Question

he Tree House has a pretax cost of debt of 6.2 percent and a return on assets of 10.9 percent. The debt–equity ratio is .55. Ignore taxes. What is the cost of equity? Multiple Choice 14.71% 13.49% 14.16% 13.92% 8.32%

Answer 1

Solution:
	Answer is 2nd option 13.49%
Working Notes:
	Using M&M Proposition II with taxes
	RS = R0+ (R0-RB)(B/S)(1- Tc)
	Where
	B/s = debt equity ratio =0.55
	RS is cost of equity capital levered = cost of equity =??
	R0 is cost of equity capital of unlevered firm = Return on assets =10.9%
	RB is Cost of Borrowing = 6.2%
	Tc = tax rate = 0%
	RS= R0+ (R0-RB)(B/S)(1-Tc)
	Rs =10.9% + (10.9% - 6.2%) x (0.55) x ( 1- 0.0)
	Rs =10.9% + (4.7%) x (0.55)
	Rs =10.9% + 2.585%
	Rs =13.485%
	Rs =13.49%
Alternatively we can also calculate using WACC method
	Cost of Equity Ke =??
	debt equity ratio = 0.55
	Weight of Debt = D/(E+D) = 0.55/ (1 +0.55) =0.55/1.55
	Weight of Equity = E / (E +D) =1/(1+0.55) = 1/1.55
	E+D = V = 1+ 0.55 = 1.55
	Cost of debt Kd=6.2%
	Tax rate = 0% as say ignore
	WACC = cost of capital for the firm in other words the firm is generating the rate of return on its assets = 10.9%
	WACC = (E/V)Ke + (D/V) (1 -Tax rate) Kd
	10.9 % = (1 /1.55) x Ke + (0.55 /1.55) x 6.2% x ( 1 -0)
	10.9 % = (1 /1.55) x Ke + 2.2%
	Ke = (10.9% - 2.2%) x 1.55
	Ke = (10.9% - 2.2%) x 1.55
	Ke = 13.485%
	Ke = 13.49%
	Cost of equity Ke = 13.49%
Please feel free to ask if anything about above solution in comment section of the question.