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Problems Set 2 1. You just purchased a bond which matures in 5 years. The bond has a face value of $1,000, an 8% coupon rate, and its current yield is 8.21%. What is the bond’s YTM? 2. One year ago, you paid $965 for a bond that had 10-years to maturity and a 5% coupon rate. If you sold the bond today and realized a total holding period return of 7%, what is the YTM on the bond today? 3. One year ago, you purchased a bond from XYZ Corp with a coupon rate of 5%. When you bought this bond, its current yield was 6.2% and it had six years until maturity. Today you sold the bond and realized a holding period return of 11.25%. At what price did you sell the bond today? 4. You hold two bonds in an investment portfolio. The first bond is a 5-year, zero coupon bond that currently yields 3.75%. The second bond is a 7-year bond with a 5.5% coupon rate and a current price of $915. If all interest rates in the economy decrease by 0.25%, what will be the capital gain (in dollars and percentage) on this portfolio? 5. The common shares of Krusty Burger, Inc. currently sell for $20. The stock just paid a dividend of $1.00 per share. Analysts expect that the dividend will grow at a constant rate of 10% per year. What is the required rate of return on the company’s stock? What stock price is expected one year from now? 6. ABC Corporation's common stock dividend yield is 3.61%, it just paid a dividend of $2.75, and is expected to pay a dividend of $2.89 one year from now. Dividends are expected to grow at a constant rate indefinitely. What is the required rate of return on ABC stock? 7. Biogenetics, Inc. plans to retain and reinvest all of their earnings for the next 30 years. Beginning in year 31, the firm will begin to pay a $30 per share dividend. The dividend will increase at an 8% rate annually thereafter. Given a required return of 18%, what should the stock sell for today? 8. When you bought a share of stock in Killnum yesterday, analysts believed that the dividend next period would be $1.50 and that dividends would grow by 5%. Today Killnum Corp. announces that the dividend for the next year will be $2.50 per share rather than the originally expected $1.50 per share. From then on, it is expected that dividends will resume their historical constant growth rate of 5% per year. If your required rate of return is 12.5%, what will be your overnight capital gains yield on this stock? 9. CBC stock is expected to sell for $25 two years from now. Supernormal growth of 5% is expected for the next 2 years. The current dividend is $1.75 and the required return is 14%. What constant growth rate is expected beginning in year 3? 10. Among Homer Simpson’s many experiences as an (failed) entrepreneur is the time that he started a firm to recycle used grease. The current dividend on this stock is $0.90, and Homer expects that the dividend growth rate will be 5% for each of the next two years, 10% in the third year, and then will remain steady at 12% thereafter. Given the risky nature of purifying grease, prospective investors require a 14% rate of return if they are to invest in the stock of this enterprise. How much is this stock worth today? Based on the above information, how much should you expect the stock to cost in three years? If you buy the stock today and then sell it in 3 years, what will be your holding period return? 11. You have estimated the following probability distributions of expected future returns for Stock X and Y: Stock X Stock Y Probability Return Probability Return 0.1 -10% 0.2 2% 0.2 10 0.2 7 0.4 15 0.3 12 0.2 20 0.2 15 0.1 40 0.1 16 a. What is the expected rate of return for Stock X? Stock Y? b. What is the standard deviation of expected returns for Stock X? For Stock Y? 1 c. Which stock would you consider to be riskier? Why? 12. You have the following information on two securities in which you have invested: Security Expected Standard Beta % Invested (w) Return Deviation Xerox 15% 4.5% 1.20 35% Kodak 12% 3.8% 0.98 65% a) Which stock is riskier in a portfolio context? Which stock is riskier if you are considering them as individual assets (not part of a portfolio)? b) Compute the expected return on the portfolio. c) If the securities have a correlation of +0.60,compute the standard deviation of the portfolio. d) Compute the beta of the portfolio. Case study #1: Investing in Springfield Instructions: You may work on and submit this assignment in a group composed of up to five students. Your group must work independently of other groups; you may not share or borrow your answers with students outside your group. Please keep your answers to the point and well written. The entire assignment must be typed and you must submit BOTH a printed copy to me, AND an electronic to my mailbox. To receive credit, your name must be on the assignment at the time of submission. You also must answer all parts of the question and show full work to receive credit for a problem. Prob of state Lil’ Lisa Slurry Spring Shield CompuGlobalMegaHyperNet β= 0.65 β= 0.825 β= 1.4 State 1 25% 10% -10% 70% State 2 50% 2.5% 25% 20% State 3 25% 25% 5% -50% Expected return on the market =12.5% 3-month T-bill rate =3.25% (a) Compute the expected return for each of the three stocks. (b) Which stock has the most total risk? Compute the total risk of each stock to support your conclusion. (c) If the covariance between Lil’ Lisa Slurry and SpringShield is –0.0075, then what are the expected return and standard deviation of a portfolio that invests $1000 in Lil’ Lisa Slurry and $1500 in SpringShield? (d) Using the beta for each stock given in the above table, what would be the beta of a portfolio that invests $1100 in Lil’ Lisa, $500 in SpringShield, and $900 in CompuGlobalMegaHyperNet? (e) What is the expected rate of return on the portfolio described in (d)? (f) What is the required rate of return on the portfolio described in (d)? (g) If you could invest in only one of the above stocks, which one would it be and why? Please provide a clear, comprehensible answer written using complete sentences and correct English. (h) Would you take any action to improve the portfolio in (d)? If so, what specific action would you take, and why? Think about expected versus required rates of return, and please provide an answer that uses correct English. (i) If you had a total of $2,500 that could be invested in Lil’ Lisa and SpringShield, how would you distribute this money across the two stocks to produce the lowest possible total portfolio risk? You should provide the portfolio weights and dollar amounts invested in each stock. Hint: Use excel to compute the total risk for a variety of portfolio weights. 2 本文来源：https://www.dywdw.cn/6be91361ddccda38376bafce.html
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2023-01-12
