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Higher leverage increases the variance in net income and makes equity investment in the firm riskierDegree of Financial Leverage Other things remaining equal, an increase in financial leverage will increase the beta of the equity in a firm. Intuitively, we would expect that the fixed interest payments on debt result in high net income in good times and low or negative net income in bad times. Higher leverage increases the variance in net income and makes equity investment in the firm riskier. If all the firms risk is borne by the stockholders (i.e., the beta of debt is zero)8 and debt has a tax benefit to the firm, then, where ?L = Levered Beta for equity in the firm ?u = Unlevered beta of the firm (i.e., the beta of the firm without any debt) t = Corporate tax rate D/E = Debt/Equity Ratio Intuitively, we expect that as leverage increases (as measured by the debt to equity ratio), equity investors bear increasing amounts of market risk in the firm, leading to higher betas. The tax factor in the equation measures the tax deductibility of interest payments. The unlevered beta of a firm is determined by the types of the businesses in which it operates and its operating leverage. It is often also referred to as the asset beta since it is determined by the assets owned by the firm. Thus, the levered beta, which is also the beta for an equity investment in a firm or the equity beta, is determined both by the riskiness of the business it operates in and by the amount of financial leverage risk it has taken on. Since financial leverage multiplies the underlying business risk, it stands to reason that firms that have high business risk should be reluctant to take on financial leverage. It also stands to reason that firms that operate in stable businesses should be much more willing to take on financial leverage. Utilities, for instance, have historically had high debt ratios but have not had high betas, mostly because their underlying businesses have been stable and fairly predictable. Illustration 8.3: Effects of Leverage on betas: Boeing From the regression for the period from 1996 to 2000, Boeing had a historical beta of 0.56. Since this regression uses stock prices of Boeing over this period, we begin by estimating the average debt/equity ratio between 1996 and 2000, using market values for debt and equity. Average Debt/Equity Ratio between 1996 and 2000 = 15.56% The beta over the 1996-2000 period reflects this average leverage. To estimate the unlevered beta over the period, we used a corporate tax rate of 35%. Current Beta 1 ? (1 - tax rate) (Average Debt/Equity) 0.56 ?? ???0.51 ?? The unlevered beta for Boeing over the 1996-2000 period is 0.51. The levered beta at different levels of debt can then be estimated. Beta???Unlevered Beta1 ???????? For instance, if Boeing were to decrease its debt equity ratio to 10%, its equity beta will be: Boeings financial leverage increases, the beta increases concurrently. levbeta.xls.This spreadsheet allows you to estimate the unlevered beta for a firm and compute the betas as a function of the leverage of the firm. Bottom Up Betas Breaking down betas into their business risk and financial leverage components provides us with an alternative way of estimating betas in which we do not need past prices on an individual firm or asset. To develop this alternative approach, we need to introduce an additional property of betas that proves invaluable. The beta of two assets put together is a weighted average of the individual asset betas, with the weights based upon market value. Consequently, the beta for a firm is a weighted average of the betas of all the different businesses it is in. We can estimate the beta for a firm in five steps. * Step 1: We identify the business or businesses the firm operates in. * Step 2: We find other publicly traded firms in these businesses and obtain their regression betas, which we use to compute an average beta for the firms, and their financial leverage. * Step 3: We estimate the average unlevered beta for the business, by unlevering the average beta for the firm by their average debt to equity ratio. Alternatively, we could estimate the unlevered beta for each firm and then compute the average of the unlevered betas. The first approach is preferable because unlevering an erroneous regression beta is likely to compound the error. * Step 4: To estimate an unlevered beta for the firm that we are analyzing, we take a weighted average of the unlevered betas for the businesses it operates in, using the proportion of firm value derived from each business as the weights. If values are not available, we use operating income or revenues as weights. This weighted average is called the bottom-up unlevered beta. where the firm is assumed to operating in k different businesses. * Step 5: Finally, we estimate the current market values of debt and equity of the firm and use this debt to equity ratio to estimate a levered beta. The betas estimated using this process are called bottom-up betas. The Case for Bottom Up Betas At first sight, the use of bottom up betas may seem to leave us exposed to all of the problems we noted with regression betas. After all, the betas for other publicly traded firms in the business are obtained from regressions. Notwithstanding these bottom up betas represent a significant improvement on regression betas for the following reasons. * While each regression beta is estimated with standard error, the average across a number of regression betas will have much lower standard error. The intuition is simple. A high standard error on a beta estimate indicates that it can be significantly higher or lower than the true beta. Averaging across these errors results in an average beta that is far more precise than the individual betas that went into it. In fact, if the estimation