Chapter 4 slides

Chapter 4
Estimating a
Firm’s
Cost of Capital

© 2016 Pearson Education, Inc. All rights reserved.4-2
Chapter Outline
• Value, Cash Flows, and Discount Rates
– Defining a Firm’s WACC
– DCF, Firm Value, and the WACC
• Using DCF to Value an Acquisition
• Estimating the WACC
– Evaluate the Firm’s Capital Structure Weights
– The Cost of Debt
– The Cost of Preferred Equity
• Example: Alabama Power Company
– The Cost of Common Equity
• Examples: Dell
• Size Premium Examples: CAKE
– WACC: Putting It All Together
• Example: Champion Energy Corporation

Introduction
• This chapter considers discount rate determination
and the cost of capital for the firm as a whole.
– The firm’s weighted average cost of capital (WACC) is the
weighted average of the expected after-tax rates of
return of the firm’s various sources of capital.
• It is the discount rate that should be used to discount the
firm’s expected free cash flows to estimate firm value.
• It can be viewed as its opportunity cost of capital.

Defining WACC

Defining WACC
• WACC is defined as the average of the estimated required
rates of return for the firm’s interest-bearing debt (kd),
preferred stock (kp), and common equity (ke). The weights
used for each source of funds are equal to the proportions in
which funds are raised.
– Note that the cost of debt financing is adjusted downward to
reflect the interest tax-shield.

Steps in a WACC
• Step 1. Estimate capital structure and determine
the weights of each component: wd, wp, we.
• Step 2. Estimate the opportunity cost of each of
the sources of financing: kd, kp, ke, and adjust for
the effects of taxes where appropriate.
• Step 3. Calculate WACC by computing a weighted
average of the estimated after-tax costs of capital
sources used by the firm.

Estimation Issues
• Use market weights
– Reflect current importance of each source of financing to
the firm.
• Use market-based opportunity costs
– Costs should reflect the current required rates of return,
rather than historical rates.
• Use forward-looking weights and opportunity costs
– WACC assumes constant capital structure, if this does not
exist (i.e. LBO) analyst should apply APV model

Estimating WACC
• The connection of the WACC to the discounted
cash flow (DCF) estimate of firm value is:
Equation 4.2 does not reflect the value of the firm’s non-operating assets, nor does it capture the value of the firm’s
excess liquidity (i.e., marketable securities). We return to the consideration of these points in Chapters 6 and 7.

Illustration – Using DCF to Value
an Acquisition
• An analyst at Morgan Stanley has a client interested in
acquiring OfficeMart Inc.
• Step 1: Forecast FCF
• Step 2: Estimate Appropriate Discount Rate
– Assumptions: 40% Debt in Capital Structure with Cost of Debt 5%; Cost of Equity
14%, Tax Rate: 20%, WACC = 10% [i.e., 5%(1 - 20%)0.4 + 14% x 0.6 = 10%].
• Step 3: Discount the Estimated FCF
– Assumption: OfficeMart’s estimated cash flow forms a level perpetuity (no
growth)

Illustration – Using DCF to Value
an Acquisition
• Step 3: Discount the Estimated FCF
– Assumption: OfficeMart’s estimated cash flow forms a
level perpetuity (no growth)
– Recall that we have estimated firm value, which is the
sum of both the firm’s debt and equity claims. If we want
to estimate the value of the firm’s equity, we need to
subtract the value of its debt claims from the $5,600,000
valuation of the firm.
– Because OfficeMart has $2,240,000 worth of debt
outstanding, the value of the firm’s equity is $5,600,000 -
$2,240,000 = $3,360,000.

Step 1: Evaluate the Firm’s
Capital Structure Weights
• We must determine the weights that are to
be used for the components of the firm’s
capital structure.
• Represented by the fraction of the firm’s
invested capital contributed by each of the
sources of capital
– Market value of interest-bearing debt, preferred
equity, and common equity

Step 2: Estimate the Cost of Debt,
Preferred & Common Equity
• Cost of Debt (kd)
– We use yield to maturity (YTM) on publicly-traded bonds
or the risk-free rate plus a default spread given actual (or
projected) debt rating
• Cost of Preferred (kp)
– Preferred generally pays a constant dividend every period
(perpetuity), so we take the perpetuity formula, rearrange
and solve for kp
• Cost of Common Equity (ke)
– We use CAPM methods or DCF approach

