CHAPTER 6
MAKING CAPITAL INVESTMENT
DECISIONS
Answers to Concepts Review and Critical Thinking Questions
1. In this context, an opportunity cost refers to the value of an asset or other input that will be used in a
2. a. Yes, the reduction in the sales of the company’s other products, referred to as erosion, should be
treated as an incremental cash flow. These lost sales are included because they are a cost (a
revenue reduction) that the firm must bear if it chooses to produce the new product.
b. Yes, expenditures on plant and equipment should be treated as incremental cash flows. These are
costs of the new product line. However, if these expenditures have already occurred (and cannot
be recaptured through a sale of the plant and equipment), they are sunk costs and are not included
as incremental cash flows.
c. No, the research and development costs should not be treated as incremental cash flows. The
costs of research and development undertaken on the product during the past three years are sunk
costs and should not be included in the evaluation of the project. Decisions made and costs
incurred in the past cannot be changed. They should not affect the decision to accept or reject the
project.
3. Item (a) is a relevant cost because the opportunity to sell the land is lost if the new golf club is
produced. Item (b) is also relevant because the firm must take into account the erosion of sales of
4. For tax purposes, a firm would choose MACRS because it provides for larger depreciation deductions
5. It’s probably only a mild over-simplification. Current liabilities will all be paid, presumably. The cash
portion of current assets will be retrieved. Some receivables won’t be collected, and some inventory
6. Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since any
7. The EAC approach is appropriate when comparing mutually exclusive projects with different lives
that will be replaced when they wear out. This type of analysis is necessary so that the projects have a
common life span over which they can be compared. For example, if one project has a three-year life
8. Depreciation is a non-cash expense, but it is tax-deductible on the income statement. Thus depreciation
causes taxes paid, an actual cash outflow, to be reduced by an amount equal to the depreciation tax
9. There are two particularly important considerations. The first is erosion. Will the “essentialized” book
displace copies of the existing book that would have otherwise been sold? This is of special concern
given the lower price. The second consideration is competition. Will other publishers step in and
produce such a product? If so, then any erosion is much less relevant. A particular concern to book
10. Definitely. The damage to Porsche’s reputation is a factor the company needed to consider. If the
reputation were to be damaged, the company would have lost sales of its existing car lines.
12. Porsche would recognize that the outsized profits would dwindle as more products come to market
and competition becomes more intense.
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
1. Using the tax shield approach to calculating OCF, we get:
OCF = (Sales – Costs)(1 – TC) + TCDepreciation
2. We will use the bottom-up approach to calculate the operating cash flow for each year. We also must
be sure to include the net working capital cash flows each year. So, the net income and total cash flow
each year will be:
Sales
Costs
Depreciation
EBT
Tax
Net income
$9,637
$10,729
$10,963
$9,325
Capital spending
–$26,300
NWC
–300
–200
–225
–150
875
Incremental cash flow
–$26,600
$9,437
$10,504
$10,813
$10,200
3. Using the tax shield approach to calculating OCF, we get:
OCF = (Sales – Costs)(1 – TC) + TCDepreciation
4. The cash outflow at the beginning of the project will increase because of the spending on NWC. At
the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the
equipment will result in a cash inflow, but we also must account for the taxes which will be paid on
5. First, we will calculate the annual depreciation for the equipment necessary for the project. The
depreciation amount each year will be:
