ten questions about bottom

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Ten Questions about Bottom-up Betas

What is a bottom-up beta?

A bottom-up beta is estimated by starting with the businesses that a firm is in, estimating the

fundamental risk or beta of each of these businesses and taking a weighted average of these

risks.

What are the steps involved in estimating bottom-up betas?There are four steps:

Step 1: Break your company down into the businesses that it operates in. A firm like GE

operates in 26 businesses but Walmart is a single business company. Do not define your

business too narrowly or you will run into trouble in step 2.

Step 2: Estimate the risk (beta) of being in each business. This beta is called an asset beta or an

unlevered beta.

Step 3: Take a weighted average of the unlevered betas of the businesses you are in, weighted

by how much value you get from each business.

Step 4: Adjust the beta for your companys financial leverage (Debt to equity ratio)

What should we use as comparable firms?While the narrow version of comparable firm defines it to be another firm in the same business

that your firm is in, the broader definition of comparable firm includes any firm whose fortunes

are tied to your firms success and failure (or vice versa). From a practical standpoint, try the

following. Definecomparable firm narrowly as a firm that is very similar to your firm.

(Thus, if your firm makes entertainment software, look for other firms that are entertainment

software firms as well.) If you get a large enough sample (see answer to question 4), stop. If

not, try expanding your sample, using any or all of the following tactics:

i. Define comparable more broadly (all software as opposed to entertainment

software).

ii. Look for global listings of companies in the same business; all entertainment

companies listed globally would be an example.

iii. Look up and down the supply chain for other companies that feed into your company

and that your company feeds into. Thus, you may start looking for software retailers that get

the bulk of their revenues from entertainment software.

How big a sample of firms do we need?

Think of this question in the following way. Any sample size greater than one is an

improvement on a regression beta. However, the more firms that you have in your sample, the

greater the potential savings in error. With a sample of 4, your standard error will be cut by

half; with a sample of 9, by two-thirds; with a sample of 16, by 75%.... Try to get to double digits

for your sample size, if you can. If you cannot, settle for 6-8 firms and you are still saving asubstantial amount in terms of estimation error.

There is clearly a trade-off between how tightly you definecomparable firm and your

sample size. If you define comparable narrowly (firms like just like yours in terms of size and

what they do), you will get a smaller sample. If you can get to double digits with a narrow

definition, stay with it. If your sample size is too small, try one of the techniques suggested in

the answer to question 3 to expand your sample.


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Business Risk beta = Unlevered beta/ (1 +Fixed Costs/ Variable Costs)

The problem from a practical standpoint is getting the fixed and variable cost breakdown.

How do we weight these unlevered betas to arrive at the beta for the company?

The weights should be market value weights of the individual businesses that the firm operates

in. However, these businesses do not trade (GE Capital does not have its own listing) and youhave to estimate the market values. You can use weight based on revenues or earnings from

each business but you are assuming that a dollar in revenues (earnings) has the same value in

every business. An alternative is to apply a multiple of revenues (earnings) to the revenues

(earnings) from each business to arrive at an estimated value. This multiple can be estimated

for the comparable firms (from which you estimated the betas). Since you are interested in the

value of the business (and not the value of equity), you should look at EV multiples (and not

equity multiples). If you use revenues, use an EV/ Sales multiple.

How do we adjust for financial leverage?

The standard adjustment for financial leverage is to assume that debt has no market risk (a beta

of zero) and to use what is called the Hamada adjustment:

Levered Beta = Unlevered beta (1 + (1- tax rate) (Debt/Equity))

You can use the current debt to equity ratio for the firm you are analyzing or even a target debt

to equity (if you feel that change is on the horizon) in making this computation.

If you feel uncomfortable about the assumption that debt has no market risk, estimate a beta

for debt and compute the levered beta as follows

Levered Beta = Unlevered Beta (1 + (1-t)(D./E)) Beta of debt (1-t)(D/E)

The tricky part is estimating the beta of debt.

Can bottom-up betas change over time for a company?

Yes, and for two reasons. One is that the mix of businesses can change over time, leading to adifferent unlevered beta. The other is that the debt to equity ratio for the firm can change over

time, leading to changes in the levered beta.

Why is a bottom-up beta better than a regression beta?

