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Chapter 9: Estimating the Cost
of Capital
Table of Content
1.The Cost of Capital
2.The Cost of Equity
3.The Cost of Debt
4.Target Weights
2
1. The Cost of Capital
 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 company’s target capital structure.
3
emd k
V
E
Tk
V
D
 )(1WACC
1.1 Successful Implementation Requires Consistency
Criteria to ensure consistency:
 It must include the opportunity costs of all investors—debt, equity, and so on—
since free cash flow is available to all investors, who expect compensation for the
risks they take.
 It must weight each security’s required return by its target market-based weight,
not by its historical book value.
 Any financing-related benefits or costs, such as interest tax shields, not included
in free cash flow must be incorporated into the cost of capital or valued separately
using adjusted present value.
 It must be computed after corporate taxes (since free cash flow is calculated in
after-tax terms), based on the same expectations of inflation, and match the
duration of the cash flows.
4
1.2 The Cost of Capital: An Example
 The weighted average cost of capital at Home Depot equals 8.5 percent. The majority of enterprise value is held by
equity holders (68.5 percent), whose CAPM-based required return equals 10.4 percent. The remaining capital is
provided by debt holders at 4.2 percent of an after-tax basis.
5
Let’s examine the components of WACC
one by one, starting with the cost of equity…
percent
After-tax Contribution to
Source of Proportion of Cost of Marginal opportunity weighted
capital total capital capital tax rate cost average
Debt 31.5 6.8 37.6 4.2 1.3
Equity 68.5 10.4 10.4 7.1
WACC 100.0 8.5
Home Depot: Weighted Average Cost of Capital
2. The Cost of Equity
 The three most common asset-pricing models differ primarily in how they define
risk.
• The capital asset pricing model (CAPM) states that a stock’s 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 stock’s 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 multifactor 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
2.1 Capital Asset Pricing Model
 A stock’s expected return is driven by three components: the risk-free rate, beta, and the expected market risk
premium.
7
)][(][ fmifi RREBRRE 
Expected
return
of stock i
Expected
market
risk premium
Risk-free
rate
Stock’s
beta
Estimating the Cost of Equity Using the CAPM
Data requirements Considerations
• Risk-free rate Use a long-term government rate dominated
in the same currency as cash flows.
• Market risk premium The market risk premium is difficult to
measure. Various models point to a risk
premium between 4.5 percent and 5.5 percent.
• Company beta To estimate beta, lever the company's
industry beta to the company's target debt-to-
equity ratio.
Source: Bloomberg.
0
1
2
3
4
5
0 5 10 15 20
Yieldtomaturity(percent)
Years to maturity
German
Eurobond
zerocoupon bonds
U.S.
Treasury
STRIPS
2.2 Risk-Free Rate: 10-Year Local Treasury
 The cost of capital must be in the same
currency as the company’s financials.
Thus, use a risk-free rate posted by the
local central bank of the company’s
country/region.
 The cost of capital must match the
duration of the cash flows in question. For
long-term project valuation and company
evaluation, use no less than the 10-year
rate.
8
Government Zero Coupon Yields, May 2009
2.3 The Market Risk Premium
 Methods to estimate the market risk premium fall into three general
categories:
1. Estimating the future risk premium by measuring and extrapolating historical
returns.
2. Using regression analysis to link current market variables, such as the
aggregate dividend-to-price ratio, to project the expected market risk
premium.
3. Using DCF valuation, along with estimates of return on investment and
growth, to reverse engineer the market’s cost of capital.
9
2.4 Using Historical Excess Returns: Best
Practices
 To best measure the risk premium using historical data, you should:
1. Calculate the premium over long-term government bonds.
 Use long-term government bonds, because they match the duration of a company’s
cash flows better than do short-term rates.
2. 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.
3. 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.
4. Adjust the result for econometric issues, such as survivorship bias.
 Predictions based on U.S. data (a successful economy) are probably too high.
10
2.5 When Possible, Use Long-Dated Holding Periods
 To correct for the bias caused by misestimating and/or 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 and geometric averages.
11
Cumulative Returns for Various Intervals, 1900–2009
percent
U.S. U.S. U.S.
U.S. government excess excess Blume
Arithmetic mean of stocks bonds returns returns estimator
1-year holding periods 11.2 5.4 6.1 6.1 6.1
2-year holding periods 23.7 11.1 12.3 6.0 6.1
4-year holding periods 50.8 23.7 24.4 5.6 6.0
5-year holding periods 66.5 30.7 31.0 5.5 6.0
10-year holding periods 170.7 73.7 69.1 5.4 5.9
Source: Morningstar SBBI data, Morningstar Dimson, Marsh, Staunton Global Returns data.
Annualized returnsAverage cumulative returns
2.6 Embedded Market Risk Premium
Key Value Driver Formula:
12
e
g
Net Income 1-
ROE
Price =
k -g
 
 
 
2.7 Estimating Beta
• According to the CAPM, a stock’s 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
company’s raw beta is the market model:
• Based on data from 1998 to 2003, Home Depot’s beta
is estimated at 1.37.
13
 mi βRaR
percent
-25
-20
-15
-10
-5
0
5
10
15
20
-20 -15 -10 -5 0 5 10 15 20
HomeDepotmonthlystockreturns
Morgan Stanley Capital Index (MSCI) global monthly returns
Regressionbeta= 1.28
Home Depot: Stock Returns, 2001–2006
Even though Home Depot matched the market in aggregate losses during 2007 and 2008 (37 percent for
Home Depot versus 35 percent for the MSCI World Index), a slight difference in timing caused the two
measures to be uncorrelated. Prior to 2007, Home Depot’s market beta was relatively stable. For this
reason, we measure unlevered beta as of 2006.
2.8 Beta Varies over Time
 Between 1985 and 2008, IBM’s beta
hovered near 0.7 in the 1980s but rose
dramatically in the mid-1990s to a peak
above 1.7 before falling back down. It now
measures near 0.8.
 This rise in beta occurred during a period
of great change for IBM, as the company
moved from hardware (such as
mainframes) to services (such as
consulting).
14
0.0
0.4
0.8
1.2
1.6
2.0
1986 1991 1996 2001 2006
Marketbeta
IBM:Market Beta, 1985-2010
hardware
services
2.9 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
stock’s 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 S&P 500 or MSCI World Index.
 Next, recalling that raw regressions provide only estimates of a company’s true beta,
we improve estimates of a company’s beta by deriving an unlevered industry beta and
then relevering the industry beta to the company’s target capital structure.
15
2.10 Operating Risk across Industries
 A company’s beta represents the
company’s exposure to changes in the
overall stock market.
 Since the stock market is closely tied
to the economy, a company’s beta
represents its revenue and cash flow
exposure to the economy’s strength.
16
2.13
1.75
1.55
1.38
1.18
1.12
1.16
1.06
1.00
0.98
0.83
0.63
0.51
Semiconductor Equipment
Life Insurance
Integrated Steel
Specialty Retail
Commodity Chemicals
Information Services
Retail Automotive
Hotel/Gaming
Aggregate Market
Homebuilding
Packaging & Container
Property Management
Water Utility
Unlevered Beta by Sector
Source: Aswath Damodaran,New York University.
2.11 Cost of Equity Using CAPM
 When the beta is high, the stock is
considered more risky than the market.
 For instance, Cisco Systems moves more
than the market, and has a beta of 1.86.
Thus, the company’s cost of equity is 10.4
percent.
 With a beta of 0.73, Raytheon’s cost of
equity is estimated at 7.8 percent.
17
Base Return
Long-Term
Treasuries
4.0%
Below
Average
Risk
Above
Average
Risk
9.2%
14.4%
Raytheon
(7.8%)
Cisco
(10.4%)
Risk-free
rate
Expected
market
return
2.12 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
company’s equity.
