UGBA 103 Final Exam PRACTICE EXAM I Time: 3 hours
Name: Student id#:
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Note: Throughout the exam, assume that there are no frictions, i.e., perfect capital markets, information is immediately incorporated into stock prices, there is no spread between borrowing and lending rates, etc. If nothing else is stated, assume that everything is in real terms. Also, if nothing else is stated, do not consider taxes. If you think that you need to make additional assumptions, please specify these.
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Circle your final numerical answers!
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1. Portfolio choice: The following table shows the possible returns for two stocks, i and j, in different states of the world. Here, pij denotes the probability for stock i returning ri and stock j returning rj. Returns ri 10% 30% 50%
rj pij
0%
20%
30%
30% 0% 0%
0% 20% 20%
0% 20% 10%
Hint: Notice that there are only 5 states of the world for which the probability to occur is greater than 0.
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a) (5 points) Calculate expected return of stock i and j respectively.
b) (5 points) Calculate the standard deviation of stock i ’s and j’s returns respectively.
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c) (5 points) The correlation coefficient between stock i’s and j’s return is 0.76. Calculate the standard deviation of the return of a portfolio of 40% in stock i and 60% in stock j.
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2. Investments: Parts a) and b) of this problem are related. Disregard taxes in this problem.
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a) (7 points): Mr. Karl Swedenborg, the patriarch owner of Swedenborg Inc., a small business had just completed reading his son’s (Gustaf’s), analysis of the possible paths forward for the company, and he was impressed. The company owned a beach on Öland, a popular tourist island off the east cost of Sweden. Its main source of revenue was from its hotel business, consisting of several small bungalows on the beach that tourists could rent. It also owned a restaurant and a supermarket close to the beach. The restaurant and supermarket businesses were very profitable, both earning a return on equity of 40%. Together, the two businesses generated annual free cash flows of 7 million Swedish Krona1, growing at a steady rate of 3% per year in the foreseeable future. The beach business, however, which used to be the most profitable part of the company, nowadays earned a lousy return on equity of 5%, corresponding to 1 million Swedish Krona per year in free cash flows, and growing at the same rate (3%) as the rest of the business. Further, the risk of the company was low: The risk-adjusted discount rate was 8% (the same across the three businesses), not much higher than the risk-free rate of 5%. Gustaf, who had just received his business degree from a U.S. school (not Haas), had completed a full analysis of three possible strategies for the beach business: 1. Continue as before.
2. Sell the beach and bungalows to a luxury hotel chain, which would build a luxury resort on the beach. The hotel chain was willing to pay 30 million Swedish Krona for the beach in cash, immediately.
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3. Rent the beach to the hotel chain, which would be willing to sign a long-term contract and pay 2 million Swedish Krona per year in the foreseeable future. Given the very low risk of the hotel chain business, these cash flows could be considered risk-free.
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“You see Papa, the world is changing, and we need to change with it. Bungalows are out, luxury hotels are in!” his son announced enthusiastically. Calculate the value of each of the three (mutually exclusive) strategies. Which strategy should the company choose?
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You can assume that these cash flows occur at the end of the year, beginning one year into the future.
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b) (6 points): Although Mr. Swedenborg loved and respected his son, he decided to get a second opinion and therefore hired a consultant. She agreed with Gustaf’s analysis, except for that she pointed out that the analysis had not taken into account that the luxury resort, by targeting a different customer group, would affect the profitability of the restaurant and supermarket businesses. The total annual cash flows from these businesses would shrink to 6 million Swedish Krona, and grow at only 2% per year in the future. Gustaf agreed with this assessment, but argued that the consultant was making a serious mistake, by mixing in value creation generated from other parts of the business. Gustaf argued that the value of the beach business must be considered on a standalone basis in the analysis.
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What was the value of each of the three strategies? Who was right?
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3. Investments: Parts a) and b) of this problem are related. Disregard taxes in this problem.
In this problem, the discounted dividend model is assumed to hold. A California based company, OldWindows, Inc. (also known as OWI) owns a unique niche in the market. It offers terminal-based software for users on computer systems with Intel 286 processors. Although not exactly known as a high-growth industry, OWI is generating steady, slightly growing profits. If it continues as before, next year the company expects to pay dividends of $15 per share (there are 10,000 shares outstanding). The company faces a risk adjusted discount rate of 12%, and its current plowback ratio is 40%.
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Recently, the CEO has come up with a strategy for growth: international expansion. By marketing the company’s software in other countries, the CEO argues that the company would be able to generate (almost) perpetual high growth. OWI is currently growing at 4% per year, but with the new strategy, it would increase its growth rate to 9%. The growth would be financed by increasing retained earnings.
a) (7 points): What is the present value of growth opportunities (PVGO) for OWI with its current (low-growth) operations?
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b) (8 points): What will be the effect on OWI’s stock price if it adopts the highgrowth strategy?
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