errors on individual firm betas are uncorrelated across firms, the savings in standard error can be stated as a function of the average standard error and the number of firms in the sample. where n is the number of firms in the sample. Thus, if the average standard error in beta estimates for software firms is 0.50 and the number of software firms is 100, the standard error of the average beta is only 0.05 (0.50/ 100). * A bottom-up beta can be adapted to reflect actual changes in a firms business mix and expected changes in the future. Thus, if a firm divested a major portion of its operations last week, the weights on the businesses can be modified to reflect the divestiture. The same can be done with acquisitions. In fact, a firms strategic plans to enter new businesses in the future can be brought into the beta estimates for future periods. * Firms do change their debt ratios over time. While regression betas reflect the average debt to equity ratio maintained by the firm during the regression period, bottom-up betas use the current debt to equity ratio. If a firm plans to change its debt to equity ratio in the future, the beta can be adjusted to show these changes. * Finally, bottom-up betas wean us from our dependence on historical stock prices. While we do need these prices to get betas for comparable firms, all we need for the firm being analyzed is a breakdown of the businesses it is in. Thus, bottom-up betas can be estimated for private firms, divisions of business and stocks that have just started trading in financial markets. Computational Details While the idea behind bottom-up betas is fairly simple, there are several computational details that are deserving of attention. a. Defining Comparable firms: First, we have to decide how narrowly we want to define a business. Consider, for instance, a firm that manufactures entertainment software. We could define the business as entertainment software and consider only companies that primarily manufacture entertainment software to be comparable firms. We could go even further and define comparable firms as firms manufacturing entertainment software with revenues similar to that of the company being analyzed. While there are benefits to narrowing the comparable firm definition, there is a large cost. Each additional criterion added on to the definition of comparable will mean that fewer firms make the list and the savings in standard error that comprise the biggest benefit to bottom-up betas become smaller. A common sense principle should therefore come into play. If there are hundreds of firms in a business, as there are in the software business, you can afford to be more selective. If there are relatively few firms, not only do you have to become less selective, you might have to broaden the definition of comparable to bring in other firms into the mix. b. Estimating Betas: Once the comparable firms in a business have been defined, you have to estimate the betas for these firms. While it would be best to estimate the regressions for all of these firms against a common and well diversified equity index, it is usually easier to use service betas that are available for each of these firms. These service betas may be estimated against different indices. For instance, if you define your business to be global telecommunications and obtain betas for global telecomm firms from Bloomberg, these betas will be estimated against their local indices. This is usually not a fatal problem, especially with large samples, since errors in the estimates tend to average out. c. Averaging Method: The average beta for the firms in the sector can be computed in one of two ways. We could use market-weighted averages, but the savings in standard error that we touted in the earlier section will be muted, especially if there are one or two very large firms in the sample. We could estimate the simple average of the betas of the companies, thus weighting all betas equally. The process weighs in the smallest firms in the sample disproportionately but the savings in standard error are likely to be maximized. There is also the issue of whether the firm being analyzed should be excluded from the group when computing the average. While the answer is yes, there will make little or no difference in the final estimate if there are more than 15 or 20 comparable firms. d. Controlling for differences: In essence, when we use betas from comparable firms, we are assuming that all firms in the business are equally exposed to business risk and have similar operating leverage. Note that the process of levering and unlevering of betas allows us to control for differences in financial leverage. If there are significant differences in operating leverage - cost structure - across companies, the differences in operating leverage can be controlled for as well. This would require that we estimate a business beta, where we take out the effects of operating leverage from the unlevered beta. Note the similarity to the adjustment for financial leverage; the only difference is that both fixed and variable costs are eligible for the tax deduction and the tax rate is therefore no longer a factor. The business beta can then be relevered to reflect the differences in operating leverage across firms. betas.xls: This dataset on the web has updated betas and unlevered betas by business sector in the United States. 