Risk & Return

1. Risk & Return

2. 2 Total risk,s P Unsystematic risk Systematic risk Systematicand Unsystematic Risk N, number ofsecurities in portfolio 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. FIN 591: Financial Fundamentals/Valuation

3. Systematic Risk • Captured by beta • Represents a risk index • Based on capital asset pricing theory • Pricing of individual securities based on the SML E(ri) = rf + b [E(rm) - rf] Market risk premium FIN 591: Financial Fundamentals/Valuation

4. The Security Market Line Expected return on asset SML rm rf O 1 b FIN 591: Financial Fundamentals/Valuation

5. Total Annual Returns, 1926-1998 Risk Premium Arithmetic (relative to U.S. Standard Series Mean Treasury bonds) Deviation Distribution Common Stocks 13.2% 7.5% 20.3% Small Company Stocks 17.4 11.7 33.8 Long-Term Corporate Bonds 6.1 0.4 8.6 Long -Term Government Bonds 5.7 9.2 Intermediate- Term Govern- ment Bonds 5.5 5.7 U.S. Treasury Bills 3.8 3.2 Inflation 3.1 4.5 * -90% 0% +90% * The 1993 small company stock total return was 142.9 percent FIN 591: Financial Fundamentals/Valuation

6. Estimating Beta • Estimate of the historical alignment of the security price with the market • Value Line, S&P, etc…routinely provide equity bs • 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 • bequity and bdebt estimated relative to the equity market portfolio. FIN 591: Financial Fundamentals/Valuation

7. 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/Valuation

8. Unlevering Beta basset = bequity S / (B + S) + bdebt (1 - tc) B / (B + S) basset = bequity S / (B + S) Probably useful to calculate basset for other firms in the industry and find an average basset. Often assume bdebt= 0 for low leverage firms. Empirical findings: 0 < bdebt < .5. FIN 591: Financial Fundamentals/Valuation

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

10. SML-Based Cost of Equity • If personal taxes ignored (NTA = 0): E(re) = rf+ bequity [E(rm) - rf ] E(re) = rf+ basset [E(rm) - rf ] + (bequity - basset)[E(rm) - rf ] . Business risk premium Financial risk premium FIN 591: Financial Fundamentals/Valuation

11. SML-Based Cost of Debt • Difficult to measure debt’s beta E(rb) = rf + bdebt [E(rm) - rf]. . FIN 591: Financial Fundamentals/Valuation

12. Pulling It Together for WACC • The result: WACC = rf + [bequitywequity + bdebt (1 - tc) wdebt] [rm - rf ] = rf + basset [rm - rf ]. FIN 591: Financial Fundamentals/Valuation

13. 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/Valuation

14. 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/Valuation

15. Solutions to OptimalCapital 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/Valuation

16. 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/Valuation

17. An Optimal Capital Structure 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 Capital structure which maximizes firm value: VL = Vu + PVTS - PVFD - PVAC. FIN 591: Financial Fundamentals/Valuation

18. The End FIN 591: Financial Fundamentals/Valuation