1. CHAPTER 13
Equity Valuation

2. 13.1 VALUATION BY COMPARABLES

3. 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

4. Models of Equity Valuation
Valuation models use comparables
Look at the relationship between price and various determinants of value for similar firms
The internet provides a convenient way to access firm data. Some examples are:
EDGAR
Finance.yahoo.com

5. Table 13.1 Microsoft Corporation Financial Highlights

6. Valuation Methods Book value Market value Liquidation value
Replacement cost

7. 13.2 INTRINSIC VALUE VERSUS MARKET PRICE

8. Expected Holding Period Return
The return on a stock investment comprises cash dividends and capital gains or losses
Assuming a one-year holding period

9. Required Return CAPM gave us required return:
If the stock is priced correctly
Required return should equal expected return

10. Intrinsic Value and Market Price
Consensus value of all potential traders
Current market price will reflect intrinsic value estimates
This consensus value of the required rate of return, k, is the market capitalization rate
Trading Signal
IV > MP Buy
IV < MP Sell or Short Sell
IV = MP Hold or Fairly Priced

11. 13.3 DIVIDEND DISCOUNT MODELS

12. å D = V + ( 1 k ) General Model V0 = Value of Stock Dt = DividendD å t = V o + ( 1 k ) t t = 1
V0 = Value of Stock
Dt = Dividend
k = required return

13. No Growth Model D = V o k
Stocks that have earnings and dividends that are expected to remain constant
Preferred Stock

14. No Growth Model: Example= V o k
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33

15. + D ( 1 g ) Vo = - k g Constant Growth Model
g = constant perpetual growth rate

16. Constant Growth Model: Example+ D ( 1 g ) o Vo = - k g
E1 = $5.00 b = 40% k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / ( ) = $42.86

17. Stock Prices and Investment Opportunities= g
ROE b
g = growth rate in dividends
ROE = Return on Equity for the firm
b = plowback or retention percentage rate
(1- dividend payout percentage rate)

18. Figure 13.1 Dividend Growth for Two Earnings Reinvestment Policies

19. Present Value of Growth Opportunities
If the stock price equals its IV, growth rate is sustained, the stock should sell at:
If all earnings paid out as dividends, price should be lower (assuming growth opportunities exist)

20. Present Value of Growth Opportunities (cont.)
Price = No-growth value per share + PVGO (present value of growth opportunities)
Where:
E1 = Earnings Per Share for period 1 and

21. Partitioning Value: Example
ROE = 20% d = 60% b = 40%
E1 = $5.00 D1 = $3.00 k = 15%
g = .20 x .40 = .08 or 8%

22. Partitioning Value: Example (cont.)3 P = =
$42 . 86 o (. 15 - . 08 ) 5
NGV = =
$33 . 33 o . 15
PVGO =
$42 . 86 -
$33 . 33 = $9 . 52
Po = price with growth
NGVo = no growth component value
PVGO = Present Value of Growth Opportunities

23. Life Cycles and Multistage Growth Models+ t + ( 1 g ) D ( 1 g ) å = + T P D 2 1 o o + t - + ( 1 k ) ( k g ) ( 1 k ) T t = 1 2
g1 = first growth rate
g2 = second growth rate
T = number of periods of growth at g1

24. Multistage Growth Rate Model: Example
D0 = $ g1 = 20% g2 = 5%
k = 15% T = 3 D1 = 2.40
D2 = D3 = D4 = 3.63
V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +
D4 / ( ) ( (1.15)3
V0 = = $30.40

25. 13.4 PRICE-EARNINGS RATIOS

26. P/E Ratio and Growth Opportunities
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

27. P/E Ratio: No expected growth1 = P k P 1 = E k 1
E1 - expected earnings for next year
E1 is equal to D1 under no growth
k - required rate of return

28. P/E Ratio: Constant GrowthD E ( 1 - b ) 1 1 P = = k - g k - ( b
ROE ) P 1 - b = E k - ( b
ROE ) 1
b = retention ration
ROE = Return on Equity

29. Numerical Example: No Growth
E0 = $ g = 0 k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
P/E = 1/k = 1/.125 = 8

30. Numerical Example with Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
k = 12.5% g = 9%
P0 = 1.09/( ) = $31.14
P/E = 31.14/2.73 = 11.4
P/E = ( ) / ( ) = 11.4

31. P/E Ratios and Stock Risk
Riskier stocks will have lower P/E multiples
Riskier firms will have higher required rates of return (higher values of k)

32. 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

33. Figure 13.3 P/E Ratios and Inflation

34. Figure 13.4 Earnings Growth for Two Companies

35. Figure 13.5 Price-Earnings Ratios

36. Figure 13.6 P/E Ratios

37. Other Comparative Valuation Ratios
Price-to-book
Price-to-cash flow
Price-to-sales
Be creative

38. Figure 13.7 Valuation Ratios for the S&P 500

39. 13.5 FREE CASH FLOW VALUATION APPROACHES

40. Free Cash Flow
One approach is to discount the free cash flow for the firm (FCFF) at the weighted-average cost of capital
Subtract existing value of debt
FCFF = EBIT (1- tc) + Depreciation – Capital expenditures – Increase in NWC
where:
EBIT = earnings before interest and taxes
tc = the corporate tax rate
NWC = net working capital

41. Free Cash Flow (cont.)
Another approach focuses on the free cash flow to the equity holders (FCFE) and discounts the cash flows directly at the cost of equity
FCFE = FCFF – Interest expense (1- tc) + Increases in net debt

42. Comparing the Valuation Models
Free cash flow approach should provide same estimate of IV as the dividend growth model
In practice the two approaches may differ substantially
Simplifying assumptions are used

43. 13.6 THE AGGREGATE STOCK MARKET

44. Earnings Multiplier Approach
Forecast corporate profits for the coming period
Derive an estimate for the aggregate P/E ratio using long-term interest rates
Product of the two forecasts is the estimate of the end-of-period level of the market

45. Figure 13.8 Earnings Yield of the S&P 500 Versus 10-year Treasury Bond Yield

46. Table 13.4 S&P 500 Index Forecasts