Estimating the Cost of Capital

1

• Estimating the Cost of Capital

2
The Cost of Capital

• To value a company using enterprise DCF, we
  discount free cash flow by the weighted average
  cost of capital (WACC). The WACC represents the
  opportunity cost that investors face for
  investing their funds in one particular business
  instead of others with similar risk.
• In its simplest form, the weighted average cost
  of capital is the market-based weighted average
  of the after-tax cost of debt and cost of equity

• To determine the weighted average cost of
  capital, we must calculate its three components
  (1) the cost of equity, (2) the after-tax cost of
  debt, and (3) the companys target capital
  structure.

3
Successful Implementation Requires Consistency

• The most important principle underlying
  successful implementation of the cost of capital
  is consistency between the components of WACC and
  free cash flow. To assure consistency,
• It must include the opportunity costs from all
  sources of capital debt, equity, and so
  onsince free cash flow is available to all
  investors.
• It must weight each securitys required return by
  its market-based target weight, not by its
  historical book value.
• It must be computed after corporate taxes (since
  free cash flow is calculated in after-tax terms).
  Any financing-related tax shields not included in
  free cash flow must be incorporated into the cost
  of capital or valued separately.
• It must be denominated in the same currency as
  free cash flow
• It must be denominated in nominal terms when cash
  flows are stated in nominal terms

4
The Cost of Capital An Example

• The weighted average cost of capital at Home
  Depot equals 9.3. The majority of enterprise
  value is held by equity holders (91.7), whose
  CAPM-based required return equals 9.9. The
  remaining capital is provided by debt holders at
  2.9 of an after-tax basis.

The Cost of Capital Home Depot
Proportion of total capital
After-tax opportunity cost
Contribution to weighted average
Source of capital
Cost of capital
Marginal tax rate
Debt Equity WACC
8.3 91.7 100.0
4.7 9.9
38.2
2.9 9.9
0.2 9.1 9.3
Lets examine the components of WACC one-by-one,
starting with the cost of equity
5
The Cost of Equity

• To estimate the cost of equity, we must determine
  the expected rate of return of the companys
  stock. Since expected rates of return are
  unobservable, we rely on asset-pricing models
  that translate risk into expected return.
• The three most common asset-pricing models differ
  primarily in how they define risk.
• The capital assets pricing model (CAPM) states
  that a stocks expected return is driven by how
  sensitive its returns are to the market
  portfolio. This sensitivity is measured using a
  term known as beta.
• The Fama-French three-factor model defines risk
  as a stocks sensitivity to three portfolios the
  stock market, a portfolio based on firm size, and
  a portfolio based on book-to-market ratios.
• The Arbitrage Pricing Theory (APT) is a
  generalized multi-factor model, but unfortunately
  provides no guidance on the appropriate factors
  that drive returns.
• The CAPM is the most common method for estimating
  expected returns, so we begin our analysis with
  that model.

6
The Capital Assets Pricing Model

• The CAPM postulates that the expected rate of
  return on a companys stock equals the risk-free
  rate plus the securitys beta times the market
  risk premium

Expected return Percent
ERi rf Bi (ERm rf)

• To estimate a stocks expected return, you need
  to measure three inputs
• The risk-free rate
• The market risk premium
• The stocks beta

Beta (systematic risk)
7
Component 1 of the CAPM The Risk Free Rate

• To estimate the risk-free rate, we look to
  government default-free bonds. For simplicity,
  most valuation analysts choose a single yield to
  maturity from one government bond that best
  matches the entire cash flow stream being valued.
  
• For U.S.-based corporate valuation, the most
  common proxy is the 10-year government bond rate.
  This rate can be found in any daily financial
  publication.

