Importance The research discusses the principles businesses should follow to choose the capital structure and make it optimal in line with their bankruptcy risks. Objectives The research pursues modifying the Modigliani-Miller theory on the basis of realistic assumptions so to update it in terms of the bankruptcy risk. Methods Using mathematical methods, I modified the classical theory of capital structure in line with the bankruptcy risk. Two obvious assumptions are used instead of those in the Modigliani-Miller theory, i.e. estimation of the complete business value using free cash flow and estimation of the weighted average cost of capital (WACC). Furthermore, to assess the required rate of return on equity, the Capital Asset Pricing Model and the Hamada equation are needed. To consider the bankruptcy risk, it is necessary to introduce WACC of adjustments associated with the risk for the required rate of return of equity and debt. Results I figured out the optimality requirements for the capital, considering the default risk. The optimal capital structure depends on the investor's sensitivity to a new debt issuance, which can result both from an increase of bankruptcy probability and reduction of debt security. The article illustrates simple criteria for determining the optimal capital structure in line with the bankruptcy risk, and provides an empirical evaluation of the average sensitivity of the investor per three sectors. Conclusions and Relevance As for the interest-bearing debt, which does not exceed the maximum security level, the principle pronouncements of the classical theory of capital structure remain valid, with the optimal structure of capital being attainable at the maximum security level of the debt. When the risk is higher than the security level, business value can grow only if investors demonstrate low sensitivity to the debt increase.
Keywords: financial risk, bankruptcy risk, capital structure, Weighted Average Cost of Capital, business value
References:
Pagano M. The Modigliani–Miller Theorems: A Cornerstone of Finance. University of Salerno, Working Paper, 2005, no. 139.
Sharpe W.F., Aleksander G.J., Bailey J.V. Investitsii [Investments]. Мoscow, INFRA-М Publ., 2006, 1028 p.
Stiglitz J. A Re-Examination of the Modigliani–Miller Theorem. American Economic Review, 1969, vol. 59, no. 5, pp. 784–793.
Fama E., French K. Testing Trade-Off and Pecking Order Predictions about Dividends and Debt. Review of Financial Studies, 2002, vol. 15, iss. 1, pp. 1–33.
Teplova T., Shutova E. A Higher Moment Downside Framework for Conditional and Unconditional CAPM in the Russian Stock Market. Eurasian Economic Review, 2011, no. 2, pp. 157–178.
Miller M. The Modigliani–Miller Proposition after Thirty Years. Journal of Economic Perspectives, 1988, vol. 2, no. 4, pp. 99–120.
Modigliani F., Miller M. Some Estimates of the Cost of Capital to the Electric Utility Industry 1954–1957. American Economic Review, 1966, pp. 261–297.
Altman E., Kishore V. Almost Everything You Wanted to Know about Recoveries on Defaulted Bonds. Financial Analysts Journal, 1996, vol. 52, no. 6, pp. 57–64.
Altman E. Financial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy. The Journal of Finance, 1968, vol. 23, no. 4, pp. 589–609.
Koller T., Goedhart M., Wessels D. Valuation: Measuring and Managing the Value of Companies. McKinsey & Company, John Wiley & Sons, Inc., 2010, 836 p.
Zhukov P.E. Default Risk and Its Effect for a Bond Required Yield and Volatility. Review of Business and Economic Studies, 2014, no. 4, pp. 87–98.
Myers S. The Capital Structure Puzzle. Journal of Finance, 1984, vol. 39, iss. 3, pp. 575–592.
Brealey R., Myers S., Allen F. Principles of Corporate Finance. 10th ed. New York, McGraw-Hill, 2010.
Myers S. Capital Structure. The Journal of Economic Perspectives, 2001, vol. 15, no. 2, pp. 81–102.
Repin D.V., Solodukhina A.V. V poiskakh resheniya zagadki struktury kapitala: povedencheskii podkhod [Trying to read a riddle of the capital structure: a behavioral approach]. Korporativnye finansy = Journal of Corporate Finance Research, 2008, no. 1, pp. 104–119.
Hamada R. The Effect of the Firm's Capital Structure on the Systematic Risk of its Common Stocks. Journal of Finance, 1972, vol. 27, iss. 2, pp. 435–440.
Zhukov P.E. Vliyanie finansovykh riskov korporatsii na stavku diskontirovaniya i veroyatnost' bankrotstva [Financial risks of corporation, discount rates, and default probability]. Nauchno-issledovatel'skii institut. Finansovyi zhurnal = Financial Research Institute. Financial Journal, 2013, no. 2, pp. 55–63.
Denzler S., Dacorogna M., Müller U., McNeil A. From Default Probabilities to Credit Spreads: Credit Risk Models Do Explain Market Price. Finance Research Letters, 2006, vol. 3, no. 2, pp. 79–85.
Cochrane J.H. Presidential Address: Discount Rates. The Journal of Finance, 2011, vol. 66, iss. 4, pp. 1046–1108.
Merton R. On the Pricing of Corporate Debt: The Risk Structure of Interest Rate. Journal of Finance, 1974, vol. 29, no. 2, pp. 449–470.
Modigliani F., Miller M. Corporate Income Taxes and the Cost of Capital: A Correction. American Economic Review, 1963, vol. 53, no. 3, pp. 147–175.
