Question

C.H.Inc currently has no debt and expects to earn $10 million in net operating income each year for the foreseeable future. The required return on assets for companies of this type is 12.5 percent, and the corporate tax rate is 40 percent. There are no taxes on dividends or interest at the personal level. Assume that the managers of this company are weighing two capital structure alteration proposals.

Proposal 1: involves borrowing $20 million at an interest rate of 6 percent and using the proceeds to repurchase an equal amount of outstanding stock. With this level of debt, the likelihood that C.H.Inc will fall into bankruptcy in any given year increases to 15 percent, and, if bankruptcy occurs, it will impose direct and indirect costs totaling $12 million.

Proposal 2: involves borrowing $30 million at an interest rate of 8 percent, also using the proceeds to repurchase an equal amount of outstanding stock. With this level of debt, the likelihood of C.H.Inc falling into bankruptcy in any given year rises to 25 percent, and the associated direct and indirect costs of bankruptcy, if it occurs, increase to $20 million.

For each proposal, calculate the overall value of the firm, assuming that there are no personal taxes on debt or equity income. If necessary, use the industry required return for discounting bankruptcy costs.

Answer 1

All financials below are in $ mn

Value of a levered firm, V_L = Value of unlevered firm, V_U + PV (Interest tax shield) - Probability of bankruptcy x PV (Bankruptcy costs)

V_U = Net operating income x (1 - Tax rate) / Unlevered cost of capital = 10 x (1 - 40%) / 12.5% = 48

PV (Interest tax shield ) = Tax rate x Debt

Under proposal 1: PV (Interest tax shield ) = Tax rate x Debt = 40% x 20 = 8

Under proposal 2: PV (Interest tax shield ) = Tax rate x Debt = 40% x 30 = 12

PV (Bankruptcy costs) = Bankruptcy cost / Pre tax cost of debt

Under proposal 1: PV (Bankruptcy costs) = Bankruptcy cost / Pre tax cost of debt = 12 / 6% = 200 and Probability of bankruptcy = 15%

Under proposal 2: PV (Bankruptcy costs) = Bankruptcy cost / Pre tax cost of debt = 20 / 8% = 250 and Probability of bankruptcy = 25%

Hence:

Proposal 1:

The overall value of the firm, V_L = V_U + PV (Interest tax shield) - Probability of bankruptcy x PV (Bankruptcy costs) = 48 + 8 - 15% x 200 = 26

Proposal 2:

The overall value of the firm, V_L = V_U + PV (Interest tax shield) - Probability of bankruptcy x PV (Bankruptcy costs) = 48 + 12 - 25% x 250 = - 2.50