10.2 Behavioral Approaches for Dealing with Risk
Behavioral approachescan be used to get a “feel” for the level of project risk,
whereas other approaches explicitly recognize project risk. Here we present a few
behavioral approaches for dealing with risk in capital budgeting: risk and cash
inflows, sensitivity and scenario analysis, and simulation. In a later section, we
consider a popular approach that explicitly recognizes risk.
Risk and Cash Inflows
In the context of capital budgeting, the term riskrefers to the chance that a pro-
ject will prove unacceptable—that is, NPV$0 or IRRcost of capital. More
formally, risk in capital budgeting is the degree of variability of cash flows. Pro-
jects with a small chance of acceptability and a broad range of expected cash
flows are more risky than projects that have a high chance of acceptability and a
narrow range of expected cash flows.
In the conventional capital budgeting projects assumed here, risk stems
almost entirely from cash inflows,because the initial investment is generally
known with relative certainty. These inflows, of course, derive from a number of
variables related to revenues, expenditures, and taxes. Examples include the level
of sales, the cost of raw materials, labor rates, utility costs, and tax rates. We will
concentrate on the risk in the cash inflows, but remember that this risk actually
results from the interaction of these underlying variables. Therefore, to assess the
risk of a proposed capital expenditure, the analyst needs to evaluate the probabil-
ity that the cash inflows will be large enough to provide for project acceptance.
EXAMPLE Treadwell Tire Company, a tire retailer with a 10% cost of capital, is considering
investing in either of two mutually exclusive projects, A and B. Each requires a
$10,000 initial investment, and both are expected to provide equal annual cash
inflows over their 15-year lives. For either project to be acceptable according to
the net present value technique, its NPV must be greater than zero. If we letCF
equal the annual cash inflow and let CF 0 equal the initial investment, the follow-
ing condition must be met for projects with annuity cash inflows, such as A and B,
to be acceptable.
NPV[CF(PVIFAk,n)]CF 0 $0 (10.1)
By substituting k10%, n15 years, and CF 0 $10,000, we can find the
breakeven cash inflow—the minimum level of cash inflow necessary for Tread-
well’s projects to be acceptable.
Table Use The present value interest factor for an ordinary annuity at 10% for
15 years (PVIFA10%,15yrs) found in Table A–4 is 7.606. Substituting this value
and the initial investment (CF 0 ) of $10,000 into Equation 10.1 and solving for
the breakeven cash inflow (CF), we get
[CF(PVIFA10%,15yrs)] $10,000$0
CF(7.606)$10,000
CF$
1
,
3
1
4
.
7
5
$10,000
7.606
breakeven cash inflow
The minimum level of cash
inflow necessary for a project
to be acceptable, that is,
NPV$0.
CHAPTER 10 Risk and Refinements in Capital Budgeting 427
risk (in capital budgeting)
The chance that a project will
prove unacceptable or, more
formally, the degree of variability
of cash flows.
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