Bottom up betas are better than a regression beta for three reasons

They are more precise. The standard error in a bottom-up beta estimate is more precise

because you are averaging across regression betas. The savings will approximate 1/ Square root

of number of firms in the sample. Thus, even if your firm is only one business and has not

changed its debt to equity ratio over time, you will be better off using bottom up betas.

If a firm has changed its business mix, you can reflect that more easily in a bottom-up betabecause you set the weights on the different businesses. A regression beta reflects past

business mix choices.

If a firm has changed its debt to equity ratio, the bottom up beta can be easily adjusted to

reflect those changes. A regression beta reflects past debt to equity choices.

THE CPA IN INDUSTRY


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May 2003

Estimating Cost of Capital Using Bottom-up BetasBy Nancy L. Beneda, PhD, CPA, University of North Dakota

Every business must assess where to invest its funds and regularly reevaluate the quality and

risk of its existing investments. Investment theory specifies that firms should invest in assets

only if they expect them to earn more than their risk-adjusted hurdle rates. Knowing a businesscost of capital allows a comparison of different ways of financing its operations. For example,

increasing the proportion of debt may allow a company to lower its cost of capital and accept

more investments.

Knowing the cost of capital also permits a company to determine its value of operations and

evaluate the effects of alternative strategies. In value-based management, a business current

value of operations is calculated as the present value of the expected future free cash flows

discounted at the cost of capital. This analysis is useful as a guide in decision making as well as

for projecting future financing needs.

The cost of capital is also used in the computation of economic value added (EVA). EVA is useful

to the managers of the company as well as to external financial analysts. It is a measure of the

economic value created by a company in a single year. EVA is computed by subtracting a capital

charge (operating invested capital multiplied by weighted average cost of capital) from after-tax

operating income.

Financial theorists agree that using a correct risk-adjusted discount rate is needed to analyze a

companys potential investments and evaluate overall or divisional performance. Risk-adjusted

discount rates should incorporate business and operating risk as well as financial risk. Business

risk is measured by the nature of the products and services the business provides (discretionary

vs. nondiscretionary), the length of the products life cycle (shorter life cycles create more risk),

and the size of the company (economies of scale can reduce risk). Operating risk is determined

by the cost structure of the firm (higher fixed assets relative to sales increases operating risk).

Financial risk is determined by a companys level of debt. For example, industries that exhibithigh operating leverage and short life cycles, and have discretionary products such as

technology, have very high beta measurements. Borrowing money will only exaggerate the

impact of the risk.

Why Use Bottom-Up Betas?

Computing the cost of capital for a growth company, however, can be problematic. Changing

product mixes, changing cost structures, rapidly changing capital structures, and increasing size

are inherent qualities of growth firms. Furthermore, because growing companies typically do

not pay dividends, using the constant dividend growth model to compute the cost of equity

yields a cost of equity equal to the companys growth rate. In light of this, there is a need to

deal more explicitly with risk when establishing hurdle rates for growth companies. Theabundance of information available on the Internet makes computing a risk-adjusted hurdle

rate simple. Yet the literature to date has provided little to explain the computation of a risk-

adjusted cost of capital using readily available information.

The use of a bottom-up beta in computing the cost of equity component of the cost of capital is

an exceptional method of capturing all types of risk. An example using Community Health

Systems, Inc., a hospital business, illustrates the procedures. The application presented would


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be especially useful to investors who hold growth stocks in their portfolios, equity research

analysts, venture capitalists, and managers of growth firms.

A bottom-up beta is estimated from the betas of firms in a specified business, thereby

addressing problems associated with computing the cost of capital. First, by eliminating the

need for historical stock prices to estimate the firms beta, the standard error, created by

regression betas, is reduced. Second, the problem of a changing product mix is eliminatedbecause the business computes a different cost of capital for each product line. Third, the

levered beta is computed from the companys current financial leverage, rather than from the

average leverage over the period of the regression.

Overall, bottom-up betas are designed to be a better measure of the market risk associated

with the industry or sector of the business. Because betas measure the risk of a firm relative to

a market index, the more sensitive a business is to market conditions, the higher its beta.

Bottom-up betas also capture the operating and financial risk of a company. Intuitively, the

more financial risk or operating risk a firm has, the higher its beta.

Developing a Bottom-Up Beta

Exhibit 1 illustrates the computation of a bottom-up beta for Community Health Systems, Inc.