 With this model, a stock’s excess returns are regressed on three factors: 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).
18
2.13 An Alternative Model: Fama & French
 Let’s use the Fama-French three-factor model to continue our Home Depot example. To determine the company’s three betas, Home
Depot stock returns are regressed against the excess market portfolio, SMB, and HML (available from professional service providers).
19
Home Depot: Fama-French Expected Returns
For Home Depot, the
Fama-French model
leads to a slightly
smaller cost of equity
than the market model.
Average Average Contribution
monthly annual to expected
premium 1
premium Regression return
Factor (percent) (percent) coefficient 2
(percent)
Market portfolio 5.4 1.39 7.5
SMB portfolio 0.23 2.8 (0.09) (0.3)
HML portfolio 0.40 5.0 (0.14) (0.7)
Premium over risk-free rate3
6.6
Risk-free rate 3.9
Cost of equity 10.5
1
SMB and HML premiums based on average monthly returns data, 1926–2009.
2
Based on monthly returns data, 2002–2006.
3
Summation rounded to one decimal point.
2.14 An Alternative Model: The Arbitrage Pricing
Theory
 The arbitrage pricing theory (APT) can be thought of as a generalized version of the Fama-French three-factor
model. In the APT, a security’s returns are fully specified by k factors and random noise:
 By creating well-diversified factor portfolios, it can be shown that a security’s expected return must equal the risk-free
rate plus its exposure to each factor times the factor’s 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.
20
eFbFbFbaR kki
~~
...
~~~
2211 
kkfi bbbrRE λ...λλ][ 2211 
3. Estimating the Cost of Debt
1. Search Bloomberg (or other financial databases) for the yield to
maturity on the company’s long-dated, option-free debt.
 To determine price and yield accurately, use only large trades (> $1 million).
2. If bonds do not trade, instead add a default premium to a benchmark
rate.
 The benchmark rate should be a long-dated local Treasury bond rate.
 The default premium is based on the company’s debt rating.
3. If your company (or client) does not have a debt rating, then use a
scoring model to estimate a rating.
21
3.1 Yield to Maturity of Debt
 When purchasing a bond, investors require compensation. The discount
factor used to value a bond is known as its yield to maturity (YTM).
 A bond’s yield to maturity (YTM) is dependent on two factors:
 Factor #1: the bond’s time to maturity (duration)
 Factor #2: the credit spread for default risk
22
NN
YTM)(1
Face
YTM)(1
1
1
YTM
Coupon
P









3.2 Home Depot: Pricing Example
 To value a bond, use the annuity formula for
coupon payments and present value for the
face value.
 Alternatively, use a spreadsheet to compute the
present value of individual cash flows.
 For U.S. bonds, coupons are paid twice a year.
Therefore, the bond-equivalent yield must be
divided by two for discounting semiannual cash
flows.
23
Home Depot Coupon 5.875
5.875 Bond, maturing 12/16/2036 Yield 5.865
Semiannual Discount Present
Period Date Coupon Yield Factor Value
1 12/16/2010 2.9375 2.9325 1.0293 2.854
2 6/16/2011 2.9375 2.9325 1.0595 2.773
3 12/16/2011 2.9375 2.9325 1.0906 2.694
4 6/16/2012 2.9375 2.9325 1.1226 2.617
5 12/16/2012 2.9375 2.9325 1.1555 2.542
6 6/16/2013 2.9375 2.9325 1.1894 2.470
7 12/16/2013 2.9375 2.9325 1.2242 2.399
8 6/16/2014 2.9375 2.9325 1.2601 2.331
9 12/16/2014 2.9375 2.9325 1.2971 2.265
10 6/16/2015 2.9375 2.9325 1.3351 2.200
… … … … … …
… … … … … …
50 6/16/2035 2.9375 2.9325 4.2425 0.692
51 12/16/2035 2.9375 2.9325 4.3670 0.673
52 6/16/2036 2.9375 2.9325 4.4950 0.654
53 12/16/2036 102.9375 2.9325 4.6268 22.248
Present value: 100.134
3.3 Method 1: Use
Financial Database
24
Home Depot Coupon 5.875
Maturity 12/16/2036
Rating BBB+/Baa1
Trade date Time Price Yield Size
6/18/2010 11:37:19 99.440 5.917 214K
6/18/2010 9:33:40 97.898 6.034 10K
6/18/2010 9:32:39 98.898 5.958 10K
6/17/2010 15:11:00 99.387 5.921 400K
6/17/2010 13:23:11 98.819 5.964 6K
6/17/2010 13:23:11 98.986 5.951 6K
6/17/2010 13:13:20 100.132 5.865 5,000K
6/17/2010 13:06:59 101.539 5.760 10K
6/17/2010 13:06:59 99.414 5.918 10K
6/17/2010 12:31:45 99.745 5.894 4,025K
CUSIP: 437076AS1
3.4 Critical Issue: Liquidity
 Not all long-dated bonds trade on a frequent basis. Consider Procter & Gamble’s 6.45 percent 2026 bond. The bond
traded only a handful of times during a two-month period.
25
Home Depot Coupon 5.875 Procter & Gamble Coupon 6.45
Maturity 12/16/2036 Maturity 1/15/2026
Rating BBB+/Baa1 Rating AA−/Aa3
Trade date Time Price Yield Size Trade date Price Yield Size
6/18/2010 11:37:19 99.440 5.917 214K 6/17/2010 12:32:21 122.615 4.424 4,925K
6/18/2010 9:33:40 97.898 6.034 10K 6/16/2010 12:43:32 117.291 4.853 550K
6/18/2010 9:32:39 98.898 5.958 10K 5/18/2010 9:20:09 114.965 5.054 10K
6/17/2010 15:11:00 99.387 5.921 400K 5/13/2010 13:27:48 113.385 5.190 10K
6/17/2010 13:23:11 98.819 5.964 6K 5/7/2010 9:10:40 117.670 4.829 25K
6/17/2010 13:23:11 98.986 5.951 6K 5/7/2010 9:05:00 119.170 4.706 25K
6/17/2010 13:13:20 100.132 5.865 5,000K 5/7/2010 9:05:00 117.670 4.829 25K
6/17/2010 13:06:59 101.539 5.760 10K 5/6/2010 15:36:04 116.575 4.919 25K
6/17/2010 13:06:59 99.414 5.918 10K 5/5/2010 11:21:49 111.250 5.378 50K
6/17/2010 12:31:45 99.745 5.894 4,025K 5/5/2010 11:21:49 110.875 5.411 50K
CUSIP: 437076AS1 CUSIP: 742718BH1
3.5 Method 2: Add Default Premium to
Benchmark
 A corporate bond’s yield to maturity depends on the benchmark rate
(often government Treasury bonds or LIBOR) plus a default premium.
 How large is the default premium?
 The default premium depends on two statistics:
1. The probability and timing of default
2. The amount recovered by bondholders following default
26
YTM = Benchmark + Default Premium
3.6 Term Structure of Interest Rates
 Often a one-year loan and a 10-year loan will carry different yield to
maturities, even if each loan is default free.
 Long-term interest rates are an average of short-term rates.
http://www.bloomberg.com/markets/rates/index.html
http://stockcharts.com/charts/YieldCurve.html
YTM=Benchmark+DefaultPremium
U.S. Treasury Yield Curve
June 2010
Source: Bloomberg
27
3.7 he Credit Spread for Default Risk
 When a bank (or investor) lends money, it worries that it will
not be paid back. Will the borrower default?
 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.
 Rating agencies, such as S&P and Moody’s, rate the default
risk of most bonds (www.standardandpoors.com and
www.moodys.com).
