Question

Assume that there is corporate tax but no other frictions. Based on the propositions of Modigliani and Miller, which statement is least accurate:

a. The optimal structure is 100%

b. The cost of equity increases as the leverage ratio increases

c. The cost of debt increases as leverage ratio increases

d. The weighted cost of capital decreases as the leverage ratio increases

e. Firm value increases as the firm takes on more debt

Answer 1

Answer is c. The cost of debt increases as leverage ratio increases

a. Modigliani Miller (MM) proposition with taxes and no other frictions states that value is maximised at 100% debt. Interest payments on debt are a pretax expense and thus reduces the tax burden on the company which is known as tax shield. This tax shield from debt increases as the proportion of debt increases and the firm value is maximised at 100% debt.

Vl = Vu + t * d

Vl = value of levered firm

Vu = value of unlevered firm

t = marginal tax rate

d = value of debt in capital structure

b. As per the MM proposition with taxes and no other frictions, the cost of equity does increase as the leverage ratio increases. Since debtholders have a priority claim on assets and income, the risk for debtholders and thereby the cost of holding debt is lower compared to the cost of holding equity. If debt increases, leading to higher leverage ratio, debtholders would have higher claim on assets and income, thus the risk to equity holders or the cost of equity increases.

c. The cost of debt does not change as it is assumed that there is no cost of financial distress in this MM theory. cost of debt increases only if there is cost of financial distress due to additional debt in the firm. This assumption of increasing cost of debt due to higher cost of financial distress is reflected in the static trade-off theory but not in the MM with taxes and no friction theory.

d. The weighted average cost of capital for a firm using MM propostion with taxes:

rwacc = D / V * rd * (1-t) + E / V * re

rwacc = weighted average cost of capital

rd = cost of debt

t = marginal tax rate

re = cost of equity

D = value of debt in the firm

E = value of equity in the firm

Thus, as leverage increases, D / V increases and the lower cost of debt rd has higher weight in the WACC calculation thereby increasing the weighted average cost of capital

e. Firm value is obtained by discounting the future cash flows by the weighted average cost of capital. Since WACC decreases as leverage ratio increases, the firm value increases as firm takes on more debt.