Chapter 13
Capital Budgeting Decisions
Solutions to Questions
13-1 A capital budgeting screening decision is
concerned with whether a proposed investment
13-2 The “time value of money” refers to the
fact that a dollar received today is more valuable
than a dollar received in the future simply
because a dollar received today can be invested
to yield more than a dollar in the future.
13-3 Discounting is the process of computing
the present value of a future cash flow.
13-4 Accounting net income is based on
13-5 Unlike other common capital budgeting
methods, discounted cash flow methods
recognize the time value of money and take into
account all future cash flows.
13-6 Net present value is the present value of
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
cash inflows are immediately reinvested at a
rate of return equal to the discount rate.
13-8 No. The cost of capital is not simply the
interest paid on long-term debt. The cost of
results in a zero net present value for the
project.
13–10 The cost of capital is a hurdle that must
be cleared before an investment project will be
accepted. In the case of the net present value
method, the cost of capital is used as the
discount rate. If the net present value of the
project’s internal rate of return is greater than
13–11 No. As the discount rate increases, the
present value of a given future cash flow
decreases. For example, the present value factor
for a discount rate of 12% for cash to be
received ten years from now is 0.322, whereas
the present value factor for a discount rate of
14% over the same period is 0.270. If the cash
to be received in ten years is $10,000, the
13–12 The internal rate of return is more than
14% because the net present value is positive.
The internal rate of return would be 14% only if
the net present value (evaluated using a 14%
13–13 The project profitability index is
computed by dividing the net present value of
the cash flows from an investment project by
13–14 The payback period is the length of time
for an investment to fully recover its initial cost
where obsolescence is very rapid.
13–15 Neither the payback method nor the
Exercise 13-1 (10 minutes)
1.
Item
Year(s)
Cash Flow
12%
Factor
Present
Value of
Cash
Flows
2.
Item
Exercise 13-2 (30 minutes)
1.
Annual savings over present method of delivery ……..
$5,400
2.
Investment required
Factor of the internal =
rate of return Annual cash inflow
$45,000
= = 5.000
$9,000
3. The cash flows are not even over the six-year life of the truck because
of the extra $13,000 cash inflow that occurs in the sixth year. Therefore,
the approach used above cannot be used to compute the internal rate of
return. Using trial-and-error or some other method, the internal rate of
return turns out to be about 11%:
Initial investment …..
$(45,000)
Annual cash inflows ..
Salvage value ………..
Exercise 13-3 (15 minutes)
The equipment’s net present value without considering the intangible
benefits would be:
Item
Year(s)
Amount of
Cash Flows
15%
Factor
Present Value
of Cash Flows
Cost of the equipment ..
Now
$(750,000)
1.000
$(750,000)
Annual cash savings …..
1-10
$100,000
5.019
501,900
Net present value ………
$(248,100)
Exercise 13-4 (10 minutes)
1. The project profitability index for each proposal is:
Proposal
A
0.40
D
0.30
Net Present
Investment
Project
Profitability
2. The ranking is:
Proposal
Project
Profitability
Index
C
0.50
A
0.40
D
0.30
B
0.25
Exercise 13-5 (10 minutes)
1. The payback period is determined as follows:
Year
Investment
Cash
Inflow
Unrecovered
Investment
1
$38,000
$2,000
$36,000
6
7
$8,000
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 13-6 (10 minutes)
The annual incremental net operating income is determined by comparing
the operating cost of the old machine to the operating cost of the new
machine and the depreciation that would be taken on the new machine:
Exercise 13-7 (15 minutes)
1. Computation of the annual cash inflow associated with the new ride:
Net operating income …………………………..
$63,000
Add: Noncash deduction for depreciation ….
27,000
2. The simple rate of return would be:
Annual incremental net operating income
Simple rate of return = Initial investment
Exercise 13-8 (10 minutes)
1. Note: All present value factors have been taken from Exhibit 13B-1 in
Appendix 13B, using a 16% discount rate.
