Problems with Cost of Capital Estimation in the Current Environment - Update1
By: Roger J. Grabowski, ASA
Date: February 4, 2009
The current economic environment has created challenges in estimating the cost of
equity capital (“COEC”) and in estimating the appropriate overall cost of capital (i.e., the
weighted average cost of capital or “WACC”). Since October 2008, new complications
have arisen in estimating the cost of capital. Traditional methods typically employed in
estimating the COEC and the WACC are subject to significant estimation and data input
problems. This article attempts to address some of these issues and offer some specific
recommendations on dealing with these issues.
First, U.S. Treasury bond (“T-bond”) yields, the typical benchmark used in either the
Capital Asset Pricing Model (“CAPM”) or the Build-up methods of estimating COEC, are
likely temporarily low, resulting in low estimates of COEC.
Second, the expected equity risk premium (“ERP”), the rate of return expected on a
diversified portfolio of common stocks in excess of the rate of return on an investment in
T-bonds, has likely increased as the broad stock market level has declined.
Third, because the stock market correction has been heavily concentrated in the
financial services sector and in highly leveraged companies, the commonly-employed
methods we use for estimating betas, the risk measure in the traditional CAPM, are
potentially flawed providing faulty estimates of risk. The result is that at the very time
when one assumes a priori that estimates of COEC have increased, the methods we
traditionally use to estimate the COEC are providing calculations that imply risk has
Fourth, current leverage ratios are likely not sustainable in the long-term for many
companies and one needs to consider estimating cost of capital with expected changing
1 This is an edited version (reflecting edits through Feb 25, 2009) of the article that appeared in the Business
Valuation E-Letter, Issue 13-05 and an update to an article that appeared in the Business Valuation E-Letter,
Issue 12-44 published by the American Society of Appraisers.
Fifth, because income subject to income taxes is and will continue to be less than zero
for many companies, one cannot automatically use an after-tax cost of debt capital (i.e.,
multiply the interest rate by one minus the income tax rate) in calculating an appropriate
Sixth, one must always test the resulting cost of capital estimates for reasonableness
and not simply apply data or formulas by rote.
Yields on Treasury Bonds as of December 31, 2008
The general notion of a “risk-free rate” is that it is equivalent to the return available on a
security that the market generally perceives as free of the risk of default as of the
valuation date.2 Analysts typically use the yield to maturity on U.S. government securities
as of the valuation date, as proxy for the risk-free rate.
Conceptually, the risk-free rate reflects a return on the following three components:
Rental rate: A real return for lending the funds over the investment period, thus foregoing
consumption for which the funds otherwise could be used; Inflation: The expected rate of
inflation over the term of the risk-free investment; Maturity risk or investment rate risk:
The risk that the principal’s market value will rise or fall during the period to maturity as a
function of changes in the general level of interest rates.3
All three of these economic factors are embedded in the yield to maturity for any given
maturity length. However, it is not possible to observe the market consensus about how
much of the total yield for any given maturity is attributable to each of these factors.
Note that the risk-free rate includes inflation expectations. Therefore, when this rate is
used to estimate a cost of capital to discount expected future cash flows, those future
cash flows also should reflect the expected effect of inflation. In the economic sense of
nominal versus real dollars, we are building a cost of capital in nominal terms, and it
should be used to discount expected returns that also are expressed in nominal terms.
2 Shannon Pratt and Roger Grabowski, Cost of Capital: Applications and Examples 3rd ed. (Wiley, 2008),
3 This risk gives rise to the so-called horizon premium.
In valuing "going concern" businesses and long-term investments made by businesses,
practitioners generally use long-term government bonds as the risk-free security and
estimate the ERP in relation to long-term government bonds. This convention represents
a realistic, simplifying assumption. Most business investments have long durations and
suffer from a comparable reinvestment risk as long-term government bonds. As such,
the use of long-term government bonds and an ERP estimated over those long-term
bonds more closely matches the investment horizon and risks confronting business
managers in capital decisions and valuators in valuation analyses relative to the use of
Treasury bills (“T-bills”). The consensus for financial analysts today is to use the 20-year
U.S. T-bonds yield to maturity as of the effective date of valuation.
Some analysts use either a 10-year or a 30-year T-bond yield; in theory one should then
develop ERP estimates based on expected returns in excess of the yields for those
maturities. However, as a practical matter these yields usually do not differ greatly from
the 20-year yield on T-bonds.4
In applying the CAPM or the Build-up method, the analyst typically begins with the T-
bond yield to maturity and adds an estimate of the ERP (in the case of the CAPM, the
ERP estimate is multiplied by the risk factor beta). The ERP estimates using historical
data are typically measured relative to the T-bond yield.
