Corporate Financial Management

Harvard Business School 9-293-095 Rev. December 8, 1994 Professor Timothy A. Luehrman prepared these exercises as the basis for class discussion rather than to illustrate either effective or ineffective handling of an administrative situation. Copyright © 2003 by the President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call 1-800-545-7685, write Harvard Business School Publishing, Boston, MA 02163, or go to http://www.hbsp.harvard.edu. No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means—electronic, mechanical, photocopying, recording, or otherwise—without the permission of Harvard Business School. 1 Corporate Financial Management: Options Exercises Problem 1. Use the Black-Scholes model to price the following call option. [You may find it convenient to use the table in the attached Appendix; alternatively, you may use the Black-Scholes formula itself and a computer, or other published tables.] a. A one-year European call option on 100 shares of XYZ Corporation. The exercise price is $50 per share. The standard deviation (!) of returns on XYZ's shares is 0.2 per year. The current stock price is $35 per share. The risk-free rate of return is 3%. b. Now vary the terms of the call on XYZ one at a time. What happens to the value of the call as ! goes from 0.2 to 0.5? As maturity goes from 0 to 3 years? As the exercise price goes from $25 to $35 to $50? As the stock price goes from $35 to $60? As the risk-free rate goes from 3% to 6%? c. What is the value of a European put on 100 shares of XYZ, with the identical terms given in part (a.) above? d. Repeat the calculations from part (b.) for the European put on XYZ. What are the intuitive explanations for the changes in value you computed? Problem 2. Project Alpha has two phases. You may invest in the first, in both, or in neither. The first phase requires an investment of $100 today. One year later, Alpha will deliver either $120 or $80, with equal probability. At that time, (after the phase 1 payout has been received) you can invest an additional $100 for phase 2. One year later phase 2 pays out either 20% more cash than phase 1 actually delivered, or (equally likely) 20% less. For investments in this business, your company normally applies a 10% hurdle rate. a. How much would Project Alpha be worth if it offered only the phase 1 cash flows, without the phase 2 opportunity? b. How much would the phase 2 opportunity be worth if you had to choose today, once and for all, whether or not to invest in it? c. Assuming you can wait to decide about phase 2, what is the total value of Project Alpha? Should you invest the first $100? Purchased by Dao Wu (wudao2001@hotmail.com) on September 11, 2012 293-095 Corporate Financial Management: Options Exercises 2 d. Project Omega has exactly the same structure as Project Alpha, and the same systematic risk, but somewhat different cash flows. For $100 invested today, Omega delivers in phase 1 either $140 or $60, with equal probability. Phase 2 requires an additional $100 investment and delivers either 40% more or 40% less than phase 1 did. What is the total value of Project Omega? Should you invest the first $100? e. Compare these two projects. Which is riskier? Which is more valuable? Which has a higher fraction of its value accounted for by "growth options," i.e., the phase 2 opportunity? Assuming both were undertaken, would you finance Alpha and Omega differently? How and why? Problem 3. You are a member of the investment committee for a large manufacturing company that three years ago licensed a new technology from a small start-up firm. Based on that technology, engineers in one of your company's divisions have developed a new product that is now ready to be manufactured and marketed. The division president has recommended proceeding with the project. Your committee has to decide whether to endorse this recommendation and approve the request for funds. If you do not proceed with the product, the licensor has the right to suspend your license and attempt to market the technology to another manufacturer. The product launch will require an initial investment of $225 million for manufacturing, marketing and distribution, and working capital. Net after-tax cash flows are expected to be $15, $20, and $25 million in the first three years of operation as new capacity comes on stream. In all successive years, net cash flow is expected to grow at 3% per year. The hurdle rate for new investment in your company's core business is 10%. However, your committee considers this project riskier than the core business and has stipulated that a 15% hurdle rate will apply. The headquarters analyst assigned to examine the project has submitted a report showing that, at 15%, the NPV of the proposed investment is negative. However, the division president has taken strong exception to this analysis. She has requested a meeting with the committee at which she and her chief engineer and marketing VP can present their arguments in favor of the project. In a memo to the committee chair, she outlined her objections to the analyst's report. First, she argued, the discount rate is wrong. The committee's insistence on 15% is unfair and, even worse, myopic. In her view, the project should be treated the same (at least) as other projects, which suggests a 10% hurdle rate. Further, given the project's strategic importance to the division, an even lower rate (she suggests 8%) would be justified. [The risk-free rate is 5%.] Second, she argued that the analyst's cash flows are wrong. The new product is an important part of the