Chapter Eight
Making Capital Investment
Decisions
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Chapter Organisation
8.1 Project Cash Flows: A First Look
8.2 Incremental Cash Flows
8.3 Project Cash Flows
8.4 More on Project Cash Flows
8.5 Special Cases of Discounted Cash Flow Analysis
Summary and Conclusions
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Chapter Objectives
• Identify incremental cash flows relevant to investment
evaluation.
• Calculate depreciation expense for tax purposes.
• Apply incremental analysis to project evaluation.
• Determine how to set the bid price and how to value
options.
• Compare mutually-exclusive projects using annual
equivalent costs.
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Project Cash Flows
• The incremental cash flows for project evaluation
consist of any and all changes in the firm’s future
cash flows that are a direct consequence of
undertaking the project.
• The stand-alone principle is the evaluation of a
project based on the project’s incremental cash flows.
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
8-4
Types of Cash Flows
• Sunk costs  a cost that has already been incurred
and cannot be removed  incremental cash flow.
• Opportunity costs  the most valuable alternative
that is given up if a particular investment is
undertaken = incremental cash flow.
• Side effects  erosion  the cash flows of a new
project that come at the expense of a firm’s existing
projects = incremental cash flow.
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8-5
Types of Cash Flows (continued)
• Financing costs  the interest rate used to discount
the cash flows reflects in part the financing costs of
the project  incremental cash flow.
• An investment of the firm in the project’s net working
capital represents an additional cost of undertaking
the investment.
• Always use after-tax incremental cash flow, since
taxes are definitely a cash flow.
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Investment Evaluation
• Step 1  Calculate the tax effect of the decision.
• Step 2  Calculate the cash flows relevant to the
decision.
• Step 3  Discount the cash flows to make the
decision.
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Example—Investment Evaluation
• Purchase price $42 000
• Salvage value $1000 at end of Year 3
• Net cash flows Year 1
$31 000
Year 2
$25 000
Year 3
$20 000
• Tax rate is 30%
• Depreciation 20% reducing balance
• Required rate of return 12%
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Solution—Depreciation Schedule
Initial cost
Dep’n – Yr 1 (20%  42 000)
Depreciated value
Dep’n – Yr 2 (20%  33 600)
Depreciated value
Dep’n – Yr 3 (20%  26 880)
Depreciated value
Salvage value
Loss on disposal
$42 000
8 400
33 600
6 720
26 880
5 376
21 504
1 000
$20 504
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Solution—Taxable Income
Year 0
Net cash flows
Depreciation
Loss on sale
Taxable income
Year 1
31 000
(8 400)
Year 2
25 000
(6 720)
$22 600
$18 280
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
Year 3
20 000
(5 376)
(20 504)
$(5 880)
8-10
Solution—Cash Flows
Year 0
Year 1
Year 2
Year 3
Tax paid
(6 780)
(5 484)
1 764
Net cash flow
31 000
25 000
20 000
Salvage value
Outlay
Cash flow
1 000
(42 000)
$(42 000)
$24 220
$19 516
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$22 764
8-11
Solution—NPV and Decision
Cash flow
Discount
PV cash flow
NPV
Year 0
(42 000)
1
($42 000)
$11 387
Year 1
24 220
0.8929
$21 626
Year 2
19 516
0.7972
$15 558
Year 3
22 764
0.7118
$16 203
Decision: NPV > 0, therefore ACCEPT.
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8-12
Interest
• As the project’s NPV is positive, the cash flows
from the investment will cover interest costs (as
long as the interest cost is less than the required
rate of return).
• Interest costs should not therefore be included as
an explicit cash flow.
• Interest costs are included in the required rate of
return (discount rate) used to evaluate the project.
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
8-13
Depreciation
• The depreciation expense used for capital budgeting
should be the depreciation schedule required for tax
purposes.
• Depreciation is a non-cash expense; consequently, it
is only relevant because it affects taxes.
• There are two methods of depreciation:
– Prime cost (straight-line method in accounting)
– Diminishing value (reducing balance method in accounting)
• Depreciation tax shield = DT
where D = depreciation expense
T = marginal tax rate.
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Disposal of Assets
• If the salvage value > book value, a gain is made on
disposal.
This gain is subject to tax (excess
depreciation in previous periods).
• If the salvage value < book value, the ensuing loss on
disposal is a tax deduction (insufficient depreciation
in previous periods).
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Capital Gains Tax
• Capital gains made on the sale of assets such as
rental property are subject to taxation.
• For taxation purposes, the calculation of a capital
gain is complicated and depends upon whether the
seller is an individual or an entity such as a company
or trust.
• Capital losses are not a tax deduction but can be
offset against future capital gains.
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Inflation
• When a project is being evaluated, anticipated
inflation would be reflected in the estimates of the
future cash flows and the interest rate used as the
discount rate in the analysis.
• As a result there will be no distortion to the analysis
by not identifying inflation specifically.
