Steel: AK Steel Holding Corporation is a producer of flat-rolled carbon, stainless, and electrical steels and tubular products through its wholly owned subsidiary, AK Steel Corporation. The recent surge in demand for steel significantly increased AK's profits,7 and it is now engaged in a research project to improve its production of rolled steel. The research involves three distinct steps, each of which must be successfully completed before the firm can implement the cost-saving new production process. If the research is completed successfully, it will save the firm $4 million. Unfortunately there is a chance that one or more of the research steps might fail, in which case the entire project would be worthless. The three steps are done sequentially, so that the firm knows whether one step was successful before it has to invest in the next step. Each step has a 0.8 probability of success and costs $500,000. The risks of failure in the three steps are uncorrelated with one another. AK Steel is a risk-neutral company. (In case you are worried about such things, the interest rate is zero.)

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?