division's future plans. After three years, once the original capacity is fully utilized, she can add twice again as much capacity for less than twice the additional expenditure. Specifically, an additional investment of $405 million will result in cash flows of $30, $40, and $50 million in the next three years, followed by a perpetuity that would start at $51.5 and grow at 3% per year. Three years after this second investment, the division can invest another $770 million and receive net cash flows of $60, $80, and $100 million in the subsequent three years, followed by a perpetuity growing at 3% per year. As before, this adds twice again the capacity at less than twice the previous investment. Thus, the memo emphasized, within ten years the division will have built a new business producing annual net cash flow of nearly $200 million. The division president was prepared to come to the meeting and argue first, that her assumptions were appropriate, and second, that the NPV of launching the product was obviously positive. The committee chair then asked the analyst to respond to the president's memo. In a second report, the analyst defended his original figures. It was perfectly legitimate, he argued, to separate the sequence of investments because each could be analyzed on its own merits. Indeed, only the first investment of $225 million was now before the committee. Nevertheless, he Purchased by Dao Wu (wudao2001@hotmail.com) on September 11, 2012 Corporate Financial Management: Options Exercises 293-095 3 claimed to be indifferent about whether he evaluated them separately (see Table A) or added them all together (see Table B). Discounting at 15%, none of the three investments had a positive NPV and so neither did the whole program. At 10%, the $225 million investment currently under consideration had a negative NPV. The other two had positive NPVs, but they might never happen and, in any event, the NPV of all three added together was still not much above zero. Of course, the program looked better at 8%, and the committee was free to accord it the special treatment requested by the division president. But the analyst respectfully observed that a new product launch could hardly be regarded as less risky than the established core business. Accordingly, he could see no justification for lowering the hurdle rate. Even if 15% was too high, surely 10% was too low. At any rate between these two, the project was unimpressive. Table A Table B a. Evaluate the proposed product launch using a standard discounted cash flow approach. In particular, compute the proposal's NPV at each of the three discount rates under consideration. What do you expect the committee to conclude, assuming it employs this basic methodology? b. Estimate the NPV of the program as a portfolio of options. Assume that, though you are unsure of the standard deviation for the return on the assets under consideration, you are confident that ! is at least 0.3 per year, and no more than 0.6. Based on this approach, what decision would you recommend to the committee? Purchased by Dao Wu (wudao2001@hotmail.com) on September 11, 2012 293-095 Corporate Financial Management: Options Exercises 4 [Hint: This problem is more complicated, but similar to the example presented in the first section of Brealey and Myers' Chapter 21.1 For simplicity, you may wish to ignore, at first, the opportunity to invest $770 million in year 6, and focus only on the first two rounds of investment.] c. How should the year 6 opportunity be incorporated into an options-based analysis of the whole program? d. How would you explain and justify the options-based approach to your fellow committee members? Problem 4. A new product has two major potential markets. The product will succeed in both or fail in both, with equal probability. The markets are otherwise independent. You may enter the markets sequentially or simultaneously either now, one year from now, or two years from now. Later entry is not feasible. Market A requires an initial investment of $100 regardless of when it is entered. If the product is successful, market A will have a present value of $150 one year after entry. If the product fails, market A will be worth $90 one year after entry. Market B requires an initial investment of $55 regardless of when it is entered. One year after entry, B will have a present value of $130 or $20 for success and failure, respectively. For simplicity, perform all discounting in this problem at 5%. a. What is the NPV for each market, assuming each is entered immediately? b. What are all the possible combinations of time and place for introducing the new product? Can any possibilities can be eliminated as suboptimal without further calculations? Why or why not? Which entry strategy is optimal? c. Can you state a general capital budgeting rule for selecting the optimal strategy in this and similar problems? d. Suppose there are three potential markets, A, B, and C, where A and B are as above and C requires an investment of $30 regardless of when entered, and promises a return of $50 or $30 one year later. Does the decision rule you formulated in part (c.) above produce the optimal decision for this revised problem? Why or why not? 1. Richard A. Brealey and Stewart C. Myers, Principles of Corporate Finance, 4th edition, (New York: McGraw-Hill, Inc., 1991), pp. 511-14. Purchased by Dao Wu (wudao2001@hotmail.com) on September 11, 2012 293-095 -5- Appendix Black-Sholes Value of a European Call Option, Expressed as a Percentage of Underlying Asset Value Purchased by Dao Wu (wudao2001@hotmail.com) on September 11, 2012