(CHS). CHS has an average three-year historical sales growth rate of 25.6%. The August 12,

2002, Fortune reported it to be one of the top 40 companies traded, based on both value and

growth indicators. It went public on June 9, 2000, and does not have a reported beta.

The first step in estimating a bottom-up beta is to identify the business and a set of comparable

established companies. Compustat, Value Line, and Hoovers.com, all report companies by

industry and sector. Panel A of Exhibit 1 shows a set of eight comparable companies identified

by Hoovers.

Second, the reported beta (reported betas are levered) and recent financial statements for

each comparable company should be obtained. Value Line and Compustat provide reported

betas. Financial statements can be obtained from Hoovers or Compustat. From the financialstatements, the marginal tax rate and the debt-to-equity ratio is determined. Using the

reported beta, the debt-to-equity ratio, and the tax rate, an unlevered beta is computed

(Exhibit 1, Panel A). The computation of an unlevered beta removes the effects of financial

leverage of the comparable firms. The unlevered beta for each comparable company is

determined using the following:

Equation 1:

Bl = Bu x [1 + (1 tax rate) x (D / E)], or

Bu = Bl / [1 + (1 tax rate) x (D / E)]

The unlevered beta (Bu) in Equation 1 is the beta of a firm with no debt and is determined by

the types of businesses in which it operates and its operating leverage (risk). The degree ofoperating leverage is a function of a companys cost structure, and is usually defined in terms of

the relationship between fixed costs and total costs. A company that has high operating

leverage (high fixed costs relative to total costs) will also have higher variability in earnings

before interest and taxes than a company producing a similar product with low operating

leverage. Other things being equal, the higher variance in operating income will lead to a higher

beta for companies with high operating leverage.
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The debt to equity ratio (D/E) in Equation 1 represents the amount of financial leverage or the

debt level of the company. Other things being equal, an increase in financial leverage will

increase the beta. The obligated payments on debt increase the variance in net income, with

higher leverage increasing income during good times and decreasing income during economic

downturns. The tax advantage of debt financing is represented in the formula by (1 tax rate).

The higher the tax rate, the more favorable the debt financing.

The third step is to compute a weighted-average unlevered beta of the comparable companies,

and from this, using Equation 1, compute the levered beta (BL) for the company being

evaluated. The computation of the unlevered beta of the comparable company is weighted

according to company size measured as the market value (MV) of equity plus debt. As shown in

Panel B of Exhibit 1, the weighted average unlevered beta for the comparable companies is

0.72.

The levered beta (BL) for CHS is then computed using the weighted-average unlevered beta of

the comparable companies. The debt-to-equity ratio and tax rate of the company under

consideration is used to lever up the unlevered beta in Equation 1. This procedure adjusts the

beta for the financial risk and tax benefits associated with the individual firm, project, or

division in question. The levered beta (BL) of a firm is a function of its operating leverage, the

type of businesses in which it operates, and its financial leverage.

The levered beta computed for CHS is 0.917. The debt-to-MV ratio of 0.42, obtained from CHSs

financial statements, is slightly higher than the debt-to-MV ratios for comparable companies

and factored into the computation of CHSs levered beta of 0.917.

Finally, operating leverage and growth should also be observed for comparable companies.

Exhibit 1, Panel C, provides a detailed explanation of the computations and sources of data for

the information in Panels A and B. The operating leverage of the entity being analyzed should

be compared to the operating leverage of the comparable companies. While operating leverageaffects betas, measuring the operating leverage of a company is difficult because fixed and

variable costs are often aggregated in income statements. It is possible to get an approximate

measure of the operating leverage of a company by looking at changes in operating income as a

function of changes in sales. For companies with high operating leverage, operating income

should change more than proportionately when sales change. Operating leverage can be

computed using the following formula:

Equation 2:

Operating leverage = (% change in operating income) / (% change in sales)

If the companys project or division being analyzed has a higher (lower) operating leverage than

the comparable firms, the unlevered beta should be adjusted upward (downward). CHSsoperating leverage of 1.1 and three-year historical growth rate of 25.6 appear to be fairly

consistent with the operating leverage and growth rates of the comparable companies. Thus

the computed levered beta for CHS is a good estimate of the companys market risk with regard

to operating leverage and growth.

The unlevered betas appear to be associated with a combination of size and operating leverage.

