For composite costs of equity in excess of 100% or below
the riskfree rate of 7.2%, NMF will be displayed. It is our opinion that
costs of equity below the riskfree rate are not meaningful. It is also
our opinion that costs of equity above a certain level are not meaningful.
We have chosen this level to be 100%.
Costs of equity above 100% or below 7.2% are included in the percentile statistics because they provide valuable information to the reader. Costs of equity to such extremes are indicative of the cost of equity model failing due to the nature of the data for companies in the industry. CAPM—Ordinary Least Squares (OLS)
where, CAPM—With Small Capitalization Premium The CAPM does not fully account for the higher returns of small company stocks. Recent research has shown that the CAPM does not fully account for returns of medium sized companies either. Ibbotson Associates’ Stock, Bonds, Bills, and Inflation 1997 Yearbook gives a detailed analysis of company size and its impact on the CAPM. The column labeled "+ Size Premium" is the OLS form of the capital asset pricing model with the small capitalization premium added. Premiums are determined by the equity capitalization of a company and are simply added to the original CAPM equation. For this publication, the following premiums were added: For midcap companies, whose equity capitalization is at or below $3,320,996,625 but greater than $774,452,250, a premium of 1.04% is added. For lowcap companies, whose equity capitalization is at or below $773,983,875, but greater than $201,911,250, a premium of 1.75% is added. For microcap companies, whose equity capitalization is at or below $201,169,500, a premium of 3.47% is added. No premium is added for largecap companies. For composites, the size premium is an equity capitalization weighted average of the size premiums of the companies included in the composite. ThreeFactor FamaFrench Model The FamaFrench Three Factor Model is a multiple linear regression model developed by Eugene Fama and Kenneth French. The model is estimated by running a time series multiple regression for each company. The dependent variable is the company’s monthly excess stock returns over Treasury bill returns. The independent variables are as follows:
The multiple regression formula can be written as follows.
The cost of equity is estimated as follows:
where, For further description reference: Fama, Eugene F. and Kenneth R. French, "Size and BooktoMarket Factors in Earnings and Returns," Journal of Finance, March 1995. Analysts SingleStage Discounted Cash Flow
where, The single stage discounted cash flow model is the Gordon growth model which is stated as:
where, In our model, we know all of the variables except k, so we have rewritten the equation to solve for the discount rate or cost of equity. If a company pays no dividends, its cost of equity is its growth rate. If individual company growth rates were not available in the ACE database, industry average growth rates were substituted. ThreeStage Discounted Cash Flow
where, CF_{Ai0} = Average
cash flow for company i; CF_{Ai0} (1 + g_{i1})^{5};
[IBEI_{5} (1 + g_{i1})^{5}]
(1 + g_{2})^{5}; Solving for the cost of equity is an iterative process. The ThreeStage model identifies three separate growth rates. A growth rate applicable to cash flows during the first five years of future performance, a growth rate applicable to cash flows over the sixth through tenth years, and a growth rate applicable to earnings for all future years following the first ten years. The first term of this model discounts to present those cash flows related to the first five years of growth. The second term discounts to present all cash flows in years six through ten. The third term discounts to present those earnings related to all future years beyond year ten. Cash flows are used in place of dividends in the first and second terms because many companies do not pay dividends. Earnings are used in place of cash flows in the third term, because over extended periods of time it is assumed that capital expenditures and depreciation will be equal. Cash flow is defined as income before extraordinary items plus depreciation less capital expenditures plus deferred taxes. Normal cash flows and income before extraordinary items are used because of the potential for anomalous years. "Normal" cash flows and income before extraordinary items are estimated by multiplying the last five years average cash flow and earnings rates, both as a percent of sales, by the most recent year's sales. This reduces the effect that an anomalous recent year would have on a longrun expected cost of equity. A cost of equity number will be calculated under this model only if both cash flow and income before extraordinary items are positive values. Companies included in the composite that do not have ACE growth rates are excluded from this calculation. In those instances where no companies in the composite have an ACE growth rate, the industry average is substituted. In limited cases, no ACE growth rates will be available for any company in the industry. In this case, the industry average growth rate for the preceding SIC code is substituted. For example, if industry 7371 has no ACE growth rates for any of the companies included in the industry, the industry average growth rate for industry 737 is substituted. 
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