Question

Question 4. (Total: 25 marks) DEF Company expects an EBIT of $19,750 every year forever. DEF currently has no debt, and its cost of equity is 15 percent. The firm can borrow at 10 percent. T he corporate tax rate is 35 percent . Assume no financial distress risk. a. W hat is the value of the firm with its existing capital structure ? b. What will the value be if the company converts to 50 percent debt? c. What are the cost of equity and WACC if the company converts to 50 perce nt debt? d. What will the value be if the company converts t o 100 percent debt? e. What is the WACC if the company converts to 100 percent debt? f. Compare the firm values and WACCs at 0%, 50%, and 100% debt. What can we conclude regarding the relationship between leverage level, firm value, and WACC? .

Answer 1

(a)

(a)

The cost of equity R = 10%

Value of the unlevered firm = EBIT(1 - tax-rate) / R
Value of the unlevered firm = 19750(1 - 0.35) / 0.15
Value of the unlevered firm = $85,583.33

(b)

Value of levered firm = Valued of unlevered firm + Value of debt*Tax-rate

Value of levered firm = 85,583.33 + 0.5*85,583.33*0.35 = $100,560.42

(c)

Cost of equity = R(Ue) + (D/E) * (R(Ue) - R(d))

R(Ue) is the unlevered cost of equity

Cost of equity = 0.15 + (1*(0.15-0.1)) = 0.2 = 20%

WACC= r(e)*w(e) + r(d)*w(d)*(1-t)

w(e), w(d) are the weights of equity and debt respectively

r(e), r(d) are the returns on equity and debt respectively

WACC = 0.5*0.2 + 0.5*0.1*(1-0.35) = 0.1325 = 13.25%

(d)

Value of levered firm = Valued of unlevered firm + Value of debt*Tax-rate

Value of levered firm = 85,583.33 + 1*85,583.33*0.35 = $115,537.50

(e)

WACC= r(e)*w(e) + r(d)*w(d)*(1-t)

WACC= 0 + 1*0.1*(1-0.35) = 0.065= 6.5%

(f)

Debt%	WACC	Firm value
0	15%	85,583.33
50	13.25%	100,560.4
100	6.50%	115,537.50

As the leverage increases, the WACC decreases (since cost of debt is lower)

As leverage increases, the firm value increases.