C. Accounting Betas

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 regressed against changes in earnings for the

market, in the same periods, to arrive at an estimate of a “market 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, resulting 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 one

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 power.

Illustration 4.10: Estimating Accounting Betas ““ Bookscape Books

Bookscape Books, even though it is a private business, has been in existence since

1980 and has accounting earnings going back to that year. Table 4.10 summarizes

accounting earnings changes at Bookscape and for the S&P 500 for each year since 1980.

Table 4.10: Earnings for Bookscape versus S&P 500

Year S&P 500 Bookscape

1980 3.55%

3.01%

1981 4.05%

1.31%

1982 -14.33%

-8.95%

1983 47.55%

-3.84%

1984 65.00%

26.69%

1985 5.05%

-6.91%

1986 8.50%

-7.93%

1987 37.00%

11.10%

1988 45.17%

42.02%

1989 3.50%

5.52%

1990 -10.50%

-9.58%

1991 -32.00%

-12.08%

1992 55.00%

-5.12%

1993 31.00%

9.37%

1994 21.06%

36.45%

55

1995 11.55%

30.70%

1996 19.88%

1.20%

1997 10.57% 16.55%

1998 -3.35% 7.10%

1999 18.13% 14.40%

2000 15.13% 10.50%

2001 -14.94% -8.15%

2002 6.81% 4.05%

2003 14.63% 12.56%

Regressing the changes in profits at Bookscape against changes in profits for the S&P

500 yields the following:

Bookscape Earnings Change = 0.1003 + 0.7329 (S & P 500 Earnings Change)

Based upon this regression, the beta for Bookscape is 0.73. In calculating this beta, we

used net income to arrive at an equity beta. Using operating earnings for both the firm

and the S&P 500 should yield the equivalent of an unlevered beta.

Technically, there is no reason why we cannot estimate accounting betas for

Disney, Aracruz Cellulose and Deutsche Bank. In fact, for Disney, we could get net

income numbers every quarter, which increases the data that we have in the regression.

We could even estimate accounting betas by division, since the divisional income is

reported. We do not attempt to estimate accounting betas for the following reasons:

1. To get a sufficient number of observations in our regression, we would need to go

back in time at least 10 years and perhaps more. The changes that many large

companies undergo over time make this a hazardous exercise.

2. Publicly traded firms smooth out accounting earnings changes even more than private

firms do. This will bias the beta estimates downwards.

spearn.xls: This data set on the web has earnings changes, by year, for the S&P

500 going back to 1960.

Market, Fundamental and Accounting Betas: Which one do we use?

For most publicly traded firms, betas can be estimated using accounting data,

market data or from fundamentals. Since the betas will almost never be the same, the

question then becomes one of choosing between these betas. We would almost never use

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accounting betas, for all of 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 and the inability of these regressions to reflect

the effects of major changes in the business and financial risk at the firm. Fundamental

betas, in our view, provide us with the best beta estimates because they are not only more

precise (because of the averaging) but also because they allow us to reflect changes in

business and financial mix. In summary, we will use the fundamental estimates of equity

betas of 1.25 for Disney, 0.82 for Bookscape, 0.70 for Aracruz and 0.98 for Deutsche

Bank.

IV. Estimating the Cost of Equity

Having estimated the riskfree 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 = Riskfree Rate + Beta * Expected Risk Premium

where the riskfree 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 = Riskfree Rate + # ! j * Risk Premium j

j "1

where the riskfree rate is the long term government bond rate, βj 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 key

implications for both equity investors in the firm and the managers of the firm. For equity

investors, it is the rate that they need to make to be compensated for the risk that they

have taken on investing in the firm. If after analyzing an investment, they conclude that

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

57

the firm, the return that investors need to make to break even on their equity investments

becomes the return that they have to try and deliver to keep these investors from

becoming restive and rebellious. Thus, it becomes the rate that they have to beat in terms

of returns on their equity investments in individual project. In other words, this is the cost

of equity to the firm.

Illustration 4.11: Estimating the Cost of Equity

In illustration 4.5, we estimated a bottom-up levered beta for Disney and each of

its divisions. Using the prevailing treasury bond rate of 4% and the historical risk

premium of 4.82% from table 4.2, we estimate the cost of equity for Disney as a

company and for each of its divisions:

Table 4.11: Levered Beta and Cost of Equity: Disney

Business Unlevered Beta D/E Ratio Levered Beta Cost of Equity

Media Networks 1.0850 26.62% 1.2661 10.10%

Parks and Resorts 0.9105 26.62% 1.0625 9.12%

Studio Entertainment 1.1435 26.62% 1.3344 10.43%

Consumer Products 1.1353 26.62% 1.3248 10.39%

Disney 1.0674 26.62% 1.2456 10.00%

Note that since none of the divisions carry their own debt, we have assumed that they are

all funded using the same mix of debt and equity as Disney as a company.45 The costs of

equity vary across the remaining divisions, with studio entertainment having the highest

beta and parks and resorts the lowest.46

To estimate the cost of equity for Deutsche Bank, we will use the same risk

premium (4.82%) that we have used for the U.S, since Deutsche™s business is still

primarily in mature markets in Europe and the United States. Using the 10-year German

Euro bond rate of 4.05% as the Euro riskfree rate47 and Deutsche Bank™s bottom up beta

of 0.98, the cost of equity for Deutsche Bank is:

45 Disney provides no breakdown of debt by division. If it did, we could use division specific debt to equity

ratios.

