Solution to Problem Set 5 ECN 134 Financial Economics Prof Farshid Mojaver Questions on Stock Valuation 2 1 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 V0 no longer equals P0 and why V0 is greater or less than P0 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 06 D1 1 06 10 60 k g 0 16 0 06 P0 b Leading P0 E1 10 60 3 18 3 33 c PVGO P0 Trailing P0 E0 10 60 3 00 3 53 E1 3 18 10 60 9 275 k 0 16 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 06 Thus V0 2 06 0 16 0 03 15 85 V0 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 Forecast industry return on equity Industry beta Government bond yield Equity risk premium 40 25 1 2 6 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 Forecasted growth in real GDP Government bond yield Equity risk premium Country A 5 10 5 Country B 2 6 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 10 rind government bond yield industry beta equity risk premium 0 06 1 2 0 05 0 12 Therefore P0 E1 0 60 0 12 0 10 30 0 b 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 a higher 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 V0 b D 0 1 g 4 1 12 101 82 k g 0 164 0 12 P1 V1 V0 1 g 101 82 1 12 114 04 E r D1 P1 P0 4 48 114 04 100 0 1852 18 52 P0 100 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 Beta Market price Intrinsic value Notes Risk free rate Expected market return QuickBrush 1 35 45 00 63 00 SmileWhite 1 15 30 00 4 50 14 50 b Ludlow estimates the following EPS and dividend growth rates for SmileWhite First 3 years Years thereafter 12 per year 9 per year Estimate the intrinsic value of SmileWhite by using the table above and the twostage DDM Dividends per share in the most recent year were 1 72 c Recommended QuickBrush or SmileWhite stock for purchase by comparing each company s intrinsic value with its current market price d Describe one strength of the two stage DDM in comparison with the constantgrowth DDM Describe one weakness inherent in all DDMs a b k rf rM rf 4 5 1 15 14 5 4 5 16 Year 2007 2008 2009 2010 2011 Dividend 1 72 1 93 2 16 2 42 2 63 1 72 1 12 1 72 1 122 1 72 1 123 1 72 1 123 1 09 Present value of dividends paid in 2008 2010 Year 2008 2009 2010 PV of Dividend 1 93 1 161 1 66 2 16 1 162 1 61 2 42 1 163 1 55 Total 4 82 D 2011 2 63 Price at year end 2010 k g 0 16 0 09 37 57 PV in 2007 of this stock price 37 57 24 07 1 16 3 Intrinsic value of stock 4 82 24 07 28 89 c 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 estimate of its intrinsic value Based on this analysis Quick Brush offers the potential for considerable abnormal returns while SmileWhite offers slightly belowmarket risk adjusted returns b Strengths of …