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UCD ECN 134 - HW5s-S10-2

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ECN 134Questions on Stock Valuation 2Risk and ReturnSolution to Problem Set 5ECN 134Financial Economics Prof. Farshid MojaverQuestions on Stock Valuation 21. 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 P/E ratio.c. Calculate the present value of growth opportunities.d. 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 0V no longer equals 0P and why 0V is greater or less than0P.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) = $1.0660$10.0.060.16$1.06gkDP10b. Leading P0/E1 = $10.60/$3.18 = 3.33 Trailing P0/E0 = $10.60/$3.00 = 3.53c.275.9$16.018.3$60.10$kEPPVGO10The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%).d. 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.2. Peninsular Research is initiating coverage of a mature manufacturing industry. John Jones, CFA, head of the research department, gathered the following fundamental industry and market data to help in his analysis:Forecast industry earnings retention rate 40%Forecast industry return on equity 25%Industry beta 1.2Government bond yield 6%Equity risk premium 5%a. Compute the price-to-earnings (P0/E1) ratio for the industry based on this fundamental data.b. Jones wants to analyze how fundamental P/E ratios might differ among countries.He gathered the following economic and market data.Fundamental Factors Country A Country BForecasted growth in real GDP 5% 2%Government bond yield 10% 6%Equity risk premium 5% 4%Determine whether each of these fundamental factors would cause P/E ratios to be generally higher for Country A or higher for Country B.a. The industry’s estimated P/E can be computed using the following model:P0/E1 = payout ratio/(r  g)However, since r and g are not explicitly given, they must be computed using the following formulas:gind = ROE  retention rate = 0.25  0.40 = 0.10rind = government bond yield + ( industry beta  equity risk premium) = 0.06 + (1.2  0.05) = 0.12Therefore:P0/E1 = 0.60/(0.12  0.10) = 30.0b. i. Forecast growth in real GDP would cause P/E ratios to be generally higher for Country A. Higher expected growth in GDP implies higher earnings growth and a higher P/E.ii. Government bond yield would cause P/E ratios to be generally higher for Country B. A lower government bond yield implies a lower risk-free rate and therefore a higher P/E.iii. Equity risk premium would cause P/E ratios to be generally higher for Country B. A lower equity risk premium implies a lower required return and ahigher P/E.3. The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.2. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $10 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 20% per year on all reinvested earnings forever.a. What is the intrinsic value of a share of Xyrong stock?a. If the market price of a share is currently $100, and you expect the market price to be equal to the intrinsic value 1 year from now, what is your expected 1-year holding-period return on Xyrong stock?a. k = rf +[E(rM ) – rf ] = 8% + 1.2(15% – 8%) = 16.4%g = b  ROE = 0.6  20% = 12%82.101$12.0164.012.14$gk)g1(DV00b. P1 = V1 = V0(1 + g) = $101.82  1.12 = $114.04%52.181852.0100$100$04.114$48.4$PPPD)r(E00114. Janet Ludlow’s firm requires all its analysts to use a two-stage dividend discount model (DDM) and the Capital Asset Pricing Model (CAPM) to value stocks. Using the CAPM and DDM, Ludlow has valued QuickBrush Company at $63 per share. She now must value SmileWhite Corporation.a. Calculate the required rate of return for SmileWhite by using the information in the following table.QuickBrush SmileWhiteBeta 1.35 1.15Market price $45.00 $30.00Intrinsic value $63.00 ?Notes:Risk-free rate 4.50%Expected market return 14.50%b. Ludlow estimates the following EPS and dividend growth rates for SmileWhite: First 3 years 12% per yearYears thereafter 9% per yearEstimate the intrinsic value of SmileWhite by using the table above, and the two-stage DDM. Dividends per share in the most recent year were $1.72.c. Recommended QuickBrush or SmileWhite stock for purchase by comparing eachcompany’s intrinsic value with its current market price.d. Describe one strength of the two-stage DDM in comparison with the constant-growth DDM. Describe one weakness inherent in all DDMs.a. k = rf + (rM) – rf ] = 4.5% + 1.15(14.5%  4.5%) = 16%b. Year Dividend2007$1.722008$1.72  1.12 = $1.932009$1.72  1.122 = $2.162010$1.72  1.123 = $2.422011$1.72  1.123  1.09 =$2.63Present value of dividends paid in 2008 – 2010:Year PV of Dividend2008$1.93/1.161 = $1.662009 $2.16/1.162 = $1.612010 $2.42/1.163 = $1.55Total = $4.82Price at year-end 201057.37$09.016.063.2$2011gkDPV in 2007 of this stock price07.24$16.157.37$3Intrinsic value of stock = $4.82 + $24.07 = $28.89c. The data in the problem indicate that Quick Brush is selling at a price substantially below its intrinsic value, while the calculations above demonstrate that SmileWhite is selling at a price somewhat above the estimateof its intrinsic value. Based on this analysis, Quick Brush offers the potential for considerable abnormal returns, while SmileWhite offers slightly below-market risk-adjusted returns.b. Strengths of


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