Hurdle Rates for Firms
04/15/08
Ch. 4
Investment Decision
 Firms should invest in projects that create
value for the firm’s shareholders
 These are projects that yield a return greater
than the minimum acceptable hurdle rate with
adjustments for project riskiness.
 Do you ever lend money and expect to get
less back? Companies should not…
2
Investment Decision
 Components of the investment decision making
process
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
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Determine the appropriate hurdle rate for the firm (Ch.
4) -- WACC
Make adjustments for project riskiness (Ch. 5)
Calculate the cash flows associated with the project –
Incremental Cash Flow
Employ the appropriate decision tools -- NPV
Evaluate project interactions (Ch.6)
 If NPV is positive go, if NPV is negative no-go
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What is a Hurdle Rate?
The hurdle rate for the firm represents the
minimum rate of return that the firm as a
whole must generate on its investments to
satisfy its investors.
 It is the implicit cost of money for the firm…
 This is also referred to as the weighted
average cost of capital (WACC) or simply
the cost of capital.
4
Weighted Average Cost of Capital
 Percent of financing times the cost of
financing for that funding source
 Sources



Equity (Owners)
Debt (Bondholders, Banks, etc.)
Preferred Stockholders (often skipped)
 WACC = (E/V) x Re + (D/V) x Rd x (1 – Tc)
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Cost of Equity
 Required rate of return for equity investors (or shareholders)
is also referred to as the cost of equity
 For publicly traded firms, we initially assume that the these
equity investors are diversified investors. Consequently,
 Only the firm’s risk relative to the market is relevant
(systematic risk)
 Firm-specific risk is assumed to be diversified away
re  rf   (rm  rf )
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Cost of Equity
 To calculate the cost of equity for a firm, we
need estimates for each of its components:
 Risk-free rate, rf
Market return, or alternatively the market
risk premium, (rm- rf)
 Firm’s beta, β

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Risk-free Rate
 With the risk-free asset, the actual return and
expected return do not vary.
 The risk-free asset assumes:


No default risk (bonds and their ratings)
No reinvestment risk (coupons reinvested)
 Ideally, this means that you should use a risk-
free asset whose maturity matches the timing
of cash flows
 Treasury securities
http://screen.yahoo.com/bonds.html
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Market Risk Premium
 The market risk premium represents the extra return
beyond that of a risk-free asset that an investor
demands for moving their funds from the risk-free
asset to the risky (market portfolio) asset.
 E(rm) – rf = market risk premium…
 Consider this payment for units of risk
 Beta as units of risk
 Increase Beta and you increase demand for extra risk
premium
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Estimating the Market Risk Premium
 There are two methods to estimate the
market risk premium.


historical risk premium
Implied risk premium
 The majority of analyses tend to employ the
historical method or some form of weighted
average between the two.
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The Historical Approach
 In most cases, historical market risk
premiums can be estimated as follows:



define a time period for the estimation (1926Present, 1962-Present....)
Arithmetic average (simple average)…Find each
year’s return, then average of the yearly returns
Geometric average (compounding)…
 Take the difference between the average return
of the market and the risk-free rate
 Look at Finance. Yahoo (ticker SPY) ‘93 to now
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Historical Premium Limitations
 The limitations of this approach are:

it assumes that the risk aversion of investors has
not changed in a systematic way across time. (The
risk aversion may change from year to year, but it
reverts back to historical averages)

it assumes that the riskiness of the “risky” portfolio
(stock index) has not changed in a systematic way
across time
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Implied Premium Approach
 The implied risk premium approach estimates a risk
premium based on current market values, dividends
and growth rates.
 We can use a basic dividend discount model (DDM)
to estimate the implied risk premium:
Index value =
Expected index dividends
(RR on the index – growth rate in dividends)
 The implied risk premium would then be:
RR on index – current risk-free rate
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Implied Premium Limitations
 The limitations of this approach are:


It assumes that the DDM is correct to value
the market.
It assumes that the market is currently
correctly valued (what other choice do we
have?)