Because the largest companies have the highest operating leverage, it appears that these


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companies attempt to balance business risk with operating risk by increasing their operating

leverage.

The unlevered betas, however, do not appear to correlate with growth rates. The annual

growth rates for the most recent three years of the comparable companies range from 2.5% to

42.7%. The five-year annual projected growth rate for 2002 through 2007 of the hospital

industry is reported by Yahoo Finance to be 16.3% (finance.yahoo.com; as of September 4,2002).

Growth companies generally tend to have significant fixed costs associated with setting up

infrastructure and developing new products. Once these costs have been incurred, however,

the variable costs are relatively low. For growth companies in high-risk industries, such as

technology, higher growth leads to higher fixed costs and higher betas. The low betas of

companies in the hospital industry indicate a low market risk, even for growth companies. This

can be explained by the industrys nondiscretionary products and longer product life cycles.

Capital Asset Pricing Model (CAPM) and the Cost of Equity

Exhibit 2shows the computation of the cost of equity for CHS using the capital asset pricing

model (CAPM), Equation 3, and the bottom-up beta computed in Exhibit 1. The components

that go into measuring the cost of equity using the CPM include the riskless rate, the market

risk premium, and the beta of the firm, product, or division.

Equation 3:

Cost of equity = (riskless rate + beta) x market risk premium

A riskless asset is one in which the investor knows the expected return with certainty.

Consequently, there is no default risk and no uncertainty about reinvestment rates. To

eliminate uncertainty about reinvestment rates, the maturity of the security should be matched

with the length of the evaluation. In practice, using a long-term government ratewhich can be

obtained from Bondsonline (www.bondsonline.com)as a riskless rate in all types of analyses

will yield a close approximation of the true value.

The market risk premium measures the extra return that would be demanded by investors forshifting their money from a riskless investment to an average-risk investment. It should be a

function of how risk-averse the investors are and how risky they perceive stocks and other risky

investments to be, in comparison to a riskless investment. The most common approach to

estimating the market risk premium is to estimate the historical premium earned by risky

investments (stocks) over riskless investments (government bonds). The average historical

market risk premium over the period 1926 to 1999 for small companies is 12.1%, as reported by

Ibbotsons.

Exhibit 2 illustrates the computation of the cost of equity for CHS. Using a risk-free rate of 5.5%,

a market risk premium of 12.1%, and the bottom-up beta of 0.917, the cost of equity for CHS is

estimated to be 16.6%.Cost of Debt

The cost of debt measures the current cost of borrowing funds to finance projects. The cost of

debt is measured by the current level of interest rates, the default risk of the company, and the

tax advantage associated with debt.

Equation 4:

Pre-tax cost of debt = Treasury bond rate + default spread of companys debt
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The default spread is the difference between the long-term Treasury bond rate and the

companys bond yield. Default spreads can be found at Bondsonline if the company has a bond

rating. Bond ratings can be found atwww.standardandpoors.com . For companies that are not

rated (CHS is not rated by Standard & Poors), the rating may be obtained by computing the

companys interest coverage ratio and adjusting for industry standards or expected future

interest coverage. The interest coverage ratio for CHS is 2, and the associated ratings for thecomparable companies indicate a bond rating of B+ for CHS. The default spread for this rating

from Bondsonline is 8.5%.Exhibit 3illustrates the computation of the cost of debt for CHS, from

Equation 4, as 14%.

Cost of Capital

The estimated cost of capital should be based on the market values of a companys debt and

equity, since a company has to earn more than its market value cost of capital to generate

value. From a practical standpoint, using the book value cost of capital will tend to understate

the cost for most companies, especially highly levered companies. These companies have more

equity in their capital structures, and equity is more likely to have a higher market value than

book value.

Equation 5:

Cost of Capital = ke [E / (D+E)] + kd [D / (D+E)]

The market value of equity (E) for CHS is $2,354 million, calculated as the number of shares

outstanding times the stock price as of December 31, 2001. The stock price can easily be

obtained from Yahoo Finance, and the number of shares outstanding is reported on the

financial statements, which can be obtained from either Hoovers or Compustat. Generally the

book value of debt is an adequate proxy for the market value unless interest rates have

changed drastically.Exhibit 4illustrates the computation of the cost of capital for CHS, which is

14.40%.
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