Yield to Maturity on Government Bonds
Ideally, each cash flow should be discounted
using a government bond with a similar maturity.
Percent
Years to maturity
Source Bloomberg
8
Component 2 of the CAPM The Market Risk Premium

• Sizing the market risk premiumthe difference
  between the markets expected return and the
  risk-free rateis arguably the most debated issue
  in finance.
• Methods to estimate the market risk premium fall
  in three general categories
• Extrapolate historical excess returns. If the
  risk premium is constant, we can use a historical
  average to estimate the future risk premium.
• Regression analysis. Using regression, we can
  link current market variables, such as the
  aggregate dividend-to-price ratio, to expected
  market returns.
• Use DCF to reverse engineer the risk premium.
  Using DCF, along with estimates of return on
  investment and growth, we can reverse engineer
  the markets cost of capital and subsequently
  the market risk premium.
• None of the methods precisely estimate the market
  risk premium. Still, based on evidence from each
  of these models, we believe the market risk
  premium as of year-end 2003 was approximately 5
  percent.

9
Method 1 Use Historical Excess Returns

• Investors, being risk-averse, demand a premium
  for holding stocks rather than bonds.
• If the level of risk aversion hasnt changed over
  the last 100 years, then historical excess
  returns are a reasonable proxy for future
  premiums. But many econometric issues quickly
  arise. For instance,
• Which risk free rate should be used to compute
  the excess return?
• Which method of averaging is better, arithmetic
  or geometric?
• Is a prediction based on U.S. data too high?

10
Using Historical Excess Returns Best Practices

• To best measure the risk premium using historical
  data, you should
• Calculate the premium over long-term government
  bonds
• Use long-term government bonds, because they
  match the duration of a companys cash flows
  better than do short-term rates.
• Use the longest period possible
• If the market risk premium is stable, a longer
  history will reduce estimation error. Since, no
  statistically significant trend is observable, we
  recommend the longest period possible.
• Use an arithmetic average of longer-dated
  intervals (such as five years)
• Although the arithmetic average of annual returns
  is the best predictor of future one year returns,
  compounded averages will be upward biased (too
  high). Therefore, use longer-dated intervals to
  build discount rates.
• Adjust the result for econometric issues, such as
  survivorship bias.
• Predictions based on U.S. data (a successful
  economy) are probably too high.

11
Geometric Versus Arithmetic Average

• Annual returns can be calculated using either an
  arithmetic average or a geometric average. An
  arithmetic (simple) average sums each years
  observed premium and divides by the number of
  observations

• A geometric (compounding) average compounds each
  years excess return and takes the root of the
  resulting product

• Arithmetic averages always exceed geometric
  averages when returns are volatile.

So which averaging method best estimates the
expected future rate of return?
12
Problems with the Arithmetic Average

• The arithmetic average of annual returns is the
  best predictor of future one year returns, but
  compounded averages will be biased upwards (i.e.
  too high).
• Consider a portfolio which can either grow by
  20 or -10 in a given period. The arithmetic
  average equals 5. If you invested 100 in this
  portfolio, what is the portfolios expected value
  after two years?

If returns are independent, the expected value is
110.3, the same as if 100 had grown
consistently at the arithmetic average of 5 for
two periods.
If returns are negatively autocorrelated, i.e.
high returns are more likely followed by low
returns, a compounded arithmetic return is too
high!
13
When Possible, Use Long-Dated Holding Periods
To correct for the bias caused negative
autocorrelation in returns, we have two choices.
First, we can calculate multi-period holding
returns directly from the data, rather than
compound single-period averages. Alternatively,
we can use an estimator proposed by Marshall
Blume, one that blends the arithmetic geometric
averages.
Arithmetic Returns for Various Intervals,
1903-2002
Cumulative returns
Annualized returns
U.S. government bonds
U.S. excess return
U.S. excess returns
Number of observations
U.S. stocks
Blume estimator
Arithmetic mean of
1-year holding periods 2-year holding
periods 4-year holding periods 5-year holding
periods 10-year holding periods
100 50 25 20 10
11.3 24.1 49.9 68.2 165.6
5.3 10.9 23.1 29.5 72.1
6.2 12.6 23.0 32.3 70.1
6.2 6.1 5.3 5.8 5.5
6.2 6.1 6.0 5.9 5.6
Source Ibbotson Associates McKinsey analysis
14
Method 2 Regression Analysis
Predicted Market Risk Premium based on the
dividend to price ratio

• Using advanced regression techniques unavailable
  to earlier authors, Jonathan Lewellen of
  Dartmouth found that observable variables, such
  as dividend yields, do predict future market
  returns.
• Plotting the models predictions reveals one
  major drawback the risk premium prediction can
  be negative!
• Other authors question the idea of using
  financial ratios, arguing unconditional
  historical averages predict better than more
  sophisticated regression techniques.