Since 2004, yields on 20-year (constant maturity) T-bonds have been:
2004 (average for 12 months)
2005 (average for 12 months)
2006 (average for 12 months)
2007 (average for 12 months)
2008 (average - first 8 months)
2008 (September 30)
2008 (October 31)
2008 (November 30)
2008 (December 31)
4 It is also noted that the 30-year T-bond was characterized in several periods during the 1990’s and 2000’s
by a lower yield-to-maturity than the 10-year T-bond. This was partially attributable to a lack of 30-year bond
issuance by the US government, which resulted in a downward kink in the yield curve – this was not
necessarily reflective of long-term risk perceptions, but rather a function of supply and demand on the 30-
December 31, 2008, is a particularly important date because many valuations are
performed as of the end of the calendar year, thus requiring COEC to be estimated as of
Most analysts would agree that the world economies are in crisis. Financial crises are
often accompanied by a “flight to quality” such that the nominal returns on “risk-free”
securities fall dramatically for reasons other than inflation expectations. Recent
macroeconomic research suggests that inflation expectations are fairly stable, and
therefore the dramatic decline in the T-bond yields in November and December 2008 is
unlikely due to expected declines in expected long-term inflation.5 In fact, long term (10-
year horizon) Consumer Price Index (CPI) expectations continued to be at 2.5 percent at
the end of 2008.6
While short-term inflation expectations have decreased,7 many commentators are
warning that long-term inflation will increase, not decrease, given the projected U.S.
budget deficit. Based on surveys of professional forecasters, yields on long-term U.S.
government bonds are also expected to increase. For example, 10-year T-bond yields
are expected to increase 1.67 percent between the spot yield on December 2008 and
the end of December 2010, returning to a more “normal level” comparable to the months
prior to November 2008.8
Another independent provider of economic forecasts the yield to maturity on the 30-year
U.S. T-bond to increase approximately 1.5 percent from December 2008 to August
2009, as presented in the following table:
5 V.V. Chari, Lawrence Christiano and Patrick J. Kehoe, “Facts and Myths about the Financial Crisis of
2008,” Federal Reserve Bank of Minneapolis Research Department working paper 666 (October 2008)
6 “Survey of Professional Forecasters”, Federal Reserve Bank of Philadelphia, November 17, 2008; “The
Livingston Survey,” Federal Reserve Bank of Philadelphia, December 9, 2008.
7 “The Livingston Survey,” Federal Reserve Bank of Philadelphia Research Department comparing the
projected increases in the producer price index for 2009 contained in June 2008 and December 2008
8 Ibid, December 9, 2008.
30-Year U.S. Treasury Bond Yield Forecast
Forecast Value (1)
(1) 30-year maturity secondary market rate. Percent
average of month.
Further, the implied forward volatility (based on options on exchange traded funds or
“ETFs”) on 20-year T-bonds in November and December 2008 increased significantly
(as shown in the following table), suggesting that the market is uncertain that the lower
yields (and correspondingly higher prices) are sustainable.
iShares Lehman 20+
S&P 500 ETF
Year Treasury Bond
30 Day (1)3 Mnth (2)
30 Day (1) 3 Mnth (2)
(1) 30 Day Implied Volatility
(2) 3 month Implied Volatility
In summary, the evidence suggests that the yield on T-bonds represents an aberration
as of December 31, 2008, overly influenced temporarily by the “flight to quality.
What should the analyst do when estimating the appropriate risk-free rate in developing
the COEC? This author suggests that one approach is to ignore the December 31, 2008,
“spot” yield on 20-year T-bonds and use a longer-term average T-bond yield (e.g., 4.5
percent)9 in developing an estimate of COEC, until such time when yields return to a
more normalized level. One should then match the T-bond yield with the appropriate
conditional ERP estimate for this stage in the business cycle.10
9 Alternatively, one could use a “forward” rate on T-bonds.
10 If one uses the apparently abnormal spot yield on 20-year T-bonds as of December 31, 2008, in
developing one’s estimate of the COEC then one should use an ERP estimate consistent with the abnormal
spot yield; see footnote 13 and Aswath Damodaran, “What is the riskfree rate? A Search for the Basic
Building Block,” working paper (December 2008).
Equity Risk Premium
A long-term study of realized premiums in excess of the return on T-bonds indicates that
realized premiums, on the average, have decreased as the T-bond yields decrease.11
But these are not ordinary times. If one simply adds an estimate of the ERP derived
during “normal” economic times to the “spot” yield on 20-year T-bonds on December 31,
2008, one will likely arrive at too low of an estimate of the COEC.
As is explained in Cost of Capital 3rd ed.,
The evidence presented above [that the long-run ERP is between 3.5% and
6%] represents a long-term average or unconditional estimate of the ERP.
That is, what is a reasonable range of ERP that can be expected over an
entire business cycle? Where in this range is the current ERP? Research
has shown that ERP is cyclical during the business cycle. We use the term
“conditional ERP” to mean the ERP that reflects current market conditions.
