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Hilltop Paving has a levered equity cost of capital of 14.92 percent. The debt-to-value ratio is .4, the assumed tax rate is 23 percent, and the pretax cost of debt is 7.2 percent. What is the estimated unlevered cost of equity

Respuesta :

Answer:

The estimated unlevered cost of equity is 12.30%.

Explanation:

Debt-to-value ratio = 0.4

Equity-to-value ratio = 1 - Debt-to-value ratio = 1 - 0.4 = 0.6

The estimated unlevered cost of equity can be calculated solving the following formula:

Levered equity cost of capital = Unlevered cost of equity + ((Debt-to-value ratio / Equity-to-value ratio) * (100% - Tax rate) * (Unlevered cost of equity - Pretax cost of debt)) .............. (1)

Substituing all the relevant values into equation (1), we have:

14.92% = Unlevered cost of equity + ((0.4/0.6) * (1 - 23%)  * (Unlevered cost of equity - 7.2%))

Let R0 = Unlevered cost of equity, we have:

14.92% = R) + ((0.4/0.6) * (1 - 23%)  * (R0 - 7.2%))

14.92% = R0 + (0.666666666666667 * 0.77 * (R0 - 7.2%))

14.92% = R0 +  (0.513333333333334 * (R0 -7.2%))

14.92% = R0 +  (0.513333333333334 * R0) - (0.513333333333334 * 7.2%)

14.92% = R0 +  (0.513333333333334 * R0) - 0.03696

14.92% + 0.03696 = R0(1 + 0.513333333333334)

0.18616 = R0(1.513333333333334)

R0 = 0.18616 / 1.513333333333334

R0 = 0.1230, or 12.30%

Therefore, the estimated unlevered cost of equity is 12.30%.