YTM=Benchmark+DefaultPremium
28
EXTREMELY STRONG capacity to meet its financial commitments. AAA is the highest issuer credit
rating assigned by Standard & Poor’s.
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 somewhat more susceptible to the adverse
effects of changes in circumstances and economic conditions than obligors in higher-rated
categories.
ADEQUATE 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.
------
LESS VULNERABLE in the near term than other lower-rated obligors. However, it faces major
ongoing uncertainties and exposure to adverse business, financial, or economic conditions that
could lead to the obligor’s inadequate capacity to meet its financial commitments.
MORE VULNERABLE to nonpayment than obligations rated BB, but the obligor currently has the
capacity to meet its financial commitments on its obligations. Adverse business, financial, or
economic conditions will likely impair the obligor’s capacity or willingness to meet its financial
commitments.
CURRENTLY VULNERABLE, and is dependent upon favorable business, financial, and economic
conditions to meet its financial commitments.
AAA/Aaa
AA/Aa
A/A
BBB/Baa
BB/Ba
B/B
CCC/Caa
3.8 S&P and Moody’s Ratings
SpeculativeInvestmentGrade
29
3.9 Home Depot: Ratings Example On July 5, 2007, Standard & Poor's ratings service lowered both the corporate credit rating on Home
Depot Inc. to BBB+ from A+ and the CP rating to A-2 from A-1. At the same time, the ratings were
removed from CreditWatch, where they had been placed on June 19, 2007, with negative implications
following the company's announced plans to use $9.5 billion of net proceeds from the sale of HD Supply
and the issuance of $12 billion of senior notes and cash to finance a $22.5 billion share repurchase
program. The CreditWatch resolution follows the company's approval by the U.S. Federal Trade
Commission to sell HD Supply to a consortium of private equity firms. The outlook is stable.
30
3.10 The Credit Spread for Default Risk
• The lower the rating,
the higher the required
yield to maturity.
• Extremely safe bonds
trade at a small
premium to Treasuries.
• “Junk bonds” can
easily yield more than
10 percent. But the
yield is far from
guaranteed!
YTM=Benchmark+DefaultPremium 3.60
4.36
4.44
4.52
4.53
4.55
4.71
4.91
5.24
5.33
6.07
6.99
7.22
7.47
7.93
8.65
8.99
Treasury
AAA
AA+
AA
AA−
A+
A
A−
BBB+
BBB
BBB−
BB+
BB
BB−
B+
B
B−
Yield to Maturity by Debt Rating
10-Year Bonds, Monthly Average
percent, 2009
31
3.11 Default Spreads over Time
 Default spreads change over time. Default spreads rise during times of economic distress. During the financial crisis
of 2008, junk bond spreads spiked from 2 percent to 12 percent.
32
0
2
4
6
8
10
12
Jan-95 Jan-98 Jan-01 Jan-04 Jan-07 Jan-10
Default Spreadby Rating
Treasury
AAA
BBB
BB
0
2
4
6
8
10
12
14
Jan-95 Jan-98 Jan-01 Jan-04 Jan-07 Jan-10
Yield to Maturity by Rating
Treasury
AAA
BBB
BB
 Predicting default is key to determining an appropriate credit rating. To this
end, Edward Altman of New York University built a linear model that
combines various financial ratios to build a Z-score.
 X1 = Working Capital/Total Assets
 X2 = Retained Earnings/Total Assets
 X3 = Earnings Before Interest and Taxes/Total Assets
 X4 = Market Value of Equity/Book Value of Total Liabilities
 X5 = Sales/Total Assets
 When the Z-score falls below 1.81, the company has a 90 percent chance of
becoming distressed within a year.
)(0.1)(6.0)(3.3)(4.1)(2.1 54321 XXXXXZ 
3.12 Method 3: Determining the Credit
Rating
33
3.13 Z-Scores and Credit Ratings
 Although rating agencies use a
combination of both financial ratios
and quantitative assessments, the Z-
score can be successfully mapped
back to ratings.
 As Z-scores rise, so do average bond
ratings.
34
6.20
4.73
3.74
2.81
2.38
1.80
0.33
AAA
AA
A
BBB
BB
B
CCC
Average Z-Score by S&P BondRating
3.14 Is the Z-Score Still Relevant?
Default Expert Altman Launches Credit Rating Tool
Default expert Edward Altman is teaming with Risk Metrics Group to offer credit ratings on North American
companies, responding to a need for better default warnings in the wake of a record bankruptcy wave. “We
are excited about it being a significant improvement over existing models that are out there and providing
probability-of-default estimates that are very important to investors," said Altman, a professor of finance at
New York University.
Default probabilities are estimated with a "Z-Metrics" credit analysis tool, a new generation of the widely
known Z-score formula introduced by Altman in 1968 to predict corporate defaults. “It's based on a much
more up-to-date sample, many more new variables, and it includes market value variables as well as
macroeconomic variables that the Z-score didn't," Altman said. "The accuracy level in terms of predicting
defaults and nondefaults is considerably higher than both rating agencies and the old Z-score models," he
said.
—March 2010
35
3.15 Determining the Credit Rating: Other
Ratios
 Market participants are keenly interested in what drives credit rating actions. Although agency models are proprietary,
they have disclosed financial ratios they believe to be important:
36
Financial ratio AAA AA A BBB BB B CCC
EBITDA/revenues (%) 22.2 26.5 19.8 17.0 17.2 16.2 10.5
Return on capital (%) 27.0 28.4 21.8 15.2 12.4 8.7 2.7
EBIT interest coverage (×) 26.2 16.4 11.2 5.8 3.4 1.4 0.4
EBITDA interest coverage (×) 32.0 19.5 13.5 7.8 4.8 2.3 1.1
Funds from operations/total debt (%) 155.5 79.2 54.5 35.5 25.7 11.5 2.5
Free operating cash flow/total debt (%) 129.9 40.6 31.2 16.1 7.1 2.2 −3.6
Debt to EBITDA 0.4 0.9 1.5 2.2 3.1 5.5 8.6
Debt/debt plus equity (%) 12.3 35.2 36.8 44.5 52.5 73.2 98.9
Source: Standard & Poor’s, CreditStats.
Adjusted Key Industrial Financial Ratios, Long-Term Debt
Three-Year (2005−2007) Medians
3.16 Below-Investment-Grade Debt
• Estimate the bond’s price by discounting expected cash flows by the cost
of debt:
• Next, to determine the bond’s yield to maturity, place promised cash
flows, rather than expected cash flows, into the numerator. Then solve
for the yield to maturity:
37
4. USING TARGET WEIGHTS TO
DETERMINE THE COST OF CAPITAL
 With our estimates of the cost of equity and after-tax cost of debt, we can now blend the two expected
returns into a single number. To do this, use the target weights of debt and equity to enterprise value, on
a market (not book) basis:
 To estimate the target capital structure for a company you are valuing from an external perspective, use a
combination of three approaches:
 Estimate the company’s current market-value-based capital structure.
 Review the capital structure of comparable companies.
 Review management’s implicit or explicit approach to financing the business and its implications for
the target capital structure.
38
Questions?
