 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-1 Equity Valuation Models Chapter 18

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-2 Basic Types of Models - Balance Sheet Models - Dividend Discount Models - Price/Earning Ratios Estimating Growth Rates and Opportunities Fundamental Stock Analysis: Models of Equity Valuation

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-3

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-4 Intrinsic Value - Self assigned Value  Eddie: IV = $10, Elin: IV = $12, Myron: IV = $14 - 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 Intrinsic Value and Market Price

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-5

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-6 V 0 = Value of Stock D t = Dividend k = required return Dividend Discount Models: General Model

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-7 Stocks that have earnings and dividends that are expected to remain constant Preferred Stock No Growth Model

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-8 E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33 No Growth Model: Example

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-9 g = constant perpetual growth rate Constant Growth Model

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill E 1 = $5.00 b = retention =40% k = 15% (1-b) = payout = 60% g = 8% Constant Growth Model: Example V 0 = 3.00 / ( ) = $42.86 D 1 = E 1 *(1-b) = $5*.60

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill g = growth rate in earnings (& dividends if g and ROE are constant) ROE = Return on Equity for the firm b = plowback or retention percentage rate (1- dividend payout percentage rate) Estimating Dividend Growth Rates

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill E 0 = $4.63b = 40% k = 15% (1-b) = 60%g = 8% Constant Growth Model: Example D 0 = 4.63*.60 = $2.78 D 1 = 2.78*1.08 = $3 E 1 = $4.63*(1.08) = $5 and D 1 = E 1 *(1-b) = $5*.60 = $3

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-13

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Constant growth example Example: - last year's EPS = $ required return = 15% - constant return on new equity investment (ROE) = 20% - constant dividend payout = 40% - Growth in earnings = ROE*retention ratio = ROE*b

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 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 Specified Holding Period Model

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Multistage Growth Models Two period model - Calculate the present value of the expected dividends over the first (or nonconstant) stage - Estimate the stock price at the end of the first stage and discount this value back to time 0 - Add these two together to estimate the value at time 0

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Multistage example last year's EPS = $3.75 & required return = 12% ROE - years 1 & 2 = 24% - year 3 = 20% - year 4 and beyond = 16% dividend payout - years 1 & 2 = 30% - year 3 = 40% - year 4 and beyond = 50% growth in earnings - years 1 & 2 = - year 3 = - year 4 and beyond =

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill PVGO = Present Value of Growth Opportunities E 1 = Earnings Per Share for period 1 Partitioning Value: Growth and No Growth Components

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8% Partitioning Value: Example

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities Partitioning Value: Example

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 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 Price Earnings Ratios

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-22

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill E 1 - expected earnings for next year - E 1 is equal to D 1 under no growth k - required rate of return P/E Ratio: No Expected Growth

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill b = retention ratio ROE = Return on Equity P/E Ratio with Constant Growth

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00 PE = 1/k = 1/.125 = 8 Numerical Example: No Growth

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 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 PE = 31.14/2.73 = 11.4 PE = (1 -.60) / ( ) = 11.4 Numerical Example with Growth

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Pitfalls in P/E Analysis Use of accounting earnings - Historical costs - May not reflect economic earnings Reported earnings fluctuate around the business cycle

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 18-28

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Inflation and Equity Valuation Inflation has an impact on equity valuations Historical costs underestimate economic costs Empirical research shows that inflation has an adverse effect on equity values - Research shows that real rates of return are lower with high rates of inflation

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Potential Causes of Lower Equity Values with Inflation Shocks cause expectation of lower earnings by market participants Returns are viewed as being riskier with higher rates of inflation Real dividends are lower because of taxes