Year 1 depreciation = $1,420,000(.3333) = $473,286
Year 2 depreciation = $1,420,000(.4445) = $631,190
Year 3 depreciation = $1,420,000(.1481) = $210,302
6. The book value of the asset is zero, so the gain on the sale is taxable.
Aftertax salvage value = $230,000 + ($0 – 230,000)(.25)
Aftertax salvage value = $172,500
To calculate the OCF, we will use the tax shield approach, so the cash flow each year is:
7. First, we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation charge = $575,000/5
Annual depreciation charge = $115,000
The aftertax salvage value of the equipment is:
IRR = 17.70%
8. First, we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation = $375,000/5
Annual depreciation = $75,000
Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or
plus) the taxes on the sale of the equipment, so:
9. The book value of the asset will be zero at the end of the project, so the aftertax salvage value is:
Aftertax salvage value = $25,000(1 – .24)
Aftertax salvage value = $19,000
Using the tax shield approach, we find the OCF for the first year of the project is:
10. To find the book value at the end of four years, we need to find the accumulated depreciation for the
first four years. We could calculate a table with the depreciation each year, but an easier way is to add
the MACRS depreciation amounts for each of the first four years and multiply this percentage times
11. We will begin by calculating the initial cash outlay, that is, the cash flow at Time 0. To undertake the
project, we will have to purchase the equipment and increase net working capital. So, the cash outlay
today for the project will be:
Using the bottom-up approach to calculating the operating cash flow, we find the operating cash flow
each year will be:
12. We will need the aftertax salvage value of the equipment to compute the EAC. Even though the
equipment for each product has a different initial cost, both have the same salvage value. The aftertax
salvage value for both is:
Aftertax salvage value = $25,000(1 – .21)
Aftertax salvage value = $19,750
13. First, we will calculate the depreciation each year, which will be:
D1 = $670,000(.2000) = $134,000
D2 = $670,000(.3200) = $214,400
D3 = $670,000(.1920) = $128,640
D4 = $670,000(.1152) = $77,184
The book value of the equipment at the end of the project is:
BV4 = $670,000 – ($134,000 + 214,400 + 128,640 + 77,184)
BV4 = $115,776
The asset is sold at a loss to book value, so this creates a tax refund. The aftertax salvage value will
be:
14. The book value of the asset is zero, so the aftertax salvage value will be:
Aftertax salvage value = $55,000 + ($0 – 55,000)(.23)
Aftertax salvage value = $42,350
So, the OCF for each year will be:
OCF1 = $245,000(1 – .23) + .23($670,000) = $342,750
OCF2 = $245,000(1 – .23) = $188,650
OCF3 = $245,000(1 – .23) = $188,650
OCF4 = $245,000(1 – .23) = $188,650
Now we have all the necessary information to calculate the project NPV. We need to be careful with
the NWC in this project. Notice the project requires $20,000 of NWC at the beginning, and $2,500
more in NWC each successive year. We will subtract the $20,000 from the initial cash flow and
subtract $2,500 each year from the OCF to account for this spending. In Year 4, we will add back the
total spent on NWC, which is $27,500. The $2,500 spent on NWC capital during Year 4 is irrelevant.
Why? Well, during this year the project required an additional $2,500, but we would get the money
15. If we are trying to decide between two projects that will not be replaced when they wear out, the proper
capital budgeting method to use is NPV. Both projects only have costs associated with them, not sales,
so we will use these to calculate the NPV of each project. Using the tax shield approach to calculate
the OCF, the NPV of System A is:
OCFA = –$73,000(1 – .23) + .23($265,000/4)
OCFA = –$40,973
16. If the equipment will be replaced at the end of its useful life, the correct capital budgeting technique
is EAC. Using the NPVs we calculated in the previous problem, the EAC for each system is:
EACA = –$402,230.27/(PVIFA7.5%,4)
EACA = –$120,092.89
17. The aftertax salvage value is:
Aftertax salvage value = $45,000(1 – .22)
Aftertax salvage value = $35,100
Tax
–64,515
28,985
Net income
–$228,735
$102,765
+ Depreciation
18. Since we need to calculate the EAC for each machine, sales are irrelevant. EAC only uses the costs of
operating the equipment, not the sales. Using the bottom up approach, or net income plus depreciation,
method to calculate OCF, we get:
Machine A
Machine B
Variable costs
–$4,340,000
–$3,720,000
Fixed costs
Depreciation
EBT
–$4,857,000
–$4,465,000
Tax
Net income
+ Depreciation
Sales
$275,000
Variable costs
96,250
Fixed costs
47,000
Depreciation
EBIT
19. When we are dealing with nominal cash flows, we must be careful to discount cash flows at the
nominal interest rate, and we must discount real cash flows using the real interest rate. Project A’s
cash flows are in real terms, so we need to find the real interest rate. Using the Fisher equation, the
real interest rate is:
1 + R = (1 + r)(1 + h)
1.11 = (1 + r)(1 + .04)
20. To determine the value of a firm, we can find the present value of the firm’s future cash flows. No
depreciation is given, so we can assume depreciation is zero. Using the tax shield approach, we can
find the present value of the aftertax revenues, and the present value of the aftertax costs. The required
return, growth rates, price, and costs are all given in real terms. Subtracting the costs from the revenues
will give us the value of the firm’s cash flows. We must calculate the present value of each separately
21. To calculate the nominal cash flows, we increase each item in the income statement by the inflation
rate, except for depreciation. Depreciation is a nominal cash flow, so it does not need to be adjusted
for inflation in nominal cash flow analysis. Since the resale value is given in nominal terms as of the
end of Year 5, it does not need to be adjusted for inflation. Also, no inflation adjustment is needed for
net working capital since it is already expressed in nominal terms. Note that an increase in required
net working capital is a negative cash flow whereas a decrease in required net working capital is a
positive cash flow. We first need to calculate the taxes on the salvage value. Remember, to calculate
the taxes paid (or tax credit) on the salvage value, we take the book value minus the market value,
times the tax rate, which, in this case, would be:
Now we can find the nominal cash flows each year using the income statement. Doing so, we find:
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Sales
$275,000
$283,250
$291,748
$300,500
$309,515
22. The present value of the company is the present value of the future cash flows generated by the
company. Here we have real cash flows, a real interest rate, and a real growth rate. The cash flows are
a growing perpetuity, with a negative growth rate. Using the growing perpetuity equation, the present
value of the cash flows is:
23. To find the EAC, we first need to calculate the PV of costs of the incremental cash flows. We will
begin with the aftertax salvage value, which is:
Taxes on salvage value = (BV – MV)TC
Taxes on salvage value = ($0 – 7,500)(.23)
Taxes on salvage value = –$1,725
Market price
Tax on sale
Aftertax salvage value
EBT
$101,000
$106,640
$112,449
$118,433
$124,596
Tax
Capital spending
NWC
24. We will calculate the aftertax salvage value first. The aftertax salvage value of the equipment will be:
Taxes on salvage value = (BV – MV)TC
Taxes on salvage value = ($0 – 30,000)(.22)
Taxes on salvage value = –$6,600
Market price
$30,000
25. Replacement decision analysis is the same as the analysis of two competing projects, in this case, keep
the current equipment, or purchase the new equipment. We will consider the purchase of the new
machine first.
