Estimating Cost of Capital in the Current Environment

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Estimating Cost of Capital in the

Current Economic Environment

Brown Bag PresentationFebruary 13, 2009

Paul Daddio

2Willamette Management Associates

Introduction• Turmoil in the economy and markets since October 2008

have created conditions that make cost of capital estimation more challenging.

• Traditional methods typically employed in estimating cost of capital are subject to significant estimation and data input problems.

• Historical data is useful only to the extent it provides a good estimate of the future.

• This presentation will cover a recent article by Roger Grabowski, “Problems with Cost of Capital Estimation in the Current Environment” (ASA Business Valuation E-Letter, 2/4/09) and portions of a recent article by Aswath Damodaran, “Equity Risk Premium (ERP): Determinants, Estimation and Implications.”


Issues To Be Addressed• Issues to be addressed in this presentation:

– Risk-free rate estimation – Equity risk premium (ERP) estimation– Impact on beta estimation of rapidly declining values of (1)

highly levered companies and (2) financial services companies– Cross-checking for reasonableness

• Issues not addressed in this presentation:– Impact on beta estimation of temporarily higher leverage

ratios of guideline companies– Loss of expected tax shield benefit of debt and use of after-

tax versus pre-tax WACC


Risk-free Rate Estimation• 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. Analysts typically use the yield to maturity on 20-year Treasury Bonds as of the valuation date, as a proxy for the risk-free rate. Treasury bond yields incorporate three components:– Rental rate (a real return for lending the funds over the investment period,

thus foregoing consumption),– Inflation (the expected rate of inflation over the term of the risk-free

investment), and– Maturity risk (risk that the principal’s market value will rise or fall during

the period to maturity).

• 20-year Treasury bond yields have declined dramatically since October 2008.Yield on 20-year (constant maturity) T-bonds

2004 Average for 12 months 5.02%2005 Average for 12 months 4.62%2006 Average for 12 months 4.98%2007 Average for 12 months 4.87%2008 Average - first 8 months 4.52%2008 September 30 4.43%2008 October 31 4.78%2008 November 30 3.72%2008 December 31 3.03%


Average Monthly Yield on 20-Year Treasury Bonds

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• It is unlikely the decrease in the 20-year Treasury Bond yield has been due primarily to a decrease in inflation expectations.– CPI projections remain at 2.5% as of 12/31/08 (same as a year

earlier).– The 30-year Treasury bond yield is projected by forecasts.org

to increase from 2.87% in December 2008 to 4.42% in August 2009.

• The recent decline in yields is more likely a reflection of the “flight to quality” witnessed in financial markets as investors have fled from risky assets into “risk-free” assets. Evidence indicates this may be an aberration.

• Therefore, use of a spot yield on Treasury bonds may cause analysts to underestimate a subject company’s actual cost of capital.

• As alternatives, it may be appropriate to use (1) a longer-term average Treasury yield (Roger Grabowski suggests 4.5%) or (2) a forward rate on Treasuries.

Risk-free Rate Estimation (continued)


Equity Risk Premium Estimation• A long-term study by Aswath Damodaran 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. 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 cost of equity capital.

• An analyst applying an arithmetic mean methodology using the 1927 to most recent year data (i.e., the period used in the SBBI Yearbook) may see the ERP decrease from 7.1% as of December 31, 2007, to an estimated 6.5% as of December 31, 2008. An analyst applying an arithmetic mean methodology using the 1963 to most recent year data (i.e., the period used in the Duff & Phelps Risk Premium Report) may see the ERP decrease from 4.85% as of December 31, 2007, to an estimated 3.9% as of December 31, 2008.

• Long-run ERP estimates typically incorporate an average of all phases of the economic cycle. However, there is evidence that ERP rises and falls with the phase of the economic cycle such that, at the top of the cycle, ERP is at the lower-most limit of its range; at the bottom, ERP is at the upper-most limit; and in between, ERP is between these limits.

• In Cost of Capital 3rd ed., Pratt and Grabowski conclude that ERP ranges from 3.5% to 6.0% and suggest 5.0% under normal economic conditions.


Equity Risk Premium Estimation (continued)

• The trend of “implied ERP” provides evidence that the ERP may be increasing, not decreasing, as ERP estimates based on historical returns would imply. The implied ERP is estimated by interpolating a discount rate that causes the price of the S&P 500 to equal the present value of expected dividends plus stock buybacks.

Source: “Equity Risk Premiums (ERP): Determinants, Estimation and Implications,” Aswath Damodaran, 9/08.

• From December 31, 2007, to December 31, 2008, the implied ERP increased from 4.37% to 6.43%.

Implied ERP

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Equity Risk Premium Estimation (continued)

• Roger Grabowski recommends using an estimated ERP of 6.0% (i.e., the top of the ERP range quoted earlier) in the current environment, higher than the 5.0% he has advocated under normal economic conditions and higher than the 4.85% indicated by the 2008 Duff & Phelps, LLC, Risk Premium Report.

