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The cost of capital (aka hurdle rate) and NPV The cost of capital (aka hurdle rate) and NPV analysisanalysis
The FirmThe Firm
The cash flow generated by those assets represents the The cash flow generated by those assets represents the payoffpayoff to creditors and shareholders. to creditors and shareholders.
PayoffPayoff = PV(CF from assets) = PV(CF from assets)
The creditors and shareholders want the The creditors and shareholders want the payoffpayoff to be to be
larger than the initial cost.larger than the initial cost.
What discount rate to use?What discount rate to use?
A fair discount rate should reflect:
• perceived project risk• inflation• time preference
A question of benchmarkA question of benchmark
If the project has “average” firm risk, use the default benchmark
ExemplificationExemplification
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 benchmarkA question of benchmark
The Benchmark is the Weighted Average Cost of Capital
WACC
WACC: CalculationWACC: Calculation
WACC = wWACC = wee (r (ree) + w) + wdd (i) (1-T) (i) (1-T)
we = weight of equity in total market value
re = cost of equity
wd = weight of debt in total market value
i = cost of debt
T = corporate tax rate
Calculating the cost of equityCalculating 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: ClarificationThe cost of equity: Clarification
The cost of equity = The required return on equity
Calculating the cost of equity: Dividend Calculating the cost of equity: Dividend growth modelgrowth model
Current stock value = PV future dividends
P = DP = D11/(r -g)/(r -g)
D1 = next expected dividend
r = required return
g = expected dividend growth rate
Calculating the cost of equity: Dividend Calculating the cost of equity: Dividend growth modelgrowth model
r = Dr = D11/P/P00 + g + g
Required return = dividend yield + capital gains
Where does "g" come from?Where does "g" come from?
We want to know how to estimate the capital gain (dividend growth) rate
Where does "g" come from?Where does "g" come from?
We know that:
EarningsEarnings11 = Earnings = Earnings00 + (Ret)Earnings + (Ret)Earnings00(ROE)(ROE)
EarningsEarnings11/Earnings/Earnings00 = 1 + (Ret)(ROE) = 1 + (Ret)(ROE)
Where does "g" come from?Where does "g" come from?
If the retention ratio (RetRet) remains constant over time, EarningsEarnings11/Earnings/Earnings00 = Dividend = Dividend11/Dividend/Dividend00 = 1+g = 1+g
Remember,
EarningsEarnings1 1 = Earnings = Earnings00 [1+(Ret)ROE] [1+(Ret)ROE]
Where does "g" come from?Where does "g" come from?
hence, 1+ g = 1 + (Ret)(ROE),1+ g = 1 + (Ret)(ROE), that is,
g = (Ret)(ROE)g = (Ret)(ROE)
The growth in dividend depends on:
• the proportion of earnings reinvested back into the company• ROE
Dividend growth model: Dividend growth model: Advantages & DisadvantagesAdvantages & Disadvantages
Simple to understand and calculateSimple to understand and calculate
Cannot be accurate without a good estimation of gCannot be accurate without a good estimation of g
Assumes the market is efficientAssumes the market is efficient
Calculating the cost of equityCalculating the cost of equity
Method 1: Dividend growth model
Method 3: Risk-return modelMethod 3: Risk-return model
Method 3: HPR approach
Method 4: ROE approach
Risk-return modelsRisk-return models
The return premium per unit of relative risk has to be constant:
(r - r(r - rff)/b = (r)/b = (rMM -r -rff)/b)/bMM
r = required return on our stock
rf = risk-free rate
rM = expected return on the market portfolio
b = the beta of our stock
bM = market beta, always equal to 1
More on risk-return modelsMore on risk-return models
CAPM: CAPM: r = rr = rff +b(r +b(rMM - r - rff))
beta = relative measure of risk:
the amount of volatility our stock adds to the volatility of the market portfolio
Calculating betaCalculating beta
Run regression with market return as independent variable and our stock return as dependent variable
rrii = a + b (r = a + b (rMM) + e) + e
estimated b = betabeta, the measure of relative risk
BetaBeta
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 modelsRisk-return models
Advantages:Advantages:Takes risk into considerationTakes risk into consideration
Disadvantages:Disadvantages:Beta and the expected market return cannot be estimated reliablyBeta and the expected market return cannot be estimated reliably
CAPM is elegant and appealing, but otherwise uselessCAPM is elegant and appealing, but otherwise useless
Calculating the cost of equityCalculating the cost of equity::
Method 1: Dividend growth model
Method 3: Risk-return model
Method 3: HPR approachMethod 3: HPR approach
Method 4: ROE approach
HPR approachHPR approach
Estimate the holding period return:
r = [(Pr = [(PEndEnd - P - PBeginningBeginning + FVDividends)/(P + FVDividends)/(PBeginningBeginning)])]1/t1/t -1 -1
HPR approachHPR approach
Advantages:
Simple to calculateSimple to calculate
Disadvantages:
Difficult to select the horizonDifficult to select the horizon
Very inaccurate approximation due to market volatilityVery inaccurate approximation due to market volatility
Calculating the cost of equityCalculating the cost of equity
Method 1: Dividend growth model
Method 3: Risk-return model
Method 3: HPR approach
Method 4: ROE approachMethod 4: ROE approach
ROE approachROE approach
Use book/market values to approximate the required rate of return:
r = NI/Equityr = NI/Equity
ROE approachROE approach
Advantages:
Easy to calculateEasy to calculate
Disadvantages:
Poor approximation due to the volatility of stock Poor approximation due to the volatility of stock pricesprices
The cost of debtThe 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)cost of debt = i(1-T)
SummarySummary
The hurdle rate has to reflect the risk of the project, not The hurdle rate has to reflect the risk of the project, not the source of fundsthe source of funds
If the risk of the project is If the risk of the project is averageaverage, use the default , use the default rate:WACCrate:WACC
If the risk of the project is above or below average, If the risk of the project is above or below average, adjust the WACC upward or downwardadjust the WACC upward or downward