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.

Stating the obviousStating the obvious

Calculating PV = discounting CFs

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

ClarificationClarification

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

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