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Risk and the Addition of Debt to the Capital Structure

Published online by Cambridge University Press:  19 October 2009

Harold Bierman Jr.
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Extract

This paper investigates how the addition of debt to the capital structure of a corporation affects the risk of the stockholders. In the first instance, we will hold the size of the firm constant and substitute debt for common stock. In the second situation, we will allow firm size to change, and will accomplish the increase in size by issuing debt. For both situations, we will first observe the effect of debt on the earnings per dollar of common stock investment. The analysis could also be made using the number of shares of common stock. Since the number of shares of common stock may be changed quite arbitrarily (as, for example, by stock dividends), we want to make the measure invariant to the number of shares outstanding. We will do this by using value of common stock and value of debt. We are then computing the variance of return on common stock investment when we compute variance of earnings per dollar of common stock investment. After considering how debt affects earnings per dollar of stockholders' investment, we will investigate the effect of debt on the total earnings of the stockholders, and on the probability of a deficit.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 3 , Issue 4 , December 1968 , pp. 415 - 426
Copyright
Copyright © School of Business Administration, University of Washington 1968

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References

1 See Beranek, W., Analysis for FinanciaL Decisions (Homewood, Ill.: Richard D. Irwin, Inc., 1963), pp. 243–248Google Scholar for a similar approach. For a different approach, see Donaldson, G., Corporate Debt Capacity (Boston, Mass.: Harvard Graduate School of Business, 1961).Google Scholar

2 See Appendix 1 to this chapter for a proof.

3 See Appendix 1 to this chapter.

4 The magnitude of the change will depend on the value of Var (X). Different investors will have different estimates of Var (X), and will interpret the issuance of debt differently.

5 See Appendix 2 at the end of this paper. We are assuming that the new earnings will be perfectly correlated with the old earnings. When we substituted debt for common stock, the variance of the earnings was Var(X).l Now that we are adding debt, the variance of the earnings is Var .

6 The advantage of using Chebyshev's inequality is that no assumption has to be made about the probability distribution of earnings.

1 We are assuming that the interest cost is certain even though the payments may be uncertain.