Purchase new machine:
The initial cash outlay for the new machine is the cost of the new machine, plus the increased net
working capital. So, the initial cash outlay will be:
Purchase new machine
–$15,600,000
Net working capital
Total
–$15,850,000
Operating expense
Depreciation
Net income
Now we can calculate the decision to keep the old machine:
Keep old machine:
The initial cash outlay for the old machine is the market value of the old machine, including any
potential tax consequence. The decision to keep the old machine has an opportunity cost, namely, the
company could sell the old machine. Also, if the company sells the old machine at its current value, it
will receive a tax benefit. Both of these cash flows need to be included in the analysis. So, the initial
cash flow of keeping the old machine will be:
Next, we can calculate the operating cash flow created if the company keeps the old machine. There
are no incremental cash flows from keeping the old machine, but we need to account for the cash flow
effects of depreciation. The income statement, adding depreciation to net income to calculate the
operating cash flow, will be:
Depreciation
$1,350,000
EBT
–$1,350,000
So, the NPV of the decision to keep the old machine will be:
Taxes
Total
–$4,373,000
There is another way to analyze a replacement decision that is often used. It is an incremental cash
flow analysis of the change in cash flows from the existing machine to the new machine, assuming the
new machine is purchased. In this type of analysis, the initial cash outlay would be the cost of the new
machine, the increased NWC, and the cash inflow (including any applicable taxes) of selling the old
machine. In this case, the initial cash flow under this method would be:
Purchase new machine
–$15,600,000
Net working capital
–250,000
The cash flows from purchasing the new machine would be the saved operating expenses. We would
also need to include the change in depreciation. The old machine has a depreciation of $1.35 million
per year, and the new machine has depreciation of $3.9 million per year, so the increased depreciation
will be $2.55 million per year. The pro forma income statement and operating cash flow under this
approach will be:
Operating expense savings
$6,300,000
Depreciation
EBT
Taxes
787,500
Net income
$2,962,500
The NPV under this method is:
NPV = –$11,477,000 + $5,512,500(PVIFA10%,4) + $250,000/1.104
NPV = $6,167,636.64
And the IRR is:
Sell old machine
Taxes on old machine
Total
–$11,477,000
26. We can find the NPV of a project using nominal cash flows or real cash flows. Either method will
result in the same NPV. For this problem, we will calculate the NPV using both nominal and real cash
flows. The initial investment in either case is $650,000 since it will be spent today. We will begin with
the nominal cash flows. The revenues and production costs increase at different rates, so we must be
careful to increase each at the appropriate growth rate. The nominal cash flows for each year will be:
Year 0
Year 1
Year 2
Year 3
Revenues
$565,000.00
$593,250.00
$622,912.50
Costs
$345,000.00
358,800.00
373,152.00
Capital spending
–$650,000
Total cash flow
–$650,000
$189,485.71
$200,467.71
$212,103.69
Year 4
Year 5
Year 6
Year 7
Revenues
$654,058.13
$686,761.03
$721,099.08
$757,154.04
Costs
388,078.08
403,601.20
419,745.25
436,535.06
Depreciation
EBT
$173,122.90
$190,302.69
$208,496.69
$227,761.83
Taxes
Net income
Capital spending
Total cash flow
Depreciation
EBT
Taxes
Net income
$189,485.71
$200,467.71
$212,103.69
So, the NPV of the project using nominal cash flows is:
We can also find the NPV using real cash flows. Since the revenues and costs are given in nominal
terms, we must find the real value for each by discounting at the inflation rate. So:
Real revenues = $565,000/(1 + .05)
Real revenues = $538,095.24
In real terms, the cost will actually decrease by .95 percent per year. So, the real cash flows will be:
Year 0
Year 1
Year 2
Year 3
Revenues
$538,095.24
$538,095.24
$538,095.24
Costs
$328,571.43
325,442.18
322,342.73
Depreciation
88,435.37
84,224.17
80,213.49
EBT
$121,088.44
$128,428.90
$135,539.02
Taxes
Net income
$92,027.21
$97,605.96
$103,009.65
$180,462.59
$181,830.13
$183,223.15
Capital spending
Total cash flow
$180,462.59
$181,830.13
$183,223.15