Percent
Source Lewellen (2004) Goyal and Welch (2003)
McKinsey analysis
15
Method 3 Reverse Engineer Discounted Cash Flow

• Using the principles of discounted cash flow,
  along with estimates of growth, various authors
  have attempted to reverse engineer the market
  risk premium.
• We use the key value driver formula to reverse
  engineer the market risk premium. After
  stripping out inflation, the expected market
  return (not excess return) is remarkably
  constant, averaging 7.0.

16
Component 3 of the CAPM Measuring Beta

• According to the CAPM, a stocks expected return
  is driven by beta, which measures how much the
  stock and market move together. Since beta cannot
  be observed directly, we must estimate its value.
  
• The most common regression used to estimate a
  companys raw beta is the market model

The Beta for Home Depot
Percent
Home Depot monthly stock returns

• Based on data from 1998-2003, Home Depots beta
  is estimated at 1.37

SP 500 monthly returns
17
Estimating Beta Best Practices

• As can be seen on the previous slide, estimating
  beta is a noisy process. Based on certain market
  characteristics and a variety of empirical tests,
  we reach several conclusions about the regression
  process
• Raw regressions should use at least 60 data
  points (e.g., five years of monthly returns).
  Rolling betas should be graphed to examine any
  systematic changes in a stocks risk.
• Raw regressions should be based on monthly
  returns. Using shorter return periods, such as
  daily and weekly returns, leads to systematic
  biases.
• Company stock returns should be regressed against
  a value-weighted, well-diversified portfolio,
  such as the SP 500 or MSCI World Index.

• Next, recalling that raw regressions provide only
  estimates of a companys true beta, we improve
  estimates of a companys beta by deriving an
  unlevered industry beta and then relevering the
  industry beta to the companys target capital
  structure.

18
When Possible, Compute a Rolling Beta

• Because estimates of beta are imprecise, plot the
  companys rolling 60-month beta to visually
  inspect for structural changes or short-term
  deviations.
• IBMs beta hovered near 0.7 in the 1980s but rose
  dramatically in the mid-1990s and now measures
  near 1.3. This rise in beta occurred during a
  period of great change for IBM.

IBM Market Beta, 1985-2004
Beta
19
Levering and Unlevering Betas

• To improve the precision of beta estimation, use
  industry, rather than company-specific, betas.
  Companies in same industry face similar operating
  risks, so they should have similar operating
  betas.
• Simply using the median of an industrys raw
  betas, however, overlooks an important factor
  leverage. A companys equity beta is a function
  of not only its operating risk, but also the
  financial risk it takes.
• The weighted average beta for operating assets
  (bu - which is called the unlevered beta) and
  financial assets (btxa) must equal the weighted
  average beta for debt (bd) and equity (be). Our
  goal is to use this to solve for bu

operating assets tax assets
debt equity
Because there are many unknowns and only one
equation, we must impose additional assumptions
to solve for bu
20
Levering and Unlevering Betas

• Method 1 Assume btxa equals bu. If you believe
  the risk associated with tax shields (bu) equals
  the risk associated with operating assets (bu),
  the risk equation can be simplified dramatically.
  Specifically,

if bd 0

• Method 2 Assume btxa equals bd. If you believe
  the risk associated with tax shields (btxa) is
  comparable to the risk of debt (bd), the equation
  can once again be arranged to solve for the
  unlevered cost of equity.

