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B.A. 130 Final Exam Fall 1996 4 points per problem 1. What is a certainty-equivalent value? 2. Suppose the standard deviation of a security’s return is 25% per year. What is its variance? 3. What is a preferred stock? 4. Consider two stocks: stock A pays a dividend of $5 a year, and its dividend is not expected to grow or shrink in the future; stock B is expected to pay a dividend of $2.50 next year, and thereafter its dividend is expected to grow at 5% per year. What are the values if the interest rate is 20% per year? 5. Consider the stocks in problem 6. At what interest rate do they sell for the same price? 6. Suppose we have two stocks, C and D. Each of reports $10 a share in earnings; the required rate of return is 10% per year. Stock C has a price of $150; stock D has a price of $100. What is the present value of growth opportunities for stock C? What is the present value of growth opportunities for stock D? 7. You believe that there is a 50% chance that stock A will rise by 20% and a 50% chance that stock A will fall by 10%. You also believe that there is a 25% chance that stock B will rise by 20%, and a 75% chance that stock B will remain constant. The correlation between the two stocks is zero. What is the expected return on stock A? What is the standard deviation? 8. Consider the stocks in problem 12. Suppose you invest half your wealth in stock A and half your wealth in stock B. What is the expected return on your portfolio? What is the standard deviation? 9. Suppose that Michaela Medical Technologies has a beta of -1. Suppose that the market’s required rate of return is 12% per year, and that the risk-free rate is 3% per year. What is the required rate of return on this stock? What do you expect the return on this stock to be in a year in which the market return is 9%? What do you expect the return to be in a year in which the market return is 6%? 10. Suppose that the standard deviation of the market return is 0.2 (20%); the standard deviation of the return on Zizzer Industries is 0.8 (80%), and that the correlation between the excess return on the market and the excess return on Zizzer is 0.5. What is Zizzer’s beta? 11. Suppose you built a diversified portfolio with the same beta as Zizzer: what would you expect the standard deviation of your portfolio to be? 12. Just what are the benefits to portfolio diversification, exactly? 13. What is the approximate net present value to the state lottery agency of a game that offers a prize of $40,000,000 ($1,000,000 a year for each of the next 40 years), for which the state lottery agency sells 30 million one-dollar tickets? The required return is 3.6% per year. 14. Your boss, a state legislator, looks at the situation in problem 13 and says: “Wait a minute! The lottery is only collecting $30 million in revenue, and it is promising $40 million in expenditures!” He calls a press conference to denounce the mismanagement of the lottery. You have one paragraph to head him off. What do you say? 15. What is the net present value at a discount rate of 12% per year of an investment made by spending $1,000,000 this year on a portfolio of stocks with an initial dividend next year of $100,000, and an expected rate of dividend growth thereafter of 4% per year? 16. What is "Monte Carlo analysis"? 17. What is a "put option"? 18. Suppose the risk-free rate is 4% per year and the market return is 8% per year. Suppose the standard deviation of the market portfolio is 20%, and the covariance of security i with the market portfolio's annual return is 0.04. Suppose, further, that the expected cash flow from security i is $1,250,000 each year forever. What is the current market price of security i? 19. Suppose the covariance of Betatron’s annual return with the market is .04, and the standard deviation of the market return is 20% per year. Suppose, further, that half of the market value of Betatron is in the form of bonds; half is held in the form of common stocks; and that Betatron’s bonds have a beta of 0.1. What is the beta of Betatron’s common stock? 20. "If the efficient market hypothesis is true, then a portfolio manager might just as well select his or her portfolio by throwing darts at an open Wall Street Journal." Is this statement correct? Why or why not? 21. In 1996, Megacorp makes a rights issue, at $10 per share, of one new share for every four shares held. Before the issue there were 50 million shares outstanding, and the share price was $12. What is the value of a right? What is the prospective post-rights issue price of the stock? 22. Suppose that you hold a call option on a share of stock, and also "owe" a share of stock--that is, you have sold it short. What is the payoff to your portfolio on the exercise date if the price of the stock is above the strike price? 23. Over the coming year the common stock of Dandelion, Inc., will either halve to $50 from its current level of $100, or rise to $200. The 1-year risk-free interest rate is 5%. What is the option delta of a one-year call option on Dandelion stock with a strike price of $170? 24. What is the net present value today at a discount rate of five percent per year of a stock that has expected next year's earnings of $5 a share, and a present value of growth opportunities of $50 a share? 25. What is the net present value at a discount rate of 8% per year of an investment made by spending $1,000,000 this year on a portfolio of stocks with an initial dividend next year of $50,000, and an expected rate of dividend growth thereafter of 3% per year? B.A. 130 Practice Final Exam Fall 1996 1. Explain why investments that carry greater systematic risk have a higher required rate of return. Because the risk cannot be diversified away--and investors are risk-averse. 