Gail's Dance Studio is currently an all equity firm that has 80,000 shares of stock outstanding with a market price of $42 a share.The current cost of equity is 12% and the tax rate is 34%.Gail is considering adding $1.25 million of debt with a coupon rate of 8% to her capital structure.The debt will be sold at par value.What is the levered value of the equity?
A)$2.5 million
B)$2.7 million
C)$3.3 million
D)$3.7 million
E)$3.9 million

Question

Quizplus · Accepted Answer

The levered value of the equity is the value of the equity after the debt has been added to the capital structure. To calculate the levered value of the equity, we need to first calculate the value of the debt. The value of the debt is equal to the present value of the coupon payments and the principal payment. The coupon payment is $1.25 million * 8% = $100,000. The principal payment is $1.25 million. The present value of the coupon payments is $100,000 / (1 + 12%)^1 + $100,000 / (1 + 12%)^2 + ... + $100,000 / (1 + 12%)^30 = $1.92 million. The present value of the principal payment is $1.25 million / (1 + 12%)^30 = $342,000. Therefore, the value of the debt is $1.92 million + $342,000 = $2.26 million.The levered value of the equity is equal to the value of the firm minus the value of the debt. The value of the firm is equal to the number of shares outstanding times the market price per share. The number of shares outstanding is 80,000. The market price per share is $42. Therefore, the value of the firm is 80,000 * $42 = $3.36 million. The levered value of the equity is $3.36 million - $2.26 million = $1.1 million.

Gail's Dance Studio Is Currently an All Equity Firm That