******************************************************************************Descriptive and Conceptual QuestionsYour Name:____________________Midterm 2Financial Economics, Spring 2010 ******************************************************************************Descriptive and Conceptual Questions[4 pts] 1. Describe one weakness inherent in all DDMs.Answer:All DDMs are very sensitive to input values. Small changes in k or g can imply large changes in estimated intrinsic value. These inputs are difficult to measure.[9 pts] 2. Identify, within the context of the constant dividend growth model, how each of the following factors would affect the P/E ratio of stock ABCa. Risk (beta) of ABCb. Estimates growth rate of earnings and dividendsc. Market risk premiumAnswer:a. The P/E ratio is a decreasing function of riskiness; as risk increases, the P/E ratio decreases. b. The P/E ratio is an increasing function of the growth rate of the firm; the higher the expected growth, the higher the P/E ratio. c. The P/E ratio is a decreasing function of the market risk premium. An increased market risk premium increases the required rate of return, lowering the price of a stock relative to its earnings. [6 pts] 3. Explain how an increase in dividend payout would affect each of the following (holding all other factors constant):a. Sustainable growth rate.b. Growth in book value.Answer:a. An increase in dividend payout will reduce the sustainable growth rate as less funds are reinvested in the firm. The sustainable growth rate (i.e., ROE x plowback) will fall as plowback ratio falls.b. The increased dividend payout rate will reduce the growth rate of book value for the same reason -- less funds are reinvested in the firm.[4 pts] 4. Provide a formal definition of beta in a SML and explain what it measures. Answer:Formal definition:Beta describes the relative variability of returns. It measures the risk contribution of a security to the market portfolio relative to the variance of the market portfolio. It is a measure of the systematic risk of a security in the market portfolio.[4 pts] 5. How is beta measured empirically? βi=Cov(ri, rM)σ2(rM)AnswerEmpirically Beta is estimated using the Characteristic Line: rit = ai + birMt + eitThe beta of the market portfolio market is equal one.[7 pts] 6. Describe the two steps in which an individual investor comes up with an optimal portfolio of risky and risk-free assets. Use a graph to make your points.Answer Short Answer questions [4 pts each]1. If the expected rate of return of the market portfolio is 15% and a stock with a beta of 1.0 paysa dividend yield of 4%, what must the market believe is the expected rate of price appreciation onthat stock?AnswerSince beta = 1.0, then k = market return = 15%Therefore: 15% = D1/P0 + g = 4% + g  g = 11%2. The common stock of Flavorful Teas has an expected return of 14.4%. The return on the market is 10% and the risk-free rate of return is 3.5%. What is the beta of this stock? AnswerE(r) = .144 = .035 +   (.10 - .035); .109 = .065;  = 1.683. The stock of Big Joe's has a beta of 1.14 and an expected return of 11.6%. The risk-free rate of return is 4%. What is the expected return on the market? Answer E(r) = .116 = .04 + 1.14 (rm - .04); .1216 = 1.14rm; rm = .1067 = 10.67%4. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.09? Answer9% = w1(12%) + (1 - w1)(5%); 9% = 12%w1 + 5% - 5%w1; 4% = 7%w1; w1 = 0.57; 1 - w1 = 0.43; verify: 0.57(12%) + 0.43(5%) = 8.99%.5. SGA Consulting had a FCFE of $3.2M last year and has 3.2M shares outstanding. SGA's required return on equity is 13%. FCFE is expected to grow at 8.5% forever. What is the intrinsicvalue of SGA's shares?$3.2M/3.2M = $1.00 FCFE per share; 1.00 * 1.085 = 1.085; 1.085/(.13 - .085) = 24.116. Fly Boy Corporation is expected have EBIT of $800k this year. Fly Boy Corporation is in the 30% tax bracket, will report $52,000 in depreciation, will make $86,000 in capital expenditures, and have a $16,000 increase in net working capital this year. What is Fly Boy's FCFF? FCFF = EBIT(1-T) + depreciation - capital expenditures - increase in NWC FCFF = 800,000(.7) + 52,000 - 86,000 - 16,000 = 510,000Problem solving questions [18 pts] 1. Stock valuation The market consensus is that Analog Electronic Corporation has an ROE=9%, has a beta of 1.25, and plans to maintain indefinitely its traditional plowback ratio of 2/3. This year’s earnings were $3 per share. The annual dividend was just paid. The consensus estimate of the coming year’s market return is 14%, and T-bills currently offer a 6% return.a. Find the price at which Analog stock should sell.b. Calculate the present value of growth opportunities.c. Suppose your research convinces you Analog will announce momentarily that it will immediately reduce its plowback ratio to 1/3. Find the intrinsic value of the stock. The market is still unaware of this decision. Explain why V0 no longer equals P0 and whyV0 is greater or less thanP0.a. k = rf + (rM) – rf ] = 6% + 1.25(14% – 6%) = 16%g = 2/3 9% = 6%D1 = E0(1 + g) (1 – b) = $3(1.06) (1/3) = $1.06P0=D1k−g=$1 . 060 . 16−0 . 06=$10 . 60b.PVGO=P0−E1k=$ 10 .60−$ 3 . 180 .16=−$ 9. 275The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%).c. Now, you revise b to 1/3, g to 1/3  9% = 3%, and D1 to:E0  1.03  (2/3) = $2.06Thus:V0 = $2.06/(0.16 – 0.03) = $15.85V0 increases because the firm pays out more earnings instead of reinvesting a poor ROE. This information is not yet known to the rest of the market.[6 pts] 2. Risk Aversion Consider a portfolio that offers an expected rate of return of 12% and a standarddeviation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversionfor which the risky portfolio is still preferred to bills?Answer)When we specify utility by U = E(r) – 0.5Aσ2, the utility level for T-bills is: 0.07The utility level for the risky portfolio is: U = 0.12 – 0.5A(0.18)2 = 0.12 – 0.0162AIn order for the risky portfolio to be preferred to bills, the following inequality must hold:0.12 – 0.0162A > 0.07  A < 0.05/0.0162 = 3.09 [6 pts] 3. Return and Risk Consider a portfolio that is invested 40% in stock Q and 60% in stock R? a. What is the expected return of the portfolio?b.