Sample Final Exam

Published: 2021-08-17 20:50:08
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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 < 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 the 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 project’s beta is different from that of the overall firm, then the: (4 pts) A. CAPM can no longer be used. B. project should be discounted using the overall firm’s 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). Jack’s 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%. Jack’s tax rate is 35%. What is Jack’s 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]

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