Optimal capital structure: Problems with the Harvard and Damodaran Approaches

In this paper we will present an analysis of the optimal capital structure using two examples: one proposed by the Harvard Business School and the other proposed by Damodaran. First, we highlight certain inconsistencies in the debt and equity costs assumed by the Harvard Business School note from a number of viewpoints. We calculate the incremental cost of debt implied in Harvard's note and we find also inconsistencies: surprisingly, the last two debt increments have a cost of 14.75% and 18.5%, while the required return to equity in the unlevered company is 12%. With respect to the cost of debt, the inconsistency is not the cost of debt (the bank can charge whatever interest it likes) but in assuming that the debt's cost is the same as its required return (or that the debt's value equals its nominal value). We also calculate the required return to incremental equity cash flow implied in Harvard's note and we find that the required return first falls, then increases, and then falls again. The required incremental return should fall as the leverage decreases. The probability of bankruptcy almost doubles beyond the optimal capital structure. The difference between the required return to equity and the required return to debt decreases for debt levels above the optimal capital structure. It is also shown that assuming no leverage costs there is no optimal structure (the company's value increases with the debt ratio) and the difference between required return to equity and the required return to debt is constant. Damodaran (1994) offers a similar approach to that of the Harvard Business School note, but applies it to a real company (Boeing in 1990) and assumes a constant cash flow growth. One problem with Damodaran's results is that the value of the firm (D+E) for debt ratios above 70% is less than the value of debt, which implies a negative value for equity. We calculate the incremental cost of debt implied in Damodaran's example. It can be seen that increasing debt to take the debt ratio from 30% to 40% implies contracting that debt at 21.5%, which is an enormous figure. Stranger still is the finding that the next debt increment (which has a higher risk) is cheaper: it costs 19%. An additional error in Damodaran's calculations is that he calculates the WACC using book values in the weighting, instead of market values. It is also shown that if it is assumed that the debt's market value is the same as its book value, then the capital structure that minimizes the WACC also maximizes the share price. However, without this assumption, the minimum value of the WACC may not occur at the same point as the maximum share price.