Cost of Debt Capital kd
• Use yield to maturity (YTM) on publicly-traded bonds
– Risk-free rate plus default spread given actual (or projected)
debt rating
• If debt is not publicly-traded, analyst should estimate Kd
using the YTM on a portfolio of bonds with similar credit
ratings and maturity.
– Reuters provides average spreads to Treasury data that is
updated daily and cross-categorized by both default rating
(Moody’s, S&P, Fitch) and years to maturity
• For debt with default risk, the expected cash flows must
reflect the probability of default (Pb) and the recovery rate
(Re) on the debt in the event of default.
• Cost of Debt Capital is after-tax: kd (1-t)

Cost of Debt Capital kd

Financial Calculator Refresher
• Using a calculator for YTM
• Target company has a bond issue currently
outstanding with 25 years left to maturity. The
coupon rate is 9% and they are paid semi-
annually. The bond is currently selling for
$908.72 per $1000 bond. What is the pre-tax kd?
N = 50; PMT = 45; FV = 1000; PV = -908.75; CPT I/Y
= 5%; YTM = 5(2) = 10%

Cost of Preferred Equity (Kp)
• The cost of straight
(nonconvertible)
preferred stock can be
calculated:
• Using the preferred
dividend and observed
price of preferred
stock, we can infer
required rate of return:

Kp Example: Alabama Power
Company
• To illustrate, consider the preferred shares issued by
Alabama Power Company (ALP-PP), which pay a 5.3%
annual dividend on a $25.00 par value, or $1.33 per share.
On February 26, 2014, these preferred shares were selling
for $24.96 per share. Consequently, investors require a
5.67% return on these shares, calculated as follows:

Cost of Common Equity (ke)
• Ke is the most difficult estimate; it is the rate of
return investors expect from investing in the firm’s
stock
– Common shareholders are the residual claimants of the
firm’s earnings, there is no promised or pre-specified
return based on a financial contract
– Returns are based on cash distributions (i.e., dividends
and cash proceeds from the sale of the stock)
• Estimation Approaches:
– Asset pricing models - variants of Capital Asset Pricing
Model (CAPM)
– Discounted cash flow approach

Traditional CAPM
• CAPM may be used to estimate a
company’s Ke based on the risk-free rate
plus a premium for equity risk.
• To understand the relation between risk
and return it is useful to decompose the
risk associated with an investment into two
components:
– Systematic risk or nondiversifiable risk
– Nonsystematic risk or diversifiable risk

Systematic Risk
• Systematic risk or nondiversifiable risk
– Variability that contributes to the risk of a
diversified portfolio
– Examples: market factors such as changes in
interest rates and energy prices that influence
almost all stocks.
– The logic of the CAPM suggests that stocks that
are very sensitive to these sources of risk should
have high required rates of return, since
these stocks contribute more to the variability of
diversified portfolios.

Nonsystematic risk
• Nonsystematic risk or diversifiable risk
– Variability that does not contribute to the risk of
a diversified portfolio.
– Examples: random firm-specific events such as
lawsuits, product defects, and various technical
innovations.
– These sources of risk should have almost no
effect on required rates of return because
they contribute very little to the overall
variability of diversified portfolios.

Traditional CAPM
• “Risk-adjusted return” CAPM takes into account
beta, the risk free rate, and the expected return
on the market. It is also the equation for the
Security Market Line:

Example: Dell Cost of Equity

• In the U.S. the risk-free rate of interest
can be estimated by using a U.S. Treasury
Rate
– Long-term (10-20 year)
– Intermediate-term
– Short-term
• It should be consistent with the market
risk premium assumption, and ideally
matches the useful economic life of the
asset to be valued.
Ke and the risk-free rate: krf

Ke and the beta: βe
• The firm’s beta represents the sensitivity of
its equity returns to variations in the rates
of return on the overall market portfolio.
– If the value of the market portfolio of risky
investments outperforms Treasury bonds by
10% during a particular month, then a stock
with a beta coefficient of 1.25 would expect to
outperform Treasury bonds by 12.5%.

