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

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%.

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