QCU and Exercise for Part 3 : 30 QCU (only one answer is right) and 1 Exercise

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1 QCU and Exercise for Part 3 : 30 QCU (only one answer is right) and 1 Exercise Risk and return Cost of equity From the cost of equity to the cost of capital Corporate Finance Master All campuses 1

2 30 QCU 1) Which of the following statements is false? A) The variance increases with the magnitude of the deviations from the mean. B) The variance is the expected squared deviation from the mean. C) Two common measures of the risk of a probability distribution are its variance and standard deviation. D) If the return is riskless and never deviates from its mean, the variance is equal to one. 2) Which of the following equations is incorrect? A) Var ( R) = SD( R) B SD( R) = ( [ ]) 2 RPR R E R C) Var ( R) = ( [ ]) 2 RPR R E R D) ER [ ] = RPR R 3) Which of the following investments offered the lowest overall return over the past eighty years? A) Small stocks B) Treasury Bills C) S&P 500 D) Corporate bonds 4) Suppose an investment is equally likely to have a 35% return or a - 20% return. The expected return for this investment is closest to: A) 7.5% B) 15% C) 5% D) 10% 2

3 Use the table for the question(s) below. Consider the following Price and Dividend data for General Electric Company: Date Price ($) Dividend ($) December 31, 2008 $14.64 January 26, 2009 $13.35 $0.10 April 28, 2009 $9.14 $0.10 July 29, 2009 $10.74 $0.10 October 28, 2009 $8.02 $0.10 December 30, 2009 $7.72 5) Assume that you purchased General Electric Company stock at the closing price on December 31, 2008 and sold it after the dividend had been paid at the closing price on January 26, Your dividend yield for this period is closest to: A) -8.15% B) 0.75% C) 0.70% D) -8.80% 6) Assume that you purchased General Electric Company stock at the closing price on December 31, 2008 and sold it after the dividend had been paid at the closing price on January 26, Your capital gains rate (yield) for this period is closest to: A) 0.75% B) 0.70% C) -8.80% D) -8.15% Use the table for the question(s) below. Consider the following realized annual returns: Year End Index Realized Return Stock A Realized Return % 46.3% % 26.7% % 86.9% % 23.1% % 0.2% % -3.2% % -27.0% % 27.9% % -5.1% % -11.3% 7) The average annual return on the Index from 2000 to 2009 is closest to: A) 7.10% B) 4.00% C) 9.75% D) 8.75% 3

4 8) The variance of the returns on the Index from 2000 to 2009 is closest to: A).0450 B).3400 C).1935 D) ) Which of the following is not a systematic risk? A) The risk that oil prices rise, increasing production costs B) The risk that the Federal Reserve raises interest rates C) The risk that the economy slows, reducing demand for your firm's products D) The risk that your new product will not receive regulatory approval 10) Which of the following is not a diversifiable risk? A) The risk that oil prices rise, increasing production costs B) The risk of a product liability lawsuit C) The risk that the CEO is killed in a plane crash D) The risk of a key employee being hired away by a competitor Use the following information to answer the problems below. Consider two banks. Bank A has 1000 loans outstanding each for $100,000, that it expects to be fully repaid today. Each of Bank A's loans have a 6% probability of default, in which case the bank will receive $0 for each of the defaulting loans. Bank B has 100 loans of $1 million outstanding, which it also expects to be fully repaid today. Each of Bank B's loans have a 5% probability of default, in which case the bank will receive $0 for each of the defaulting loans. The chance of default is independent across all the loans. 11) The expected overall payoff to Bank A is: A) $5,000,000 B) $6,000,000 C) $94,000,000 D) $95,000,000 12) The expected overall payoff to Bank B is: A) $5,000,000 B) $6,000,000 C) $94,000,000 D) $95,000,000 13) The standard deviation of the overall payoff to Bank A is closest to: A) $689,000 B) $751,000 C) $2,179,000 D) $2,375,000 4