If the dollar level of debt is constant and debt
is risk free,
21
Determining the Industry Beta

• To estimate an industry-adjusted company beta
• First, regress each companys stock returns
  against the SP 500 to determine raw beta.
• Next, to unlever each beta, calculate each
  companys market-debt-to-equity ratio.
• Determine the industry unlevered beta by
  calculating the median (in this case, the median
  and average betas are the same).
• Relever the industry unlevered beta is to each
  companys target debt-to-equity ratio

Home Depot
Lowes
Capital structure
Debt Operating leases Excess cash Total net
debt Shares outstanding (Mil) Share price
() Market value of equity Debt/equity Raw
beta (step 1) Unlevered beta (step 2) Industry
average (step 3) Relevered beta (step 4)
1,365 6,554 (1,609) 6,310 2,257 35.49
80,101 0.079 1.37 1.27 1.14 1.23

3,755 2,762 (948) 5,569 787 55.39 43,592
0.128 1.15 1.02 1.14 1.30
Home Depot
Lowes
Beta calculations
22
Applying the CAPM

• The CAPM postulates that the expected rate of
  return on a companys stock equals the risk free
  rate plus the securitys beta times the market
  risk premium.
• To estimate the risk-free rate in developed
  economies, use highly liquid, long-term
  government securities, such as the 10-year
  zero-coupon strip.
• Based on historical averages and forward-looking
  estimates, the appropriate market risk premium is
  currently between 4.5 and 5.5 percent.
• To estimate a companys beta, use industry
  derived betas levered to the companys target
  capital structure.
• For Home Depot

ERi rf Bi (ERm rf)
ERi 4.34 1.23 (4.5) 9.9
23
An Alternative Model Fama French

• In 1992, Eugene Fama and Kenneth French published
  a paper in the Journal of Finance that received a
  great deal of attention because they concluded,

In short, our tests do not support the most
basic prediction of the SLB Sharpe-Lintner-Black
Capital Asset Pricing Model that average stock
returns are positively related to market betas.

• Based on prior research and their own
  comprehensive regressions, Fama and French
  concluded that
• Equity returns are inversely related to the size
  of a company (as measured by market
  capitalization).
• Equity returns are positively related to the
  ratio of the book value to market value of the
  companys equity.
• With this model, a stocks excess returns are
  regressed on excess market returns, the excess
  returns of small stocks over big stocks (SMB),
  and the excess returns of high book-to-market
  stocks over low book-to-market stocks (HML).

24
An Alternative Model Fama French

• Lets use the Fama-French three-factor model to
  continue our Home Depot example. To determine the
  companys three betas, Home Depot stock returns
  are regressed against the excess market
  portfolio, SMB, and HML (available from
  professional service providers).

Home Depot Fama French Expected Returns
Contribution to expected return
Factor
Market risk premium SMB premium HML
premium Premium over risk free rate Risk free
rate Cost of equity
6.1 (0.1) (0.5) 5.5 4.3 9.8
For HD, the FF model leads to a slightly smaller
cost of equity than the CAPM.
25
An Alternative Model The Arbitrage Pricing Theory

• The Arbitrage Pricing Theory (APT) can be thought
  of as a generalized version of the Fama-French
  3-Factor model. In the APT, a securitys returns
  are fully specified by k factors and random noise

• By creating well-diversified factor portfolios,
  it can be shown that a securitys expected return
  must equal the risk free rate plus its exposure
  to each factor times the factors excess return
  (denoted by lambda)

• Implementation of the APT however has been
  elusive, as there is little agreement on either
  the number of factors, what the factors
  represent, or how to measure the factors.

26
The Cost of Debt

• The weighted average cost of capital represents
  the blended rate of return for a companys
  investors, both debtholders and equity holders

• To compute the WACC, we must estimate the cost of
  debt (kd). To do this we look to the yield to
  maturity (YTM). Although YTM represents a
  promised yield, it is a good approximation for
  expected return for investment grade companies.
• To compute yield-to-maturity, you have two
  options
• Compute the yield-to-maturity on long-term bonds
  by reverse engineering the discount rate needed
  to set DCF equal to the price.
• Compute the yield-to-maturity indirectly by
  adding a default premium (based on the companys
  rating) to the risk free rate.

Lets examine the indirect method
27
Component 1 of YTM The Risk Free Rate

• The yield-to-matrurity can be estimated by adding
  a default premium (based on the companys rating)
  to the risk free rate. The first component of
  yield-to-maturity is the risk free rate.
• Regardless of the maturity structure for the
  companys debt, use a long-term risk free rate
  when estimating a companys cost of capital.
  Using short-term debt yields to approximate the
  cost of debt ignores the fact that future debt
  will have different yields.

