Question

Jason is considering developing a process innovation. It requires an initial investment of $100,

then another investment of $40 after one year. Jason thinks the probability it will turn out to be

feasible after two years is 0.7. If it is feasible, it will then take another expenditure of $50 (2

years from the initial investment) to complete. It will then be ready to demonstrate 3 years from

the initial investment. Jason thinks there is a 0.05 probability that with a successful

demonstration he will sell his innovation for $1,000 and a 0.5 probability he will sell it for $400,

and that otherwise there will be no interest. The annual discount rate (riskless rate of return) is

5%. There are no other costs and Jason is risk neutral.

a. Illustrate the decision(s) to be made with a decision tree.

b. What is the present expected value of the project?

c. What probability of selling the project for $400 would make Jason indifferent between

pursuing it or not, assuming P(1000) stays the same?

d. Jason may obtain an expert’s opinion of the feasibility of his idea for a fee. Suppose the

consultant’s studied opinion is completely accurate and Jason thinks there is a 70% chance they

will find the innovation feasible. How much is the opinion worth?

e. Suppose, having dealt with consultants on similar projects, Jason guestimates there is a 0.7

probability the consultant will report the innovation is probably feasible and otherwise the

consultant will report the idea is probably not feasible. Jason thinks that if the consultant says the

idea is probably not feasible, the probability it is feasible is 0.19 and that if the consultant says

the idea is probably feasible, the probability it is feasible is 0.92. How much is the opinion

worth?

Answer 1

a. Illustrate the decision(s) to be made with a decision tree.
Image - Attached

b. What is the present expected value of the project?

Present Value of Project = {(1000/1.05^3)-[(100+(40/1.05)+(50/1.05^2)*50%] + [(400/1.05^3)- [100+(40/1.05)+(50/1.05^2)]*50%]}/2

= $ 1025.93/2=512.96

c. What probability of selling the project for $400 would make Jason indifferent between

pursuing it or not, assuming P(1000) stays the same?

As the Present value of both the probabilities is $ 512.96 which is higher than $ 400, no probability would make Jason indifferent