Chapter Common Stock Valuation McGraw Hill Irwin Copyright 2008 by The McGraw Hill Companies Inc All rights reserved Common Stock Valuation Our goal in this chapter is to examine the methods commonly used by financial analysts to assess the economic value of common stocks These methods are grouped into three categories Dividend discount models Residual Income models Price ratio models 6 2 Security Analysis Be Careful Out There Fundamental analysis is a term for studying a company s accounting statements and other financial and economic information to estimate the economic value of a company s stock The basic idea is to identify undervalued stocks to buy and overvalued stocks to sell In practice however such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst 6 3 The Dividend Discount Model The Dividend Discount Model DDM is a method to estimate the value of a share of stock by discounting all expected future dividend payments The basic DDM equation is V 0 D 1 D 2 D 3 D T L 1 k 1 k 2 1 k 3 1 k T In the DDM equation V 0 the present value of all future dividends D t the dividend to be paid t years from now k the appropriate risk adjusted discount rate 6 4 Example The Dividend Discount Model Suppose that a stock will pay three annual dividends of 200 per year and the appropriate risk adjusted discount rate k is 8 In this case what is the value of the stock today V 0 D 1 D 2 D 3 1 k 1 k 2 1 k 3 200 200 200 V 0 515 42 2 3 1 0 08 1 0 08 1 0 08 6 5 The Dividend Discount Model the Constant Growth Rate Model Assume that the dividends will grow at a constant growth rate g The dividend next period t 1 is D t 1 D t 1 g So D 2 D 1 1 g D 0 1 g 1 g For constant dividend growth the DDM formula becomes T D 0 1 g 1 g V 0 1 k g 1 k if k g V 0 T D 0 if k g 6 6 Example The Constant Growth Rate Model Suppose the current dividend is 10 the dividend growth rate is 10 there will be 20 yearly dividends and the appropriate discount rate is 8 What is the value of the stock based on the constant growth rate model T D 0 1 g 1 g V 0 1 k g 1 k if k g 20 10 1 10 1 10 V 0 243 86 1 08 10 1 08 6 7 The Dividend Discount Model the Constant Perpetual Growth Model Assuming that the dividends will grow forever at a constant growth rate g For constant perpetual dividend growth the DDM formula becomes V 0 D 0 1 g D 1 k g k g Important g k 6 8 Example Constant Perpetual Growth Model Think about the electric utility industry In mid 2005 the dividend paid by the utility company American Electric Power AEP was 1 40 Using D 0 1 40 k 7 3 and g 1 5 calculate an estimated value for DTE V 0 1 40 1 015 24 50 073 015 Note the actual mid 2005 stock price of AEP was 38 80 What are the possible explanations for the difference 6 9 The Dividend Discount Model Estimating the Growth Rate The growth rate in dividends g can be estimated in a number of ways Using the company s historical average growth rate Using an industry median or average growth rate Using the sustainable growth rate 6 10 The Historical Average Growth Rate Suppose the Kiwi Company paid the following dividends 2000 1 50 2001 1 70 2002 1 75 2003 1 80 2004 2 00 2005 2 20 The spreadsheet below shows how to estimate historical average growth rates using arithmetic and geometric averages Year 2005 2004 2003 2002 2001 2000 Dividend 2 20 2 00 1 80 1 75 1 70 1 50 Pct Chg 10 00 11 11 2 86 2 94 13 33 Arithmetic Average 8 05 Geometric Average 7 96 Year 2000 2001 2002 2003 2004 2005 Grown at 7 96 1 50 1 62 1 75 1 89 2 04 2 20 6 11 The Sustainable Growth Rate Sustainabl e Growth Rate ROE Retention Ratio ROE 1 Payout Ratio Return on Equity ROE Net Income Equity Payout Ratio Proportion of earnings paid out as dividends Retention Ratio Proportion of earnings retained for investment 6 12 Example Calculating and Using the Sustainable Growth Rate In 2005 American Electric Power AEP had an ROE of 14 59 projected earnings per share of 2 94 and a per share dividend of 1 40 What was AEP s Retention rate Sustainable growth rate Payout ratio 1 40 2 94 476 So retention ratio 1 476 524 or 52 4 Therefore AEP s sustainable growth rate 1459 52 4 7 645 6 13 Example Calculating and Using the Sustainable Growth Rate Cont What is the value of AEP stock using the perpetual growth model and a discount rate of 7 3 Recall the actual mid 2005 stock price of AEP was 38 80 V 0 1 40 1 07645 436 82 38 80 073 07645 Clearly there is something wrong because we have a negative price What causes this negative price Suppose the discount rate is appropriate What can we say about g 6 14 The Two Stage Dividend Growth Model The two stage dividend growth model assumes that a firm will initially grow at a rate g1 for T years and thereafter grow at a rate g2 k during a perpetual second stage of growth The Two Stage Dividend Growth Model formula is T T D 0 1 g1 1 g1 1 g1 D 0 1 g2 V 0 1 k g1 1 k 1 k k g2 6 15 Using the Two Stage Dividend Growth Model I Although the formula looks complicated think of it as two parts Part 1 is the present value of the first T dividends it is the same formula we used for the constant growth model Part 2 is the present value of all subsequent dividends So suppose MissMolly com has a current dividend of D 0 5 which is expected to shrink at the rate g1 10 for 5 years but grow at the rate g2 4 forever With a discount rate of k 10 what is the present value of the stock 6 16 Using the Two Stage Dividend Growth Model II T T D 0 1 g1 1 g1 1 g1 D 0 1 g 2 V 0 1 k g1 1 k 1 k k g2 5 5 5 00 0 90 0 90 0 90 5 00 1 0 04 V 0 1 0 10 0 10 1 0 10 1 0 10 0 10 0 04 14 25 31 78 46 03 The total value of 46 03 is the sum of a 14 25 present …