If the market is not correctly valued how do we
adjust for the errors of the many?
Would we even care to estimate the correct value
or would we “exploit” this error of the many?
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Looking at Beta
 Co-movement with the market (regression)
 Estimated with stock returns of the individual
company as the dependent variable


Return = [(PriceT+! + Dividends)/ PriceT] – 1
Why add dividends to price?
 Independent variable is usually large market
index
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S&P 500 is very popular
Return of S&P 500, should add in dividends
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Regression to Find Beta
 Independent Variable is Market Return
 Dependent Variable is Individual Stock Return
 Regression estimates slope and intercept
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
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Slope, beta = Covariance (y, x) / Variance of X
Intercept, alpha = mean (y) – beta x mean (x)
R2 = (beta times variance of x) / variance (y)
 Problem #12 – AnaDome

Beta 0.735, intercept -0.0015, R-squared 0.29
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Issues with Beta Estimation
 Time period of returns
 Longer periods provide more data
 Longer periods introduce problems with shifts
in the beta of the company (all firms moving to
a beta of 1?)
 What is the right return interval? Daily,
Monthly, Quarterly, Annual…more data better
 What is the Market Return? What do you use
for the market? Should be all assets…we use
S&P 500 for US stocks and we are “happy”
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Bottom-up betas
 The bottom-up approach relies on the fundamental
characteristics of the firm to determine the riskiness of the firm
and thus the firm beta.
 These fundamental characteristics include:
 Type of Business: Firms in more cyclical businesses or that sell
products that are more discretionary to their customers will have
higher betas than firms that are in non-cyclical businesses or sell
products that are necessities or staples.

Operating Leverage: Firms with greater fixed costs (as a
proportion of total costs) will have higher betas than firms with
lower fixed costs (as a proportion of total costs)

Financial Leverage: Firms that borrow more (higher debt, relative
to equity) will have higher betas than firms that borrow less.
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Bottom-up betas
 The first component of a firm’s risk is that
associated with its operations:

We can measure this risk by calculating the
firm’s unlevered beta (βU), i.e., a beta that
removes the effect of financial leverage.
 This unlevered beta is also referred to as an
asset beta as it represents the riskiness of
a firm’s assets.
 βU = Current Beta / (1+(1-TC)(D/E))
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Equity Betas and Leverage
 The following equation provides us with the mathematical
relationship between the unlevered and levered beta:
u 
L
1  1  TC D / E 
where
L = Levered Beta
u = Unlevered Beta
t = Corporate marginal tax rate
D = Debt Value
E = Equity Value
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Cost of Equity
 Once we know
 Risk-free Rate
 Market Premium
 Beta of the firm…
 Calculate the Cost of Equity
re  rf   (rm  rf )
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What is debt?
 General Rule: Debt generally has the following
characteristics:


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Commitment to make fixed payments in the future
The fixed payments are tax deductible
Failure to make the payments can lead to either default or
loss of control of the firm to the party to whom payments are
due.
 As a consequence, debt should include
 Any interest-bearing liability, whether short term or long term.
 Any lease obligation, whether operating or capital.
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Cost of debt vs. required rate of return
for debtholders
 The required rate of return for bondholders of a
particular firm is a function of:


Current interest rate for the risk-free asset
Default risk associated with the firm, i.e., how likely is the
firm to go bankrupt (risk premium).
 Bondholders are compensated in interest payments
(or coupon payments) for this required rate of return.
 Because from the firm’s perspective interest expense
is tax-deductible, the after-tax cost of debt (rd) is:
rd * (1 – tax rate)
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Estimating the cost of debt
 Depending on whether or not the firm in question has
bonds that are publicly traded and on available
information, there are three ways (in order of
preference) to estimate the before-tax cost of debt:
 Look for prices and yields of bonds outstanding
 Estimate the cost of debt from the firm’s credit
rating
 Estimate the cost of debt by calculating a synthetic
credit rating
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Estimating the cost of debt
 If the firm has bonds outstanding, and the bonds are
traded, the yield to maturity (YTM) on a long-term,
straight (no special features) bond can be used as
the before tax cost of debt.
http://screen.yahoo.com/bonds.html
FV
P
N
1  YTM 

1
1 N

1  YTM 

 Coupon 
YTM



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Estimating the cost of debt
 If the firm is rated, use the credit rating and a
typical default spread on bonds with that
rating to estimate the cost of debt.
 See page 139 of text for default spreads by
rating
 Start again with risk-free rate and add default
spread
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Back to WACC
 Once we know the required return for equity
and debt
 And we know the percentage of each funding
 And we know the tax rate…
 We can estimate the hurdle rate by
calculating the WACC
 (E/V) x Re + (D/V) x Rd x (1 – Tc)
 Note…the riskiness of the cash flows will be
implied by beta and the bond rating
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Homework
 Chapter 4 -
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5,
8,
9,
14,
19,
and 23
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