8.3: Estimating a Bottom-up Beta for Vans Shoes - January 2001 Vans Shoes is a shoe manufacturing firm with a market capitalization of $191 million. To estimate the bottom up beta for Vans Shoes, we consider the betas of all publicly traded shoe. In addition to the betas for each firm, we report the market debt to equity ratio, the effective tax rate and a measure of operating leverage obtained by dividing S,G&A expenses (which we consider fixed) by other operating expenses (which we consider variable). We can estimate the unlevered beta for the business using the averages for these values. Average Beta = 0.79 Average Debt to Equity Ratio = 75.04% Using the effective tax rate of 25.95%, we can estimate the unlevered beta. The beta for Vans Shoes can then be obtained, using the firms marginal tax rate of 34.06% and market debt to equity ratio of 9.41%. This levered beta is based on the implicit assumption that all shoe manufacturers have similar operating leverage. In fact, we could adjust the unlevered beta for the average fixed cost/variable cost ratio for the business and then relever back at the operating leverage for Vans Shoes. We can then use Vans fixed cost to variable cost ratio of 31.16% to estimate an adjusted unlevered and levered beta. By having a debt to equity ratio and an operating leverage that is lower than the average for the industry, Vans Shoes ends up with a beta much lower than that of the industry. 8.4: Estimating a Bottom-up Beta for Boeing: September 2000 Boeing has undergone a significant change in both its business mix and its financial leverage over the last 5 years. Not only did it acquire Rockwell and McDonnell Douglas, giving it a major foothold in the defense business, but it borrowed substantial amounts to make these acquisitions. Since these events have occurred in the last few years, the historical regression beta does not fully reflect the effects of these changes. To estimate Boeings beta today, we broke its business into two areas. * Commercial Aircraft, which is Boeings core business of manufacturing commercial jet aircraft and providing related support services. * Information, Space and Defense Systems (ISDS), which includes research, development, production and support of military aircraft, helicopters and missile systems. Each of these areas of business has very different risk characteristics and we estimated the unlevered beta for each business by looking at comparable firms in each business. Table 8.3 summarizes these estimates. ISDS, we used 17 firms that derived the bulk of their revenues from defense contracting and computed the average beta and debt/equity ratio for these firms. The unlevered beta was computed using these averages. For commercial aircraft, there are no truly comparable firms. We looked at Boeings own beta prior to its expansion in the defense business and computed the unlevered beta using this estimate. The values for each of the divisions was estimated using the revenues9 from each segment and a typical revenue multiple10 for that type of business. The unlevered beta for Boeing as a company in 2000 can be estimated by taking a value-weighted average of the betas of each of the different business areas. This is reported in the last column to be 0.8774. The equity beta can then be estimated using the current financial leverage for Boeing as a firm. Combining the market value of equity of $55.2 billion and the market value of debt of $7.85 billion, using a 35% tax rate for the firm, we arrive at the current beta for Boeing. This is very different from the historical beta of 0.56 that we obtained from the regression, but it is, in our view, a much truer reflection of the risk in Boeing. 8.5: Estimating a Bottom-up Beta for Titan Cements - January 2000 To estimate a beta for Titan Cements, we began by defining comparable firms as other cement companies in Greece but found only one comparable firm. When we expanded the list to include cement companies across Europe, we increased our sample to nine firms. Since we did not see any reason to restrict our comparison to just European firms, we decided to look at the average beta for cement companies globally. There were 108 firms in this sample with an average beta of 0.99, an average tax rate of 34.2% and an average debt to equity ratio of 27.06%. We used these numbers to arrive at an unlevered beta of 0.84. We then used Titans market values of equity (566.95 million Gdr) and debt (13.38 million GDr) to estimate a levered beta for its equity: We used a tax rate of 24.14% in this calculation. How well do betas travel? Often, when analyzing firms in small or emerging markets, we have to estimate betas by looking at firms in the same business but traded on other markets. This is what we did when estimating the beta for Titan Cements. Is this appropriate? Should the beta for a steel company in the United States be comparable to that of a steel company in Indonesia? We see no reason why it should not. But the company in Indonesia has much more risk, you might argue. We do not disagree, but the fact that we use similar betas does not mean that we believe that the costs of equity are identical across all steel companies. In fact, using the approach described in the last chapter, the risk premium used to estimate the cost of equity for the Indonesian company will incorporate a country risk premium, whereas the cost of equity for the U.S. company will not. Thus, even if the betas used for the two companies are identical, the cost of equity for the Indonesian company will be much higher. There are a few exceptions to this proposition. Recall that one of the key determinants of betas is the degree to which a product or service is discretionary. It is entirely possible that products or services that are discretionary in one market (and command high betas) may be non-discretionary in another market (and have low betas). For instance, phone service is viewed as a non-discretionary product in most developed markets, but is a discretionary product in emerging markets. Consequently, the average beta estimated by looking at telecom firms in developed markets will understate the true beta of a telecomm firm in an emerging market. Here, the comparable firms should be restricted to include only telecomm firms in emerging markets. |
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