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The cost of capital (aka hurdle rate) and NPV analysis

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The Firm The cash flow generated by those assets represents the payoff to creditors and shareholders. Payoff = PV(CF from assets) The creditors and shareholders want the payoff to be larger than the initial cost.

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Stating the obvious Calculating PV = discounting CFs

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What discount rate to use? A fair discount rate should reflect: perceived project risk inflation time preference

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A question of benchmark If the project has “average” firm risk, use the default benchmark

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Clarification “Average” risk = Risk comparable to that of firm’s other projects

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Exemplification Coca-Cola building a new bottling plant in Lennoxville would be a project of average risk Ford planning to launch a satellite would be a project of above average risk Sprint expanding in Eastern Europe with the help of government contracts would be a project of below average risk

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A question of benchmark The Benchmark is the Weighted Average Cost of Capital WACC

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WACC: Calculation WACC = w e (r e ) + w d (i) (1-T) w e = weight of equity in total market value r e = cost of equity w d = weight of debt in total market value i = cost of debt T = corporate tax rate

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Calculating the cost of equity Method 1: Dividend growth model Method 3: Risk-return model Method 3: HPR approach Method 4: ROE approach

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The cost of equity: Clarification The cost of equity = The required return on equity

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Calculating the cost of equity: Dividend growth model Current stock value = PV future dividends P = D 1 /(r -g) D 1 = next expected dividend r = required return g = expected dividend growth rate

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Calculating the cost of equity: Dividend growth model r = D 1 /P 0 + g Required return = dividend yield + capital gains

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Where does "g" come from? We want to know how to estimate the capital gain (dividend growth) rate

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Where does "g" come from? We know that: Earnings 1 = Earnings 0 + (Ret)Earnings 0 (ROE) Earnings 1 /Earnings 0 = 1 + (Ret)(ROE)

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Where does "g" come from? Ret Earnings 1 /Earnings 0 = Dividend 1 /Dividend 0 = 1+g If the retention ratio (Ret) remains constant over time, Earnings 1 /Earnings 0 = Dividend 1 /Dividend 0 = 1+g Remember, Earnings 1 = Earnings 0 [1+(Ret)ROE]

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Where does "g" come from? 1+ g = 1 + (Ret)(ROE), hence, 1+ g = 1 + (Ret)(ROE), that is, g = (Ret)(ROE) The growth in dividend depends on: the proportion of earnings reinvested back into the company ROE

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Dividend growth model: Advantages & Disadvantages Simple to understand and calculate Cannot be accurate without a good estimation of g Assumes the market is efficient

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Calculating the cost of equity Method 1: Dividend growth model Method 3: Risk-return model Method 3: HPR approach Method 4: ROE approach

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Risk-return models The return premium per unit of relative risk has to be constant: (r - r f )/b = (r M -r f )/b M r = required return on our stock r f = risk-free rate r M = expected return on the market portfolio b = the beta of our stock b M = market beta, always equal to 1

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More on risk-return models CAPM: r = r f +b(r M - r f ) beta = relative measure of risk: the amount of volatility our stock adds to the volatility of the market portfolio

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Calculating beta Run regression with market return as independent variable and our stock return as dependent variable r i = a + b (r M ) + e beta estimated b = beta, the measure of relative risk

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Beta beta < 1, our stock has below average risk beta = 1, our stock has average market risk beta > 1, our stock has above average risk

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Risk-return models Advantages: Takes risk into consideration Disadvantages: Beta and the expected market return cannot be estimated reliably CAPM is elegant and appealing, but otherwise useless

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Calculating the cost of equity: Method 1: Dividend growth model Method 3: Risk-return model Method 3: HPR approach Method 4: ROE approach

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HPR approach Estimate the holding period return: r = [(P End - P Beginning + FVDividends)/(P Beginning )] 1/t -1

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HPR approach Advantages: Simple to calculate Disadvantages: Difficult to select the horizon Very inaccurate approximation due to market volatility

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Calculating the cost of equity Method 1: Dividend growth model Method 3: Risk-return model Method 3: HPR approach Method 4: ROE approach

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ROE approach Use book/market values to approximate the required rate of return: r = NI/Equity

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ROE approach Advantages: Easy to calculate Disadvantages: Poor approximation due to the volatility of stock prices

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The cost of debt The yield-to-maturity or the interest on bank loans Has to be adjusted for the tax-saving effect of debt cost of debt = i(1-T)

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Summary The hurdle rate has to reflect the risk of the project, not the source of funds If the risk of the project is average, use the default rate:WACC If the risk of the project is above or below average, adjust the WACC upward or downward

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