Alternatives for beta: βe
• Firm’s historical or predicted βe
– Estimated by regressing the firm’s excess stock
returns on the excess returns of a market
portfolio, where excess returns are defined as
the returns in excess of the risk-free return
– Analysts typically estimate using historical
returns
– We must ensure this accurately reflects the
relationship between risk and return in the
future

Alternatives for beta: βe
• Beta estimate based on βe of comparable firms
– Publicly-traded peers selected by business mix and
relative risk
– Involves adjustments for differences in capital structure
– Involves “unlevering” the betas for each of the sample
firms to remove the influence of capital structure
– The average βUnlevered are “relevered” to reflect the capital
structure of the target firm
– Preferred estimation method for privately-held firms

Beta example using sample of
comparable firms

• Factors favoring historical company beta
– Using current capital structure in developing weights
– No change expected in business mix
• Factors favoring historical industry beta
– Change in business mix expected
– Firm in Chapter 11
– Firm betas vary substantially by source
– Firm not publicly-traded
• Factors favoring forecasted beta
– Using future weights, not historical weights to estimate
WACC
– Projecting change in business mix
The Equity Beta

• Time Frame for measurement of βe:
– Most publicly available betas are estimated with
short-term risk-free rates or simply by
regressing stock returns on market returns.
– If a long-term maturity is used for the risk-free
rate to match the maturity of the cash flows it is
also advisable that the beta estimate should
reflect the longer-maturity risk-free rate.
– A longer time frame (5 years) smoothes out
irregularities in the market, which may be
present over shorter periods of time.

• Time Frame for measurement of βe:
– A shorter period (2 years) may be more appropriate for
companies in dynamic, high growth industries or for
recently restructured companies.
– Typically at least 3 years is used to capture statistically
significant return experience.

Ke and the expected equity risk
premium: (km – krf)
• Equity risk premium is an estimate of
excess returns above the risk-free rate.
• The discount rate must reflect the
opportunity cost of capital, which is in turn
determined by the rate of return associated
with investing in other risky investments.

• If one believes that the stock market will
generate high returns over the next 10
years, then the required rate of return on a
firm’s stock will also be quite high.
– Historical data suggest that the equity risk premium for the
market portfolio has averaged 6% to 8% a year over the past 75
years. However, there is good reason to believe that, looking
forward, the equity risk premium will not be this high.
– Current equity risk premium forecasts can be as low as 4%.
– 5% is commonly used in practice.

• Historical equity risk premium
– Many analysts use history as a guide to estimate the future
market return premium. Ibbotson Associates calculates
historical risk premiums over several time periods.

Problems with CAPM
• Academic research has failed to find a significant cross-sectional
relation between the beta estimates of stocks and their future rates
of return.
• Firm characteristics, like market capitalization and book-to-market
ratios, provide much better predictions of future returns than do
betas.
• Proposed modifications of CAPM – i.e. size premium
• Ibbotson Associates, divides firms into discrete groups based on the
total market value of their equity (the following is based on the
2013 Ibbotson NYSE Decile-Size Premium Data):
– Large-cap: firms with market value of equity above $7.687B - no size
premium.
– Mid-cap: firms with market value of equity between $7.687B and
$1.912B – apply size premium of 1.12%.
– Low-cap: firms with market value of equity between $1.912B and
$5141M – apply size premium of 1.85%
– Micro-cap: firms with market value of equity below $514M - apply size
premium of 3.81%.

• The Cheesecake Factory (NasdaqGS:CAKE)
– Equity Market Capitalization as of 1/2/2015: 2.38B (Mid-cap)
– Operates upscale, casual dining restaurants under The
Cheesecake Factory and Grand Lux Café brands with $1.96B
Revenue; $168M Net Income in 2014
Size Premium Example: CAKE
CAKE Required Return – Cost of Equity (Ke):
Risk Free Rate (10-year T-Bond Yield) as of 1/2/2015 2.24%
CAKE Beta (Finance.yahoo.com) 0.63
Equity Risk Premium (assumed) 5.0%
Mid-Cap Premium 1.12%
KCAKE = 2.24% + 0.63 * 5.0% + 1.12% = 6.51%

Factor models:
• Another approach to estimate ke is through the use of multifactor risk
models that capture the risk of investments with multiple betas and factor
risk premiums.
• Risk factors:
– Macroeconomic variables: changes in interest rates, inflation, or GDP
– Factor portfolios
• The Fama-French three-factor model is the most widely used
• It attempts to capture the determinants of equity returns using three risk
premiums:
– The equity risk premium of the CAPM: RMRF – return on equity index minus 30
day T-bills
– A size risk premium: SMB (small minus big) – return on small cap portfolio minus
return on large cap portfolio
– A risk premium related to the relative value of the firm when compared to its book
value (historical cost-based value): HML (high minus low)

Fama-French example: Dell
The resulting estimate of Apple’s ke is 5.98%, which is very different from the 7.1% we obtained
using the standard CAPM (illustrated in Figure 4-4)

Fama-French example: Apple
Inc.
using the standard CAPM.

