Amajor use of decision tree analysis is to estimate the expected value of information. we will use the following simple example to illustrate the application process.

a ceo needs to decide whether to invest $5 million to improve an existing product, which is sure to yield a profit of $7 million, or to develop a new product, which will yield a profit of $15 million if successful or $0 if not successful. a consultant offers to conduct a market forecast for the new product for a fee of $0.5 million. should the ceo hire the consultant and in which product should the ceo invest?

a 2-stage tree shown below describes the decision process: the first stage is to decide whether to acquire the information; the second stage is to decide which product to invest. for simplicity, we assume that the ceo is risk-neutral and wants to maximize the expected net profit.

the estimation process

to remove any distraction that may be imposed by the fee, the ceo should estimate the expected value of the information in consultant’s forecast without considering the proposed fee.

the consultant should be hired only if the fee is less than the expected value of the information.

1.for the estimation, the ceo starts with p(s), the prior probability of the new product’s success and the track records of the consultant’s precious forecasts:

p(f|s) = % favorable forecast for similar products proven successful in the market.

p(u|n) = % unfavorable forecast for similar products proven not successful in the market.

2.compute the expected net profit of the new product without market forecast:

enpn = p(s)(10) + p()

compare it with the net profit of the existing product, enpe

expected value without information (market forecast) = evw/oi = max (enpn, enpe)

3.compute p(s|f), p(n|f), p(s|u), p(n|u) as well as p(f) and p(u)

4.for the event of favorable forecast (f), compute the expected net profit of the new product:

enpfn = p(s|f)(10) + p(n|)

expected value with favorable information = evwfi = max (enpfn, enpe)

5.for the event of unfavorable forecast (u), compute the expected net profit of the new product:

enpun = p(s|u)(10) + p(n|)

expected value with unfavorable information = evwui = max (enpun, enpe)

6.expected value with information = evwi = p(f)evwfi + p(u)evwui

7. expected value of information = evwi – evw/oi

homework 8

let the prior probability of success for the new product, p(s), be 0.6, what is the maximum worth of the consultant if her track records have been one of the following:

8a. (5 points) perfect information, i. e., p(f|s)=1 and p(f|n)=0

8b. (5 points) wishy-washy, i. e., p(f|s)=0.5 and p(f|n)=0.5

8c. (5 points) reasonable, e. g., p(f|s)=0.8 and p(f|n)=0.3

8d. (5 points) perfect wrong information, i. e., p(f|s)=0 and p(f|n)=1