Principles of Managerial Finance

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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