Chapter 13
Capital Budgeting Decisions
Solutions to Questions
13-1 A capital budgeting screening decision is
two or more alternative investment projects,
because a dollar received today can be invested
the present value of a future cash flow.
13-5 Unlike other common capital budgeting
methods, discounted cash flow methods
cash inflows less the present value of the cash
13-7 One assumption is that all cash flows
occur at the end of a period. Another is that all
13-8 No. The cost of capital is not simply the
13-9 The internal rate of return is the rate of
13–10 The cost of capital is a hurdle that must
discount rate. If the net present value of the
13–11 No. As the discount rate increases, the
present value of a given future cash flow
decreases. For example, the present value factor
to be received in ten years is $10,000, the
13–12 The internal rate of return is more than
© The McGraw-Hill Companies, Inc., 2015
2 Managerial Accounting, 15th Edition
13–13 The project profitability index is
computed by dividing the net present value of
the cash flows from an investment project by
for an investment to fully recover its initial cost
The payback method is also used in industries
where obsolescence is very rapid.
13–15 Neither the payback method nor the
The Foundational 15
1. The depreciation expense of $595,000 is the only non-cash expense.
2. The annual net cash inflows are computed as follows:
Net operating income …………………………..
$ 405,000
Add: Noncash deduction for depreciation ….
595,000
Annual net cash inflow ………………………….
$1,000,000
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
The Foundational 15 (continued)
3. The project’s net present value is computed as follows:
Now
1
2
3
4
5
Purchase of
equipment …………….
$(2,975,000)
Sales ……………………
$2,735,000
$2,735,000
$2,735,000
$2,735,000
$2,735,000
Variable expenses …..
(1,000,000)
(1,000,000)
(1,000,000)
(1,000,000)
(1,000,000)
Out-of-pocket costs …
__________
(735,000)
(735,000)
(735,000)
(735,000)
(735,000)
Total cash flows (a) ..
$(2,975,000)
$1,000,000
$1,000,000
$1,000,000
$1,000,000
$1,000,000
Discount factor (b) ….
1.000
0.877
0.769
0.675
0.592
0.519
Present value
(a)×(b) ………………..
$(2,975,000)
$877,000
$769,000
$675,000
$592,000
$519,000
Net present value …..
$457,000
4. In question 2, the present value of the annual net cash inflows is $3,433,000. In question 3, the
present value of the annual net cash inflows is $3,432,000. The $1,000 difference arises because
The Foundational 15 (continued)
5. The project profitability index for the project is:
Item
Net Present
Value
(a)
Investment
Required
(b)
Project
Profitability
Index
(a) ÷ (b)
Project
$457,000
$2,975,000
0.15*
* The answer of 0.1536 was rounded to 0.15.
6. The project’s internal rate of return is:
Investment required
Factor of the internal =
rate of return Annual cash inflow
$2,975,000
= = 2.975
$1,000,000
Looking in Exhibit 13B-2, and scanning along the five-year line, we can
see that the factor computed above, 2.975, is closest to 2.991, the
factor for the 20% rate of return. Therefore, to the nearest whole
percent, the internal rate of return is 20%.
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
$1,000,000
$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.
The Foundational 15 (continued)
8. The simple rate of return is computed as follows:
Annual incremental net operating income
Simple rate =
of return Initial investment
9. If the discount rate was 16%, instead of 14%, the project’s net
present value would be lower because the discount factors would be
smaller.
11. The net present value would be higher because a $300,000 salvage
12. The simple rate of return would be higher. The salvage value would
lower the annual depreciation expense by $60,000 ($300,000 ÷ 5
The Foundational 15 (continued)
13. The new annual variable expense would be $1,230,750 ($2,735,000 × 45%). The project’s actual
net present value would be computed as follows:
Now
1
2
3
4
5
Purchase of
equipment …………….
$(2,975,000)
Sales ……………………
$2,735,000
$2,735,000
$2,735,000
$2,735,000
$2,735,000
Variable expenses …..
(1,230,750)
(1,230,750)
(1,230,750)
(1,230,750)
(1,230,750)
Out-of-pocket costs …
__________
(735,000)
(735,000)
(735,000)
(735,000)
(735,000)
Total cash flows (a) ..
$(2,975,000)
$ 769,250
$ 769,250
$ 769,250
$ 769,250
$ 769,250
Discount factor (b) ….
1.000
0.877
0.769
0.675
0.592
0.519
Present value
(a)×(b) ………………..
$(2,975,000)
$674,632
$591,553
$519,244
$455,396
$399,241
Net present value …..
$(334,934)
The Foundational 15 (continued)
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
$769,250
$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
Exercise 13-1 (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
of the cash inflow in the last year has no effect on the payback period.
Exercise 13-2 (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 13B-2 in Appendix 13B.
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