Chapter 12 Risk and
Refinements on CB
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10-1
Introduction to Risk in Capital
Budgeting
• Thus far, we have assumed that all investment projects
have the same level of risk as the firm.
• In other words, we assumed that all projects are equally
risky, and the acceptance of any project would not change
the firm’s overall risk.
• In actuality, these situations are rare—projects are not
equally risky, and the acceptance of a project can affect
the firm’s overall risk.
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12-2
Behavioral Approaches for Dealing
with Risk: Risk and Cash Inflows
• Behavioral approaches can be used to get a “feel” for the
level of project risk, whereas other approaches try to
quantify and measure project risk.
• Risk (in capital budgeting) refers to the uncertainty
surrounding the cash flows that a project will generate or,
more formally, the degree of variability of cash flows.
• In many projects, risk stems almost entirely from the cash
flows that a project will generate several years in the
future, because the initial investment is generally known
with relative certainty.
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12-3
Behavioral Approaches for Dealing
with Risk: Scenario Analysis
• Scenario analysis is a behavioral approach that uses
several possible alternative outcomes (scenarios), to
obtain a sense of the variability of returns, measured here
by NPV.
• In capital budgeting, one of the most common scenario
approaches is to estimate the NPVs associated with
pessimistic (worst), most likely (expected), and optimistic
(best) estimates of cash inflow.
• The range can be determined by subtracting the
pessimistic-outcome NPV from the optimistic-outcome
NPV.
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12-4
Table 12.2 Scenario Analysis of
Treadwell’s Projects A and B
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12-5
Project Risk
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12-6
Behavioral Approaches for
Dealing with Risk: Simulation
Simulation is a statistics-based behavioral approach that
applies predetermined probability distributions and random
numbers to estimate risky outcomes.
The Monte Carlo Method: The Forecast Is for Less Uncertainty
– To combat uncertainty in the decision-making process, some companies use a
Monte Carlo simulation program to model possible outcomes.
– A Monte Carlo simulation program randomly generates values for uncertain
variables over and over to simulate a model.
– One of the problems with using a Monte Carlo program is the difficulty of
establishing the correct input ranges for the variables and determining the
correlation coefficients for those variables.
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12-7
International Risk
Considerations
• Exchange rate risk is the danger that an unexpected change in the
exchange rate between the dollar and the currency in which a
project’s cash flows are denominated will reduce the market value
of that project’s cash flow.
– In the short term, much of this risk can be hedged
– Long-term exchange rate risk can best be minimized by
financing the project in whole or in part in the local currency.
• Political risk is much harder to protect against.
– Governments can seize the firm’s assets, or otherwise interfere with a
project’s operation.
– They can do so either by adjusting a project’s expected cash inflows to
account for the probability of political interference or by using risk-adjusted
discount rates in capital budgeting formulas.
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12-8
Risk-Adjusted Discount Rates
Risk-adjusted discount rates (RADR) are rates of return
that must be earned on a given project to compensate the
firm’s owners adequately—that is, to maintain or improve
the firm’s share price.
The higher the risk of a project, the higher the RADR—and
thus the lower a project’s NPV.
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12-9
Risk-Adjusted Discount Rates:
Review of CAPM
Using beta, bj, to measure the relevant risk of any asset j, the
CAPM is
rj = RF + [bj  (rm – RF)]
where
rj
RF
bj
rm
=
=
=
=
required return on asset j
risk-free rate of return
beta coefficient for project j
return on the market portfolio of assets
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12-10
Figure 12.2
CAPM and SML
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12-11
How do we get the RADR
• Managers can characterize projects by
– Risk indexes
– Risk classes
• How this is done varies
– Could be subjective
– Could be statistical
• Lets say a CV > 2.7 = risk class 4
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or risk index 7
12-12
Risk-Adjusted Discount Rates:
Applying RADRs (cont.)
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12-13
Table 12.3 Bennett Company’s
Risk Classes and RADRs
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12-14
Risk-Adjusted Discount Rates:
Portfolio Effects
• As noted earlier, individual investors must hold
diversified portfolios because they are not rewarded for
assuming diversifiable risk.
• Because business firms can be viewed as portfolios of
assets, it would seem that it is also important that they too
hold diversified portfolios.
• Surprisingly, however, empirical evidence suggests that
firm value is not affected by diversification.
• In other words, diversification is not normally rewarded
and therefore is generally not necessary.
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12-15
Capital Budgeting Refinements:
Comparing Projects With Unequal Lives
• But when unequal-lived projects are mutually
exclusive, the impact of differing lives must be
considered because they do not provide service
over comparable time periods.
– This is particularly important when continuing service is
needed from the projects under consideration.
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12-16
Capital Budgeting Refinements: Comparing
Projects With Unequal Lives (cont.)
The AT Company, a regional cable-TV firm, is evaluating
two projects, X and Y. The projects’ cash flows and
resulting NPVs at a cost of capital of 10% is given below.
Project X
Year
Project Y
Cash Flow s
0
$
1
$
28,000
$
35,000
2
$
33,000
$
30,000
3
$
38,000
$
25,000
4
$
-
$
20,000
5
$
-
$
15,000
6
$
-
$
10,000
NPV
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(70,000) $
$11,277
(85,000)
$19,013
12-17
Capital Budgeting Refinements: Comparing
Projects With Unequal Lives (cont.)
Annualized NPV (ANPV)
CB: Unequal Lives
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12-18
Capital Rationing
• Firm’s often operate under conditions of capital
rationing—they have more acceptable independent
projects than they can fund.
• In theory, capital rationing should not exist—firms should
accept all projects that have positive NPVs.
• However, in practice, most firms operate under capital
rationing.
• Generally, firms attempt to isolate and select the best
acceptable projects subject to a capital expenditure budget
set by management.
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12-19
Capital Rationing
• The internal rate of return approach is an approach to
capital rationing that involves graphing project IRRs in
descending order against the total dollar investment to
determine the group of acceptable projects.
• The graph that plots project IRRs in descending order
against the total dollar investment is called the
investment opportunities schedule (IOS).
• The problem with this technique is that it does not
guarantee the maximum dollar return to the firm.
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12-20
Capital Rationing
Tate Company, a fast growing plastics company with a cost
of capital of 10%, is confronted with six projects competing
for its fixed budget of $250,000.
Project
Initial Investm ent
IRR
PV of Inflow s
$
80,000
12%
$
B
70,000
20%
112,000
42,000
C
100,000
16%
145,000
45,000
D
40,000
8%
36,000
(4,000)
E
60,000
15%
79,000
19,000
F
110,000
11%
126,500
16,500
A
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100,000
NPV
$
20,000
12-21
IRR Approach
Assume the firm’s
cost of capital
is 10% and has
a maximum of
$250,000 available
for investment.
Ranking the
projects according
to IRR, the
optimal set of
projects for
Tate is B, C,
and E,
However project A and F are
acceptable project!s! They have an
IRR greater than the cost of capital!!
CB: Capital Rationing
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12-22
Figure 12.4 Investment
Opportunities Schedule
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12-23
Capital Rationing (cont.)
• The net present value approach is an approach to capital
rationing that is based on the use of present values to
determine the group of projects that will maximize
owners’ wealth.
• It is implemented by ranking projects on the basis of IRRs
and then evaluating the present value of the benefits from
each potential project to determine the combination of
projects with the highest overall present value.
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12-24
NPV Approach
Now we will rank by NPV.
With the $250,000 limit in
investment we will only do
projects C, B, and A
While projects E & F clearly
will add wealth to the
shareholder.
Why?
CB: Capital Rationing
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12-25