a. Draw the decision tree for the firm.
b. If the firm proceeds with this project, what is the probability that it will succeed in implementing the new production process?
c. If the research were costless, what would be the firm’s expected gain from it before the project began?
d. Should the firm begin the research, given that each step costs $500,000?
e. Once the research has begun, should the firm quit at any point even if it has had no failures? Should it ever continue the research even if it has had a failure?
After the firm has successfully completed the first two steps, it discovers an alternate production process that would cost $150,000 and would lower production costs by $1 million with certainty. This process, however, is a substitute for the three-step cost-saving process; they cannot be used simultaneously. Furthermore, to have this process available, the firm must spend the $150,000 before it knows if it will successfully complete the third step of the three-step research project.
f. Draw the augmented decision tree that includes the possibility of pursuing this alternate production process.
g. If the firm continues the three-step project, what is the chance it would get any value from also developing the alternate production process?
h. If developing the alternate production process were costless and if the firm continues the three-step project, what is the expected value that it would get from having the alternate production process available (at the beginning of the third research step)? (This is known as the option value of having this process available.)
i. Should the firm
i. Pursue only the third step of the three-step project?
ii. Pursue only the alternate production process?
iii. Pursue both the third step of the three-step project and the alternate production process?
j. If the firm had known of the alternate production process before it began the three-step research project, what should it have done?