Chapter 8. Forecasting Performance
39

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Chapter 9 on Valuation and Reporting in Organization

  • 1. Chapter 9: Estimating the Cost of Capital
  • 2. Table of Content 1.The Cost of Capital 2.The Cost of Equity 3.The Cost of Debt 4.Target Weights 2
  • 3. 1. The Cost of Capital  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 company’s target capital structure. 3 emd k V E Tk V D  )(1WACC
  • 4. 1.1 Successful Implementation Requires Consistency Criteria to ensure consistency:  It must include the opportunity costs of all investors—debt, equity, and so on— since free cash flow is available to all investors, who expect compensation for the risks they take.  It must weight each security’s required return by its target market-based weight, not by its historical book value.  Any financing-related benefits or costs, such as interest tax shields, not included in free cash flow must be incorporated into the cost of capital or valued separately using adjusted present value.  It must be computed after corporate taxes (since free cash flow is calculated in after-tax terms), based on the same expectations of inflation, and match the duration of the cash flows. 4
  • 5. 1.2 The Cost of Capital: An Example  The weighted average cost of capital at Home Depot equals 8.5 percent. The majority of enterprise value is held by equity holders (68.5 percent), whose CAPM-based required return equals 10.4 percent. The remaining capital is provided by debt holders at 4.2 percent of an after-tax basis. 5 Let’s examine the components of WACC one by one, starting with the cost of equity… percent After-tax Contribution to Source of Proportion of Cost of Marginal opportunity weighted capital total capital capital tax rate cost average Debt 31.5 6.8 37.6 4.2 1.3 Equity 68.5 10.4 10.4 7.1 WACC 100.0 8.5 Home Depot: Weighted Average Cost of Capital
  • 6. 2. The Cost of Equity  The three most common asset-pricing models differ primarily in how they define risk. • The capital asset pricing model (CAPM) states that a stock’s 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 stock’s 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 multifactor 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
  • 7. 2.1 Capital Asset Pricing Model  A stock’s expected return is driven by three components: the risk-free rate, beta, and the expected market risk premium. 7 )][(][ fmifi RREBRRE  Expected return of stock i Expected market risk premium Risk-free rate Stock’s beta Estimating the Cost of Equity Using the CAPM Data requirements Considerations • Risk-free rate Use a long-term government rate dominated in the same currency as cash flows. • Market risk premium The market risk premium is difficult to measure. Various models point to a risk premium between 4.5 percent and 5.5 percent. • Company beta To estimate beta, lever the company's industry beta to the company's target debt-to- equity ratio.
  • 8. Source: Bloomberg. 0 1 2 3 4 5 0 5 10 15 20 Yieldtomaturity(percent) Years to maturity German Eurobond zerocoupon bonds U.S. Treasury STRIPS 2.2 Risk-Free Rate: 10-Year Local Treasury  The cost of capital must be in the same currency as the company’s financials. Thus, use a risk-free rate posted by the local central bank of the company’s country/region.  The cost of capital must match the duration of the cash flows in question. For long-term project valuation and company evaluation, use no less than the 10-year rate. 8 Government Zero Coupon Yields, May 2009
  • 9. 2.3 The Market Risk Premium  Methods to estimate the market risk premium fall into three general categories: 1. Estimating the future risk premium by measuring and extrapolating historical returns. 2. Using regression analysis to link current market variables, such as the aggregate dividend-to-price ratio, to project the expected market risk premium. 3. Using DCF valuation, along with estimates of return on investment and growth, to reverse engineer the market’s cost of capital. 9
  • 10. 2.4 Using Historical Excess Returns: Best Practices  To best measure the risk premium using historical data, you should: 1. Calculate the premium over long-term government bonds.  Use long-term government bonds, because they match the duration of a company’s cash flows better than do short-term rates. 2. 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. 3. 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. 4. Adjust the result for econometric issues, such as survivorship bias.  Predictions based on U.S. data (a successful economy) are probably too high. 10
  • 11. 2.5 When Possible, Use Long-Dated Holding Periods  To correct for the bias caused by misestimating and/or 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 and geometric averages. 11 Cumulative Returns for Various Intervals, 1900–2009 percent U.S. U.S. U.S. U.S. government excess excess Blume Arithmetic mean of stocks bonds returns returns estimator 1-year holding periods 11.2 5.4 6.1 6.1 6.1 2-year holding periods 23.7 11.1 12.3 6.0 6.1 4-year holding periods 50.8 23.7 24.4 5.6 6.0 5-year holding periods 66.5 30.7 31.0 5.5 6.0 10-year holding periods 170.7 73.7 69.1 5.4 5.9 Source: Morningstar SBBI data, Morningstar Dimson, Marsh, Staunton Global Returns data. Annualized returnsAverage cumulative returns
  • 12. 2.6 Embedded Market Risk Premium Key Value Driver Formula: 12 e g Net Income 1- ROE Price = k -g      
  • 13. 2.7 Estimating Beta • According to the CAPM, a stock’s 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 company’s raw beta is the market model: • Based on data from 1998 to 2003, Home Depot’s beta is estimated at 1.37. 13  mi βRaR percent -25 -20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20 HomeDepotmonthlystockreturns Morgan Stanley Capital Index (MSCI) global monthly returns Regressionbeta= 1.28 Home Depot: Stock Returns, 2001–2006 Even though Home Depot matched the market in aggregate losses during 2007 and 2008 (37 percent for Home Depot versus 35 percent for the MSCI World Index), a slight difference in timing caused the two measures to be uncorrelated. Prior to 2007, Home Depot’s market beta was relatively stable. For this reason, we measure unlevered beta as of 2006.
  • 14. 2.8 Beta Varies over Time  Between 1985 and 2008, IBM’s beta hovered near 0.7 in the 1980s but rose dramatically in the mid-1990s to a peak above 1.7 before falling back down. It now measures near 0.8.  This rise in beta occurred during a period of great change for IBM, as the company moved from hardware (such as mainframes) to services (such as consulting). 14 0.0 0.4 0.8 1.2 1.6 2.0 1986 1991 1996 2001 2006 Marketbeta IBM:Market Beta, 1985-2010 hardware services
  • 15. 2.9 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 stock’s 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 S&P 500 or MSCI World Index.  Next, recalling that raw regressions provide only estimates of a company’s true beta, we improve estimates of a company’s beta by deriving an unlevered industry beta and then relevering the industry beta to the company’s target capital structure. 15
  • 16. 2.10 Operating Risk across Industries  A company’s beta represents the company’s exposure to changes in the overall stock market.  Since the stock market is closely tied to the economy, a company’s beta represents its revenue and cash flow exposure to the economy’s strength. 16 2.13 1.75 1.55 1.38 1.18 1.12 1.16 1.06 1.00 0.98 0.83 0.63 0.51 Semiconductor Equipment Life Insurance Integrated Steel Specialty Retail Commodity Chemicals Information Services Retail Automotive Hotel/Gaming Aggregate Market Homebuilding Packaging & Container Property Management Water Utility Unlevered Beta by Sector Source: Aswath Damodaran,New York University.
  • 17. 2.11 Cost of Equity Using CAPM  When the beta is high, the stock is considered more risky than the market.  For instance, Cisco Systems moves more than the market, and has a beta of 1.86. Thus, the company’s cost of equity is 10.4 percent.  With a beta of 0.73, Raytheon’s cost of equity is estimated at 7.8 percent. 17 Base Return Long-Term Treasuries 4.0% Below Average Risk Above Average Risk 9.2% 14.4% Raytheon (7.8%) Cisco (10.4%) Risk-free rate Expected market return
  • 18. 2.12 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 company’s equity.  With this model, a stock’s excess returns are regressed on three factors: 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). 18
  • 19. 2.13 An Alternative Model: Fama & French  Let’s use the Fama-French three-factor model to continue our Home Depot example. To determine the company’s three betas, Home Depot stock returns are regressed against the excess market portfolio, SMB, and HML (available from professional service providers). 19 Home Depot: Fama-French Expected Returns For Home Depot, the Fama-French model leads to a slightly smaller cost of equity than the market model. Average Average Contribution monthly annual to expected premium 1 premium Regression return Factor (percent) (percent) coefficient 2 (percent) Market portfolio 5.4 1.39 7.5 SMB portfolio 0.23 2.8 (0.09) (0.3) HML portfolio 0.40 5.0 (0.14) (0.7) Premium over risk-free rate3 6.6 Risk-free rate 3.9 Cost of equity 10.5 1 SMB and HML premiums based on average monthly returns data, 1926–2009. 2 Based on monthly returns data, 2002–2006. 3 Summation rounded to one decimal point.
