**Unformatted text preview: **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 probability that the cash inflows will be large enough to provide for project acceptance.
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 let CF
equal the annual cash inflow and let CF0 equal the initial investment, the following condition must be met for projects with annuity cash inflows, such as A and B,
to be acceptable.
NPV breakeven cash inflow
The minimum level of cash
inflow necessary for a project
to be acceptable, that is,
NPV $0. [CF (PVIFAk, n)] CF0 $0 (10.1) By substituting k 10%, n 15 years, and CF0 $10,000, we can find the
breakeven cash inflow—the minimum level of cash inflow necessary for Treadwell’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 (CF0) of $10,000 into Equation 10.1 and solving for
the breakeven cash inflow (CF ), we get
[CF (PVIFA10%,15yrs)]
CF $10,000
(7.606)
CF $0
$10,000
$10,000
7.606 $1,314.75 428 PART 3 Long-Term Investment Decisions Input
10000 Function
PV 15 N 10 I
CPT Calculator Use Recognizing that the initial investment (CF0) is the present value
(PV), we can use the calculator inputs shown at the left to find the breakeven
cash inflow (CF ), which is an ordinary annuity (PMT ).
Spreadsheet Use The breakeven cash inflow also can be calculated as shown on
the following Excel spreadsheet....

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