For example, when the economy is near or in recession (and reflected in
recent relatively low returns on stocks), the conditional ERP is more likely at
the higher end of the range. When the economy improves (with expectations
of improvements reflected in recent increasing stock returns), the conditional
ERP moves toward the mid-point of the range. When the economy is near its
peak (and reflected in recent relatively high stock returns), the conditional
ERP is more likely at the lower end of the range.12
As the stock market has fallen in late 2008, the ERP implied by the S&P 500 has
increased.13 In one analysis, the implied ERP has risen to the high end of the range
cited in the above quote.14
11 Aswath Damodaran, “Equity Risk Premiums: Determinants, Estimation and Implications,” (September
2008 with an October update reflecting the market crisis), pp. 56-57.
12 Pratt and Grabowski, op. cit., Chapter 9.
13 Damodaran, op. cit., pp. 54. The implied ERP is the discount rate that equates the S&P 500 index with
expected dividends plus stock buybacks.
14 Damodaran On-Line Update, January 2009. Damodaran reports that the implied ERP as of January 1,
2009, equals 6.43 percent (measured from the “below normal” yield on 10-year T-bonds) while the ERP
estimate based on historic returns equals 3.88 percent. The implied ERP at January 26 stood at
approximately 7 percent (measured from the “below normal” yields on 10-year T-bonds).
What should the analyst do in estimating the ERP? This author suggests that, given
current market conditions, one should consider using an estimated ERP of 6.0 percent,
the upper end of the range of the research on long-term (normal) ERP.15 As expected
economic conditions improve and stock prices increase; the ERP can be expected to
decrease in the future.
The following page contains a summary of beta estimates for a sample publicly traded
company (“Sample Company #1”). Sample Company #1’s market capitalization has
ranged between $1 billion and $3 billion in recent years. The company has zero long-
term debt so its beta estimates only operating risk and no financial risk. We are
displaying various beta estimates at each month end from December 2006 to December
Beta Estimates for Sample Company #1
R2 (60 Month
R2 (260 Week
R2 (Sum Beta)
15 If one uses the apparently abnormal spot yield on 20-year T-bonds as of December 31, 2008, in
developing one’s estimate of the COEC and a higher ERP estimate consistent with the abnormal spot yield,
one will need to update (reduce) their ERP estimate once spot yields return to more normal levels and not
simply adjust their ERP estimate annually as is common practice.
Prior to May 2008, the ordinary least squares regression estimate of beta (“OLS Beta”)
was 2.0 or greater.16 These estimates result from a regression and are made “with
estimation error.” Total Beta has exceeded 4.0 during that same period17. One
interpretation of Total Beta is a beta estimate corrected for estimation error.
But after May 2008 we see OLS Beta estimates have decreased to a range of
approximately 1.3 to 1.8.
What happened? Overall stock market indices such as the S&P 500 have been overly
influenced by financial stocks and stocks of highly leveraged companies. The relative
volatility of returns for Subject Company #1 with no debt has declined relative to a
market whose returns (negative) are over-weighted by financial companies. The Subject
Company #1 business risk relative to the overall economy did not change during this
period. But relative to a market over-weighted by financial companies, it appears to
have decreased in risk.
The graph below helps explain these relationships. One can see the severe downward
adjustment to the financial sector stocks, which initially dragged the S&P 500 down even
as the other sectors were bouncing back. Ultimately, other sectors followed suit as
economic conditions in other sectors of the economy deteriorated further.
16 Estimating beta over a 60-month “look-back” period; see Pratt and Grabowski, op.cit., Chapter 10.
17 Total Beta equals [beta / R] or [σs / σm], the relative standard deviation of the returns on the subject
security to the standard deviation of returns on the market. See: Chris Tofallis, “Investment Volatility: A
Critique of Standard Beta Estimation and a Simple Way Forward,” working paper (January 2008).
Price Return on Various S&P Indices Over Time
S&P 500 Index
S&P 500 Financial Index
S&P 500 Health Care Index
S&P Industrial Index
S&P Information Technology Index
During these past months, we have in essence observed a process of re-pricing of the
stock market in general and, in particular, of many stocks at new lower prices. The low
beta estimates for some stocks, such as Subject Company #1, derived from analyzing
stock returns during a “look-back period” result from the negative returns on the stock
market portfolio and many other stocks as the stock market seeks its new, lower
equilibrium price. The low beta estimate currently observed above is not from a change
in the underlying long-term relative business risk of Subject Company #1 to the business
risk of the economy as represented by the stock market. For example, prices of financial
sector stocks (and their returns) have trended downwards looking for new equilibrium
levels; once those levels are reached, the relative volatility of these stocks to the stock
market will return to “normal”. But during this adjustment period, prices of stocks such
as Sample Company #1 have moved downward relatively little (or not as much as the
market portfolio), making their observed beta estimates lower than historic norms and
lower than what one might expect in the future after the market portfolio is finished re-
pricing at a new, lower equilibrium level.
While such adjustments in pricing occur for some stocks during all time periods, over
these past few months we have seen the stock market (as represented by the S&P 500
for example) experience a major re-pricing led by financial sector stocks and highly