Question

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 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?

i have the answer for this question. it was:

Vl= (80,000*42) + (0.34*1M) = 3.7M   

Ve= 3.7m - Debt 1m= 2.7M

that was the answers, but i have two doubts here:

first: from what i know, Vl=Vu + tax shield. and Vu is, suppose perpetual cash flow is: EBIT* (1-T)/ R0 then we add D*T (TAX shild)

why in this question above the VL= market capt + Tax shield? ( why market cap not EBIT*(1-T)/ R0 ?

second doubt: what is Ve ? why it is VL- Debt ? (what does Ve stand for, why do we do that in this question?)

Answer 1

(1)

you already know that ,

Vl=Vu + tax shield

where ;

Vl = value of levered firm

Vu = value of unlevered firm

now when you calculate Vu , you are basically calculating value of the firm as if it had no debt and the firm were an all-equity firm. From this we know that Vu is the value of equity of the firm or the value of the firm since it had only equity in its capital structure

Now, since Vu is the value of equity

And value of equity = No. of shares outstanding * Current price per share

This is also equal to market capitalization

since EBIT is not given in the question , you cannot calculate Vu by using the formula :  EBIT* (1-T)/ R0

(2)

Ve is the value of the equity of the levered firm , that is the value of equity of a firm that has both debt and equity in its capital structure now

Now consider the following equation:

Total value of levered firm( Vl) = Value of equity + value of debt

from the above equation

Value of equity = Total value of levered firm - value of debt

since we now want to calculate value of equity of a firm which has both debt and equity , we will take the value of levered firm (Vl) calculated from the first equation ,Vl=Vu + tax shield, and subtract the value of debt given in the question from Vl to get the value of equity of the firm when it includes debt in its capital structure