Questions: Capital Structure and the Modigliani-Miller Theorems

Question 1

An all-equity firm has a cost of capital r_U = 10%. It borrows half its value at r_D = 5% and uses the proceeds to buy back shares, so D/E = 1. With no taxes, what is the new cost of equity?

• A. 10%
• B. 12.5%
• C. 15%
• D. 20%

Answer: (C)

By MM Proposition II, r_E = r_U + (D/E)(r_U − r_D) = 10% + 1 × (10% − 5%) = 15%. The WACC is 0.5 × 15% + 0.5 × 5% = 10%, unchanged from the all-equity firm.

Question 2

Under the Modigliani-Miller assumptions with no taxes, two firms with identical operating cash flows but different debt levels must have the same total market value.

• T. True
• F. False

Answer: True

If the values differed, investors could buy the cheaper firm's securities and use personal borrowing or lending to replicate the other firm's payoffs, earning an arbitrage profit. Competition removes the gap, so total values are equal.

Question 3

When interest payments are tax-deductible at corporate rate τ_c and the firm keeps permanent debt D, the 1963 Modigliani-Miller result states that firm value equals:

• A. V_U
• B. V_U + τ_c D
• C. V_U − τ_c D
• D. V_U × (1 − τ_c)

Answer: (B)

Each year the firm saves τ_c × r_D × D in taxes. Discounted at r_D as a perpetuity, the present value of these savings is τ_c D, so levered firm value is the unlevered value plus the value of the interest tax shield.

Question 4

If debt creates a tax shield, why do most firms not finance themselves almost entirely with debt?

Model answer: More debt raises the probability and expected cost of financial distress, including legal costs of bankruptcy, lost customers and suppliers, and distorted investment incentives. The tradeoff theory holds that firms choose leverage where the marginal tax benefit of debt equals the marginal expected cost of distress.

Agency costs between shareholders and creditors and the information problems behind pecking-order behavior also limit debt in practice.