6QQMN566 advanced Corporate Finance
Workshop Questions - Real Options II
Q1.
You own a coppermine. The price of copper is currently $1.50 per pound. The mine produces 1 million pounds of copper per year and costs $2 million per year to operate. It has enough copper to operate for 100 years. Shutting the mine down would entail bringing the land up to EPA standards and is expected to cost $5 million. Reopening the mine once it is shut down would be impossible given current environmental standards. The price of copper has an equal (and independent) probability of going up or down by 25% each year for the next two years and then will stay at that level forever. Calculate the NPV of continuing to operate the mine if the cost of capital is fixed at 15%. Is it optimal to abandon the mine or keep it operating?
Q2.
Genenco is developing a new drug that will slow the aging process. In order to succeed, two breakthroughs are needed: one to increase the potency of the drug, and the second to eliminate toxic side effects. Research to improve the drug’s potency is expected to require an upfront investment of $10 million and take 2 years; the drug has a 5% chance of success. Reducing the drug’s toxicity will require a $30 million upfront investment, take 4 years, and has a 20% chance of success. If both efforts are successful, Genenco can sell the patent for the drug to a major drug company for $2 billion. All risk is idiosyncratic, and the risk-free rate is 6%.
(a) What is the NPV of launching both research efforts simultaneously? (b) What is the optimal order to stage the investments?
(c) What is the NPV with the optimal staging?
Homework:
Q3.
You are an analyst working for Goldman Sachs, and you are trying to value the growth potential of a large, established company, Big Industries. Big Industries has a thriving R&D division that has consistently turned out successful products. You estimate that, on average, the R&D division generates two new product proposals every three years, so that there is a 66% chance that a project will be proposed every year. Typically, the investment opportunities the R&D division produces require an initial investment of $10 million and yield profits of $1 million per year that grow at one of three possible growth rates in perpetuity: 3%, 0%, and −3%. All three growth rates are equally likely for any given project. These opportunities are always “take it or leave it” opportunities: If they are not undertaken immediately, they disappear forever.
(a) Assume that the cost of capital will always remain at 12% per year. What is the present value of all future growth opportunities Big Industries will produce?
(b) Assume that all the probabilities are risk-neutral probabilities, which means the cost of capital is always the risk-free rate and risk-free rates are as follows: The current interest rate for a risk-free perpetuity is 8%; in one year, there is a 64.375% chance that all risk-free interest rates will be 10% and stay there forever, and a 35.625% chance that they will be 6% and stay there forever. The current one- year risk-free rate is 7%.
Q4.
Your engineers are developing a new product to launch next year that will require both software and hardware innovations. The software team requests a budget of $5 million and forecasts an 80% chance of success. The hardware team requests a $10 million budget and forecasts a 50% chance of success. Both teams will need 6 months to work on the product, and the semi-annual risk-free interest rate is 2%.
(a) Which team should work on the project first?
(b) Suppose that before anyone has worked on the project, the hardware team comes back and revises their proposal, changing the estimated chance of success to 75% based on new information. Will this affect your decision in (a)?