CHAPTER 8
MAKING CAPITAL INVESTMENT
DECISIONS
Answers to Concept Questions
1. In this context, an opportunity cost refers to the value of an asset or other input that will be used in a
project. The relevant cost is what the asset or input is actually worth today, not, for example, what it
cost to acquire.
2. a. Yes, the reduction in the sales of the company’s other products, referred to as erosion, should be
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
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
project.
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 cash flow,
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
or losses that result in either a tax credit or liability.
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 from the existing
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. Notice that the
choice between MACRS and straight-line is purely a time value issue; the total depreciation is the
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
will not be sold, of course. Counterbalancing these losses is the fact that inventory sold above cost
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
debt, and the firm’s overall capital structure would remain unchanged, financing costs are not relevant
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 two
projects on an equal footing, implying that one project will be repeated five times and the other will
be repeated three times. Note the shortest common life may be quite long when there are more than
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
shield, tcD. A reduction in taxes that would otherwise be paid is the same thing as a cash inflow, so
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
11. One company may be able to produce at lower incremental cost or market better. Also, of course, one
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
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
OCF = [2,400($7 – 2)](1 – .34) + .34($33,000/6)
So, the NPV of the project is:
Since the NPV is positive, the company should accept the project.
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 total cash flow each year will
be:
Year 1
Year 2
Year 3
Year 4
Sales
$14,200
$15,900
$15,700
$12,900
Costs
2,100
2,100
2,100
2,100
Depreciation
7,750
7,750
7,750
7,750
EBT
$4,350
$6,050
$5,850
$3,050
Tax
1,479
2,057
1,989
1,037
Net income
$2,871
$3,993
$3,861
$2,013
OCF
$10,621
$11,743
$11,611
$9,763
Capital spending
–$31,000
NWC
–450
–175
–250
–275
1,150
Incremental cash flow
–$31,450
$10,446
$11,493
$11,336
$10,913
The NPV for the project is:
NPV = $2,043.08
3. Using the tax shield approach to calculating OCF, we get:
So, the NPV of the project is:
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:
Cash Flow
–$4,400,000
= –$3,950,000 – 450,000
1,578,833
1,578,833
2,402,583
= $1,578,833 + 450,000 + 575,000 + (0 – 575,000)(.35)
And the NPV of the project is:
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 = $3,950,000(.3333) = $1,316,535
Year 2 depreciation = $3,950,000(.4445) = $1,755,775
Year 3 depreciation = $3,950,000(.1481) = $584,995
So, the book value of the equipment at the end of three years, which will be the initial investment
minus the accumulated depreciation, is:
To calculate the OCF, we will use the tax shield approach, so the cash flow each year is:
OCF = (Sales – Costs)(1 – tC) + tCDepreciation
Year
Cash Flow
0
–$4,400,000
= –$3,950,000 – 450,000
1
1,578,787
= $1,720,000(.65) + .35($1,316,535)
2
1,732,521
= $1,720,000(.65) + .35($1,755,775)
3
2,248,942
= $1,720,000(.65) + .35($584,995) + $450,000 + 476,193
6. First, we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation charge = $625,000/5
Annual depreciation charge = $125,000
The aftertax salvage value of the equipment is:
IRR = 20.90%
7. First, we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation = $267,000/5
Annual depreciation = $53,400
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:
Very often, the book value of the equipment is zero as it is in this case. If the book value is zero, the
equation for the aftertax salvage value becomes:
Aftertax salvage value = $19,800
Using the tax shield approach, we find the OCF for the project is:
