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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
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
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
d. Yes, the annual depreciation expense must be taken into account when calculating the cash
flows related to a given project. While depreciation is not a cash expense that directly affects
e. No, dividend payments should not be treated as incremental cash flows. A firm’s decision to
pay or not pay dividends is independent of the decision to accept or reject any given investment
f. Yes, the resale value of plant and equipment at the end of a project’s life should be treated as an
incremental cash flow. The price at which the firm sells the equipment is a cash inflow, and any
g. Yes, salary and medical costs for production employees hired for a project should be treated as
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
existing products when a new product is introduced. If the firm produces the new club, the earnings
4. For tax purposes, a firm would choose MACRS because it provides for larger depreciation
deductions earlier. These larger deductions reduce taxes, but have no other cash consequences.
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
6. Management’s discretion to set the firm’s capital structure is applicable at the firm level. Since any
one particular project could be financed entirely with equity, another project could be financed with
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 and the other has a five-year life, then a 15-year horizon is the minimum necessary to place the
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
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
10. Definitely. The damage to Porsche’s reputation is a factor the company needed to consider. If the
11. One company may be able to produce at lower incremental cost or market better. Also, of course,
12. Porsche would recognize that the outsized profits would dwindle as more products come to market
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:
Year 1 Year 2 Year 3 Year 4
Sales $12,900 $14,000 $15,200 $11,200
Costs 2,700 2,800 2,900 2,100
OCF $9,061 $9,721 $10,447 $8,335
Capital spending –$27,400 0 0 0 0
NWC –300 –200 –225 –150 875
Incremental cash flow –$27,700 $8,861 $9,496 $10,297 $9,210
The NPV for the project is:
3. Using the tax shield approach to calculating OCF, we get:
OCF = (Sales – Costs)(1 – tC) + tCDepreciation
OCF = ($1,240,000 – 485,000)(1 – .35) + .35($1,650,000 / 3)
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
this sale. So, the cash flows for each year of the project will be:
Year Cash Flow
0 – $1,935,000 = –$1,650,000 – 285,000
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 = $1,650,000(.3333) = $549,945
Year 2 depreciation = $1,650,000(.4445) = $733,425
The asset is sold at a gain to book value, so this gain is taxable.
Year Cash Flow
0 – $1,935,000 = –$1,650,000 – 285,000
1 683,230.75 = ($755,000)(.65) + .35($549,945)
6. First, we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation charge = $530,000 / 5
The aftertax salvage value of the equipment is:
Using the tax shield approach, the OCF is:
Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting
this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This
reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end
7. First, we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation = $345,000 / 5
Annual depreciation = $69,000
Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus
Aftertax salvage value = MV + (0 – MV)tc
Aftertax salvage value = MV(1 – tc)
Using the tax shield approach, we find the OCF for the project is:
OCF = $85,000(1 – .34) + .34($69,000)
OCF = $79,560
8. 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 the cost of the asset. We can then subtract this from the asset cost. Doing so, we get:
9. 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:
Equipment –$3,900,000
Using the bottom-up approach to calculating the operating cash flow, we find the operating cash flow
each year will be:
Sales $2,350,000
Costs 587,500
Net income $511,875
The operating cash flow is:
To find the NPV of the project, we add the present value of the project cash flows. We must be sure
to add back the net working capital at the end of the project life, since we are assuming the net
10. 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:
Both cases: aftertax salvage value = $20,000(1 – .35) = $13,000
To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for
Techron I is:
And the OCF and NPV for Techron II is:
OCF = – $48,000(1 – .35) + .35($315,000 / 5)
OCF = –$9,150
The two milling machines have unequal lives, so they can only be compared by expressing both on
an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II
because it has the lower (less negative) annual cost.
Intermediate
11. First, we will calculate the depreciation each year, which will be:
D1 = $730,000(.2000) = $146,000
D2 = $730,000(.3200) = $233,600
The book value of the equipment at the end of the project is:
The asset is sold at a loss to book value, so this creates a tax refund. The aftertax salvage value will
be:
So, the OCF for each year will be:
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 $3,500
more in NWC each successive year. We will subtract the $20,000 from the initial cash flow and
subtract $3,500 each year from the OCF to account for this spending. In Year 4, we will add back the
total spent on NWC, which is $30,500. The $3,500 spent on NWC capital during Year 4 is irrelevant.
12. 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:
And the NPV of System B is:
If the system will not be replaced when it wears out, then System A should be chosen, because it has
the less negative NPV.
13. 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:
14. 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 –$4,725,000 –$4,050,000
Fixed costs –204,000 –165,000
The NPV and EAC for Machine A is:
NPVA = –$3,100,000 – $3,023,017(PVIFA10%,6)
NPVA = –$16,266,025.68
15. 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:
So, the NPV of Project A’s real cash flows, discounting at the real interest rate, is:
We should accept Project A if the projects are mutually exclusive since it has the highest NPV.
16. 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 since each is growing at a different rate. First, we will find the present value of the
revenues. The revenues in Year 1 will be the number of bottles sold, times the price per bottle, or:
The real aftertax costs in Year 1 will be:
Costs will grow at .8 percent per year in real terms forever. Applying the growing perpetuity
formula, we find the present value of the costs is:
