Question

Company P's market value of equity is $10120 million and the company has no debt. Suppose that Company P decides to borrow $1470 million at an interest rate of 4.8% and use the proceeds to perform a share buyback. Following the debt issuance and share repurchase Company P will maintain the same dollar amount of debt in perpetuity. Without any debt Company P's cost of equity is 8.1%. The corporate tax rate is 21%.

Subsequent to borrowing and repurchase of shares, what is Company P's cost of equity?

A: between 7.10% and 7.50%

B: between 7.50% and 7.90%

C: between 7.90% and 8.30%

D: between 8.30% and 8.70%

E: between 8.70% and 9.10%

F: answer not in this range.

Answer 1

As per Modigilani Approach Preposition I (With No Taxes), value of the enterprise does not depend on the capital structure of the firm. This preposition assumes no tax environment. The approach assumes that any reduction on cost of debt, in turn increases the cost of equity such that overall cost of capital is unchanged thereby the value of the firm is unchanged.

Cost of Levered Equity = Cost of Unlevered Equity + Debt / Equity (Cost of un-levered equity - Cost of Debt)

Under the Modigilani Approach Preposition I (With No Taxes), the value of the firm will increase if the tax picture is considered. Hence value of firm will only increase by the tax portion of debt. The second preposition states that, the cost of equity has a direct relation with the level of debt. As level of debt increases, the default risk increases so does the cost of equity. However, it should be noted that the tax shield available due to taxes makes it less sensitive to changes in level of debt.

Cost of Levered Equity = Cost of Unlevered Equity + {Debt (1- Tax)  / Equity} * (Cost of unlevered equity - Cost of Debt)

Hence we solve,

Cost of levered equity = 8.1 + {1470 (1- 0.21) / (10120 - 1470)} * (8.1 - 4.8)

= 8.1 + 1161.3 / 8650 * 3.3

= 8.1 + 0.4430

= 8.54%

Hence correct option D between range of 8.30% and 8.70%