5 14) The standard deviation of the overall payoff to Bank B is closest to: A) $751,000 B) $2,179,000 C) $2,375,000 D) $21,794,000 15) Consider a portfolio that consists of an equal investment in 20 firms. For each of these firms, there is a 70% probability that the firms will have a 16% return and a 30% that they will have a - 8% return. Each of these firms returns are independent of each other. The standard deviation of this portfolio is closest to: A) 2.5% B) 4.2% C) 8.8% D) 11.0% Use the following information to answer the question(s) below. Company Ticker Beta Ford Motor Company F 2.77 International Business Machines IBM 0.73 Merck MRK ) If the market risk premium is 6% and the risk-free rate is 4%, then the expected return of investing in Ford Motor Company is closest to: A) 10.0% B) 16.2% C) 17.1% D) 20.6% 17) If the market risk premium is 6% and the risk-free rate is 4%, then the expected return of investing in Merck is closest to: A) 5.4% B) 9.4% C) 10.0% D) 10.4% 18) If the expected return on the market is 11% and the expected return of investing in Merck is 10.35%, then the risk-free rate must be: A) 3.0% B) 4.0% C) 4.5% D) 5.0% 5

6 19) If the risk-free rate is 5% and the expected return of investing in Merck is 11.3%, then the expected return on the market must be: A) 8.0% B) 10.0% C) 10.4% D) 12.0% Use the information for the question(s) below. Suppose that in the coming year, you expect Exxon-Mobil stick to have a volatility of 42% and a beta of 0.9, and Merck's stock to have a volatility of 24% and a beta of 1.1. The risk free interest rate is 4% and the markets expected return is 12%. 20) Which stock has the highest total risk? A) Merck since it has a lower volatility B) Merck since it has a higher Beta C) Exxon-Mobil since it has a higher volatility D) Exxon-Mobil since it has a lower beta 21) Which stock has the highest systematic risk? A) Merck since it has a higher Beta B) Exxon-Mobil since it has a lower beta C) Exxon-Mobil since it has a higher volatility D) Merck since it has a lower volatility 22) The beta for the market portfolio is closest to: A) 1 B) 0 C) Unable to answer this question without knowing the markets expected return D) Unable to answer this question without knowing the markets volatility 23) The beta for the risk free investment is closest to: A) 1 B) 0 C) Unable to answer this question without knowing the risk free rate D) Unable to answer this question without knowing the markets volatility 6

7 Use the figure for the question(s) below. Consider the following graph of the security market line: 24) Stock "A" A) has a relatively lower expected return than predicted. B) is underpriced. C) falls below the SML. D) is overpriced. 25) Stock "D" A) is less risky than the market portfolio. B) is overpriced. C) has a beta equal to 1. D) falls above the SML. 26) The market portfolio A) is underpriced. B) has a beta equal to 2. C) is overpriced. D) falls on the SML. 27) Which of the following statements is false? A) The tax deductibility of interest lowers the effective cost of debt financing for the firm. B) When a firm uses debt financing, the cost of the interest it must pay is offset to some extent by the tax savings from the interest tax shield. C) With tax-deductible interest, the effective after-tax borrowing rate is r(τc). D) The WACC represents the cost of capital for the free cash flow generated by the firm s assets. 7

8 Use the information for the question(s) below. Flagstaff Enterprises expected to have free cash flow in the coming year of $8 million, and this free cash flow is expected to grow at a rate of 3% per year thereafter. Flagstaff has an equity cost of capital of 13%, a debt cost of capital of 7%, and it is in the 35% corporate tax bracket. 28) If Flagstaff currently maintains a.5 debt to equity ratio, then Flagstaff's WACC is closest to: A) 10.00% B) 10.25% C) 9.50% D) 8.75% 29) If Flagstaff currently maintains a.5 debt to equity ratio, then the value of Flagstaff is closest to: A) $114 million B) $100 million C) $111 million D) $140 million 30) Consider the following equation: E D rwacc = re + rd ( 1 τ c ) E+ D E+ D the term E in this equation is A) the amount of equity. B) the amount of debt. C) the required rate of return on debt. D) the required rate of return on equity. 8

9 Exercise Exercise 1 Suppose the risk-free interest rate is 5%, and the stock market will return either 40% or 20% each year, with each outcome equally likely. Compare the following two investment strategies: (1) invest for one year in the risk-free investment, and one year in the market, or (2) invest for both years in the market. a. Which strategy has the highest expected final payoff? b. Which strategy has the highest standard deviation for the final payoff? c. Does holding stocks for a longer period decrease your risk? 9

