Chapter 6: Making capital
investment decisions
Corporate Finance
Ross, Westerfield, and
Jaffe
Outline
1. Relevant/incremental cash flows
2. An example
3. The equivalent annual cost method
TVM
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We need to evaluate a new project using the
TVM technique.
That is, we should discount future expected
cash flows (specifically, FCFs) back to
present time and compare PV to initial costs:
whether NPV > 0?
Discount cash flows, not earnings.
Relevant cash flows
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But before we do this, a few notions about
cash flows need to be addressed.
The cash flows in the capital-budgeting time
line need to be relevant cash flows; that is
they need to be incremental in nature.
Incremental cash flows: those cash flows that
will only occur if the project is accepted.
Ask the right question
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You should always ask yourself “Will this
cash flow occur ONLY if we accept the
project?”
–
–
If the answer is “yes”, it should be included in the
analysis because it is incremental.
If the answer is “no”, it should not be included in
the analysis because it will occur anyway.
Sunk costs
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A sunk cost is a cost that has already
occurred regardless of whether the project is
accepted.
Example: consulting fee for evaluating a
project.
Sunk costs should not be taken into
consideration when evaluating a project.
Opportunity costs
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Opportunity costs (OCs) are the costs of
giving up the second best use of resources.
Example: a vacant land.
Opportunity costs should be taken into
consideration when evaluating the project.
Side effects
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Accepting a new project may have side
effects.
Erosion occurs when a new project reduces
the sales and cash flows of existing projects.
Synergy occurs when a new project
increases the sales and cash flows of
existing projects.
Cash flows due to erosion and synergy are
incremental cash flows.
An example, I
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Baldwin Company is considering an investment
project: producing colored bowling balls.
The estimated life of the project: 5 years.
The cost of test marketing: $250,000.
Would be produced in a vacant building owned by
the firm; the property can be sold for $150,000 after
taxes.
The cost of a new machine: $100,000.
The estimated market value of the machine at the
end of 5 years: $30,000.
An example, II
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Production by year for the 5-year life: 5,000
units, 8,000 units, 12,000 units, 10,000 units,
and 6,000 units.
The price of bowling balls in the first year:
$20.
The price of bowling balls will increase at 2%
per year.
No debt financing; no interest expenses.
An example, III
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First-year production costs: $10 per unit.
Production costs will increase at 10% per year.
Incremental/marginal corporate tax rate: 34%.
An initial investment (at year 0) in net working
capital: $10,000.
NWC at the end of each year will be equal to 10% of
sales for that year.
NWC at the end of the project is zero.
An example, IV
Year
1
2
3
4
5
Units Price/unit Revenue Cost/unit Cost
5000
20
100000
10
50000
8000
20.4
163200
11
88000
12000 20.808 249696 12.1 145200
10000 21.22416 212241.6 13.31 133100
6000 21.648643 129891.9 14.641 87846
Depreciation
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Depreciation for tax purpose in the U.S. is
based on the Modified Accelerated Cost
Recovery System (MACRS).
See Table 6.3 (p. 176) for IRS depreciation
schedule.
For a 5-year depreciation, the depreciation
schedule is: 20% (year 1), 32% (year 2),
19.2% (year 3), 11.5% (year 4), 11.5% (year
5), and 5.8% (year 6).
An example, V
Year 1
Sales
100000
Costs
50000
Dep.
20000
Income before tax 30000
Tax
10200
Net Income
19800
OCF
39800
NWC
10000
Year 2 Year 3
Year 4
Year 5
163200 249696 212241.6 129891.9
88000 145200 133100
87846
32000 19200
11500
11500
43200 85296 67641.6 30545.86
14688 29001 22998.14 10385.59
28512 56295 44643.46 20160.27
60512 75495 56143.46 31660.27
16320 24970 21224.16
After-tax salvage cash flow
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OCF = sales – costs – taxes.
The estimated salvage market value of the machine
is 30% of $100,000; that is, $30,000.
The machine will have been depreciated to 5.8% of
$100,000 at that time; that is, $5,800.
The taxable amount is $24,200 ($30,000 - $5,800).
The after-tax salvage cash flow is: $30,000 – (34% ×
$24,200) = $21,772.
An example, VI
Year 0
OCF
Capital
OC
NWC
ΔNWC
Salvage
Total CF
IRR
Year 1 Year 2 Year 3 Year 4 Year 5
39800 60512 75495 56143 31660
-100000
-150000
150000
10000 10000 16320 24970 21224
-10000
0 -6320 -8650 3745 21224
21772
-260000 39800 54192 66846 59889 224656
16%
Decision
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If the nominal discount rate (cost of equity) is
less than 16%, we accept the project.
In other words, if the discount rate is higher
than 16%, we have a negative NPV.
NPV
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The firm uses no debt. Thus the appropriate
discount rate is the cost of equity.
Suppose that cost of equity is 15%.
NPV = 5473.43 (> 0).
An example, VII
Year 0
OCF
Capital
OC
NWC
ΔNWC
Salvage
Total CF
Re
NPV
Year 1 Year 2 Year 3 Year 4 Year 5
39800 60512 75495 56143 31660.3
-100000
-150000
150000
10000 10000 16320 24970 21224
-10000
0 -6320 -8650 3745 21224.2
21772
-260000 39800 54192 66846 59889 224656
15%
5473.43
Alternative definitions of OCF
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In our previous calculation, we used the topdown approach to compute OCF ( = sales –
costs – taxes).
Another 2 alternative methods: the bottom-up
method, and the tax shield method.
See pp. 186-189.
The equivalent annual cost method
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This method is useful (1) when one tries to
choose between 2 machines of unequal
lives, or (2) whether one should replace an
existing machine with a new one.
Whereas a general capital budgeting
problem is often computed in nominal terms,
the equivalent annual cost (EAC) method
works best in real terms.
Nominal vs. real
Time
0
1
2
Nominal CF
-1000 600
650
Expected Inflation 5%
Real CF
-1000 571.43 589.57
2 machines with unequal lives
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Revenues per year are the same, regardless
of machine.
The nominal discount rate (NR) is 13.3%.
The expected inflation rate (E(I)) is 3%. The
real discount rate (RR) is 10%.
(1 + NR) = (1 + RR) × (1 + E(I))
(1 + 13.3%) = (1 + 10%) × (1 + 3%).
Real cost outflows w/ real
discount rate
Time 0 Time 1 Time 2 Time 3 Time 4
Machine A
500
120
120
120
Machine B
600
100
100
100
100
Discount
10%
PV_A
798.42
PV_B
916.99
Equivalent annual cost
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One needs to use real (nominal) discount
rate to discount real (nominal) cash flows.
For A, the EAC is $321.05.
798.42 PV; 3 N; 10 I/Y; CPT PMT.
For B, the EAC is $289.28.
916.99 PV; 4 N; 10 I/Y; CPT PMT.
B has a lower equivalent annual cost. We
should choose B.
End-of-chapter
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Concept questions: 1-12.
Questions and problems: 1-20.