Chapter 16 – Capital Expenditure Decisions
CHAPTER 16
Capital Expenditure Decisions
ANSWERS TO REVIEW QUESTIONS
16-1 “Time is money” is an apt phrase for the evaluation of capital investment projects. A
16-2 Acceptance-or-rejection decisions involve managers deciding whether they should
undertake a particular capital investment project. In such a decision, the required
16-3 This statement is false. As the discount rate increases, the present value of a future
cash flow decreases. A higher discount rate means a higher return on funds that are
16-4 In a discounted-cash-flow (DCF) analysis, all cash flows over the life of an
investment are discounted to their present value. The discounting process makes
16-5 (1) The decision rule used to accept or reject an investment proposal under the net–
(2) The decision rule used to accept or reject an investment proposal under the
16-6 The return on an investment is equal to the amount of the unrecovered investment
multiplied by rate of return. The cash flow from the investment in a particular time
Chapter 16 – Capital Expenditure Decisions
16-7 Two advantages of the net-present-value method over the internal-rate-of-return
method are as follows:
16-8 Four assumptions underlying discounted-cash-flow analysis are as follows:
(4) A discounted-cash-flow analysis assumes a perfect capital market. In a perfect
16-9 In the total-cost approach, every cash flow for each project under consideration is
16–10 In a postaudit of an investment project, information is gathered about the actual cash
Chapter 16 – Capital Expenditure Decisions
16–11 Depreciation expense is an example of a noncash expense. A noncash expense has
16–13 A depreciation tax shield is the reduction in income taxes that results from the fact
16–14 An example of a cash flow that is not on the income statement is the acquisition cost
16–15 Under an accelerated depreciation method, the depreciation expense for an asset is
higher in the earlier years and lower in the later years than it would be under the
16–16 A gain on disposal of an asset increases income. Therefore, it increases income tax
and will increase the cash outflow for income tax. In a capital-budgeting analysis, the
16–17 The net-present-value method and the internal-rate-of-return method may yield
different rankings for investments with different lives because they make different
16–18 The profitability index (PI) is defined as the present value of cash flows, exclusive of
16–19 A project’s payback period is the number of years required for the cash inflows from
the project to accumulate to an amount equal to the initial acquisition cost for the
16–20 The payback method of evaluating investment proposals fails to consider the time
16–21 There are two ways to define an investment project’s accounting rate of return:
• Accounting rate of return = (average incremental revenue – average incremental
16–22 The chief drawback of the accounting-rate-of-return method as an investment
criterion is that it fails to account for the time value of money. Revenues and
16–23 There are two correct methods of net-present-value analysis in an inflationary
period. (1) The analyst can use real cash flows and discount them at a real discount
Chapter 16 – Capital Expenditure Decisions
SOLUTIONS TO EXERCISES
EXERCISE 16-24 (15 MINUTES)
Acquisition cost of site (time 0) ………………………………………………………………………
$(234,000
)
Preparatory work (time 0) ……………………………………………………………………………….
)
Total cost at time 0 ………………………………………………………………………………………..
$(322,080
)
EXERCISE 16-25 (15 MINUTES)
Acquisition cost of site (time 0) ………………………………………………………………………
$234,000
Preparatory work (time 0) ……………………………………………………………………………….
Find 6.710 in the 10-year row of Table IV in Appendix A. This annuity discount factor falls in
Chapter 16 – Capital Expenditure Decisions
EXERCISE 16-26 (45 MINUTES)
Year
1
2
3
4
5
6
7
8
9
10
(2) Cost savings during year
48,000
48,000
48,000
48,000
48,000
48,000
48,000
48,000
48,000
48,000
25,766
23,988
22,067
19,992
17,751
15,332
12,718
(3) Return on unrecovered
row (3) amount]
22,234
24,012
25,933
28,008
30,249
32,668
35,282
38,104
41,153
44,445
85,590
44,437
(5) Unrecovered investment
at end of year [row (1)
EXERCISE 16-27 (20 MINUTES)
Table III includes three discount rates between 8 and 16 percent. We could begin with 10,
12, or 14 percent. For completeness, the following solution computes the net present value
of the overhaul using all three discount rates.
Present Value at
Year
Repair Costs
Avoided by
Overhaul
10%
12%
14%
1
3,000 euros
3,000 euros .893
2,679 euros
2
5,000 euros
5,000 euros .826
b
4,130 euros
aTable III in Appendix A: r = 10%, n = 1.
EXERCISE 16-28 (30 MINUTES)
Answers will vary widely, depending on the project selected.
