1. Chapter 12 Equity Valuation

2. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Fundamental Stock Analysis: Models of Equity Valuation Basic Types of Models Balance Sheet Models Dividend Discount Models Price/Earning Ratios Estimating Growth Rates and Opportunities

3. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

4. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

5. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. No Growth Model V D k o  Stocks that have earnings and dividends that are expected to remain constant Preferred Stock

6. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. No Growth Model: Example E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33 V D k o 

7. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Constant Growth Model Vo Dg kg o    ()1 g = constant perpetual growth rate

8. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 / (.15 -.08) = $42.86

9. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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)

10. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Shifting Growth Rate Model VD g k Dg kgk oo t t t T T T         () () () ()() 1 1 1 1 1 1 2 2 g 1 = first growth rate g 2 = second growth rate T = number of periods of growth at g 1

11. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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 / (.15 -.05) ( (1.15) 3 V 0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

12. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Specified Holding Period Model 0 1 1 2 2 111 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

13. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

14. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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%

15. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. V NGV PVGO o o      3 1508 86 5 15 33 863352 (..) $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

16. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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

17. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. P/E Ratio: No expected growth P E k P Ek 0 1 0 1 1   E 1 - expected earnings for next year E 1 is equal to D 1 under no growth k - required rate of return

18. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. P/E Ratio with Constant Growth P D kg Eb kbROE P E b kb 0 11 0 1 1 1         () () () b = retention ration ROE = Return on Equity

19. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Numerical Example: No Growth E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00 PE = 1/k = 1/.125 = 8

20. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 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/(.125-.09) = $31.14 PE = 31.14/2.73 = 11.4 PE = (1 -.60) / (.125 -.09) = 11.4

21. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Pitfalls in Using PE 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

22. McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Other Valuation Ratios & Approaches Price-to-book Price-to-cash flow Price-to-sales Present Value of Free Cash Flow