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Chapter 18. Equity Valuation. 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. Dividend Discount Models: General Model. V 0 = Value of Stock
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Chapter18 Equity Valuation
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
Dividend Discount Models:General Model • V0 = Value of Stock • Dt = Dividend • k = required return
No Growth Model • Stocks that have earnings and dividends that are expected to remain constant • Preferred Stock
No Growth Model: Example E1 = D1 = $5.00 k = .15 V0 = $5.00 / .15 = $33.33
Constant Growth Model • g = constant perpetual growth rate
Constant Growth Model: Example E1 = $5.00 b = 40% k = 15% (1-b) = 60% D1 = $3.00 g = 8% V0 = 3.00 / (.15 - .08) = $42.86
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)
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%
Specified Holding Period Model • PN = the expected sales price for the stock at time N • N = the specified number of years the stock is expected to be held
Partitioning Value: Growth and No Growth Components • PVGO = Present Value of Growth Opportunities • E1 = Earnings Per Share for period 1
Partitioning Value: Example • ROE = 20% d = 60% b = 40% • E1 = $5.00 D1 = $3.00 k = 15% • g = .20 x .40 = .08 or 8%
Partitioning Value: Example Vo = value with growth NGVo = no growth component value PVGO = Present Value of Growth Opportunities
Free Cash Flow to Equity 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 • 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.
Let’s look at an example http://faculty.etsu.edu/trainor/FNCE%203300/Lowes.doc Another interesting site you may want to use: http://caps.fool.com/Ticker.aspx?source=icaedilnk9950012&ticker=LOW
Free Cash flow to the Firm • 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.
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
P/E Ratio: No expected growth • E1 - expected earnings for next year • E1 is equal to D1 under no growth • k - required rate of return
P/E Ratio with Constant Growth • b = retention ration • ROE = Return on Equity
Numerical Example: No Growth E0 = $2.50 g = 0 k = 12.5% P0 = D/k = $2.50/.125 = $20.00 PE = 1/k = 1/.125 = 8
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/(.125-.09) = $31.14 PE = 31.14/2.73 = 11.4 PE = (1 - .60) / (.125 - .09) = 11.4
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
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.