Spectronix Inc.operates in a world of perfect capital markets,has no debt,and has a required rate of return on equity of 10%.An executive manager has suggested that borrowing money to buy back outstanding stock is a good idea because it would replace equity financing with less expensive debt financing,thus increasing the value of the firm.Assume the firm issues new debt with a required return of of 5% to repurchase 30% of the outstanding stock.What is the cost of equity at the conclusion of this transaction?
A)21.67%
B)12.14%
C)16.43%
D)45.00%

Question

Quizplus · Accepted Answer

In a world of perfect capital markets, the Modigliani-Miller theorem (without taxes) suggests that the value of the firm is not affected by its capital structure. The cost of equity increases when debt is introduced because equity becomes riskier. The new cost of equity can be calculated using the formula: $r_E = r_0 + (r_0 - r_D) \times (D/E)$, where $r_0$ is the unlevered cost of equity (10%), $r_D$ is the cost of debt (5%), and $D/E$ is the debt-to-equity ratio after the transaction. After repurchasing 30% of the outstanding stock, the debt-to-equity ratio becomes 0.3/0.7 = 0.4286. Plugging these values into the formula gives: $r_E = 10\% + (10\% - 5\%) \times 0.4286 = 12.14\%$.