46 If we consider cash as a division, the cost of equity is the riskfree rate because cash is invested in

commercial paper and treasuries.

47 There are about 8 countries that issue 10-year Euro denominated bonds. We used the German Euro bond

rate as the riskfree rate, not because Deutsche Bank was a German company, but because the German Euro

bond rate was the lowest of the government bond rates. The Greek and Spanish 10-year Euro bond rates

58

Table 4.12: Cost of Equity for Deutsche Bank

Cost of

Equity

Business Beta Weights

Commercial Banking 0.7345 7.59% 69.03%

Investment Banking 1.5167 11.36% 30.97%

Deutsche Bank 8.76%

Note that the cost of equity for investment banking is significantly higher than the cost of

equity for commercial banking, reflecting the higher risks.

For Aracruz, we will add the country risk premium estimated for Brazil of 7.67%,

estimated earlier in the chapter, to the mature market premium, estimated from the U.S,

of 4.82% to arrive at a total risk premium of 12.49%. The cost of equity in U.S. dollars

for Aracruz as a company can then be computed using the bottom up beta estimated in

illustration 4.7:

Cost of Equity = Riskfree Rate in US $ + Beta * Risk Premium

= 4% + 0.7040 (12.49%) = 12.79%

As an emerging market company, Aracruz clearly faces a much higher cost of equity than

its competitors in developed markets. We can also compute a cost of equity for Aracruz

in real terms, by using a real riskfree rate in this calculation. Using the 10-year inflation-

index U.S. treasury bond of 2% as the real riskfree rate, Aracruz™s real cost of equity is:

Cost of Equity = 2% + 0.7040 (13.70%) = 10.79%

If we want to compute the cost of equity in nominal BR terms, the adjustment is more

complicated and requires estimates of expected inflation rates in Brazil and the United

States. If we assume that the expected inflation in BR is 8% and in U.S. dollars is 2%, the

cost of equity in BR terms is:

(1+ Inflation Rate Brazil )

Cost of Equity in BR =(1+ Cost of Equity in $) -1

(1+ Inflation Rate US )

(1.08)

= (1.1279) -1 = .1943 or 19.43%

(1.02)

!

Note that these estimates of cost of equity are affected by the cash holdings of Aracruz.

We can estimate the cost of equity for the paper and pulp business of Aracruz

!

were about 0.20% higher, reflecting the perception of default risk in those countries. We would continue to

59

(independent of the cash holdings) by using the levered beta of 0.7576 for the business

estimated in illustration 4.7:

Real Cost of Equity (paper business) = 2.00% + 0.7576 (12.49%) = 11.46%

US $ Cost of Equity (paper business) = 4.00% + 0.7576 (12.49%) = 13.46%

(1.08)

Nominal BR Cost of Equity (paper business) 1.1346 -1 = 20.14%

(1.02)

Finally, for Bookscape, we will use the beta of 0.82 estimated from illustration

4.6 in conjunction with the riskfree rate and risk premium for the US:

!

Cost of Equity = 4% + 0.82 (4.82%) = 7.73%

This cost of equity may seem incongruously low for a small, privately held business but it

is legitimate if we assume that the only risk that matters is non-diversifiable risk.

In Practice: Risk, Cost of Equity and Private Firms

Implicit in the use of beta as a measure of risk is the assumption that the marginal

investor in equity is a well diversified investor. While this is a defensible assumption

when analyzing publicly traded firms, it becomes much more difficult to sustain for

private firms. The owner of a private firm generally has the bulk of his or her wealth

invested in the business. Consequently, he or she cares about the total risk in the business

rather than just the market risk. Thus, for a business like Bookscape, the beta that we

have estimated of 0.82 (leading to a cost of equity of 7.73%) will understate the risk

perceived by the owner of Bookscape. There are two solutions to this problem:

1. Assume that the business is run with the near-term objective of sale to a large

publicly traded firm. In such a case, it is reasonable to use the market beta and cost of

equity that comes from it.

2. Add a premium to the cost of equity to reflect the higher risk created by the owner™s

inability to diversify. This may help explain the high returns that some venture

capitalists demand on their equity investments in fledgling businesses.

Adjust the beta to reflect total risk rather than market risk. This adjustment is a relatively

simple one, since the R squared of the regression measures the proportion of the risk

that is market risk. Dividing the market beta by the square root of the R squared

(which is the correlation coefficient) yields a total beta. In the Bookscape example,

use the German Euro bond rate to value Greek and Spanish companies in Euros.

60

the regressions for the comparable firms against the market index have an average R

squared of about 16%. The total beta for Bookscape can then be computed as follows:

Market Beta 0.82

Total Beta = = 2.06

=

R squared .16

Using this total beta would yield a much higher and more realistic estimate of the cost of

equity.

!

Cost of Equity = 4% + 2.06 (4.82%) = 13.93%

Thus, private businesses will generally have much higher costs of equity than their

publicly traded counterparts, with diversified investors. While many of them

ultimately capitulate by selling to publicly traded competitors or going public, some

firms choose to remain private and thrive. To do so, they have to diversify on their

own (as many family run businesses in Asia and Latin America did) or accept the