Principles of Corporate Finance_ 12th Edition

Chapter 9 Risk and the Cost of Capital 239

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flow in perpetuity of $250,000 a year after taxes. If they are not successful, the project will

have to be dropped.

The expected cash flows (in thousands of dollars) are

C 0 = −125

C 1 = 50% chance of − 1,000 and 50% chance of 0

= .5(−1,000) + .5(0) = −500

Ct for t = 2, 3, ... = 50% chance of 250 and 50% chance of 0

= .5(250) + .5(0) = 125

Management has little experience with consumer products and considers this a project of

extremely high risk.^22 Therefore management discounts the cash flows at 25%, rather than at

Vegetron’s normal 10% standard:

NPV = −125 − ____^500

1.25

+ ∑

t = 2

∞

______^125

(1.25)t

= −125, or −$125,000

This seems to show that the project is not worthwhile.

Management’s analysis is open to criticism if the first year’s experiment resolves a high

proportion of the risk. If the test phase is a failure, then there is no risk at all—the project is

certain to be worthless. If it is a success, there could well be only normal risk from then on.

That means there is a 50% chance that in one year Vegetron will have the opportunity to invest

in a project of normal risk, for which the normal discount rate of 10% would be appropriate.

Thus the firm has a 50% chance to invest $1 million in a project with a net present value of

$1.5 million:

Success → NPV = −1,000 + ____^250

.10

= +1500 (50% chance)

Pilot production

and market tests

Failure → NPV = 0 (50% chance)

Thus we could view the project as offering an expected payoff of .5(1,500) + .5(0) = 750,

or $750,000, at t = 1 on a $125,000 investment at t = 0. Of course, the certainty equivalent

of the payoff is less than $750,000, but the difference would have to be very large to jus-

tify rejecting the project. For example, if the certainty equivalent is half the forecasted cash

flow (an extremely large cash flow haircut) and the risk-free rate is 7%, the project is worth

$225,500:

NPV = C 0 +

CEQ 1

_____

1 + r

= −125 +

.5(750)

______

1.07

= 225.5, or $225,500

This is not bad for a $125,000 investment—and quite a change from the negative-NPV that

management got by discounting all future cash flows at 25%.

(^22) We will assume that they mean high market risk and that the difference between 25% and 10% is not a fudge factor introduced to
offset optimistic cash-flow forecasts.