  • 20. 2.14 An Alternative Model: The Arbitrage Pricing Theory  The arbitrage pricing theory (APT) can be thought of as a generalized version of the Fama-French three-factor model. In the APT, a security’s returns are fully specified by k factors and random noise:  By creating well-diversified factor portfolios, it can be shown that a security’s expected return must equal the risk-free rate plus its exposure to each factor times the factor’s 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. 20 eFbFbFbaR kki ~~ ... ~~~ 2211  kkfi bbbrRE λ...λλ][ 2211 
  • 21. 3. Estimating the Cost of Debt 1. Search Bloomberg (or other financial databases) for the yield to maturity on the company’s long-dated, option-free debt.  To determine price and yield accurately, use only large trades (> $1 million). 2. If bonds do not trade, instead add a default premium to a benchmark rate.  The benchmark rate should be a long-dated local Treasury bond rate.  The default premium is based on the company’s debt rating. 3. If your company (or client) does not have a debt rating, then use a scoring model to estimate a rating. 21
  • 22. 3.1 Yield to Maturity of Debt  When purchasing a bond, investors require compensation. The discount factor used to value a bond is known as its yield to maturity (YTM).  A bond’s yield to maturity (YTM) is dependent on two factors:  Factor #1: the bond’s time to maturity (duration)  Factor #2: the credit spread for default risk 22 NN YTM)(1 Face YTM)(1 1 1 YTM Coupon P         
  • 23. 3.2 Home Depot: Pricing Example  To value a bond, use the annuity formula for coupon payments and present value for the face value.  Alternatively, use a spreadsheet to compute the present value of individual cash flows.  For U.S. bonds, coupons are paid twice a year. Therefore, the bond-equivalent yield must be divided by two for discounting semiannual cash flows. 23 Home Depot Coupon 5.875 5.875 Bond, maturing 12/16/2036 Yield 5.865 Semiannual Discount Present Period Date Coupon Yield Factor Value 1 12/16/2010 2.9375 2.9325 1.0293 2.854 2 6/16/2011 2.9375 2.9325 1.0595 2.773 3 12/16/2011 2.9375 2.9325 1.0906 2.694 4 6/16/2012 2.9375 2.9325 1.1226 2.617 5 12/16/2012 2.9375 2.9325 1.1555 2.542 6 6/16/2013 2.9375 2.9325 1.1894 2.470 7 12/16/2013 2.9375 2.9325 1.2242 2.399 8 6/16/2014 2.9375 2.9325 1.2601 2.331 9 12/16/2014 2.9375 2.9325 1.2971 2.265 10 6/16/2015 2.9375 2.9325 1.3351 2.200 … … … … … … … … … … … … 50 6/16/2035 2.9375 2.9325 4.2425 0.692 51 12/16/2035 2.9375 2.9325 4.3670 0.673 52 6/16/2036 2.9375 2.9325 4.4950 0.654 53 12/16/2036 102.9375 2.9325 4.6268 22.248 Present value: 100.134
  • 24. 3.3 Method 1: Use Financial Database 24 Home Depot Coupon 5.875 Maturity 12/16/2036 Rating BBB+/Baa1 Trade date Time Price Yield Size 6/18/2010 11:37:19 99.440 5.917 214K 6/18/2010 9:33:40 97.898 6.034 10K 6/18/2010 9:32:39 98.898 5.958 10K 6/17/2010 15:11:00 99.387 5.921 400K 6/17/2010 13:23:11 98.819 5.964 6K 6/17/2010 13:23:11 98.986 5.951 6K 6/17/2010 13:13:20 100.132 5.865 5,000K 6/17/2010 13:06:59 101.539 5.760 10K 6/17/2010 13:06:59 99.414 5.918 10K 6/17/2010 12:31:45 99.745 5.894 4,025K CUSIP: 437076AS1
  • 25. 3.4 Critical Issue: Liquidity  Not all long-dated bonds trade on a frequent basis. Consider Procter & Gamble’s 6.45 percent 2026 bond. The bond traded only a handful of times during a two-month period. 25 Home Depot Coupon 5.875 Procter & Gamble Coupon 6.45 Maturity 12/16/2036 Maturity 1/15/2026 Rating BBB+/Baa1 Rating AA−/Aa3 Trade date Time Price Yield Size Trade date Price Yield Size 6/18/2010 11:37:19 99.440 5.917 214K 6/17/2010 12:32:21 122.615 4.424 4,925K 6/18/2010 9:33:40 97.898 6.034 10K 6/16/2010 12:43:32 117.291 4.853 550K 6/18/2010 9:32:39 98.898 5.958 10K 5/18/2010 9:20:09 114.965 5.054 10K 6/17/2010 15:11:00 99.387 5.921 400K 5/13/2010 13:27:48 113.385 5.190 10K 6/17/2010 13:23:11 98.819 5.964 6K 5/7/2010 9:10:40 117.670 4.829 25K 6/17/2010 13:23:11 98.986 5.951 6K 5/7/2010 9:05:00 119.170 4.706 25K 6/17/2010 13:13:20 100.132 5.865 5,000K 5/7/2010 9:05:00 117.670 4.829 25K 6/17/2010 13:06:59 101.539 5.760 10K 5/6/2010 15:36:04 116.575 4.919 25K 6/17/2010 13:06:59 99.414 5.918 10K 5/5/2010 11:21:49 111.250 5.378 50K 6/17/2010 12:31:45 99.745 5.894 4,025K 5/5/2010 11:21:49 110.875 5.411 50K CUSIP: 437076AS1 CUSIP: 742718BH1
  • 26. 3.5 Method 2: Add Default Premium to Benchmark  A corporate bond’s yield to maturity depends on the benchmark rate (often government Treasury bonds or LIBOR) plus a default premium.  How large is the default premium?  The default premium depends on two statistics: 1. The probability and timing of default 2. The amount recovered by bondholders following default 26 YTM = Benchmark + Default Premium
  • 27. 3.6 Term Structure of Interest Rates  Often a one-year loan and a 10-year loan will carry different yield to maturities, even if each loan is default free.  Long-term interest rates are an average of short-term rates. http://www.bloomberg.com/markets/rates/index.html http://stockcharts.com/charts/YieldCurve.html YTM=Benchmark+DefaultPremium U.S. Treasury Yield Curve June 2010 Source: Bloomberg 27
  • 28. 3.7 he Credit Spread for Default Risk  When a bank (or investor) lends money, it worries that it will not be paid back. Will the borrower default?  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.  Rating agencies, such as S&P and Moody’s, rate the default risk of most bonds (www.standardandpoors.com and www.moodys.com). YTM=Benchmark+DefaultPremium 28
  • 29. EXTREMELY STRONG capacity to meet its financial commitments. AAA is the highest issuer credit rating assigned by Standard & Poor’s. 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 somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than obligors in higher-rated categories. ADEQUATE 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. ------ LESS VULNERABLE in the near term than other lower-rated obligors. However, it faces major ongoing uncertainties and exposure to adverse business, financial, or economic conditions that could lead to the obligor’s inadequate capacity to meet its financial commitments. MORE VULNERABLE to nonpayment than obligations rated BB, but the obligor currently has the capacity to meet its financial commitments on its obligations. Adverse business, financial, or economic conditions will likely impair the obligor’s capacity or willingness to meet its financial commitments. CURRENTLY VULNERABLE, and is dependent upon favorable business, financial, and economic conditions to meet its financial commitments. AAA/Aaa AA/Aa A/A BBB/Baa BB/Ba B/B CCC/Caa 3.8 S&P and Moody’s Ratings SpeculativeInvestmentGrade 29
  • 30. 3.9 Home Depot: Ratings Example On July 5, 2007, Standard & Poor's ratings service lowered both the corporate credit rating on Home Depot Inc. to BBB+ from A+ and the CP rating to A-2 from A-1. At the same time, the ratings were removed from CreditWatch, where they had been placed on June 19, 2007, with negative implications following the company's announced plans to use $9.5 billion of net proceeds from the sale of HD Supply and the issuance of $12 billion of senior notes and cash to finance a $22.5 billion share repurchase program. The CreditWatch resolution follows the company's approval by the U.S. Federal Trade Commission to sell HD Supply to a consortium of private equity firms. The outlook is stable. 30
  • 31. 3.10 The Credit Spread for Default Risk • The lower the rating, the higher the required yield to maturity. • Extremely safe bonds trade at a small premium to Treasuries. • “Junk bonds” can easily yield more than 10 percent. But the yield is far from guaranteed! YTM=Benchmark+DefaultPremium 3.60 4.36 4.44 4.52 4.53 4.55 4.71 4.91 5.24 5.33 6.07 6.99 7.22 7.47 7.93 8.65 8.99 Treasury AAA AA+ AA AA− A+ A A− BBB+ BBB BBB− BB+ BB BB− B+ B B− Yield to Maturity by Debt Rating 10-Year Bonds, Monthly Average percent, 2009 31
