# Leverage and Optimal Capital Structure

Two firms, No Leverage, Inc., and High Leverage, Inc, have equal levels of operating risk and differ only in their capital structure. No Leverage is unlevered and High Leverage has $500,00 of perpetual debt in its capital structure. Assume that the perpetual annual income of both firms available for stockholders is paid out as dividends. Hence, the growth rate for both firms is zero. The income tax rate for both firms is 40 percent. Assume that there are no financial distress costs or agency costs. Given the following data:

No Leverage Inc High Leverage Inc

Equity in capital structure $1,000,000 $500,000

Cost of equity Ke 10% 13%

Debt in capital structure - $500,000

Pretax cost of debt, Kd - 7%

Net operating income (EBIT) $100,000 $100,000

determine the:

a. Market value of No Leverage, Inc

b. Market value of High Leverage, Inc

c. Present value of the tax shield to High Leverage Inc.

Jersey Computer Company has estimated the costs of debt and equity capital (with bankruptcy and agency costs) for various proportions of debt in its capital structure:

Proportion of debt After tax cost Debt Ki Cost of Equity Ke

0.00 - 12.0%

0.10 4.7% 12.1%

0.20 4.9% 12.5%

0.30 5.1% 13.0%

0.40 5.5% 13.9%

0.50 6.1% 15.0%

0.60 7.5% 17.0%

a. Determine the firm's optimal capital structure, assuming a marginal income tax rate (T) of 40 percent.

b. Suppose that the firm's current capital structure consists of 30 percent debt (and 70 percent equity). How much higher is its weighted cost of capital than at the optimal capital structure?

#### Solution Preview

a. Market value of No Leverage, Inc

Since all income is paid out as dividend and the growth rate is zero, the income stream is a perpetuity and the market value would be the present value of the perpetuity.

For a perpetuity the present value = Annual income/required return

For no leverage, the required return would be the cost of equity as there is no debt in the capital structure.

The net income would be EBIT X (1-tax rate) as there is no interest

Net Income = 100,000 X (1-0.4) = 60,000

Required ...

#### Solution Summary

The solution explains how to determine the market value of a firms differing in leverage and how to determine the optimal capital structure