Sample Final Exam Essay Example for Free

Sample Final Exam Essay The company currently has earnings per share of $8. 25. The company has no growth and pays out all earnings as dividends. It has a new project which will require an investment of $1. 60 per share today (at time zero). The project will increase the earnings by $0. 40 per share indefinitely starting one year after the investment. Investors require a 10 percent return on XYZ stock. Assume the firm just paid the dividend of $8. 25 yesterday. a) What is the value per share of the company’s stock assuming the firm does not undertake the investment opportunity? 5 pts) b) If the company does undertake the investment what is the value per share now? (10 pts) c) What will the value per share be 3 years from now? (5 pts) Solution: a) P = Dividend / R = 8. 25 / 0. 1 = $ 82. 5 b) NPVGO = (-1. 60 + 0. 40 / 0. 1) = $ 2. 40 So the stock price will be: 82. 5 + 2. 40 = 84. 90 c) (8. 25 + 0. 40) / 0. 1 = 86. 5 Question 3 – Portfolio Variance Suppose the expected returns and standard deviation of stocks A and B are E(Ra) = 0. 13, E(Rb) = 0. 19, ? a = 0. 38, ? b = 0. 62 respectively. ) Calculate the expected return and standard deviation for a portfolio that is composed of 45 percent A and 55 percent B when the correlation coefficient between the returns on A and B is 0. 5 (10 pts) b) How does the correlation coefficient between the returns on A and B affect the standard deviation of the portfolio? (3 pts) c) Provide a range for the correlation coefficient where we obtain diversification benefits. (i. e, The portfolio standard deviation is less than the weighted average of the individual standard deviations of the stocks? ) Provide a range where we don’t have diversification benefits. 3 + 2 pts) d) For some values of correlation coefficient, we can achieve a portfolio standard deviation of almost zero. TRUE or FALSE? ( 2 pts) Solution: a) The expected return of the portfolio is the sum of the weight of each asset times the expected return of each asset, so: E(RP) = wAE(RA) + wBE(RB) E(RP) = . 45(. 13) + . 55(. 19) E(RP) = . 1630 or 16. 30% The variance of a portfolio of two assets can be expressed as: ([pic] = w[pic]([pic] + w[pic]([pic] + 2wAwB(A(B(A,B ([pic] = . 452(. 382) + . 552(. 622) + 2(. 45)(. 55)(. 38)(. 62)(. 50) ([pic] = . 20383 So, the standard deviation is: (P = (. 20383)1/2 = . 4515 or 45. 15% b) As Stock A and Stock B become less correlated, or more negatively correlated, the standard deviation of the portfolio decreases. c) corr lt; 1 (strictly less), corr = 1 d) TRUE Question 4 – CAPM and SML Suppose that you observe the following information. Assume these securities are correctly priced. Beta Expected Return XYZ Corp: 1. 4 0. 150 ABC Corp: 0. 9 0. 115 a) What is the risk free rate and the expected return on the market? 3 + 3 pts) b) What is the expected return on an asset with a beta 1. 6? (4 pts) c) What is the beta on a portfolio consisting of 30% XYZ, 30% ABC, 20% risk free asset and 20% market portfolio? (5 pts) d) If a security has beta 1. 8 and expected return 18%, is this security above or below SML? Over or under priced? ( 2 + 3 pts) Solution: a) Here we have the expected return and beta for two assets. We can express the returns of the two assets using CAPM. If the CAPM is true, then t he security market line holds as well, which means all assets have the same risk premium. Setting the reward-to-risk ratios of the assets equal to each other and solving for the risk-free rate, we find: (. 15 – Rf)/1. 4 = (. 115 – Rf)/. 90 .90(. 15 – Rf) = 1. 4(. 115 – Rf) .135 – . 9Rf = . 161 – 1. 4Rf .5Rf = . 026 Rf = . 052 or 5. 20% Now using CAPM to find the expected return on the market with both stocks, we find: .15 = . 0520 + 1. 4(RM – . 0520). 115 = . 0520 + . 9(RM – . 0520) RM = . 1220 or 12. 20%RM = . 1220 or 12. 20% b) 5. 20% + 1. 6 (12. 20% – 5. 20%) = 5. 20% + 11. 20% = %16. 40 c) 0. 30 * 1. 4 + 0. 30*0. 9 + 0. 2*1 +0. *0 = 0. 89 d) According to SML 5. 20% + 1. 8 (12. 20% 5. 20%) = 5. 20% + 12. 60% = 17. 80%. The security is above SML. It is underpriced. Question 5 1). For a multi-product firm, if a projects beta is different from that of the overall firm, then the:Â  (4 pts) A. CAPM can no longer be used. B. project should be discounted using the overall firms beta. C. project should be discounted at a rate commensurate with its own beta. D. project should be discounted at the market rate. E. project should be discounted at the T-bill rate. 2). Jacks Construction Co. as 80,000 bonds outstanding that are selling at par value. Bonds with similar characteristics are yielding 8. 5%. The company also has 4 million shares of common stock outstanding. The stock has a beta of 1. 1 and sells for $40 a share. The U. S. Treasury bill is yielding 4% and the market risk premium is 8%. Jacks tax rate is 35%. What is Jacks weighted average cost of capital? (8 pts) A. 7. 10% B. 7. 39% C. 10. 38% D. 10. 65% E. 11. 37% Re = . 04 + (1. 1 ( . 08) = . 128 Debt: 80,000 ( $1,000 = $80m Common: 4m ( $40 = $160m Total = $80m + $160m = $240m [pic]