McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Equity Valuation CHAPTER 12

12-2 Fundamental Stock Analysis: Models of Equity Valuation Basic Types of Models –Balance Sheet Models –Dividend Discount Models –Price/Earnings Ratios Estimating Growth Rates and Opportunities

12-3 Intrinsic Value and Market Price Intrinsic Value –Self assigned Value –Variety of models are used for estimation Market Price –Consensus value of all potential traders Trading Signal –IV > MP Buy –IV < MP Sell or Short Sell –IV = MP Hold or Fairly Priced

12-4 Dividend Discount Models: General Model V D k o t t t      ()1 1 V 0 = Value of Stock D t = Dividend k = required return

12-5 No Growth Model V D k o  Stocks that have earnings and dividends that are expected to remain constant Preferred Stock

12-6 No Growth Model: Example E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33 V D k o 

12-7 Constant Growth Model Vo Dg kg o    ()1 g = constant perpetual growth rate

12-8 Constant Growth Model: Example Vo Dg kg o    ()1 E 1 = $5.00b = 40% k = 15% (1-b) = 60%D 1 = $3.00 g = 8% V 0 = 3.00 / ( ) = $42.86

12-9 Estimating Dividend Growth Rates gROEb  g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate – (1- dividend payout percentage rate)

12-10 Figure 12.1 Dividend Growth for Two Earnings Reinvestment Policies

12-11 Shifting Growth Rate Model VD g k Dg kgk oo t t t T T T         () () () ()() g 1 = first growth rate g 2 = second growth rate T = number of periods of growth at g 1

12-12 Shifting Growth Rate Model: Example D 0 = $2.00 g 1 = 20% g 2 = 5% k = 15% T = 3 D 1 = 2.40 D 2 = 2.88 D 3 = 3.46 D 4 = 3.63 V 0 = D 1 /(1.15) + D 2 /(1.15) 2 + D 3 /(1.15) 3 + D 4 / ( ) ( (1.15) 3 D 4 / ( ) ( (1.15) 3 V 0 = = $30.40

12-13 Specified Holding Period Model V D k D k DP k NN N    ()()()... P N = the expected sales price for the stock at time N N = the specified number of years the stock is expected to be held

12-14 Partitioning Value: Growth and No Growth Components V E k PVGO Dg kg E k o o       1 1 1() () PVGO = Present Value of Growth Opportunities E 1 = Earnings Per Share for period 1

12-15 Partitioning Value: Example ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8%

12-16 V NGV PVGO o o      (..) $42.. $33. $42.$33.$9. Partitioning Value: Example V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities

12-17 Price Earnings Ratios P/E Ratios are a function of two factors –Required Rates of Return (k) –Expected growth in Dividends Uses –Relative valuation –Extensive use in industry

12-18 P/E Ratio: No expected growth P E k P Ek   E 1 - expected earnings for next year –E 1 is equal to D 1 under no growth k - required rate of return

12-19 P/E Ratio with Constant Growth P D kg Eb kbROE P E b kb         () () () b = retention ration b = retention ration ROE = Return on Equity ROE = Return on Equity

12-20 Numerical Example: No Growth E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00 P/E = 1/k = 1/.125 = 8

12-21 Numerical Example with Growth b = 60% ROE = 15% (1-b) = 40% E 1 = $2.50 (1 + (.6)(.15)) = $2.73 D 1 = $2.73 (1-.6) = $1.09 k = 12.5% g = 9% P 0 = 1.09/( ) = $31.14 P/E = 31.14/2.73 = 11.4 P/E = (1 -.60) / ( ) = 11.4

12-22 Figure 12-3 P/E Ratio of the S&P 500 Index and Inflation

12-23 Pitfalls in Using P/E Ratios Flexibility in reporting makes choice of earnings difficult Pro forma earnings may give a better measure of operating earnings Problem of too much flexibility

12-24 Figure 12-4 Earnings Growth for Two Companies

12-25 Figure 12-5 Price-Earnings Ratios

12-26 Figure 12-6 P/E Ratios

12-27 Other Valuation Ratios & Approaches Price-to-book Price-to-cash flow Price-to-sales Present Value of Free Cash Flow

12-28 Figure 12-7 Market Valuation Statistics

12-29 Figure 12-8 Earnings Yield of the S&P 500 Versus 10-year Treasury Bond Yield