Question

The correct answer to the following question is WACC= 4.55%. Please explain with full details & thank you:

2. A company has a market value of equity of $3,200,000 and one million shares outstanding. The company also has issued bonds with a face value of $2 million. The bonds have a coupon rate of 4% p.a. and coupons are paid every six months. A coupon was just paid today. The bonds were issued five years ago and have a maturity date in exactly nine years' time. The company has a beta of 0.6, the current yield on the bonds is 3% p.a., the return on the market portfolio is 9%, the risk-free return is 2% p.a. and the company tax rate is 30%. What is the company's weighted average cost of capital (WACC)?

Answer 1

1]	After tax cost of debt = Before tax cost*(1-tax rate) = 3%*(1-30%) =	2.10%
	[Before tax cost of debt = Current yield on bonds, which is
	given as 3%]
2]	Cost of equity per CAPM = Risk free rate+beta*(Return on market portfolio-Risk free rate) = 2%+0.6*(9%-2%) =	6.20%
3]	WACC = After tax cost of debt*Weight of debt+Cost of equity*Weight of equity
	The WACC is caculated in the table below:
	Component	Market Value	Weight	Component Cost	WACC
	Debt [calculated below]	$    21,56,726	40.26%	2.10%	0.85%
	Equity [given]	$    32,00,000	59.74%	6.20%	3.70%
	Total	$    53,56,726	100.00%		4.55%
	WACC = 4.55%
	CALCULATION OF MARKET VALUE OF DEBT:
	Market value of debt is the sume of the following:
	a] The maturity value of $2000000 discounted at 1.5% for
	18 half years.
	b] The PV of the half yearly interest of $40000 for 18 half
	years. Those interest payments constitute an annuity.
	The discount rate is 3%/2 = 1.5%.
	Hence, the market value of debt = 2000000/1.015^18+40000*(1.015^18-1)/(0.015*1.015^18) =	$    21,56,726