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Incremental Form of Analysis
• The description ‘incremental’ is often replaced by
‘marginal’.
• The advantage of using a marginal form of analysis is
that there will only be one calculation and not two.
• By using a marginal form we are implicitly analysing
one option: that is, to do nothing.
• The sign of the NPV tells us whether it is sensible to
change or not.
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Example—Incremental Cash
Flows
A firm is currently considering replacing a machine purchased two
years ago with an original estimated useful life of five years. The
replacement machine has an economic life of three years. Other
relevant data is summarised below:
Initial cost
Annual revenues
Annual costs
Annual depreciation
Salvage value
Tax rate
Required rate of return
Existing Machine
$240 000
$100 000
$60 000
$48 000
$80 000 (now)
30%
10%
New Machine
$360 000
$150 000
$70 000
$120 000
$100 000 (End year 3)
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Solution—Taxable Income
Year 0
Increased revenues
Increased costs
Dep’n Existing
Dep’n New
Loss on sale (existing) (64 000)
Gain on sale (new)
Taxable income
$(64 000)
Year 1
50 000
(10 000)
48 000
(120 000)
$(32 000)
Year 2
50 000
(10 000)
48 000
(120 000)
Year 3
50 000
(10 000)
48 000
(120 000)
$(32 000)
100 000
$68 000
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Solution—Cash Flows
Year 0
19 200
Tax
Increased revenues
Increased costs
Salvage values
80 000
Outlay
(360 000)
Cash flow
$(260 800)
Year 1
9 600
50 000
(10 000)
Year 2
9 600
50 000
(10 000)
Year 3
(20 400)
50 000
(10 000)
100 000
$49 600
$49 600
$160 400
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Solution—NPV and Decision
Year 0
Cash flow
(260 800)
Discount
1
PV of cash flow $(260 800)
NPV
($54 212)
Year 1
49 600
0.9091
$45 091
Year 2
49 600
0.8264
$40 989
Year 3
160 400
0.7513
$120 508
Decision: NPV < 0, therefore REJECT.
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8-22
A Note on Cash Flows
• Cash flows do not always conveniently occur at the
end of the period.
• Taking revenue at the period end is a conservative
approach to evaluation.
• If the facts made it necessary to take cash flows as
occurring at the beginning of the period this only
requires a minor adjustment to the analysis.
• The period examined could be yearly, monthly or
even weekly. If so, the discount rate must match the
period (e.g. a weekly analysis needs a weekly rate).
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Setting the Bid Price
• How to set the lowest price that can be profitably
charged.
• Cash outflows are given.
• Determine cash inflows that result in zero NPV at the
required rate of return.
• From cash inflows, calculate sales revenue and price
per unit.
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Setting the Option Value
• A buy option is an arrangement that gives the holder
the right to buy an asset at a fixed price sometime in
the future.
• Option value =
Asset value × Probability of the Value
–
Present value of the exercise price × Probability the exercise
price will be paid.
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Annual Equivalent Cost (AEC)
• When comparing two mutually-exclusive projects with
different lives, it is necessary to make comparisons
over the same time period.
• AEC is the present value of each project’s costs
calculated on an annual basis.
• NPVs are calculated and then converted to AECs
using the relevant PVIFA (present value interest
factor for annuities).
• Select the project with the lowest AEC.
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Example—AEC
• Project A costs $3000 and then $1000 per annum for
the next four years.
• Project B costs $6000 and then $1200 for the next
eight years.
• Required rate of return for both projects is 10 per
cent.
• Which is the better project?
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Solution—Project A
NPV  C  PVIFA 4, 0.10   C0
  $1000  3.1699   $3000
  $3170  $3000
  $6170
PV of costs
AEC 
PVIFA 4, 0.10 
 $6 170

3.1699
  $1 946
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PPTs t/a Fundamentals of Corporate Finance 4e, by Ross, Thompson, Christensen, Westerfield & Jordan
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Solution—Project B
NPV  C  PVIFA 8, 0.10   C0
  $1 200  5.3349   $6000
  $6402  $6000
  $12 402
PV of costs
AEC 
PVIFA 8, 0.10 
 $12 402

5.3349
  $2325
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Solution—Interpretation
‘Project A is better because it costs $1946 per year
compared to Project B’s $2325 per year’.
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Annual Equivalent Benefit (AEB)
• The AEB is used when comparing projects with cash
inflows and outflows but with unequal lives.
• The steps required to calculate the AEB are the same
as those used for AEC.
• Select the project with the highest AEB.
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Summary and Conclusions
• Discounted cash flow (DCF) analysis is a standard
tool in the business world.
• The information provided for a specific decision may
be complex; however the analysis reduces to three
distinct steps:
- Step 1  Calculate the taxable income
- Step 2  Calculate the cash flows relevant to the decision
- Step 3  Discount the cash flows to make the decision.
• Cash flows should be identified in a way that makes
economic sense.
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8-32