2. What is 6% of $100 million? What are the annual interest payments on a coupon bond with an interest rate of 6% and a face value of $100 million? $6 million; $6 million a year. 3. Consider two stocks: stock F pays a dividend of $1 a year, and its dividend is not expected to grow or shrink in the future; stock G is expected to pay a dividend of $0.50 next year, and thereafter its dividend is expected to grow at 5% per year. What are the values of these two stocks if the interest rate is 10%? Explain the connection between their dividends and their prices. Use the growing perpetuity formula: P = D/(r-g). 4. Suppose we have two stocks, H and J. Each of them will pay $5 a share in dividends next year; each of them reports $10 a share in earnings; the required rate of return is 10% per year. Stock C has a price of $50; stock D has a price of $25. What is the present value of growth opportunities for stock C? What is the present value of growth opportunities for stock D? How can two stocks with identical current earnings and dividends sell for different prices? An ambiguity in the question: the firms cannot be “earning” $10 a share and have the dividend payout ratios that the quetsion indicates 5. You believe that there is a 50% chance that stock A will rise by 20% and a 50% chance that stock A will fall by 10%. You also believe that there is a 25% chance that stock B will rise by 20%, and a 75% chance that stock B will remain constant. The correlation coefficient between the two stocks is zero. (a) What is the expected rate of return on stock A? What is the standard deviation? (b) What is the expected rate of return on stock B? What is the standard deviation? (c) Suppose you invest half your wealth in stock A and half your wealth in stock B. What is the expected return on your portfolio? What is the standard deviation of your portfolio? Expected returns of 5% on both stocks; standard deviations of 15% and 8.6%; the 50-500 portfolio has a standard deviation of 8.6% 6. Why is diversification important for investors? In what sense is a “diversified” portfolio better than an “undiversified” portfolio? It allows them to get rid of systematic risk; a diversified portfolio has higher return for the same risk as an undiversified portfolio. 7. What is a certainty-equivalent value? The certain cash flow value that one would see as having the same presnt value as a risky cash flow at that point in time. 8. What is a variance? A measure of risk; the square of the standard deviation; the expected value of the squared difference between the realization of a variable and the variable’s expected value. 9. What is a preferred stock? Stock that (a) comes before common stock in dividend payouts and in bankruptcy proceedings, in that the preferred shareholders must be paid before the common shareholders can be paid; (b) doesn’t have many rights to vote in corporate elections. 10. What is an initial public offering? The first issue of a company’s stock to the public, as opposed to the founders. 11. What is an annuitized annual cost? The average annual value of the cost of maintaining a machine... 12. Suppose that Tyrannosaur Technologies has a beta of -1. Suppose that the market’s required rate of return is 12% per year, and that the risk-free rate is 3% per year. What is the required rate of return on this stock? What do you expect the return on this stock to be in a year in which the market return is 12%? What do you expect the return on this stock to be in a year in which the market return is 3%. -6%; -6%; 3%. 13. Suppose that the standard deviation of the market return is 0.3 (30%); the standard deviation of the return on Zizzer Industries is 0.6 (60%), and that the correlation between the excess return on the market and the excess return on Zizzer Industries is 0.5. What is Zizzer Industries’ beta? Suppose you constructed a diversified portfolio of stocks with the same beta as Zizzer Industries: what would you expect the standard deviation of your portfolio to be? beta = 1; 0.30% 14. Just what are the benefits to portfolio diversification, exactly? the reduction in unsystematic, diversifiable risk. 15. You have the opportunity to undertake an investment with the following set of cash flows: Year 0 1 2 3 4 5 6 7 Cash Flow: -$10 $1.2 $6.2 $0.6 $0.6 $0.6 $3.1 $2.8 Your financial advisors say that this investment carries an incremental beta of two. The risk-free rate is 2%; the market’s required rate of return is 7%. Will undertaking this project raise or lower your company’s total stock market value? By how much? It has a zero NPV, and so undertaking this project will not change your company’s stock market value (although it will probably change your beta) 16. What is the expected net present value to the state lottery agency of a game that has a prize of infinity—a prize of $1,000,000 a year payable for every year in the future until the end of time—for which the state lottery agency expects to sell 18 million one-dollar tickets? The required rate of return is 5% per year. NPV = -$2,000,000 17. Suppose that the price of Carbonics stock can go up by 15% or down by 13% in the next year from the current stock price of $60, and that only these two outcomes are possible. Suppose, further, that the safe interest rate is 10% per year. What is the option delta of a call option on Carbonics stock with a strike price of $60? delta = 9/16.50 = .5 +.75/16.50 = .545454... 18. Suppose that you hold a call option on a share of stock, and also "owe" a share of stock--that is, you have sold it short. What is the total payoff to your portfolio on the exercise date if the price of the stock is above the strike price? Payoff equals minus the strike price 19. What is a "rights issue"? An issue of stock made on such terms that current shareholders must buy them in order to avoid losing money; turning your shareholders into your sales force. 20. What is "Monte Carlo analysis"? A statistical decision-making tool that involves running lots of simulations for lots of randomly- drawn values of the parameters describing a situation, and then looking at the distribution of outcomes.