• Aswath Damodaran has said that ERP based on historical data that incorporates 2008 market returns is too low to reflect actual expectations of ERP for the future in the current economic environment.


Beta Estimation• One must remember that beta is an estimate of the expected future

relationship between changes in the returns on the subject company’s stock to changes in the stock market returns. In other words, the application of CAPM requires the use of a forward-looking beta as a measure of future risk.

• As such, analysts should be cautious that the beta they use for valuing a given company makes sense relative to the underlying risk of the subject and not rely on “spot” estimates using a single beta estimation methodology derived from returns during a look-back period that may not represent the expected relationship of returns in the future.

• According to Roger Grabowski, betas calculated using historical data that incorporate returns since October 2008 are lower than what they have been historically.

• The severe volatility exhibited by stocks of financial services companies and highly leveraged companies have disproportionately impacted the market as a whole even while non-financial companies with relatively low debt levels have generally experienced relatively lower levels of volatility.

• After stocks of financial companies and highly leveraged companies have finished being re-priced and have reached a new equilibrium, betas incorporating the new equilibrium will return to normal levels.


Beta Estimation (continued)

Measuring beta at time 2 will result in an invalid estimate of beta because the “look-back period includes an aberrant time period (period B). A better estimate may be derived at time 1, even if the valuation date is time 2.


Beta Estimation (continued)• Alternative beta estimation methods

• Flawed alternatives:

• Barra projected betas begin with ordinary least squares (“OLS”) beta estimates. Therefore, the flaws discussed earlier in the presentation tend to carry over to Barra projected betas. Barra projected betas also appear to not correctly adjust for errors in estimating the betas of smaller cap companies.

• Bloomberg adjusted betas are “adjusted” somewhat arbitrarily toward 1.0, under the premise that eventually every company’s beta will converge to the market beta.


Cross-checking For Reasonableness• Logically, the cost of equity capital should exceed the yield

investors expect on the company’s debt capital (i.e., pre-tax). Equity capital is riskier than debt capital and the market will price each component based on its relative risk. In “normal times,” one would examine spreads over T-bonds. In the current economic environment, with yields on T-bonds artificially low, spreads are not meaningful.

• Rather, one should look at the absolute level of market yield on the subject company’s debt (market yield for the debt rating on the subject company’s debt level, either actual or target, based on the actual or synthetic debt rating of the subject company) and the cost of equity capital should exceed that yield on debt.

• Another course of action may be to use the data provided in the Duff & Phelps Risk Premium Report to estimate the cost of equity capital. The Risk Premium Report provides equity risk premium data for use in a build-up model that is independent of estimates of beta.


Cross-checking For Reasonableness (continued)

• Has the cost of equity capital for most companies increased?– Grabowski suggests that the market is divided between

companies with no or limited debt and companies with high levels of debt.

– Absolute yields on the debt of Aaa and Aa rated companies have increased only slightly since the onset of the economic crisis. Meanwhile, absolute yields on lower-rated debt have risen substantially, implying the cost of equity capital for these companies has increased as well.

Yields on Long-Term Bonds20 Year Treasury

BondA-Rated Corporate

BondsAa-Rated

Corporate BondsAaa-Rated

Corporate BondsBaa-Rated

Corporate BondsHigh Yield

Corporate Bonds

12/31/07 4.50% 6.39% 6.26% 5.70% 6.64% 9.64%12/31/08 3.03% 6.95% 5.61% 5.86% 8.62% 19.50%


Conclusions• Estimating the appropriate cost of capital is always difficult as pricing

risk is a difficult exercise. But in today’s environment it is even more challenging and requires extreme care on the part of the analyst.

• Any concluded cost of capital estimation must balance the correct application of various models, including associated inputs, with the basic theory of finance and common sense over the long-term.

• A mechanical application of the (1) Treasury bond yields and (2) historical ERP may result in estimation error.

• Severe declines in the values of (1) highly levered companies and (2) financial services companies may have distorted beta estimates based on a “look-back” period for some companies.

SBBI Example12/31/07 12/31/08

Risk-free Rate 4.5% 3.1%Equity Risk Premium 7.1% 6.5%Average Market Rate of Return 11.6% 9.6%


Conclusions (continued)• Roger Grabowski does not suggest changing or straying

from the traditional models typically employed in estimating the cost of equity capital, but rather, advises analysts to take a closer look at the inputs that go into these models. It is likely temporary aberrations in several of the inputs to traditional models during this period of economic crisis require analysts to apply more rigor and scrutiny in developing cost of capital estimate.

• In presenting cost of capital estimates, analysts may want to separately identify the adjustments made due to temporary aberrations from the more long-term assumptions they typically use in their models; some analysts describe such adjustments as adding/subtracting an “alpha” from the estimate arrived at applying assumptions derived from data sources or in “standard” analyses.

Documents

Estimating Cost of Capital in the Current Environment