Yield to Maturity on Government Bonds
In 2003, the 10-year yield to maturity was 4.3
in the U.S. and in Europe.
Percent
Years to maturity
Source Bloomberg
28
SP and Moody Ratings Classes

• In order to be compensated for default risk,
  lenders charge a premium over the default-free
  benchmark rate to risky customers. The higher
  the chance of default, the higher the premium
  will be.
• Professional firms, such as SP and Moodys, rate
  the default risk of most bonds. Lets examine
  the ratings defined by Standard Poors

SP / Moodys
EXTREMELY STRONG capacity to meet its financial
commitments. AAA is the highest Issuer Credit
Rating assigned by Standard Poors. VERY
STRONG capacity to meet its financial
commitments. It differs from the highest rated
obligors only in small degree. STRONG capacity
to meet its financial commitments but is somewhat
more susceptible to the adverse effects of
changes in circumstances and economic conditions
than obligors in higher-rated categories. ADEQUAT
E capacity to meet its financial commitments.
However, adverse economic conditions or changing
circumstances are more likely to lead to a
weakened capacity of the obligor to meet its
commitments. Speculative debt is rated BB, B,
and CCC. In these case, YTM is a poor proxy for
the cost of debt.
AAA / Aaa AA / Aa A/ A BBB / Baa
Investment Grade
29
Component 2 of YTM The Corporate Yield Spread

• Once a bond rating has been identified, convert
  the rating into a yield to maturity.
• Lets examine U.S. corporate yield spreads over
  U.S. government bonds. All quotes are presented
  in basis points, where 100 basis points equals
  1.
• Since Home Depot is rated Aa3 by Moodys and AA
  by SP, we estimate that the 10-year yield to
  maturity is between 34 and 37 basis points over
  the 10-year Treasury.

Yield Spread in Basis Points, December 2003
Maturity in years
Rating Aaa/AAA Aa1/AA Aa2/AA Aa3/AA A2/A Baa2/BB
B Ba2/BB B2/B
1 34 37 39 40 57 79 228 387
3 35 33 34 36 49 96 260 384
5 21 34 35 37 57 108 257 349
7 22 40 42 43 65 111 250 332
10 28 29 34 37 48 102 236 303
30 50 62 64 65 82 134 263 319
Source Bloomberg
30
The Cost of Debt at Distressed Companies

• Yield to maturity is not an expected return. It
  is the return earned if the obligation is paid on
  time and in full. Since distressed companys
  have a significant chance of default, the
  yield-to-maturity is a poor proxy for expected
  return.
• One alternative for computing expected return is
  the CAPM. Since most bonds dont trade enough to
  generate a reliable beta, however, we compute
  index betas instead.

Beta by Bond Rating

• High yield debt has only a slightly higher beta
  than investment grade debt.
• If the market risk premium equals 5, this
  difference translates to only a 50 basis point
  differential in expected return!

Asset class Treasury bonds Investment-grade
corporate debt High-yield corporate debt
Beta 0.19 0.27 0.37
Source Lehman Brothers Global Family of
Indices, Fixed Income Research Morgan Stanley
Capital International U.S. Treasury Paul
Sweeting
31
Use Market-Based Target Weights

• With our estimates of the cost of equity (ke) and
  cost of debt (kd), we can now blend the two
  expected returns into a single number. To do
  this, we use the target weights of debt (and
  equity) to enterprise value, on a market (not
  book) basis

D/V equals the companys market-based, target
debt-to-value ratio

• To develop a target capital structure for a
  company,
• Estimate the companys current market-value-based
  capital structure.
• Review the capital structure of comparable
  companies.
• Review managements implicit or explicit approach
  to financing the business and its implications
  for the target capital structure.

32
Typical Market Weights Across Industries
Median Debt-to-Value, 2003

• To place the companys current capital structure
  in the proper context, compare its capital
  structure with those of similar companies.
• Industries with heavy fixed investment in
  tangible assets tend to have higher debt levels.
• High-growth industries, especially those with
  intangible investments, tend to use very little
  debt.

In percent
Note Market value of debt proxied by book
value. Enterprise value proxied by book value of
debt plus market value of equity