8. To find the BV 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:
Aftertax salvage value = $1,507,504
9. We will begin by calculating the initial cash outlay, that is, the cash flow at Year 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
–$3,750,000
NWC
–575,000
Total
–$4,325,000
Sales
$2,100,000
Costs
630,000
Depreciation
937,500
EBT
$532,500
Tax
186,375
Net income
$346,125
The operating cash flow is:
OCF = Net income + Depreciation
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:
Aftertax salvage value = $76,000(1 – .35) = $49,400
To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron
I are:
11. First, we will calculate the depreciation each year, which will be:
D1 = $485,000(.2000) = $97,000
D2 = $485,000(.3200) = $155,200
The book value of the equipment at the end of the project is:
BV4 = $485,000 – ($97,000 + 155,200 + 93,120 + 55,872) = $83,808
So, the OCF for each year will be:
OCF1 = $179,000(1 – .35) + .35($97,000) = $150,300
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 $15,000 of NWC at the beginning, and $4,000
more in NWC each successive year. We will subtract the $15,000 from the initial cash flow, and
Why? Well, during this year the project required an additional $4,000, but we would get the money
back immediately. So, the net cash flow for additional NWC would be zero. With all this, the equation
for the NPV of the project is:
NPV = –$485,000 – 15,000 + ($150,300 – 4,000)/1.09 + $170,670 – 4,000)/1.092
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:
OCFA = –$135,000(1 – .34) + .34($490,000/4)
And the NPV of System B is:
OCFB = –$119,000(1 – .34) + .34($685,000/6)
If the system will not be replaced when it wears out, then System A should be chosen, because it has
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:
EACA = –$637,211.05/(PVIFA11%,4)
If the conveyor belt system will be continually replaced, we should choose System B since it has the
less negative EAC.
14. Since we need to calculate the EAC for each machine, revenue is irrelevant. The sales figure is only
used to calculate the variable costs since EAC only uses the costs of operating the equipment, not the
get:
Machine A
Machine B
Variable costs
–$4,025,000
–$3,450,000
Fixed costs
–1,580,000
–1,750,000
Depreciation
–483,333
–494,444
EBT
–$6,088,333
–$5,694,444
Tax
2,130,917
1,993,056
Net income
–$3,957,417
–$3,701,389
+ Depreciation
483,333
494,444
OCF
–$3,474,083
–$3,206,944
The NPV and EAC for Machine A is:
NPVA = –$2,900,000 – $3,474,083(PVIFA10%,6)
And the NPV and EAC for Machine B is:
NPVB = –$4,450,000 – 3,206,944(PVIFA10%,9)
You should choose Machine B since it has a more positive EAC.
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:
1 + R = (1 + r)(1 + h)
So, the NPV of Project A’s real cash flows, discounted at the real interest rate, is:
NPV = –$67,000 + $34,000/1.0673 + $37,000/1.06732 + $23,000/1.06733
Project B’s cash flow are in nominal terms, so the NPV discounted at the nominal interest rate, is:
NPV = –$74,000 + $34,000/1.11 + $45,000/1.112 + $29,000/1.113
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
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:
Aftertax revenue in Year 1 in real terms = (6,500,000 × $1.03)(1 – .34)
Revenues will grow at 2 percent per year in real terms forever. Apply the growing perpetuity formula,
we find the present value of the revenues is:
PV of revenues = C1/(R – g)
Now we can find the value of the firm, which is:
Value of the firm = PV of revenues – PV of costs
17. 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
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. The nominal aftertax
salvage value is:
Market price
$75,000
Tax on sale
–25,500
Aftertax salvage value
$49,500
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
$265,000
$275,600
$286,624
$298,089
$310,013
Expenses
77,000
80,080
83,283
86,615
90,079
Depreciation
123,000
123,000
123,000
123,000
123,000
EBT
$65,000
$72,520
$80,341
$88,474
$96,933
Tax
22,100
24,657
27,316
30,081
32,957
Net income
$42,900
$47,863
$53,025
$58,393
$63,976
OCF
$165,900
$170,863
$176,025
$181,393
$186,976
Capital spending
–$615,000
$49,500
NWC
–30,000
30,000
Total cash flow
–$645,000
$165,900
$170,863
$176,025
$181,393
$266,476
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