The Gift Mart is an all-equity firm with a current cost of equity of 19.6 percent. The estimated earnings before interest and taxes are $239,000 annually forever. Currently, the firm has no debt but is in the process of borrowing $400,000 at 9.5 percent interest. The tax rate is 30 percent. What is the value of the unlevered firm?

Question

Quizplus · Accepted Answer

First, we need to calculate the value of the firm with debt. We can use the WACC formula for this:

WACC = (E/V) x Re + (D/V) x Rd x (1 - Tc)

Where:
E/V = percentage of equity in the capital structure
Re = cost of equity
D/V = percentage of debt in the capital structure
Rd = cost of debt
Tc = corporate tax rate

We can assume that the firm's capital structure will be 100% debt after borrowing $400,000. Therefore, E/V = 0 and D/V = 1.

WACC = (0/1) x 0.196 + (1/1) x 0.095 x (1 - 0.30) = 0.1235 or 12.35%

Next, we can use the perpetuity formula to calculate the value of the firm:

PV = EBIT / WACC

PV = $239,000 / 0.1235 = $1,934,866.22

Finally, we need to remove the value of debt from this amount to get the unlevered firm value:

Unlevered firm value = $1,934,866.22 - $400,000 = $1,534,866.22, which is closest to option B, $853,571.

The Gift Mart Is an All-Equity Firm with a Current