Corporate Finance, Module 22: “Real Options”

Homework Assignment

(The attached PDF file has better formatting.)

Use the practice problem on trade shows and real options to answer this homework assignment.

Ten pharmaceutical firms compete to produce a drug to cure Alzheimer’s disease. The capitalization rate is 12% per annum.

●    The expected cost for research and development is $1.77 billion a year for 15 years; at the capitalization rate for pharmaceutical projects, the present value cost is $12.05 billion.
●    The first firm that obtains a patent gains the entire market; all other firms get no return.
●    The firms are certain that one of them will obtain a patent and the drug will be successful, but they don’t know which firm will obtain the patent. If the firm’s research is good, it may develop the drug in 10 years and obtain the patent; if its research is not good, it may take 20 years and its research will be wasted. After 10 years, one firm obtains the patent and all research stops, for an average present value cost of $10 billion per firm.
●    The expected profit has a present value of $85 billion.

A.    Why might a firm want to keep its research secret? (If a competitor might steal research findings, why would a firm want to keep its research method secret?)
B.    If all firms keep their research secret, what is the expected net present value of the project to each firm? Assume all firms are identical, so each has a 10% chance of obtaining the patent. Is this a positive NPV project?
C.    Assume that firms have a good idea how their research is going and whether it is likely to succeed. If the firms know the relative research progress of all the competitors, after the first year, the least successful firm realizes it has little chance of obtaining the patent and drops out; after the second year, a second firm drops out, and so forth. Why might a firm want to publicize its research findings if all the other firms agree to publicize theirs? Assume the firms announce their progress, not their methods, so they cannot steal research ideas from each other. They are learning who is likely to succeed, not how to produce the drug.
D.    If one firm informs a competitor that it has a promising drug, how might both firms gain?
E.    With an annual trade fair to inform all firms of the research progress of each, is the research a positive NPV investment? (One could work out the exact present value of the total research costs for the ten firms, but this is not necessary. If all ten firms do their research independently, the total cost is $10 billion × 10 = $100 billion for 10 × 15 = 150 years of research. With the annual trade shows, one firm spends one year, a second firm spends two years, a third firm spends three years, and so forth; the winning firm spends 10 years. The total research time is 55 years, though the present value is more than 55% × $100 = $55 billion. The present value is about $65 billion. The research is a negative NPV project for nine firms and a positive NPV project for one firm; the average is positive.)

Use the discussion on trade shows (in the practice problems) for this assignment. Write one or two sentences to show that you understand the real option in this scenario.

Question: One candidate writes on the discussion forum: “I believe there is a problem with the answer that problems C and D are trying to extract. If the company that drops out has no chance of success, then the probabilities of success for your company does NOT change. This is a classic Monte Hall problem. The company that drops out is the door with the goat. All the other companies are the other doors. Their chance increase...your chances do not.
Of course, your chance does go up if the company that dropped out still had some chances left.” What does this mean?

Answer: Suppose ten firms compete in the market; each has a 10% chance of producing the medication first. Firm Z’s lead researcher quits, and it now has no chance of being first. It drops out of the market, leaving nine firms with an 11.1% chance for each to be first. The candidate correctly points out that

●    The other firms’ chances increased when the lead researcher quit.
●    Nothing happens when Firm Z pulls out of the market.

Question: How does this relate to the homework assignment?

Answer: The homework assignment differs. For the homework assignment, the lead researcher for the Firm Z gets a bad flu and spends two weeks in bed. When he comes back to work, the firm realizes that it has fallen behind its competitors. Firm Z reasons:

●    With a 10% chance of being first, our research project has a positive NPV.
●    With an 8% chance of being first, our research project has a negative NPV.

Firm Z stops its research and pulls out of this market. In this case, the lead researcher’s illness has a slight effect on the chances of the other firms. The major effect comes when Firm Z ends it research efforts.

Question: How does Firm Z estimate its chances?

Answer: The homework assignment deals with this question. The trade fairs and other inter-company activities let each firm know where the others stand.

Question: Can you give an insurance (actuarial) example of this?

Answer: Suppose General Motors wants to buy insurance: group health, general liability, workers’ compensation, commercial automobile, and executive life insurance. It seeks proposals from the major insurers in the United States.

Each insurer considers three items:

●    The cost of preparing a proposal.
●    The chance of winning the contract.
●    The expected profit if it wins the contract.

The NPV depends on who is competing.

■    If no other firms compete, it can submit a short proposal, it has a high chance of winning, and it can charge a high premium and make a large profit.
■    If many other firms compete, it must prepare a better proposal, it has a small chance of winning, and it will have to propose a lower premium.

Each firm wants one of two things:

●    Other firms should give up.
●    If another firm will not give up, it should make its intentions clear, so the first firm may decide to give up.

Anybody know how to approach Part E?  It is a little confusing.

[NEAS: The sentences in parentheses give the answer; write one or two sentences of your own to show that you understand what the real option is.]

Jacob: Why do we discuss real options? They are confusing, and even courses on options pricing rarely discuss real options.

Rachel: Real options are the reason for the entire discussion of options in the textbook. Discounted cash flow analysis works for most projects, but not for projects that involve real options. Many business projects have a real option embedded in them. The primary objective of the textbook is to teach you how to identify real options; actually pricing them is not easy.

Are the costs for research and development in Part B a given for EACH for or a collective value for all firms? I am a little confused how these costs play into determining the PV and NPV of the research project.

I believe the NPV will be negative in either scenario for Part B, but R&D would certainly affect the NPV for the restated market plan in Part E.

[NEAS: The R&D costs are for a single firm.]

So for Part B, do we use the $12.05 billion present value for the 15 years, or the $10 billion listed in the third bullet of the question? My guess is that we use NPV = -$10 billion + (.1)($85 billion) = -$9.15 billion.

[NEAS: Use the $10 billion.]

I think you are correct, UGA, although I would redo your math.

(0.1)(85) = 8.5 billion, not 0.85 billion

Shouldn't part E be a decreasing annuity-due?  I see this as

-1.77(10 + 9v + 8v² + .... + v⁹) = -1.77(10 - a₁₀)/d = -71.86B

not as 55% of the total hours if no firm drops out.

Part B:

My understanding is that there's a 10% chance of a NPV profit of $85b, and a 90% chance of a NPV cost of $10b. Therefore, the expected value of the NPV is (.10)*($85)+(.90)*(-$10)=-$0.5b

I'm assuming the R&D costs for the successful firm (-$12.05b) are already accounted for in the $85b profit.

yes, it does.  since the problem only stated that there's 10% chance of 85 billion profit, and did not include "OTHERWISE the PROFIT is 0", then we have to assume that it's also a 90% chance of a 10 mil loss.  so yes, the expected NPV is -0.5 million.  In either case, it's a negative NPV

I think this is the right approach - except if you evaluate the original claim - 15 years of research at 1.77B/ year @12% = 12.05 billion, it becomes clear that spending starts at the end of the first year, and the formula becomes:

-1.77(10v + 9v² + 8v + .... + v¹⁰) = -64.16

Either way, since profit is 85B, it is now +NPV overall.