return is greater
11-10 No. As the discount rate increases, the
decreases. For example, the present value factor
for a discount rate of 12% for cash to be
to be received in ten years is $10,000, the
present value in the first case is $3,220, but only
11-11 The internal rate of return is more than
would be less than 14% if the net present value
11-12 The project profitability index is
computed by dividing the net present value of
the cash flows from an investment project by
11-13 The payback period is the length of time
for an investment to fully recover its initial cost
investment proposals. The payback method is
useful when a company has cash flow problems.
The payback method is also used in industries
method ignores all cash flows that occur after
the initial investment has been recovered.
The Foundational 15
1. The depreciation expense of $535,000 is the only non-cash expense.
2. The annual net cash inflows are computed as follows:
Net operating income …………………………..
$ 465,000
Add: Noncash deduction for depreciation ….
535,000
Annual net cash inflow ………………………….
$1,000,000
3. The present value of the annual net cash inflows is computed as
follows:
Item
Year(s)
Cash Flow
14%
Factor
Present
Value of
Cash Flows
Annual net cash
inflows ………………
1-5
$1,000,000
3.433
$3,433,000
4. The present value of the equipment’s salvage value is computed as
follows:
Item
Year(s)
Cash Flow
14%
Factor
Present
Value of
Cash Flows
Salvage value of
the equipment …….
5
$300,000
0.519
$155,700
5. The project’s net present value is computed as follows:
Item
Year(s)
Amount of
Cash Flows
14%
Factor
Present Value
of Cash Flows
Cost of the equipment ……………
Now
$(2,975,000)
1.000
$(2,975,000)
Annual net cash inflows ………….
1-5
$1,000,000
3.433
3,433,000
Salvage value of the
equipment …………………………
5
$300,000
0.519
155,700
Net present value ………………….
$ 613,700
The Foundational 15 (continued)
6. The project profitability index for the project is:
Item
Net Present
Value
(a)
Investment
Required
(b)
Project
Profitability
Index
(a) ÷ (b)
Project
$613,700
$2,975,000
0.21*
* The answer of 0.2063 was rounded to 0.21.
7. The payback period is determined as follows:
Year
Investment
Cash
Inflow
Unrecovered
Investment
1
$2,975,000
$1,000,000
$1,975,000
2
$1,000,000
$975,000
3
$1,000,000
$0
4
$1,000,000
$0
5
$1,300,000
$0
The investment in the project is fully recovered in the 3rd year. To be
more exact, the payback period is approximately 2.98 years.
8. The simple rate of return is computed as follows:
Annual incremental net operating income
Simple rate =
of return Initial investment
$465,000
= = 15.63%
$2,975,000
The Foundational 15 (continued)
9. If the discount rate was 16% instead of 14% the project’s net present
10. The payback period would be the same because the initial investment
11. The net present value would be higher because a higher salvage value
value.
12. The first step in computing the simple rate of return is to realize that if
the salvage value increases by $200,000, then the annual depreciation
expense will decrease by $40,000 ($200,000 ÷ 5 year useful life). The
$505,000
= = 16.97%
$2,975,000
The Foundational 15 (continued)
13. The new contribution margin would be $2,735,000 × 55% =
$1,504,250. The new net operating income would be $1,504,250 –
$1,270,000 = $234,250. The remaining calculations are as follows:
Net operating income …………………………..
$234,250
Add: Noncash deduction for depreciation ….
535,000
Annual net cash inflow ………………………….
$769,250
Item
Year(s)
Amount of
Cash Flows
14%
Factor
Present Value
of Cash Flows
Cost of the equipment ……………
Now
$(2,975,000)
1.000
$(2,975,000)
Annual net cash inflows ………….
1-5
$769,250
3.433
2,640,835
Salvage value of the
equipment …………………………
5
$300,000
0.519
155,700
Net present value ………………….
$ (178,465)
14. The payback period is computed as follows:
Year
Investment
Cash
Inflow
Unrecovered
Investment
1
$2,975,000
$769,250
$2,205,750
2
$769,250
$1,436,500
3
$769,250
$667,250
4
$769,250
$0
5
$1,069,250
$0
The investment in the project is fully recovered in the 4th year. To be
more exact, the payback period is approximately 3.87 years.
15. The simple rate of return is computed as follows:
Annual incremental net operating income
Simple rate =
of return Initial investment
$234,250
= = 7.87%
$2,975,000
Exercise 11-1 (10 minutes)
1. The payback period is determined as follows:
Year
Investment
Cash Inflow
Unrecovered
Investment
1
$15,000
$1,000
$14,000
2
$8,000
$2,000
$20,000
3
$2,500
$17,500
4
$4,000
$13,500
5
$5,000
$8,500
6
$6,000
$2,500
7
$5,000
$0
8
$4,000
$0
9
$3,000
$0
10
$2,000
$0
The investment in the project is fully recovered in the 7th year. To be
more exact, the payback period is approximately 6.5 years.
2. Because the investment is recovered prior to the last year, the amount
Exercise 11-2 (10 minutes)
1.
Now
1
2
3
4
5
Purchase of machine ………………….
$(27,000)
Reduced operating costs …………….
________
$7,000
$7,000
$7,000
$7,000
$7,000
Total cash flows (a) …………………..
$(27,000)
$7,000
$7,000
$7,000
$7,000
$7,000
Discount factor (12%) (b) …………..
1.000
0.893
0.797
0.712
0.636
0.567
Present value (a)×(b) ………………..
