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been won during Gerald Ford’s presidency or sooner.) As money is spent and

failures continue to mount, the decision maker must realistically revise down-

ward the probability of success. Thus, one would expect the success probabili-

ties to decreasestage by stage.

With declining probabilities, the firm should give up the investment (irre-

spective of how much money has been sunk) when the revised probability of

success falls sufficiently low. This stopping rule can be summarized by a cutoff

probability (call this p*) below which the firm should not invest. In fact, the cut-

off value for the multistage decision is exactly the same as for the single-stage

problem; it must satisfy the zero-profit condition

or, equivalently,

where denotes the profit upon success and c is the investment cost. At p*, the

investment is a break-even proposition (i.e., the expected profit is zero). For

any lower probability of success, the investment earns an expected loss and

should not be pursued. For example, let $20 million, c $3 million, and

the success probabilities be .25, .21, .17, .13, .07, and .01. Since the cutoff value

is p* 3/20  .15, the firm should invest up to $9 million (three investments),

if necessary, before abandoning the program.

p*cƒ,

p*c0,

FIGURE 13.3

A Sequential R&D Decision

Because the odds of success increase with each investment, the firm’s best strategy is to continue to invest in

the project. Its overall expected profit is $1 million.

First

investment

Second

investment

Third

investment

Fourth

investment

Fifth

investment

1 1 –1/2 –1/2 –2 –2 –3.5 –3.5 –5 –5

Do not

invest^0

1/5

7

Quit

–3

1/4

4

Quit

–6

1/3

1

Quit

–9

1/2

–2

Quit

–12

4/5 3/4 2/3 1/2

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