10 30 QCU :Answer 1) Answer: D Explanation: D) If the return is riskless and never deviates from its mean, the variance is equal to zero. 2) Answer: A Explanation: A) SD( R) = Var ( R) 3) Answer: B 4) Answer: A Explanation: A) ER [ ] P R ( ) ( ) = =.50 35% % = 7.5% 5) Answer: C Explanation: C) = div / P0 =.10 / =.0068 R R 6) Answer: C Explanation: C) = (P1 - P0) / P0 = ( ) / = ) Answer: D Explanation: D) R annual = R 1 + R R N N 8) Answer: D Explanation: D) R annual = R 1 + R R N N Index Year Realized End Return ( R - R ) ( R R) % 14.78% % 15.88% % 21.68% % 0.18% 3.24E % % % % % % % 23.38% % -4.42% % -1.42% = R 1 + R R = R 1 + R R = = 8.82% = = 8.82% Variance = SUM of ( ) 2 R R / T - 1 = / 9 = ) Answer: D 10) Answer: A 10

11 11) Answer: C Explanation: C) E[payoff] = (.06)(1000)($0) + (1 -.06)(1000)($100,000) = $94,000,000 12) Answer: D Explanation: D) E[payoff] = (.05)(100)($0) + (1 -.05)(100)($1,000,000,000) = $95,000,000 13) Answer: B Explanation: B) E[payoff] = (.06)(1000)($0) + (1 -.06)(1000)($100,000) = $94,000,000 ( ) ( ) ( ) 2 2 SD Payoff =.06 $0 $ $100 $94 = million 23,748,684 SD( Overall Payoff ) = = $750, ) Answer: B Explanation: B) E[payoff] = (.05)(100)($0) + (1 -.05)(100)($1,000,000) = $95,000,000 ( ) ( ) ( ) 2 2 SD Payoff =.05 $0 $ $100 $95 = million 21,794, 495 SD( Overall Payoff ) = = $2,179, ) Answer: A Explanation: A) E[return] = (.70)(16%) + (.30)(-8%) = 8.8% ( ) ( ) ( ) t 2 2 SD R =.70 16% 8.8% % 8.8% = % % SD( R portfolio ) = = % 20 16) Answer: D Explanation: D) Return = (.06) = ) Answer: B Explanation: B) Return = (.06) = ) Answer: C Explanation: C) Return =>.1035 = + 0.9(.11 - X) =>.1X = (.11) => = ) Answer: D Explanation: D) Return =>.113 = (X -.05) =>.9X = => =.12 20) Answer: C 21) Answer: A 22) Answer: A Explanation: A) ( ) ( ) Beta of the Market Portfolio = Cov R,R mkt mkt SD R mkt = SD ( R mkt )Corr R mkt,r mkt SD R mkt ( ) ( ) = Corr(Rmkt,Rmkt) = 1 The market is perfectly correlated with itself. 11

12 23) Answer: B Explanation: B) Since the risk free investment has zero volatility, the Beta must equal zero. 24) Answer: B 25) Answer: B 26) Answer: D 27) Answer: C Explanation: C) With tax-deductible interest, the effective after-tax borrowing rate is r(1 - τc). 28) Answer: B E D E+ D E+ D 1.5 r WACC = ( 1.35) = Explanation: B) r = r + r ( 1 τ ) WACC E D c 29) Answer: C E D E+ D E+ D 1.5 r WACC = ( 1.35) = Explanation: C) r = r + r ( 1 τ ) Value Flagstaff = 30) Answer: A WACC E D c FCF Wacc g = $8 = $ million

13 Exercise : Answer Exercise 1 R(i) : (1.05)(1.40)-1 = 47% or (1.05)(0.80) 1 = 16% R(ii) : = 96%, = 12%, =12%, = 36% a. ER(i) = (47% 16%)/2 = 15.5% ER(ii) = (96% + 12% + 12% 36%)/4 = 21% b. Vol(i) =sqrt(1/2 (47% 15.5%) 2 + 1/2( 16% 15.5%) 2 ) = 31.5% Vol(ii)=sqrt(1/4 (96%-21%) 2 + ½(12% 21%) 2 + 1/4( 36% 21%) 2 ) = 47.5% c. No 13

Financial Markets 11-1

Financial Markets Laurent Calvet calvet@hec.fr John Lewis john.lewis04@imperial.ac.uk Topic 11: Measuring Financial Risk HEC MBA Financial Markets 11-1 Risk There are many types of risk in financial transactions