  • 32. 3.11 Default Spreads over Time  Default spreads change over time. Default spreads rise during times of economic distress. During the financial crisis of 2008, junk bond spreads spiked from 2 percent to 12 percent. 32 0 2 4 6 8 10 12 Jan-95 Jan-98 Jan-01 Jan-04 Jan-07 Jan-10 Default Spreadby Rating Treasury AAA BBB BB 0 2 4 6 8 10 12 14 Jan-95 Jan-98 Jan-01 Jan-04 Jan-07 Jan-10 Yield to Maturity by Rating Treasury AAA BBB BB
  • 33.  Predicting default is key to determining an appropriate credit rating. To this end, Edward Altman of New York University built a linear model that combines various financial ratios to build a Z-score.  X1 = Working Capital/Total Assets  X2 = Retained Earnings/Total Assets  X3 = Earnings Before Interest and Taxes/Total Assets  X4 = Market Value of Equity/Book Value of Total Liabilities  X5 = Sales/Total Assets  When the Z-score falls below 1.81, the company has a 90 percent chance of becoming distressed within a year. )(0.1)(6.0)(3.3)(4.1)(2.1 54321 XXXXXZ  3.12 Method 3: Determining the Credit Rating 33
  • 34. 3.13 Z-Scores and Credit Ratings  Although rating agencies use a combination of both financial ratios and quantitative assessments, the Z- score can be successfully mapped back to ratings.  As Z-scores rise, so do average bond ratings. 34 6.20 4.73 3.74 2.81 2.38 1.80 0.33 AAA AA A BBB BB B CCC Average Z-Score by S&P BondRating
  • 35. 3.14 Is the Z-Score Still Relevant? Default Expert Altman Launches Credit Rating Tool Default expert Edward Altman is teaming with Risk Metrics Group to offer credit ratings on North American companies, responding to a need for better default warnings in the wake of a record bankruptcy wave. “We are excited about it being a significant improvement over existing models that are out there and providing probability-of-default estimates that are very important to investors," said Altman, a professor of finance at New York University. Default probabilities are estimated with a "Z-Metrics" credit analysis tool, a new generation of the widely known Z-score formula introduced by Altman in 1968 to predict corporate defaults. “It's based on a much more up-to-date sample, many more new variables, and it includes market value variables as well as macroeconomic variables that the Z-score didn't," Altman said. "The accuracy level in terms of predicting defaults and nondefaults is considerably higher than both rating agencies and the old Z-score models," he said. —March 2010 35
  • 36. 3.15 Determining the Credit Rating: Other Ratios  Market participants are keenly interested in what drives credit rating actions. Although agency models are proprietary, they have disclosed financial ratios they believe to be important: 36 Financial ratio AAA AA A BBB BB B CCC EBITDA/revenues (%) 22.2 26.5 19.8 17.0 17.2 16.2 10.5 Return on capital (%) 27.0 28.4 21.8 15.2 12.4 8.7 2.7 EBIT interest coverage (×) 26.2 16.4 11.2 5.8 3.4 1.4 0.4 EBITDA interest coverage (×) 32.0 19.5 13.5 7.8 4.8 2.3 1.1 Funds from operations/total debt (%) 155.5 79.2 54.5 35.5 25.7 11.5 2.5 Free operating cash flow/total debt (%) 129.9 40.6 31.2 16.1 7.1 2.2 −3.6 Debt to EBITDA 0.4 0.9 1.5 2.2 3.1 5.5 8.6 Debt/debt plus equity (%) 12.3 35.2 36.8 44.5 52.5 73.2 98.9 Source: Standard & Poor’s, CreditStats. Adjusted Key Industrial Financial Ratios, Long-Term Debt Three-Year (2005−2007) Medians
  • 37. 3.16 Below-Investment-Grade Debt • Estimate the bond’s price by discounting expected cash flows by the cost of debt: • Next, to determine the bond’s yield to maturity, place promised cash flows, rather than expected cash flows, into the numerator. Then solve for the yield to maturity: 37
  • 38. 4. USING TARGET WEIGHTS TO DETERMINE THE COST OF CAPITAL  With our estimates of the cost of equity and after-tax cost of debt, we can now blend the two expected returns into a single number. To do this, use the target weights of debt and equity to enterprise value, on a market (not book) basis:  To estimate the target capital structure for a company you are valuing from an external perspective, use a combination of three approaches:  Estimate the company’s current market-value-based capital structure.  Review the capital structure of comparable companies.  Review management’s implicit or explicit approach to financing the business and its implications for the target capital structure. 38

Editor's Notes

  1. 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. 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 equals the weighted average of the after-tax cost of debt and cost of equity (the equation is in the slide) where D/V =target level of debt to enterprise value using market-based (not book) values E/V =target level of equity to enterprise value using market-based values kd =cost of debt ke =cost of equity Tm =company’s marginal income tax rate The equation shows the three critical components of theWACC: the cost of equity, the after-tax cost of debt, and the target mix between the two securities
  2. The most important principle underlying successful implementation of the cost of capital is consistency between the components of WACC and free cash flow. Since free cash flow is the cash flow available to all financial investors, the company’s WACC must also include the required return for each investor. To assure consistency among these elements, the cost of capital must meet the criteria listed in the slide. Bearing these criteria in mind, to determine the weighted average cost of capital for a particular enterprise, you need to estimate the WACC’s three components: the cost of equity, the after-tax cost of debt, and the company’s target capital structure. Since none of the variables are directly observable, we employ various models, assumptions, and approximations to estimate each component. These models estimate the expected return on alternative investments with similar risk using market prices. This is why the term expected return is used interchangeably with cost of capital. Since the cost of capital is also used for allocating capital within the firm, it can also be referred to as a required return or hurdle rate.
  3. 5
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  5. Because the CAPM is discussed at length in modern finance textbooks, we will not delve into the theory here. Instead, we focus on best practices for implementation. The CAPM postulates that the expected rate of return on any security equals the risk-free rate plus the security’s beta times the market risk premium. In the CAPM, the risk-free rate and market risk premium, defined as the difference between E(Rm) andrf, are common to all companies; only beta varies across companies. Beta represents a stock’s incremental risk to a diversified investor, where risk is defined as the extent to which the stock covaries with the aggregate stock market. Although the CAPM is based on solid theory (the 1990 Nobel Prize in economics was awarded to the model’s primary author, William Sharpe), the model provides little guidance for its use in valuation. For instance, when valuing a company, which risk-free rate should you use? How do you estimate the market risk premium and beta? In the following section, we address these issues. The general conclusions are the following: - To estimate the risk-free rate in developed economies, use highly liquid, long-term government securities, such as the 10-year zero-coupon STRIPS. - Based on historical averages and forward-looking estimates, the appropriate market risk premium is between 4.5 and 5.5 percent. - To estimate a company’s beta, use an industry-derived unlevered beta relevered to the company’s target capital structure. Company-specific betas vary too widely over time to be used reliably.
