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The expected return on an equity investment in a firm, given its risk, has strong implications for both equity investors in the firm and the managers of the firmCalculating Betas after A Major Restructuring The bottom-up process of estimating betas provides a solution when firms go through a major restructuring that change both their business mix and leverage. In these cases, the regression betas are misleading because they do not reflect fully the effects of these changes. Boeings beta, estimated using the bottom up approach, is likely to provide a more precise estimate than the historical beta from a regression of Boeings stock prices, given Boeings acquisitions of Rockwell and McDonnell Douglas and its increase in leverage. In fact, a firms beta can be estimated even before the restructuring becomes effective using the bottom-up approach. In the illustration that follows, for instance, we estimate Boeings beta just before and after its acquisition of McDonnell Douglas, allowing for the changes in both the business mix and the leverage. 8.6: Beta of a Firm After an Acquisition: Boeing and McDonnell Douglas In 1997, Boeing announced that it was acquiring McDonnell Douglas, another company involved in the aerospace and the defense business. At the time of the acquisition, the two firms had the following market values and betas: Note that the market values of equity used for the two firms reflect the market values after the acquisition announcement and reflect the acquisition price agreed upon for McDonnell Douglas shares. In order to evaluate the effects of the acquisition on Boeings beta, we first examine the effects of the merger on the business risk of the combined firm, by estimating the unlevered betas of the two companies and calculating the combined firms unlevered beta. Boeings acquisition of McDonnell Douglas was accomplished by issuing new stock in Boeing to cover the value of McDonnell Douglass equity of $12,555 million. Since no new debt was used to finance the deal, the debt outstanding in the firm after the acquisition is just the sum of the debt outstanding at the two companies before the acquisition. Debt = McDonnell Douglas Old Debt + Boeings Old Debt = $3,980 + $2,143 = $6,123 million Equity = Boeings Old Equity + New Equity used for Acquisition = $32,438 + $12,555 = $44,993 million The debt/equity ratio can then be computed as follows D/E Ratio = $ 6,123/44,993 = 13.61% This debt/equity ratio in conjunction with the new unlevered beta for the combined firm yields a new beta. A third approach is to estimate the market risk parameters from accounting earnings rather than from traded prices. Thus, changes in earnings at a division or a firm, on a quarterly or annual basis, can be related to changes in earnings for the market, in the same periods, to arrive at an estimate of an accounting beta to use in the CAPM. While the approach has some intuitive appeal, it suffers from three potential pitfalls. First, accounting earnings tend to be smoothed out relative to the underlying value of the company, as accountants spread expenses and income over multiple periods. This results in betas that are biased down, especially for risky firms, or biased up, for safer firms. In other words, betas are likely to be closer to 1.00 for all firms using accounting data. Second, accounting earnings can be influenced by non-operating factors, such as changes in depreciation or inventory methods and by allocations of corporate expenses at the divisional level. Finally, accounting earnings are measured, at most, once every quarter and often only once every year, resulting in regressions with few observations and not much explanatory power (low R-squared, high standard errors). 8.7: Estimating Accounting Betas --Defense Division of Boeing - 1995 Having operated in the defense business for decades, Boeing has a record of its profitability. These profits are reported in Table 8.4, together with earnings changes for companies in the S&P 500 going back to 1980. Source: Bloomberg the changes in profits in the defense division (?EarningsDefense) against changes in profits for the S&P 500 (?EarningsS&P ) yields the following: 0.03??0.65?EarningsS&P Based upon this regression, the beta for the defense division is 0.65. We can now estimate the cost of equity for the defense division, with a riskless rate of 5% and a risk premium of 5.5%, as follows. Cost of Equity for the Defense Division = 5% + 0.65 (5.5%) = 8.58% accbeta.xls: This spreadsheet allows you to estimate the accounting beta on a division or firm. spearn.xls: This dataset on the web has earnings changes, by year, for the S&P 500 going back to 1960. , Bottom-up and Accounting Betas: Which one do we use? For most publicly traded firms, betas can be estimated using accounting data or market data or from the bottom-up approach. Since the betas will almost never be the same using these different approaches, the question is which one do we use? We would almost never use accounting betas, for all the reasons specified above. We are almost as reluctant to use historical market betas for individual firms because of the standard errors in beta estimates, the failures of the local indices (as is the case with most emerging market companies) and the inability of these regressions to reflect the effects of major changes in the business mix and financial risk at the firm. Bottom-up betas, in our view, provide us with the best beta estimates because: 1. They allow us to consider changes in business and financial mix, even before they occur. 