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Chapter 8Risk and Rates of Return Stand-Alone Risk Portfolio Risk Risk and Return: CAPM/SML 8-2
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Selected Realized Returns, 1926-2007 Average Standard Return DeviationSmall-company stocks 17.1% 32.6%Large-company stocks 12.3 20.0L-T corporate bonds 6.2 8.4L-T government bonds 5.8 9.2U.S. Treasury bills 3.8 3.1Source: Based on Stocks, Bonds, Bills, and Inflation: (ValuationEdition) 2008 Yearbook (Chicago: Morningstar, Inc., 2008), p28. 8-3
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Comparing Standard Deviations Probability Distributions Prob. T-bill Corporate Bonds Stocks 0 3.8 6.2 12.3 Rate of Return (%) 8-4
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Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return. ˆ r Expected rate of return N ˆ r ri Pi i 1 Standard deviation CV Expected return ˆ r 8-5
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Calculating Portfolio Expected Return ˆ rp is a weighted average : N ^ ˆ rp wi ri i 1 ˆ rp 0.5 (12.3%) 0.5 (6.2%) 9.3% 8-6
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Illustrating Diversification Effects of a StockPortfolio Stand-alone risk = Market risk + Diversifiable risk Diversifiable risk – portion that can be eliminated through proper diversification. Market risk – portion that cannot be eliminated through diversification. Measured by beta. 8-8
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Capital Asset Pricing Model (CAPM) Model linking risk and required returns. ri = rRF + (rM – rRF)bi If beta = 1.0, as risky as the average stock. If beta > 1.0, riskier than average. If beta < 1.0, less risky than average. Most stock betas are between 0.5 to 1.5. 8-9
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Illustrating the Security Market Line SML: ri = 5.5% + (5.0%)bi ri (%) SML rM = 10.5 rRF = 5.5 . T-bills Risk, bi -1 0 1 2 8-10
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Chapter 9Stocks and Their Valuation Features of Common Stock Determining Common Stock Values Preferred Stock 9-11
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Discounted Dividend Model Value of a stock is the present value of the future dividends expected to be generated by the stock. ˆ0 D1 D2 D3 D P 1 2 3 ... (1 rs ) (1 rs ) (1 rs ) (1 rs ) D 0 (1 g) D1Gordon Growth Model: ˆ P0 rs g rs g Where g = (1 – k) * ROE And r is derived from CAPM equation. 9-12
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What would the expected price todaybe, if g = 0?The dividend stream would be a perpetuity. 0 1 2 3 rs = 13% 2.00 2.00 2.00 ˆ PMT $2.00 P0 $15.38 r 0.13 9-13
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Supernormal Growth: What if g = 30% for 3 years before achieving long-run growth of 6%? 0 r = 13% 1 2 3 4 s g = 30% g = 30% g = 30% g = 6%D0 = 2.00 2.600 3.380 4.394 4.658 2.301 2.647 3.045 ˆ 4.658 46.114 P3 $66.54 0.13 0.06 ˆ 54.107 = P0 9-14
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Components of return Dividend yield= D1/P0 Capital gains yield = (P1 – P0)/P0 Total return (rs) = Dividend yield + Capital gains yield 9-15
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Corporate Valuation Model(aka Free Cash Flow Model) Value of the entire firm equals the present value of the firm’s free cash flows.1. Find the market value (MV) of the firm, by finding the PV of the firm’s future FCFs.2. Subtract MV of firm’s debt and preferred stock to get MV of common stock.3. Divide MV of common stock by the number of shares outstanding to get intrinsic stock price (value). 9-16
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Firm Multiples Method Analysts often use the following multiples to value stocks. P/E P/CF P/Sales 9-17
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Preferred Stock Hybrid security. Like bonds, fixed dividend that must be paid before common stock dividends are paid. However, payments can be skipped or postponed in unprofitable years. D Vp rp 9-18
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Chapter 10 The Cost of Capital Sources of Capital Component Costs WACC Adjusting for Flotation Costs Adjusting for Risk 10-19
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What sources of long-term capital dofirms use? Long-Term CapitalLong-Term Preferred Common Debt Stock Stock Retained New Common Earnings Stock 10-20
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Calculating the Weighted Average Costof Capital WACC = wdrd(1 – T) + wprp + wcrs The w’s refer to the firm’s capital structure weights. The r’s refer to the cost of each component. 10-21
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Component Cost of Debt WACC = wdrd(1 – T) + wprp + wcrs rd is the marginal cost of debt capital. Often estimated as YTM on long-term debt Why tax-adjust; i.e., why rd(1 – T)? Example: 15-yr, 12% bond selling for $1154.INPUTS 30 -1154 60 1000 N I/YR PV PMT FVOUTPUT 5 10-22
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Component Cost of Preferred Stock WACC = wdrd(1 – T) + wprp + wcrs rp is the marginal cost of preferred stock, which is the return investors require on a firm’s preferred stock. Preferred dividends are not tax-deductible, so no tax adjustments necessary. Just use nominal rp. Our calculation ignores possible flotation costs. 10-23
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Component Cost of Equity WACC = wdrd(1 – T) + wprp + wcrs rs is the marginal cost of common equity using retained earnings. The rate of return investors require on the firm’s common equity using new equity is re. What are flotation costs? 10-24
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Three Ways to Determine the Cost ofCommon Equity, rs CAPM: rs = rRF + (rM – rRF)b DCF: rs = (D1/P0) + g Own-Bond-Yield-Plus-Risk-Premium: rs = rd + RP 10-25
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Find the Cost of Common Equity Usingthe CAPM ApproachThe rRF = 7%, RPM = 6%, and the firm’s beta is1.2. rs = rRF + (rM – rRF)b = 7.0% + (6.0%)1.2 = 14.2% 10-26
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Find the Cost of Common Equity Usingthe DCF ApproachD0 = $4.19, P0 = $50, and g = 5. D1 = D0(1 + g) = $4.19(1 + 0.05) = $4.3995 rs = (D1/P0) + g = ($4.3995/$50) + 0.05 = 13.8% 10-27
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Find rs Using the Own-Bond-Yield-Plus-Risk-Premium Methodrd = 10% and RP = 4. This RP is not the same as the CAPM RPM. This method produces a ballpark estimate of rs, and can serve as a useful check. rs = rd + RP rs = 10.0% + 4.0% = 14.0% 10-28
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What is a reasonable final estimate of rs? Method Estimate CAPM 14.2% DCF 13.8% rd + RP 14.0% Average 14.0% 10-29
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What factors influence a company’scomposite WACC? Market conditions. The firm’s capital structure and dividend policy. The firm’s investment policy. Firms with riskier projects generally have a higher WACC. Should the company use the composite WACC as the hurdle rate for each of its projects? 10-31
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