Designing a new cancer drug requires successfully completing two research steps, to be carried by two separate labs. Lab A will work on the curing ability of the drug (call this step A). With probability 0.5, they will succeed in developing a version that is effective against cancer. With probability 0.5 they will fail to develop anything useful. This part of research will take one year to complete. The proposed drug has some side effects for the digestive system, which would prevent an FDA approval even if the drug turned out to be effective against cancer. A second team, Lab B, will work on this issue (call this step B). With probability 0.9, they will develop a technique to eliminate the side effect. With probability 0.1, they will fail to do so. The task of Lab B will be complete in one year as well. The uncertainties in these two steps (represented by the failure probabilities) are completely independent of each other.

Each lab requires an investment of $1 million. If both steps are completed successfully, the drug will generate a one-time cash flow of $4.5 million. The risk-free rate is 5%.

We need to decide whether to pursue the project or abandon it.

(a.) Calculate the NPV of the project if we invest in both steps now (year 0), so that if both steps are successful, we will get a cash flow of $4.5 million a year from now. Is it a good idea to pursue the project?

(b.) Calculate the NPV if we invest in B now, and make the decision about step A only after observing the outcome of step B. Notice that under this scenario, if step B turns out to be successful in year 1, and if we decide to invest in step A afterwards, then the cash flow, provided that step A is also successful, will be received in year 2. Is this implementation of the project better or worse that in part a? Why? Is it a good idea to pursue the project now?

(c.) Calculate the NPV if we invest in step A first, observe its outcome in year 1, and make our decision about step B only if step A turns out to be successful.

(d.) Among the three implementations above, which ones create and which ones destroy value? What is the best implementation? Comment on why the best implementation creates more value than others.

Hint: In most real-option examples we had to deal with systematic (i.e., priced) risk, which made it necessary to use tracking portfolio of financial assets. In this question, we are not given any information about returns on financial assets such as market portfolio. But notice that the uncertainty surrounding steps A and B of this project is completely technical and hence it is idiosyncratic (i.e., whether a given step is a failure or success has nothing to do with the return on the market portfolio.) In this case once you find out expected cash flows in the future, you can discount them at the risk-free rate. In parts b and c, however, you should be careful about the year-1 decisions. If the first step we invest in is a failure, then obviously the project will be terminated. But if the first step is successful, then there is a valuation problem you need to solve to decide whether you should invest in the second step.