2. They use average betas across large numbers of firms, which tend to be less noisy than individual firm betas. 3. They allow us to calculate betas by area of business for a firm, which is useful both in the context of investment analysis and valuation. From Betas to Cost of Equity Having estimated the riskless rate, the risk premium(s) and the beta(s), we can now estimate the expected return from investing in equity at any firm. In the CAPM, this expected return can be written as: Expected Return = Riskless Rate + Beta * Expected Risk Premium the riskless rate would be the rate on a long-term government bond, the beta would be either the historical, fundamental or accounting betas described above and the risk premium would be either the historical premium or an implied premium. In the arbitrage pricing and multi-factor model, the expected return would be written as follows: j?n Expected Return = Riskless Rate + *Risk Premiumj where the riskless rate is the long term government bond rate, ??j is the beta relative to factor j estimated using historical data or fundamentals and Risk Premiumj is the risk premium relative to factor j, estimated using historical data. The expected return on an equity investment in a firm, given its risk, has strong implications for both equity investors in the firm and the managers of the firm. For equity investors, it is the rate they need to earn to be compensated for the risk they have taken in investing in the equity of the firm. If, after analyzing an investment, they conclude they cannot make this return, they would not buy this investment; alternatively, if they decide they can make a higher return, they would make the investment. For managers in the firm, the return that investors need to make to break even on their equity investments becomes the return they have to try to deliver to keep these investors from becoming restive and rebellious. Thus, it becomes the rate they have to beat in terms of returns on their equity investments in projects. In other words, this is the cost of equity to the firm. 8.8: Estimating the Cost of Equity for Boeing - June 2000 Now that we have an estimate of beta of 0.9585 for Boeing, based upon the bottom-up estimates, we can estimate its cost of equity. To make the estimate, we used the prevailing treasury bond rate of 5% and a historical risk premium of 5.51%. Cost of Equity = 5.00% + 0.9585 (5.51%) = 10.28% There are two points making about this estimate. The first is that the cost of equity would have been significantly lower, if we had chosen to use the implied equity premium at the time of this analysis which was about 2.87% (See chapter 7). Cost of Equity = 5.00% + 0.9585 (2.87%) = 7.75% The second point is that we are not considering the exposure that Boeing has to emerging market risk from its business. If the exposure is significant, we should be adding a country risk premium to the cost of equity estimate. 8.9: Estimating the Cost of Equity for Embraer - March 2001 Embraer is a Brazilian aerospace firm. To estimate its cost of equity, we first estimated the unlevered beta by looking at aerospace firms globally. Unlevered Beta for aerospace firms = 0.87 Embraers debt to equity ratio11 at the time of this analysis was 2.45%, resulting in a levered beta for Embraer: Levered beta for Embraer = 0.87 (1 + (1-0.33)0.0245) = 0.88 To estimate the cost of equity for Embraer in U.S. dollar terms, we began with the treasury bond rate of 5% at the time of the analysis, but incorporated the country risk associated with Brazil into the risk premium. Using the approach described in chapter 7, we estimated a country risk premium of 10.24%. In conjunction with a mature market risk premium of 5.59%, estimated for the United States, this yields a cost of equity of 18.93%. of Equity for Embraer = 5% + 0.88 (5.51% + 10.24%) = 18.86% Again, there are several points that are worth making on this estimate. The first is that this cost of equity can be expected to change over time as Brazil matures as a market and country risk declines. The second is that we have assumed that betas measure exposure to country risk. A company like Embraer that derives the bulk of its revenues outside Brazil could argue that it is less exposed to country risk. We could have derived ?as a measure of exposure to country risk for Embraer by looking at the proportion of its revenues that it derives in Brazil and comparing it to the proportion of revenues derived by a typical company in Brazil. In 2000, for instance, this would have yielded the following: Proportion of Revenues from Brazil Embraer The final point is that the cost of equity in dollar terms can be converted into a nominal real cost of equity fairly simply by considering the differences in expected inflation rates in Brazil and the United States. For instance, if the expected inflation rate in Brazil is 10% and the differential inflation rate in the United States is 2%, the cost of equity in nominal real is as follows: Implicitly, we assume that real riskfree rates around that world are the same with this approach and that the risk premium scales up with inflation as well. The alternative is to estimate a cost of equity from scratch, beginning with a nominal real risk free rate (which was 14% at the time of this analysis) and adding the premiums from above: Cost of EquityNominal Real = Riskfree rate + Beta (Mature Market Risk Premium ) + ?(Country Risk Premium) = 14% + 0.88 (5.51%) + 0.15 (10.24%) = 20.39% Substituting in a real riskfree rate in the equation above would yield a real cost of equity. |
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