$(27,000)
$6,251
$5,579
$4,984
$4,452
$3,969
Net present value ……………………..
$(1,765)
Note: The annual reduction in operating costs can also be converted to its present value using the
discount factor of 3.605 as shown in Exhibit 11B-2 in Appendix 11B.
2.
Item
Cash
Flow
Years
Total
Cash
Flows
Annual cost savings ..
$7,000
5
$ 35,000
Initial investment …..
$(27,000)
1
(27,000)
Net cash flow ………..
$ 8,000
Exercise 11-3 (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
Exercise 11-4 (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 11–5 (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 11-6 (15 minutes)
1. Computation of the annual cash inflow associated with the new
electronic games:
Net operating income ……………………………………
$40,000
Add noncash deduction for depreciation …………….
35,000
Annual net cash inflow …………………………………..
$75,000
The payback computation would be:
Investment required
Payback period = Annual net cash inflow
$300,000
= = 4.0 years
$75,000 per year
Yes, the games would be purchased. The payback period is less than
the maximum 5 years required by the company.
2. The simple rate of return would be:
Annual incremental net income
Simple rate =
of return Initial investment
Exercise 11-7 (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
raise.
Exercise 11–8 (10 minutes)
Now
1
2
3
Purchase of stock…………………………
$(13,000)
Annual cash dividend ……………………
$420
$420
$ 420
Sale of stock …………………………..…..
_______
____
____
16,000
Total cash flows (a) ……………………..
$(13,000)
$420
$420
$16,420
Discount factor (14%) (b) ……………..
1.000
0.877
0.769
0.675
Present value (a)×(b) …………………..
$(13,000)
$368
$323
$11,084
Net present value ………………………..
$(1,225)
No, Kathy did not earn a 14% return on the Malti Company stock. The negative net present value
indicates that the rate of return on the investment is less than the minimum required rate of return of
14%.
Problem 11-9 (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
Problem 11-9 (continued)
3. Oxford Company’s opportunities for reinvesting funds as they are
released from a project will determine which ranking is best. The
internal rate of return method assumes that any released funds are
reinvested at the rate of return shown for a project. This means that
funds released from project D would have to be reinvested in another
Exercise 11-10 (15 minutes)
1. The payback period is:
Investment required
Payback period = Annual net cash inflow
$432,000
= = 4.8 years
$90,000
No, the equipment would not be purchased because the payback period
(4.8 years) exceeds the company’s maximum payback time (4.0 years).
2. The simple rate of return would be computed as follows:
Annual cost savings ………………………………………..
$90,000
Less annual depreciation ($432,000 ÷ 12 years) ……
36,000
Annual incremental net operating income ……………
$54,000
Annual incremental net operating income
Simple rate of return = Initial investment
$54,000
= = 12.5%
$432,000
No, the equipment would not be purchased because its 12.5% rate of
return is less than the company’s 14% required rate of return.
Exercise 11–11 (10 minutes)
Project X:
Now
1
2
3
4
5
6
Initial investment …………..
$(35,000)
Annual cash inflows ……….
________
$12,000
$12,000
$12,000
$12,000
$12,000
$12,000
Total cash flows (a) ……….
$(35,000)
$12,000
$12,000
$12,000
$12,000
$12,000
$12,000
Discount factor (18%) (b) .
1.000
0.847
0.718
0.609
0.516
0.437
0.370
Present value (a)×(b) …….
$(35,000)
$10,164
$8,616
$7,308
$6,192
$5,244
$4,440
Net present value ………….
$6,964
Initial investment …………..
$(35,000)
Single cash inflow ………….
_______
______
______
90,000
Total cash flows (a) ……….
$(35,000)
Discount factor (18%) (b) .
0.847
0.718
0.609
0.516
0.437
Present value (a)×(b) …….
$(35,000)
Net present value ………….
Problem 11-12A (20 minutes)
Now
1
2
3
4
Purchase of equipment ……….
$(275,000)
Working capital investment …
(100,000)
Annual net cash receipts …….
$120,000
$120,000
$120,000
$120,000
Road construction ……………..
(40,000)
Working capital released …….
100,000
Salvage value of equipment …
__________
________
_______
_______
65,000
Total cash flows (a) …………..
$(375,000)
$120,000
$120,000
$80,000
$285,000
Discount factor (20%) (b) …..
1.000
0.833
0.694
0.579
0.482
Present value (a)×(b) ………..
$(375,000)
$99,960
$83,280
$46,320
$137,370
Net present value ……………..
$(8,070)
Problem 11-13A (20 minutes)
1. The net present value is computed as follows:
Now
1
2
3
4
5
Purchase of
equipment …………….
$(3,500,000)
Sales ……………………
$3,400,000
$3,400,000
$3,400,000
$3,400,000
$3,400,000
Variable expenses …..
(1,600,000)
(1,600,000)
(1,600,000)
(1,600,000)
(1,600,000)
Out-of-pocket costs …
__________
(700,000)
(700,000)
(700,000)
(700,000)
(700,000)
Total cash flows (a) ..
$(3,500,000)
$1,100,000
$1,100,000
$1,100,000
$1,100,000
$1,100,000
Discount factor (b) ….
1.000
0.862
0.743
0.641
0.552
0.476
Present value
(a)×(b) ………………..
$(3,500,000)
$948,200
$817,300
$705,100
$607,200
$523,600
Net present value …..
$101,400