EXERCISE 16-29 (15 MINUTES)
1. Net present value calculations:
Discount
Rate
Annuity
Discount
Factor*
Annual
Savings
Present Value
of
Annual
Savings
Acquisition
Cost
Net
Present
Value†
8%
5.747
$27,000
$155,169
$129,750
$25,419
10%
5.335
27,000
144,045
129,750
14,295
12%
4.968
14%
4.639
(4,497
)
Notice that the net present value in the right-hand column declines as the discount rate
increases. A higher discount rate means greater urgency associated with having each cash
flow earlier rather than later.
EXERCISE 16-30 (15 MINUTES)
The annuity discount factor in Table IV of the Appendix (for r = 12% and n = 8) is 4.968. The
theater’s board of directors will be indifferent about replacing the lighting system if its net
present value is zero.
Net present value
=
−
cost
nacquisitio
savings
annual
factor discount
annuity
Therefore, the annual savings associated with the new lighting system could be as low as
$26,117.15 before the board would reject the proposal.
Chapter 16 – Capital Expenditure Decisions
EXERCISE 16-30 (CONTINUED)
Check (not required):
EXERCISE 16-31 (5 MINUTES)
(a) Acquisition cost = $36,000
EXERCISE 16-32 (10 MINUTES)
EXERCISE 16-33 (30 MINUTES)
(1)
Year
(2)
MACRS
Accelerated
Depreciation
(3)
Cash Flow:
Tax Savings
[Col. (2) .30]
(4)
Present Value
of Cash Flow
[Col. (3) Col. (8)]
(5)
MACRS
Straight-Line
Depreciation*
(6)
Cash Flow:
Tax Savings
[Col. (5) .30]
(7)
Present Value
of Cash Flow
[Col. (6) Col. (8)]
(8)
Discount
Factor
(r = .12)†
1
$36,663 (33.33% $110,000)
$10,999
$ 9,822
**
$18,333**
$ 5,500**
$ 4,912
.893
2
**
.797
3
**
.712
4
**
.636
EXERCISE 16-34 (15 MINUTES)
2. Loss on sale = book value – sales proceeds
3.
Reduced cash outflow for taxes ($1,900 .45) ………………………………………
$ 855
EXERCISE 16-35 (15 MINUTES)
Discount Rate
8%
10%
12%
Present value of after-tax savings:
$4,800 6.710*
$32,208
$4,800 5.650*
$27,120
Chapter 16 – Capital Expenditure Decisions
EXERCISE 16-36 (20 MINUTES)
1. Payback period =
flow cash tax–after annual
investment initial
2. Net-present-value analysis:
Discount Rate
10%
12%
14%
Present value of after-tax savings:
$27,000 4.868* ……………………………………….
$131,436
$123,228
$27,000 4.288* ……………………………………….
$115,776
Initial investment …………………………………………
)
)
)
3. Conclusion: The automatic teller machines are a sound economic investment if the
after-tax hurdle rate is 10 percent, but not if it is 12 percent or 14 percent. The pay-
Chapter 16 – Capital Expenditure Decisions
EXERCISE 16-37 (25 MINUTES)
1. The project’s payback period is 2.25 years, calculated as follows:
Year
After-Tax
Cash Flows
1 …………………………………………………………………………………..
$ 50,000
2 …………………………………………………………………………………..
45,000
3 (1st quarter) ………………………………………………………………..
Total …………………………………………………………………………….
$105,000
Initial cost …………………………………………………………………….
$105,000
2. The accounting rate of return is 18.1%, calculated as follows:
Accounting rate of return
=
investment initial
income net average
3. Net present value calculations:
Year
After-Tax
Cash Flow
Discount
Factor*
Present
Value
0
$(105,000)
1.000
$(105,000)
1
50,000
.862
43,100
2
45,000
.743
33,435
3
40,000
.641
25,640
4
35,000
.552
19,320
5
30,000
.476
14,280
EXERCISE 16-38 (20 MINUTES)
1.
Year
Cash Flow
in Real
Dollars
Discount Factor*
(real interest rate = .20)
Present
Value
0
$(150,000)
1.000
$(150,000)
1
45,000
.833
37,485
2
.694
3
.579
4
.482
5
.402
6
.335
7
.279
12,555
8
.233
2. Net present value = $22,665 (See preceding table.)
EXERCISE 16-39 (35 MINUTES)
1.
Nominal interest rate:
Real interest rate ………………………………………………………………….
.20
Inflation rate …………………………………………………………………………
.10
Nominal interest rate …………………………………………………………….
.32
2.
