816  Appendix D To simplify the expression further, divide both the numerator and denomina- tor of the complex fraction by kd: E k k D V k t d u d u d NI PE PE + = + − −    ( ) 1 1 1 1 Finally, multiply the numerator and denominator of the second term by -1: E k k D V k t d d u d u NI PE PE + = + −     ( ) − 1 1 1 1 As this final equation shows, a company’s P/E is a function of its unle- vered P/E, its cost of debt, and its debt-to-value ratio. When the unlevered P/E equals the reciprocal of the cost of debt, the numerator of the second frac- tion equals zero, and leverage has no effect on the P/E. For companies with large unlevered P/Es, P/E systematically increases with leverage. Conversely, companies with small unlevered P/Es would exhibit a drop in P/E as lever- age rises. 817 Appendix E Other Capital Structure Issues This appendix discusses alternative models of capital structure and credit rating estimations. These models offer some interesting insights but tend to be less useful in practice for designing a company’s capital structure. Finally, the appendix shows the similarities and differences between widely used credit ratios such as leverage, coverage, and solvency. Pecking-Order Theory An alternative to the view that there are trade-offs between equity and debt is a school of thought in finance theory that sees a pecking order in financing.1 According to this theory, companies meet their investment needs first by using internal funds (from retained earnings), then by issuing debt, and finally by is- suing equity. One of the causes of this pecking order is that investors interpret financing decisions by managers as signals of a company’s financial prospects. For example, investors will interpret an equity issue as a signal that manage- ment believes shares are overvalued. Anticipating this interpretation, rational managers will turn to equity funding only as a last resort, because it could cause the share price to fall. An analogous argument holds for debt issues, although the overvaluation signal is much smaller because the value of debt is much less sensitive to a company’s financial success.2 1 See G. Donaldson, “Corporate Debt Capacity: A Study of Corporate Debt Policy and the Determina- tion of Corporate Debt Capacity” (Harvard Graduate School of Business, 1961); and S. Myers, “The Capital Structure Puzzle,” Journal of Finance 39, no. 3 (1974): 575–592. 2 An exception is, of course, the value of debt in a financially distressed company. 818  Appendix  E According to the theory, companies will have lower leverage when they are more mature and profitable, simply because they can fund internally and do not need any debt or equity funding. However, evidence for the theory is not conclusive. For example, mature companies generating strong cash flows are among the most highly leveraged, whereas the pecking-order the- ory would predict them to have the lowest leverage. High-tech start-up com- panies are among the least leveraged, rather than debt loaded, as the theory would predict.3 Empirical research shows how the signaling hypotheses un- derlying the pecking-order theory are more relevant to financial managers in selecting and timing specific funding alternatives than for setting long-term capital structure targets.4 Surveys among financial executives confirm these findings.5 Market-Based Rating Approach Alternative metrics to credit ratings have been developed based on the notion that equity can be modeled as a call option on the company’s enterprise value, with the debt obligations as the exercise price.6 Using option valuation models and market data on price and volatility of the shares, these approaches esti- mate the future probability of default—that is, the probability that enterprise value will be below the value of debt obligations.7 The advantage is that all information captured by the equity markets is directly translated into the de- fault estimates. Traditional credit ratings tend to lag changes in a company’s performance and outlook because they aim to measure credit quality “through the cycle”8 and are less sensitive to short-term fluctuations in quality. The disadvantage of market-based ratings is that no fundamental analysis is performed on the company’s underlying business and financial health. If 3 See M. Barclay and C. Smith, “The Capital Structure Puzzle: The Evidence Revisited,” Journal of Ap- plied Corporate Finance 17, no. 1 (2005): 8–17; and M. Baker and J. Wurgler, “Market Timing and Capital Structure,” Journal of Finance 52, no. 1 (2002): 1–32. 4 See also A. Hovakimian, T. Opler, and S. Titman, “The Debt-Equity Choice,” Journal of Financial and Quantitative Analysis 36, no. 1 (2001): 1–24, for evidence that the pecking-order theory predicts short- term movements in corporate debt levels but that long-term changes are more in line with the trade- offs discussed earlier in this section. 5 J. Graham and H. Campbell, “How Do CFOs Make Capital Budgeting and Capital Structure Deci- sions?” Journal of Applied Corporate Finance 15, no. 1 (2002): 8–23. 6 This is because equity is a residual claim on the enterprise value after payment of principal and in- terest for debt. It has value only to the extent that enterprise value exceeds debt commitments. See R. Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance 29 (1974): 449–470; or for an introduction, R. Brealey, S. Myers and F. Allen, Principles of Corporate Finance, 13th ed. (New York: McGraw-Hill, 2020), chap. 23. 7 See P. Crosbie and J. Bohn, “Modeling Default Risk” (Moody’s KMV White Paper, December 2003). 8 See E. Altman and H. Rijken, “How Rating Agencies Achieve Rating Stability,” Journal of Banking and Finance 28, no. 11 (2004): 2679–2714.