Question

alberto anonymizers inc has a debt-equity ratio of 1.75. if the firm had zero debt, the cost of equity would be 9%. its cost of debt is 7% and tax rate is 50%. what is the cost of equity with the current capital structure?

Answer 1

To calculate the cost of equity with a debt-equity ratio of 1.75, the formula from the Modigliani-Miller theorem is used. Assuming a tax rate of 50% and an initial cost of equity of 9%, the calculation yields a new cost of equity of 18.625% with the current capital structure.

Step-by-step explanation:

The question involves calculating the cost of equity for a company with a debt-equity ratio of 1.75, given the cost of debt and the tax rate. To find the cost of equity with the company's current capital structure, we need to apply the Modigliani-Miller theorem with tax considerations, also known as the MM Proposition II with taxes.

Let E represent the cost of equity with no debt (9%), D represent the cost of debt (7%), T represent the tax rate (50%), and Re represent the cost of equity with the current capital structure. According to the MM Proposition II formula:

Re = E + (E - D(1-T))(Debt/Equity)

We are given the debt-equity ratio, which is 1.75. Using the formula, we substitute the values as:

Re = 9% + (9% - 7%(1-0.5))(1.75)

After calculating:

Re = 9% + (9% - 3.5%)(1.75)

Re = 9% + 9.625%

Re = 18.625%

So the cost of equity with the current capital structure is 18.625%.