  6. To estimate the risk-free rate, we look to government default-free bonds. Government bonds come in many maturities. For instance, the U.S. Treasury issues bonds with maturities ranging from one month to 30 years. However, different maturities can generate different yields to maturity. Which maturity should you use? Ideally, each cash flow should be discounted using a government bond with the same maturity. For instance, a cash flow generated 10 years from today should be discounted by a cost of capital derived from a 10-year zero coupon government bond (known as STRIPS). Government STRIPS are preferable because long-term government bonds make interim interest payments, causing their effective maturity to be shorter than their stated maturity. In reality, few practitioners discount each cash flow using a matched maturity. For simplicity, most choose a single yield to maturity from the government STRIPS that best matches the entire cash flow stream being valued. The plot shows the yield to maturity for various U.S. and German zero-coupon STRIPS versus their years to maturity (a relationship commonly known as the yield curve or term structure of interest rates). As of May 2009, 10-year U.S. Treasury STRIPS were trading at 3.9 percent, and German zero coupon bonds were trading at 3.7 percent. If you are valuing a company or long-term project, do not use a short term Treasury bill to determine the risk-free rate. When introductory finance textbooks calculate the CAPM, they typically use a short-term Treasury rate because they are estimating expected returns for the next month. As can be seen in the plot, short-term Treasury bills (near the y-axis) traded well below 10-year bonds in May 2009. Investors typically demand higher interest rates from long-term bonds when they believe short-term interest rates will rise over time. Using the yield from a short-term bond as the risk-free rate in a valuation fails to recognize that a bondholder can probably reinvest at higher rates when the short-term bond matures. Thus, the short-term bond rate misestimates the opportunity cost of investment for longer-term projects.
  7. Sizing the market risk premium—the difference between the market’s expected return and the risk-free rate—is arguably the most debated issue in finance. The ability of stocks to outperform bonds over the long run has implications for corporate valuation, portfolio composition, and retirement savings. But similar to a stock’s expected return, the expected return on the market is unobservable. And since no single model for estimating the market risk premium has gained universal acceptance, we present the results of various models. Methods to estimate the market risk premium fall into three general categories presented on the slide None of today’s models precisely estimate the market risk premium. Still, based on evidence from each of these models, the market risk premium varies continually between 4.5 and 5.5 percent and as of May 2009 equaled 5.4 percent. We step through the three models next.
  8. Historical market risk premium Investors, being risk averse, demand a premium for holding stocks rather than bonds. If the level of risk aversion hasn’t changed over the past 100 years, then historical excess returns should be a reasonable proxy for future premiums. For the best measurement of the risk premium using historical data, follow these guidelines: - Calculate the premium relative to long-term government bonds. When calculating the market risk premium, compare historical market returns with the return on 10-year government bonds. As we discussed, long-term government bonds better match the duration of a company’s cash flows than do short-term bonds. - Use the longest period possible. When using historical observations to predict future results, how far back should you look? If the market risk premium is stable, a longer history will reduce estimation error. Alternatively, if the premium changes and estimation error is small, a shorter period is better. To determine the appropriate historical period, consider any trends in the market risk premium compared with the noise associated with short-term estimates. To test for the presence of a long-term trend, we regress the U.S. market risk premium against time. Over the past 108 years, no statistically significant trend is observable. Based on regression results, the average excess return has fallen by 4.2 basis points a year, but this result cannot be statistically distinguished from zero. In addition, premiums calculated over shorter periods are extremely noisy. For instance, U.S. stocks outperformed bonds by 18 percent in the 1950s but offered no premium in the 1970s. Given the lack of any discernible trend and the significant volatility of shorter periods, you should use the longest time series possible. Use an arithmetic average of longer-dated intervals (such as 10 years). When reporting market risk premiums, most data providers report an annual number, such as 6.1 percent per year. But how do they convert a century of data into an annual number? And is the annualized number even relevant? No matter how we annualize excess returns, group the aggregation windows, or simulate estimators, the excess return on U.S. stocks over government bonds generally falls between 5 and 6 percent. - Adjust the result for econometric issues, such as survivorship bias Other statistical difficulties exist with historical risk premiums. According to one argument even properly measured historical premiums can’t predict future premiums, because the observable sample includes only countries with strong historical returns. Statisticians refer to this phenomenon as survivorship bias. Zvi Bodie writes, “There were 36 active stock markets in 1900, so why do we only look at two, [the UK and U.S. markets]? I can tell you—because many of the others don’t have a 100-year history, for a variety of reasons.” Since it is unlikely that the U.S. stock market will replicate its performance over the next century, we adjust downward the historical market risk premium.
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  10. Using the key value driver formula, we can reverse engineer the cost of equity. After inflation is stripped out, the expected market return (not excess return) is remarkably constant in the United States, averaging 7 percent. For the United Kingdom, the real market return is slightly more volatile, averaging 6 percent. To determine the market risk premium, subtract the real interest rate from the real cost of equity using Treasury inflation-protected securities (TIPS). Based on this formula, we used the long-run return on equity (13.5 percent) and the long-run growth in real gross domestic product (GDP) (3.5 percent) to convert a given year’s S&P 500 median earnings-to-price ratio into the cost of equity. The plot shows the nominal and real expected market returns between 1962 and 2008. The results are striking. After inflation is stripped out, the expected market return (not excess return) is remarkably constant, averaging 7 percent. For the United Kingdom, the real market return is slightly more volatile, averaging 6 percent. Based on these results, we estimate the current market risk premium by subtracting the current real long-term risk-free rate from the real equity return of 7 percent (for U.S. markets). In May 2009, the yield on a U.S. Treasury inflation-protected securities (TIPS) equaled 1.6 percent. Subtracting 1.6 percent from 7.0 percent gives an estimate of the risk premium at 5.4 percent.
  11. According to the CAPM, a stock’s expected return is driven by beta, which measures how much the stock and entire market move together. Since beta cannot be observed directly, you must estimate its value. To do this, begin by measuring a raw beta using regression, and then improve the estimate by using industry comparables and smoothing techniques. Even with a robust estimation process, judgment is still required. When necessary, consider how the industry is likely to move with the economy, in order to bound your results. Start with the empirical estimation of beta. The most common regression used to estimate a company’s raw beta is the market model presented in the slide. In the market model, the stock’s return (Ri), not price, is regressed against the market’s return. We plot 60 months of Home Depot stock returns versus Morgan Stanley Capital International (MSCI) World Index returns between 2001 and 2006. The solid line represents the “best fit” relationship between Home Depot’s stock returns and the stock market. The slope of this line is commonly denoted as beta. For Home Depot, the company’s raw beta (slope) is 1.28. Since typical betas range between 0 and 2, with the value-weighted average beta equaling 1, this raw result implies Home Depot is riskier than the typical stock.
