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2. Total Bet Verificare Bilet
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4. Total Betrayal
5. Total Betty

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Estimating the cost of equity for a private company

Inassessing the cost of equity for publicly traded firms, we looked at the riskof investments through the eyes of the marginal investors in these firms. Withthe added assumption that these investors were well diversified, we were ableto define risk in terms of risk added on to a diversified portfolio or marketrisk. The beta (in the CAPM) and betas (in the multi-factor models) thatmeasure this risk are usually estimated using historical stock prices. Theabsence of historical price information for private firm equity and the failureon the part of many private firm owners to diversify can create seriousproblems with estimating and using betas for these firms.

Approachesto Estimating Market Betas

Thestandard process of estimating the beta in the capital asset pricing modelinvolves running a regression of stock returns against market returns.Multi-factor models use other statistical techniques, but they also requirehistorical price information. In the absence of such information, as is thecase with private firms, there are three ways in which we can estimate betas.

1.Accounting Betas

While price information is not availablefor private firms, accounting earnings information is. We could regress changesin a private firm’s accounting earnings against changes in earnings for anequity index (such as the S&P 500) to estimate an accounting beta.

DEarnings_{Private firm} = a + b D Earnings_{S&P 500}

The slope of the regression (b) is theaccounting beta for the firm. Using operating earnings would yield an unleveredbeta, whereas using net income would yield a levered or equity beta.

There are two significant limitations with this approach.The first is that private firms usually measure earnings only once a year,leading to regressions with few observations and limited statistical power. Thesecond is that earnings are often smoothed out and subject to accountingjudgments, leading to mismeasurement of accounting betas.

2.Fundamental Betas

There have been attempts made byresearchers to relate the betas of publicly traded firms to observablevariables such as earnings growth, debt ratios and variance in earnings.Beaver, Kettler, and Scholes (1970) examined the relationship between betas andseven variables - dividend payout, asset growth, leverage, liquidity, assetsize, earnings variability and the accounting beta. Rosenberg and Guy (1976)also attempted a similar analysis. The following is a regression that we ranrelating the betas of NYSE and AMEX stocks in 1996 to four variables:coefficient of variation in operating income (CV_OI), bookdebt/equity (D/E), historical growth in earnings (g) and the book value oftotal assets (TA).

Beta = 0.6507+ 0.25 CV_OI+0.09 D/E + 0.54 g - 0.000009 TAR²=18%

where

CV_OI= Coefficient of Variation in Operating Income

= StandardDeviation in Operating Income/ Average Operating Income

We could measure each of these variablesfor a private firm and use these to estimate the beta for the firm. While thisapproach is simple, it is only as good as the underlying regression. The low R²suggests that the beta estimates that emerge from it are likely to have largestandard errors.

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3.Bottom-up Betas

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When valuing publicly traded firms, weused the unlevered betas of the businesses that the firms operated in toestimate bottom-up betas – the costs of equity were based upon these betas. Wedid so because of the low standard errors on these estimates (due to theaveraging across large numbers of firms) and the forward looking nature of theestimates (because the business mix used to weight betas can be changed). Wecan estimate bottom-up betas for private firms and these betas have the sameadvantages that they do for publicly traded firms. Thus, the beta for a privatesteel firm can be estimated by looking at the average betas for publicly tradedsteel companies. Any differences in financial or even operating leverage can beadjusted for in the final estimate.

In making the adjustment of unleveredbetas for financial leverage, we do run into a problem with private firms,since the debt to equity ratio that should be used is a market value ratio.While many analysts use the book value debt to equity ratio to substitute forthe market ratio for private firms, we would suggest one of the followingalternatives.

a. Assume that the private firm’s market leverage willresemble the average for the industry. If this is the case, the levered betafor the private firm can be written as:

bb_unlevered (1 + (1 - tax rate) (Industry AverageDebt/Equity))

bb_unlevered (1 + (1 - tax rate) (Optimal Debt/Equity))

The adjustment for operating leverage issimpler and is based upon the proportion of the private firm’s costs that arefixed. If this proportion is greater than is typical in the industry, the betaused for the private firm should be higher than the average for the industry.

Adjustingfor Non-Diversification

Betasmeasure the risk added by an investment to a diversified portfolio.Consequently, they are best suited for firms where the marginal investor isdiversified. With private firms, the owner is often the only investor and thuscan be viewed as the marginal investor. Furthermore, in most private firms, theowner tends to have much of his or her wealth invested in the private businessand does not have an opportunity to diversify. Consequently, it can be arguedthat betas will understate the exposure to market risk in these firms.

Atthe limit, if the owner has all of his or her wealth invested in the privatebusiness and is completely undiversified, that owner is exposed to all risk inthe firm and it is not just the market risk (which is what the beta measures).There is a fairly simple adjustment that can allow us to bring in thisnon-diversifiable risk into the beta computation. To arrive at this adjustment,assume that the standard deviation in the private firm’s equity value (whichmeasures total risk) is s_j and that the standarddeviation in the market index is s_m. If the correlation betweenthe stock and the index is defined to be r_jm, the market beta can bewritten as:

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Market beta

Tomeasure exposure to total risk (s_j), we could divide the marketbeta by r_jm. This would yield the following.

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Thisis a relative standard deviation measure, where the standard deviation of theprivate firm’s equity value is scaled against the market index’s standarddeviation to yield what we will call a total beta.

Total Beta

Thetotal beta will be higher than the market beta and will depend upon thecorrelation between the firm and the market – the lower the correlation, thehigher the total beta.

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Youmight wonder how a total beta can be estimated for a private firm, where theabsence of market prices seems to rule out the calculation of either a marketbeta or a correlation coefficient. Note though, that we were able to estimatethe market beta of the sector by looking at publicly traded firms in thebusiness. We can obtain the correlation coefficient by looking at the samesample and use it to estimate a total beta for a private firm.

Thequestion of whether the total beta adjustment should be made cannot be answeredwithout examining why the valuation of the private firm is being done in thefirst place. If the private firm is being valued for sale, whether and how muchthe market beta should be adjusted will depend upon the potential buyer orbuyers. If the valuation is for an initial public offering, there should be noadjustment for non-diversification, since the potential buyers are stock marketinvestors. If the valuation is for sale to another individual or privatebusiness, the extent of the adjustment will depend upon the degree to which thebuyer’s portfolio is diversified; the more diversified the buyer, the higherthe correlation with the market and the smaller the total beta adjustment.