Investment in the equipment ………………
$134,650
Present value of Year 3 cash inflow ………
$ 51,280
Less present value of Year 1 and
Exercise 13-9 (30 minutes)
1.
Item
Year(s)
Amount of
Cash Flows
15%
Factor
Present Value
of Cash Flows
Initial investment …..
Now
$(40,350)
1.000
$(40,350)
2.
Investment required
Factor of the internal =
rate of return Net annual cash inflow
3.
Investment required
Factor of the internal =
rate of return Net annual cash inflow
Exercise 13-10 (30 minutes)
1.
Required investment
Factor of the internal =
rate of return Annual cash inflow
2.
Item
Year(s)
Amount of
Cash Flows
16%
Factor
Present Value
of Cash Flows
Initial investment ………
Now
$(136,700)
1.000
$(136,700)
Annual net cash inflows
1-14
$25,000
5.468
136,700
Net present value ………
$ 0
3.
Required investment
Factor of the internal =
rate of return Annual cash inflow
Exercise 13-11 (10 minutes)
Item
Year(s)
Amount of
Cash Flows
16%
Factor
Present
Value of
Cash Flows
Project A:
Investment required .
Now
$(15,000)
1.000
$(15,000)
Annual cash inflows ..
1-10
$4,000
4.833
19,332
Net present value …..
$ 4,332
Investment …………..
Now
$(15,000)
1.000
$(15,000)
Cash inflow …………..
0.227
Net present value …..
Exercise 13-12 (15 minutes)
1. The payback period is:
Investment required
Payback Period = Net annual cash inflow
2. The simple rate of return would be computed as follows:
Annual cost savings ………………………………………..
$37,500
Less annual depreciation ($180,000 ÷ 12 years)……
15,000
Annual incremental net operating income ……………
$22,500
Exercise 13-13 (10 minutes)
Required investment
Factor of the internal =
rate of return Annual cash inflow
Exercise 13-14 (15 minutes)
Item
Year(s)
Amount
of Cash
Flows
20%
Factor
Present
Value of
Cash
Flows
Project A:
Cost of the equipment ……………
Now
$(300,000)
1.000
$(300,000)
Annual cash inflows ……………….
1-7
$80,000
3.605
288,400
Salvage value of the equipment .
7
$20,000
0.279
5,580
Net present value ………………….
$ (6,020)
Project B:
Working capital investment ……..
Now
$(300,000)
1.000
$(300,000)
Annual cash inflows ……………….
1-7
$60,000
3.605
216,300
Working capital released …………
Net present value ………………….
The $300,000 should be invested in Project B rather than in Project A.
Exercise 13-15 (10 minutes)
Year(s)
Amount of
Cash Flows
12%
Factor
Present Value
of Cash Flows
Purchase of the stock ….
Now
$(18,000)
1.000
$(18,000)
Annual dividends*………
1-4
$720
3.037
2,187
Sale of the stock ………..
4
$22,500
0.636
14,310
Net present value ………
$( 1,503)
Problem 13-16 (15 minutes)
Item
Year(s)
Amount
of Cash
Flows
14%
Factor
Present
Value of
Cash
Flows
Cost of equipment required ……
Now
$(850,000)
1.000
$(850,000)
Working capital required ……….
Now
$(100,000)
1.000
(100,000)
Annual net cash receipts ……….
3.433
Cost of road repairs ……………..
0.675
Net present value ………………..
Problem 13-17 (30 minutes)
1. The formula for the project profitability index is:
Net present value
Project profitability index = Investment required
2. a., b., and c.
Net Present
Value
Project
Profitability
Index
Internal Rate
of Return
First preference ……..
1
3
4
Second preference ….
2
2
3
Third preference …….
4
1
1
Fourth preference …..
3
4
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
would have to be reinvested at a rate of return of 19%, but another
project yielding such a high rate of return might be difficult to find.