(1)
Year
(2)
Cash Flow
in
Real
Dollars*
(3)
Price
Index
(4)
Cash Flow in
Nominal
Dollars
[Col. (2) Col. (3)]
(5)
Discount
Factor
(nominal interest
rate = .32)†
(6)
Present
Value
[Col. (4)
Col. (5)]
0
$(150,000)
1.0000
$(150,000)
1.000
$(150,000
)
1
45,000
(1.10)1 = 1.1000
49,500
.758
37,521
2
(1.10)2 = 1.2100
54,450
.574
31,254
3
45,000
(1.10)3 = 1.3310
59,895
.435
26,054
4
45,000
(1.10)4 = 1.4641
65,885
.329
21,676
5
(1.10)5 = 1.6105
72,473
.250
18,118
6
45,000
(1.10)6 = 1.7716
79,722
.189
15,067
7
45,000
(1.10)7 = 1.9487
.143
12,540
8
45,000
(1.10)8 = 2.1436
96,462
.108
3. Net present value = $22,648. See the preceding table. The $17 difference between the
Chapter 16 – Capital Expenditure Decisions
SOLUTIONS TO PROBLEMS
PROBLEM 16-40 (30 MINUTES)
1. Yes. This is a long-term decision, with cash flows that occur over a five-year period.
Given that the cash flows have a “value” dependent on when they take place (e.g.,
2. Community Challenges is better off to manufacture the igniters.
Outsource:
$(24,800,000)
Annuity discount factor (Table IV*: r = .14, n = 5)……
x 3.433
$(85,138,400)
Manufacture in-house:
Annual variable manufacturing costs (400,000 units
x $60)…………………………………………………….
$(24,000,000)
(95,000)
$(24,095,000)
x 3.433
$(82,718,135)
(60,000)
Equipment sale: $12,000 x .519 (Table III: r = .14,
6,228
$(82,779,944)
3. The company would be financially indifferent if the net present value (NPV) of the
manufacture alternative equals the NPV of the outsource alternative. Thus:
Let X = purchase price
Chapter 16 – Capital Expenditure Decisions
PROBLEM 16-41 (60 MINUTES)
Time 0
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
Contract with Diagnostic
Testing Services
Flat fee
$ (80,000)
$ (80,000)
$ (80,000)
$ (80,000)
$ (80,000)
$ (80,000)
$ (80,000)
$ (80,000)
$ (80,000)
$ (80,000)
Total cash flow
Present value
Establish In-House
Testing Lab
Rental of storage space
$ (30,000)
$ (30,000)
$ (30,000)
$ (30,000)
$ (30,000)
$ (30,000)
$ (30,000)
$ (30,000)
$ (30,000)
$ (30,000)
Equipment
Staff
Fixed operating costs
Total cash flow
Present value
PROBLEM 16-42 (45 MINUTES)
The only cash flows listed in the problem that are not annual cash flows are the purchases
of equipment for the proposed lab at time 0 (now) and at the end of year 4. Therefore, the
most efficient way to apply the incremental cost approach is to calculate the incremental
annual cash flows with the proposed lab, and then use the annuity discount factor to
compute the present value.
Incremental annual cash flows associated with proposed diagnostic testing lab:
Rental of storage space …………………………..………………………………….
$ (30,000
)
Staff compensation ……………………………………………………………………..
(200,000
)
Fixed operating costs ………………………………………………………………….
(50,000
)
(250,000
)
100,000
Subtotal ……………………………………………………………………………………..
$(430,000
)
Flat fee ……………………………………………………………………….
400,000
Subtotal ……………………………………………………………………………………..
Add: Contribution margin on cases
currently referred elsewhere ……………………………………………..
100,000
Incremental annual cash flow with proposed lab …………………………..
$ 150,000
Annuity discount factor (Table IV in Appendix A: r = .12, n = 10) ……
5.650
Present value of incremental annual cash flows …………………………...
$ 847,500
Deduct: Present value of equipment purchases:
Net present value of incremental cash flows
*
A tabular presentation of the incremental cost approach, along the lines of Exhibit
16-5, would be more cumbersome than necessary given the equivalent annual cash flows
(excluding the equipment purchases).
PROBLEM 16-43 (50 MINUTES)
1. See the following table.
2. See the following table.
3. See the following table.
Chapter 16 – Capital Expenditure Decisions
PROBLEM 16-43 (CONTINUED)
Type of Cash Flow
20×0
20×1
20×2
20×3
20×4
20×5
20×6
20×7
20×8
20×9
(1) Construction of clinic
$(390,000)
$(390,000)
(2) Equipment purchase
(3) Staffing
$(800,000)
$(800,000)
$(800,000)
$(800,000)
$(800,000)
$(800,000)
$(800,000)
$(800,000)
(4) Other operating costs
250,000
250,000
250,000
250,000
250,000
250,000
250,000
250,000
(6) Cost savings at hospital
(7) Cost of refurbishment
(5) Increased charitable
(9) Salvage value
290,000
$(390,000)
$(540,000)
$ 70,000
1.000
.893
.797
.712
.636
.567
.507
.452
.404
.361
$(390,000)
$(482,220)