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

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

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.

Stating the obvious Calculating PV = discounting CFs

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

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

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

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

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

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

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

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

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

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

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

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

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]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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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