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 = we (re) + wd (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 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 = D1/(r -g)
D1 = next expected dividend
r = required return
g = expected dividend growth rate
Calculating the cost of equity: Dividend
growth model
r = D1/P0 + 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:
Earnings1 = Earnings0 + (Ret)Earnings0(ROE)
Earnings1/Earnings0 = 1 + (Ret)(ROE)
Where does "g" come from?
If the retention ratio (Ret) remains constant over time,
Earnings1/Earnings0 = Dividend1/Dividend0 = 1+g
Remember,
Earnings1 = Earnings0 [1+(Ret)ROE]
Where does "g" come from?
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 - rf)/b = (rM -rf)/bM
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 models
CAPM: r = rf +b(rM - rf)
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
ri = a + b (rM) + e
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 = [(PEnd - PBeginning + FVDividends)/(PBeginning)]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