,solving for r in the following equation)Implied Equityik pmium = Expectd retur on stocks - Trery bond rate 7.78% - 3.95% = 3.83%129.323905.65 = 116.13 144.01160.37178.59178.59(1.0395)+ ( 1+ r)2 + ( 1+ r)3+ (1+ r)4+ ( 1+ r)5+(1+ r)(r.0395)(1+r)5Aswath32Damodaran

Aswath33DamodaranEstimating Beta• The standard procedure for estimating betas is to regress stock returns (Rj)against market returns (Rm) -Rj= a + b Rmwhere a is the intercept and b is the slope of the regression.The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock.This beta has three problems:It has high standard errorIt reflects the firm’s business mix over the period of the regression, not the current mixIt reflects the firm’s average financial leverage over the period rather than the current leverage.Aswath33Damodaran

Aswath34DamodaranBeta Estimation: The Noise Problem

Aswath35DamodaranBeta Estimation: The Index EffectAswath35Damodaran

Aswath36DamodaranSolutions to the Regression Beta ProblemModify the regression beta bychanging the index used to estimate the betaadjusting the regression beta estimate, by bringing in information about the fundamentals of the companyEstimate the beta for the firm usingthe standard deviation in stock prices instead of a regression against an indexaccounting earnings or revenues, which are less noisy than market prices.Estimate the beta for the firm from the bottom up without employing the regression technique. This will requireunderstanding the business mix of the firmestimating the financial leverage of the firmUse an alternative measure of market risk not based upon a regression.

Aswath37DamodaranThe Index Game...Aswath37Damodaran

Aswath38DamodaranDeterminants of Betas

Aswath39DamodaranIn a perfect world... we would estimate the beta of a firm bydoing the followingAswath39Damodaran

Aswath40DamodaranAdjusting for operating leverage...Within any business, firms with lower fixed costs (as a percentage of total costs) should have lower unlevered betas. If you can compute fixed and variable costs for each firm in a sector, you can break down the unlevered beta into business and operating leverage components.¥ Unlevered beta = Pure business beta * (1 + (Fixed costs/ Variable costs))The biggest problem with doing this is informational. It is difficult to get information on fixed and variable costs for individual firms.In practice, we tend to assume that the operating leverage of firms within a business are similar and use the same unlevered beta for every firm.

Aswath41DamodaranEquity Betas and LeverageConventional approach: If we assume that debt carries no market risk (has a beta of zero), the beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratioL=(1+ ((1-t)D/E))uIn some versions, the tax effect is ignored and there is no (1 -t) in the equation.

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