Question

An unlevered company with a cost of equity of 11% generates $8 million in earnings before interest and taxes (EBIT) each year. The decides to alter its capital structure to include debt by adding $4 million in debt with a pre-tax cost of 7% to its capital structure and using the proceeds to reduce equity by a like amount as to keep total invested capital unchanged. The firm pays a tax rate of 35%.

Assuming that the company's EBIT stream can be earned into perpetuity and that the debt can be perpetually issued (or rolled), what will be the firm's new cost of equity?

An unlevered company (just common stock, no preferred) with a cost of equity of 13% generates $5 million in earnings before interest and taxes (EBIT) each year. The decides to alter its capital structure to include debt by adding $4 million in debt with a pre-tax cost of 7% to its capital structure and using the proceeds to reduce equity by a like amount as to keep total invested capital unchanged. The firm pays a tax rate of 33%.

Assuming that the company's EBIT stream can be earned into perpetuity and that the debt can be perpetually issued (or rolled), what is the firm's new weighted average cost of capital?

Answer 1

All financials are in $ million.

Value of the unlevered firm = V_ul = EBIT x (1 - T) / k_ul = 8 x (1 - 35%) / 11% = 47.27

The decides to alter its capital structure to include debt by adding $4 million in debt with a pre-tax cost of 7% to its capital structure and using the proceeds to reduce equity by a like amount as to keep total invested capital unchanged.

After capital restructuring,

D = 4; E = 47.27 - 4 = 43.27

To find the levered cost of equity we use the M&M Proposition 2 with taxes:

Firm's new cost of equity = Levered cost of equity, k_e = k_ul + [k_ul - k_D] x [D/E] x [1 – t] = 11% + (11% - 7%) x 4/43.27 x (1 - 35%) = 11.24%

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Value of the unlevered firm = V_ul = EBIT x (1 - T) / k_ul = 5 x (1 - 33%) / 13% = 25.77

The decides to alter its capital structure to include debt by adding $4 million in debt with a pre-tax cost of 7% to its capital structure and using the proceeds to reduce equity by a like amount as to keep total invested capital unchanged.

After capital restructuring,

D = 4; E = 25.77 - 4 = 21.77

Wd = D / (D + E) = 15.52%

We = E / (D + E) = 1 - 15.52% = 84.48%

To find the levered cost of equity we use the M&M Proposition 2 with taxes:

Levered cost of equity, k_e = k_ul + [k_ul - k_D] x [D/E] x [1 – t] = 13% + (13% - 7%) x 4/21.77 x (1 - 33%) = 13.74%

Hence, the firm's new weighted average cost of capital, WACC = Wd x k_d x (1 - T) + We x k_e = 15.52% x 7% x (1 - 33%) + 84.48% x 13.74% = 12.33%