  12. Measurement period Although there is no common standard for the appropriate measurement period, we follow the practice of data providers such as Morningstar Ibbotson, which use five years of monthly data to determine beta. Using five years of monthly data originated as a rule of thumb during early tests of the CAPM.24 In subsequent tests of optimal measurement periods, researchers confirmed five years as appropriate. Not every data provider uses five years. The data service Bloomberg, for instance, creates raw betas using two years of weekly data. Because estimates of beta are imprecise, plot the company’s rolling 60-month beta to visually inspect for structural changes or short-term deviations. For instance, changes in corporate strategy or capital structure often lead to changes in risk for stockholders. In this case, a long estimation period would place too much weight on irrelevant data. In the slide, we graph IBM’s raw beta between 1985 and 2008. As the exhibit shows, IBM’s beta hovered near 0.7 in the 1980s and most of the 1990s but rose dramatically in the late 1990s to a peak above 1.6 in 2007. This rise in beta occurred during a period of great change for IBM, as the company moved from hardware (such as mainframes) to services (such as consulting). Subsequently, using a long estimation period (for instance, 10 years) would underestimate the risk of the company’s new business model.
  13. But why did we choose to measure Home Depot’s returns in months? Why did we use five years of data? And how precise is this measurement? The CAPM is a one-period model and provides little guidance on how to use it for valuation. Yet following certain market characteristics and the results of a variety of empirical tests leads to several guiding conclusions: - The measurement period for raw regressions should include at least 60 data points (e.g., five years of monthly returns). Rolling betas should be graphed to search for any patterns or systematic changes in a stock’s risk. - Raw regressions should be based on monthly returns. Using more frequent return periods, such as daily and weekly returns, leads to systematic biases. - Company stock returns should be regressed against a value-weighted, well-diversified market portfolio, such as the MSCIWorld Index, bearing in mind that this portfolio’s value may be distorted if measured during a market bubble. Next, recalling that raw regressions provide only estimates of a company’s true beta, improve the results from the regression by deriving an unlevered industry beta and then relevering the industry beta to the company’s target capital structure. If no direct competitors exist, you should adjust raw company betas by using a smoothing technique. We describe the basis for our conclusions next.
  14. Estimating beta is an imprecise process. Earlier, we used historical regression to estimate Home Depot’s raw beta at 1.28. But the regression’s R-squared was only 37 percent, and the standard error of the beta estimate was 0.216. Using two standard errors as a guide, we feel confident Home Depot’s true beta lies between 0.85 and 1.71—hardly a tight range. To improve the precision of beta estimation, use industry, rather than company-specific, betas. Companies in the same industry face similar operating risks, so they should have similar operating betas. As long as estimation errors across companies are uncorrelated, overestimates and underestimates of individual betas will tend to cancel, and an industry median (or average) beta will produce a superior estimate. Simply using the median of an industry’s raw regression betas, however, overlooks an important factor: leverage. A company’s beta is a function of not only its operating risk, but also the financial risk it takes. Shareholders of a company with more debt face greater risks, and this increase is reflected in beta. Therefore, to compare companies with similar operating risks, you must first strip out the effect of leverage. Only then can you compare betas across an industry.
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  18. The weighted average cost of capital blends the cost of equity with the after-tax cost of debt. To estimate the cost of debt for investment-grade companies, use the yield to maturity of the company’s long-term, option-free bonds. Multiply your estimate of the cost of debt by 1 minus the marginal tax rate to determine the cost of debt on an after-tax basis. Technically speaking, yield to maturity is only a proxy for expected return, because the yield is actually a promised rate of return on a company’s debt (it assumes all coupon payments are made on time and the debt is paid in full). An enterprise valuation based on the yield to maturity is therefore theoretically inconsistent, as expected free cash flows should be discounted by an expected return, not a promised yield. For companies with investment-grade debt, the probability of default is so low that this inconsistency is immaterial, especially when compared with the estimation error surrounding beta and the market risk premium. Thus, for estimating the cost of debt for a company with investment grade debt (debt rated at BBB or better), yield to maturity is a suitable proxy. For companies with below-investment-grade debt, we recommend using adjusted present value (APV) based on the unlevered cost of equity rather than the WACC to value the company.
  19. To solve for yield to maturity (YTM), reverse engineer the discount rate required to set the present value of the bond’s promised cash flows equal to its price:
  20. The slide presents TRACE data for Home Depot’s 5.875 percent bonds due in December 2036. TRACE reports four data items: when the trade occurred, the size of the trade, the bond price, and the implied yield to maturity. As can be seen in the exhibit, the 2036 bond trades infrequently—only nine times in four hours. Home Depot’s short-maturity debt trades more frequently, but at only five years to maturity, its duration is a poor match for the company’s long-term cash flows. When measuring the yield to maturity, use trades greater than $1 million, as smaller trades are unreliable. Large trades for Home Depot’s 2036 bond were completed at 7.62 percent (3.23 percent above the 30-year U.S. Treasury bond). For companies with only short-term bonds or bonds that rarely trade, determine yield to maturity by using an indirect method. First, determine the company’s credit rating on unsecured long-term debt. Next, examine the average yield to maturity on a portfolio of long-term bonds with the same
  21. To find the yield to maturity for companies with liquid corporate debt, search for trading data on the company’s long-term bonds (greater than 10 years). In the United States, corporate bond trades are reported to the National Association of Securities Dealers, through its Trade Reporting and Compliance Engine (TRACE) system. Only trades greater than $1 million dollars should be considered. Consider trade data on bonds from Home Depot (2036 5.875 percent bond).
  22. In practice, few financial analysts distinguish between expected and promised returns. But for debt below investment grade, using the yield to maturity as a proxy for the cost of debt can cause significant error. To understand the difference between expected returns and yield to maturity, consider the following example. You have been asked to value a one-year zero-coupon bond whose face value is $100. The bond is risky; there is a 25 percent chance the bond will default and you will recover only half the final payment. Finally, the cost of debt (not yield to maturity), estimated using the CAPM, equals 6 percent. Based on this information, you estimate the bond’s price by discounting expected cash flows by the cost of debt: Solving for YTM, the $82.55 price leads to a 21.1 percent yield to maturity. This yield to maturity is much higher than the cost of debt. So what drives the yield to maturity? Three factors: the cost of debt, the probability of default, and the recovery rate after default. When the probability of default is high and the recovery rate is low, the yield to maturity will deviate significantly from the cost of debt. Thus, for companies with high default risk and low ratings, the yield to maturity is a poor proxy for the cost of debt. When a company is rated BB (non-investment-grade) or below, we do not recommend using the weighted average cost of capital to value the company. Instead, use adjusted present value (APV). The APV model discounts projected free cash flow at the company’s industry-based unlevered cost of equity and adds the present value of tax shields.
  23. Using market values to weight expected returns in the cost of capital follows directly from the formula’s derivation. But consider a more intuitive explanation: the WACC represents the expected return on an alternative investment with identical risk. Rather than reinvest in the company, management could return capital to investors, who could reinvest elsewhere. To return capital without changing the capital structure, management can repay debt and repurchase shares, but must do so at their market value. Conversely, book value represents a sunk cost, so it is no longer relevant. The cost of capital should rely on target weights, rather than current weights, because at any point, a company’s current capital structure may not reflect the level expected to prevail over the life of the business. The current capital structure may merely reflect a short-term swing in the company’s stock price, a swing that has yet to be rebalanced by management. Thus, using today’s capital structure may cause you to overestimate (or underestimate) the value of tax shields for companies whose leverage is expected to drop (or rise). Many companies are already near their target capital structure. If the company you are valuing is not, decide how quickly the company will achieve the target. In the simplest scenario, the company will rebalance immediately and maintain the new capital structure. In this case, using the target weights and a constant WACC (for all future years) will lead to a reasonable valuation. If you expect the rebalancing to happen over a significant period of time, then use a different cost of capital each year, reflecting the capital structure at the time. In practice, this procedure is complex; you must correctly model the weights, as well as the changes in the cost of debt and equity (because of increased default risk and higher betas). For extreme changes in capital structure, modeling enterprise DCF using a constantWACC can lead to significant error. In this case, value the company with adjusted present value (APV).