• Limitations of cost of equity estimates
based on historical returns
– Historical security returns are highly variable.
– Market conditions are changing.
– Historical returns exhibit survivor bias.
Issues with Ke estimates based
on historical returns

DCF or Imputed Rate of Return
Approaches
• Instead of using the
DCF model to
determine the value of
an investment, the
method takes observed
values and estimated
cash flows and
estimates the internal
rate of return, or the
implied cost of equity
capital.
• Single-stage DCF
growth model:
• Reduces down to:
• Ke can be found by
solving:

Example: DCF or Imputed Rate of
Return Approach for DUK
• To illustrate, consider the case of Duke Energy Corporation (DUK).
Duke is involved in a number of businesses, including natural gas
transmission and electric power production. In 2013, the company
paid a dividend of $3.12 per share, and on February 26, 2014, the
firm’s stock closed trading at a price of $70.91.
• The analysts’ expected rate of growth in earnings for 2014 through
2019 is 3.92% per annum.
• Because Equation 4.11c assumes that the firm’s dividends grow
forever at a constant rate, we use the five-year estimate to
estimate Duke’s cost of equity capital as follows:

Calculating the WACC - Putting It All
Together for Champion Energy
• Champion Energy Corporation was founded in 1987 and is based in
Houston, Texas. The company provides midstream energy services, including
natural gas gathering, intrastate transmission, and processing in the
southwestern Louisiana and Texas Gulf Coast regions. The company operates
approximately 5,500 miles of natural gas gathering and transmission
pipelines and seven natural gas processing plants.
• Step 1: Capital Structure
Weights - Champion’s total
invested capital is equal to
$10 billion, which includes
interest-bearing debt of $2
billion and the firm’s equity
capitalization of $8 billion
($20.00 per share multiplied
by 400 million shares).
Consequently, the capital
structure weights are 20%
debt and 80% equity.

• Step 1: Cost of Debt
– Based on current yields to maturity for Champion’s new debt offering, we estimate
the before-tax cost of debt financing to be 5.25%. Because Champion enjoys an
investment-grade bond rating, we can use the yield to maturity as a reasonable
approximation to the cost of new debt financing. Adjusting the 8.25% yield for the
firm’s 25% tax rate produces an after-tax cost of debt of 3.94% = 5.25%(1 - .25).
• Step 2: Cost of Equity
– To calculate the cost of equity, three estimates were used: the CAPM, the three-
factor Fama-French, and the three-stage DCF models. The average of the resulting
estimates is 7.35% based on the three models:

• Step 3: The WACC for Champion’s proposed capital structure is
calculated as follows:
– Therefore, we estimate Champion’s WACC to be 9.23%, based on its planned use
of debt financing and operating plans.

Taking a Stand on the Issues
• Capital Structure
– Use market value weights for capital structure
– If a change is expected, target weights should
replace current weights
• Cost of Capital Best Practices
– Yield on a long-term bond in the estimation of
the market risk premium, as well as in
calculating the excess market returns that are
used in the estimation of beta
– Use multiple methods for estimating ke
– The focus of our analysis should be forward-
looking; but should not ignore historical data.

Summary
• A firm’s weighted average cost of capital (WACC) provides the rate
that is used to discount a firm’s future cash flows and determine
how it is likely to be valued in the financial marketplace. The
estimation of a firm’s WACC involves three fundamental activities:
evaluating the composition of the firm’s capital structure,
estimating the opportunity cost of each source of capital, and
calculating a weighted average of the after-tax cost of each source
of capital.
• Our main focus is on how firms evaluate investment opportunities.
In this regard, the WACC plays a key role.
– When firms evaluate opportunities to acquire other firms, they calculate the WACC
of the acquisition candidate. We will be discussing this in more detail in Chapter 9.
When firms evaluate an investment project, they need a discount rate that we will
refer to as the project WACC. A discussion of the project WACC is the focus of
Chapter 5.

Extensions and Refinements:
kd default risk example

Extensions and Refinements: Cost of
Debt - default risk example

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