Chapter 18 Equity Valuation

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Dividend Discount Models: General Model V 0 = Value of Stock D t = Dividend k = required return

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

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Constant Growth Model g = constant perpetual growth rate

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Constant Growth Model: Example E 1 = $5.00b = 40% k = 15% (1-b) = 60%D 1 = $3.00 g = 8% V 0 = 3.00 / ( ) = $42.86

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Estimating Dividend Growth Rates g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate (1- dividend payout percentage rate)

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Estimating Growth via historical info. Dividend in 2000 was $1. Dividend in 2006 was $1.80 Growth is (1.80/1)^(1/6)-1 = 10.29%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Specified Holding Period Model 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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Partitioning Value: Growth and No Growth Components PVGO = Present Value of Growth Opportunities E 1 = Earnings Per Share for period 1

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%

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Partitioning Value: Example V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. A much better model is to apply discount models to FCFE which may more accurately reflect a firms value. FCFE = Net Income + depreciation – Cap. Expend. – change in working capital – principal debt repayments + new debt issues. Apply model as per usual. Free Cash Flow to Equity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. If the firm finances a fixed percentage of its capital spending and investments in working capital with debt, the calculation of FCFE is simplified. Let DR be the debt ratio, debt as a percentage of assets. In this case, FCFE can be written as FCFE = NI – (1 – DR)(Capital Spending + change in Working Capital – Depreciation) When building FCFE valuation models, the logic, that debt financing is used to finance a constant fraction of investments, is very useful. This equation is pretty common. F ree Cash Flow to Equity

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. 00/Lowes.doc Another interesting site you may want to use: caedilnk &ticker=LOW Let’s look at an example

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. FCFF = EBIT(1-tax rate) + Dep. – Cap. Expenditures – Change in WC – Change in other assets. Again, proceed as normal(replace dividends with FCFF) but discount at firms cost of capital. You find value of firm. To find value of equity, simply subtract off debt. Free Cash flow to the Firm

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

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. P/E Ratio with Constant Growth b = retention ration ROE = Return on Equity

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

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/( ) = $31.14 PE = 31.14/2.73 = 11.4 PE = (1 -.60) / ( ) = 11.4

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

McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved. Other types of Valuation Use Price/sales Price/Cash flow All relative valuation models rely on the market to be fairly valued. What is a good Price/Sales ratio? Relies on comparisons which may or may not be valued accurately.