Risk & Return

FIN 591: Financial Fundamentals/Valuation2 Systematic and Unsystematic Risk Total risk decreases as the number of securities in the portfolio rises. This drop occurs only in the unsystematic-risk component. Systematic risk is unaffected by diversification. Total risk,  2 P Unsystematic risk Systematic risk N, number of securities in portfolio

FIN 591: Financial Fundamentals/Valuation3 Systematic Risk Captured by beta Represents a risk index Based on capital asset pricing theory Pricing of individual securities based on the SML E(r i ) = r f +  [E(r m ) - r f ] Market risk premium

FIN 591: Financial Fundamentals/Valuation4 The Security Market Line Expected return on asset SML r m r f O 1 

FIN 591: Financial Fundamentals/Valuation5 Total Annual Returns, Risk Premium Arithmetic(relative to U.S.Standard SeriesMeanTreasury bonds)Deviation Distribution Common Stocks 13.2%7.5%20.3% Small Company Stocks Long-Term Corporate Bonds Long -Term Government Bonds Intermediate- Term Govern- ment Bonds U.S. Treasury Bills Inflation * The 1993 small company stock total return was percent * -90% 0% +90%

FIN 591: Financial Fundamentals/Valuation6 Estimating Beta Estimate of the historical alignment of the security price with the market Value Line, S&P, etc…routinely provide equity  s There are significant and persistent differences in equity betas between industries The more pronounced the growth orientation, the higher the equity beta is likely to be  equity and  debt estimated relative to the equity market portfolio.

FIN 591: Financial Fundamentals/Valuation7 Estimating Risk Premium Risk premium = Expected nominal return on the market - treasury nominal rate Assume E(risk premium) = past risk premium Why? Recall the “rational expectations” argument Long-term market risk premium is about 7.5% See slide #5 See Exhibits 10.4 & 10.5, pages 217 and 218 of text.

FIN 591: Financial Fundamentals/Valuation8 Unlevering Beta  asset =  equity S / (B + S) +  debt (1 -  c ) B / (B + S)  asset =  equity S / (B + S) Probably useful to calculate  asset for other firms in the industry and find an average  asset. Often assume  debt = 0 for low leverage firms. Empirical findings: 0 <  debt <.5.

FIN 591: Financial Fundamentals/Valuation9 Unlevering Beta: Another Way  equity =  asset [1 + (1 -  c ) B/S] (1)  asset =  equity / [1 + (1 -  c ) B/S] (2) Approach: Identify comparable firms Their betas are levered betas if they have debt Solve eqn. (2) to find the asset beta,  asset Substitute  asset in eqn. (1) to find equity  equity. Hamada: Assumes that debt is risk free (  d = 0) & tax rate is constant.

FIN 591: Financial Fundamentals/Valuation10 SML-Based Cost of Equity If personal taxes ignored (NTA = 0): E(r e ) = r f +  equit y [E(r m ) - r f ] E(r e ) = r f +  asset [E(r m ) - r f ] + (  equity -  asset )[E(r m ) - r f ]. Business risk premium Financial risk premium

FIN 591: Financial Fundamentals/Valuation11 SML-Based Cost of Debt Difficult to measure debt’s beta E(r b ) = r f +  debt [E(r m ) - r f ]..

FIN 591: Financial Fundamentals/Valuation12 Pulling It Together for WACC The result: WACC = r f + [  equity w equity +  debt (1 -  c ) w debt ] [r m - r f ] = r f +  asset [r m - r f ].

FIN 591: Financial Fundamentals/Valuation13 WACC Industry Comparison If the company is not publicly traded Find comparable companies If the company is publicly traded Comparing WACCs with comparable firms is still valuable WACC is only an estimate and includes error How large are the deviations for the firm from industry averages?

FIN 591: Financial Fundamentals/Valuation14 Build-Up Approach Based on work done by PricewaterhouseCoopers Model: Current long-term risk-free rate Add historical equity risk premium (7.5%) Add a size premium Smaller firms are riskier (up to about 16% points) CAPM understates expected return for all firms other than the very large companies Handout re: size premia.

FIN 591: Financial Fundamentals/Valuation15 Solutions to Optimal Capital Structure M&M world: Firms should rely almost exclusively on debt to finance their operations Reality: Few firms rely mostly on debt financing Why? Personal income taxes We’ve discussed the Miller hypothesis Financial distress Agency costs.

FIN 591: Financial Fundamentals/Valuation16 Costs of Financial Distress & Agency Costs Direct Costs Legal and administrative costs Trivial magnitude for large firms Indirect Costs Quite significant U.S. courts usually deviate from absolute priority rule Impaired ability to conduct business Lost sales, jobs, firm value, etc... Agency costs Incentive to take large risks Incentive to under-invest.

FIN 591: Financial Fundamentals/Valuation17 An Optimal Capital Structure Capital structure which maximizes firm value: V L = V u + PVTS - PVFD - PVAC. The tax shield increases the value of the levered firm. Financial distress costs and agency costs lower the value of the levered firm. The two offsetting factors produce an optimal amount of debt. Tax Shield

FIN 591: Financial Fundamentals/Valuation18 The End