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##### CHAPTER 18

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**CHAPTER 18**Equity Valuation Models**Balance Sheet Models**Book Value Dividend Discount Models Price/Earning Ratios Models of Equity Valuation**Table 18.1 Financial Highlights for Microsoft Corporation,**October 25, 2007**Limitations of Book Value**Book value is an application of arbitrary accounting rules Can book value represent a floor value? Better approaches Liquidation value Replacement cost**Expected Holding Period Return**The return on a stock investment comprises cash dividends and capital gains or losses Assuming a one-year holding period**Required Return**CAPM gave us required return: If the stock is priced correctly Required return should equal expected return**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 Intrinsic Value and Market Price**PH = the expected sales price for the stock at time H**H = the specified number of years the stock is expected to be held Specified Holding Period**V0 = Value of Stock**Dt= Dividend k = required return Dividend Discount Models: General Model**Stocks that have earnings and dividends that are expected to**remain constant Preferred Stock No Growth Model**E1 = D1 = $5.00**k = .15 V0 = $5.00 /.15 = $33.33 No Growth Model: Example**g = constant perpetual growth rate**Constant Growth Model**E1 = $5.00 b = 40% k = 15%**(1-b) = 60% D1= $3.00 g = 8% V0 = 3.00 / (.15 - .08) = $42.86 Constant Growth Model: Example**g = growth rate in dividends**ROE = Return on Equity for the firm b = plowback or retention percentage rate (1- dividend payout percentage rate) Estimating Dividend Growth Rates**Figure 18.1 Dividend Growth for Two Earnings Reinvestment**Policies**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)**Present Value of Growth Opportunities Continued**Price = No-growth value per share + PVGO (present value of growth opportunities)**ROE = 20% d = 60% b = 40%**E1 = $5.00 D1 = $3.00 k = 15% g = .20 x .40 = .08 or 8% Partitioning Value: Example**Partitioning Value: Example Continued**Vo = value with growth NGVo = no growth component value PVGO = Present Value of Growth Opportunities**Life Cycles and Multistage Growth Models**g1 = first growth rate g2 = second growth rate T = number of periods of growth at g1**Multistage Growth Rate Model: Example**D0 = $2.00 g1= 20% g2= 5% k = 15% T = 3 D1= 2.40 D2 = 2.88 D3= 3.46 D4= 3.63 V0= D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 + D4 / (.15 - .05) ( (1.15)3 V0= 2.09 + 2.18 + 2.27 + 23.86 = $30.40**Figure 18.2 Value Line Investment Survey Report on Honda**Motor Co.**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**E1 - expected earnings for next year**E1 is equal to D1 under no growth k - required rate of return P/E Ratio: No Expected Growth**b = retention ratio**ROE = Return on Equity P/E Ratio: Constant 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: No 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 Numerical Example: Growth**Table 18.3 Effect of ROE and Plowback on Growth and the P/E**Ratio**P/E Ratios and Stock Risk**Holding all else equal Riskier stocks will have lower P/E multiples Higher values of k; therefore, the P/E multiple will be lower**Pitfalls in P/E Analysis**Use of accounting earnings Earnings Management Choices on GAAP Inflation Reported earnings fluctuate around the business cycle**Other Comparative Value Approaches**Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio**Free Cash Flow Approach**Discount the free cash flow for the firm Discount rate is the firm’s cost of capital Components of free cash flow After tax EBIT Depreciation Capital expenditures Increase in net working capital**Comparing the Valuation Models**In practice Values from these models may differ Analysts are always forced to make simplifying assumptions**The Aggregate Stock Market**Explaining Past Behavior Forecasting the Stock Market**Figure 18.8 Earnings Yield of S&P 500 versus 10-Year**Treasury-Bond Yield