Question

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)?

Important: please show formulas and explain your answers/calculations thoroughly

Answer 1

Firstly we will calculate the Market value of debt :-

Market value of debt = Present value of all cash outflows from the bond

Here 18 half yearly payments and at end of ninth year face of debt paid that is 2,000,000

Haft yearly interest payment = 2,000,000 * 4% /2 = 40,000

Here dicount rate is used current yield on bond 3%, half yearly payments involves discount rate = 3%/ 2 = 1.5%

Market value of debt = Half yearly interest payment * PVAF(1.5%,18 periods) + 2,000,000 * PVF ( 1.5% , 18 periods)

= 40,000 * [ 1 - 1/( 1.015)18 ] / 0.015 + 2,000,000 / (1.015)18

= 40,000 * 15.67256 + 2,000,000 / 1.307341

Market value of debt = $ 2,156,725.61

market value of equity = $ 3,200,000

total value of firm = $ 5,356,725.61

Weight of equity = Market value of equity / total value of firm = 3,200,000 / 5,356,725.61 = 0.5974

Weight of debt =  1 - weight of equity = 1 - 0.5974 = 0.4026

Calculation of cost of debt after tax :-

After tax cost of debt = Current yield on debt * ( 1 - tax rate ) = 3% * ( 1 - 0.30) = 2.1%

Calculation of the cost of equity :-

Cost of equity = Rf + Beta * ( Rm - Rf) = 2% + 0.60 * ( 9% - 2%) = 2% + 4.2% = 6.2%

Calculation of the Weighted average cost of capital :-

Component	Cost	Weight	WACC
Debt	2.10%	0.4026	0.8455%
Equity	6.20%	0.5974	3.7039%
WACC	4.5493%