Question

Young Corporation has an expected EBIT of $19,750 every year forever. The company currently has no debt, and its cost of equity is 15 percent.

a) What is the current value of the company?

b) Suppose that the company can borrow at 10 percent. If the corporate tax rate is 35 percent what will the value of the firm be if the company takes on debt equal to 50 percent of its unlevered value?

c) Calculate the cost of equity, and WACC after the proposed recapitalization in question b.

Answer 1

(a) current value of the company = EBIT / cost of equity

current value of the company = $19,750 / 0.15

current value of the company = $131667 ( Also Known as Unleveraged Value since company currently has no debt)

(b) Value of Firm = ( EBIT(1 - tax rate) / cost of equity )+ (Tax Rate x Debt Amount)

Since debt is equal to 50 percent of its unlevered value (i.e. 50% of $131667 = $65833)

Therefore :-

  Value of Firm =( $19750(1 - 0.35) / 0.15 ) + (0.35 x $65833)

Value of Firm = $85583 + $23042

  Value of Firm(Leveraged) = $108625

(c) cost of equity after the proposed recapitalization = cost of equity before recapitalization + (cost of equity before recapitalization - cost of debt) x Debt(1 - tax rate) / Equity

cost of equity before recapitalization = 15%

cost of debt = 10%

Debt = $65833

Equity = Value of Firm(Leveraged) in part (b) above - Debt Amount

Equity = $108625 - $65833

Equity = $42792

Therefore :-

cost of equity after the proposed recapitalization = 15 + (15 - 10) x $65833(1 - 0.35) / $42792

cost of equity after the proposed recapitalization = 15 + (5) x 42792 / 42792

cost of equity after the proposed recapitalization = 20%.

WACC after the proposed recapitalization = EBIT(1 - Tax) / Value of Firm(Leveraged)

WACC after the proposed recapitalization =[ $19750 (1 - 0.35) / $108625] x 100

WACC after the proposed recapitalization = 11.82%