For the decision tree of the expected value of information discussed in class, let the prior probability of success for the new product, P(S), be 0.65, 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)=0.85 and P(F|N)=0.1

8d. (5 points) Perfect wrong information, i.e., P(F|S)=0 and P(F|N)=1

You don't need to draw the decision tree.

DECISION TREE ANALYSIS FOR EXPECTED VALUE OF INFORMATION A major 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. Stage 1 Stage 2 Profit Net Profit P(S) Success $15 million $10 million New, $5 million No -$ 5 million P(N) Existing, $5 million $7 million $ 2 million No consultant Hire consultant, P(S F) $0.5 million Success $15 million $10 million P(F) New, $5 million No $0 -$ 5 million P(NF) Existing, $5 million Favorable $7 million $ 2 million prediction P(SJU) Success $15 million $10 million Unfavorable prediction No $0 -$ 5 million P(NU) New, $5 million P(U) Existing, $5 million $7 million $ 2 million