Question

FIN Ltd has decided to use the weighted average cost of capital (WACC) to discount the after-tax cash flows associated with project evaluation. You have been given the task of determining the after-tax WACC of the firm. You are informed that FIN Ltd uses the following securities to fund its operations:

• 7,000 individual bonds with a face value of $1000 that will mature in 10 years’ time offer a coupon that is paid half-yearly. The coupon rate for these bonds is 8% per annum. The current market interest rate for these bonds is 9% per annum.

• 500,000 ordinary shares, which recently paid a dividend of 20 cents. Dividends are expected to grow at 5% per annum. The beta of FIN Ltd is 1.2, the risk-free rate is currently 3% per annum, and the expected return on the market is 12% per annum.

• 400,000 preference shares, which pay an annual dividend of 1% on a stated value of $100. Each preference share is trading at a market price of $8.

• The company tax rate is 30 percent.

a) Compute the WACC based on the above information.

Answer 1

C = Semi annual interest rate = $1,000 * 8%/2 = $40

r = semi annual interest rate = 9%/2 = 4.5%

n = 10*2 = 20 compoundings

Market Value of bond = [C * [1 - (1+r)^-n] / r] + [Par value / (1+r)^n]

= [$40 * [1 - (1+4.5%)^-20] / 4.5%] + [$1,000 / (1+4.5%)^20]

= [$40 * 0.58535714 / 0.045] + [$1,000 / 2.41171402]

= $520.317458 + $414.642861

= $934.960319

= $934.96

Cost of equity = ke = risk free rate (rf) + beta *[(market risk rate(rm) - risk free rate(rf)]

= 3% + 1.2 * (12%-3%)

= 3% + 10.8%

= 13.8%

Current dividend = D0 = $0.20

g = growth rate = 5%

Dividend in Year 1 = D1 = D0 * (1+g) = $0.20 * (1+5%) = $0.21

Current Stock price = P0 = D1 / (ke - g)

= $0.21 / (13.8% - 5%)

= $2.38636364

= $2.39

Preference dividend = $100 *1% = $1

rp = Cost of preference stock = Preference dividend / market price of preferecne stock

= $1 / $8

= 0.125

= 12.5%

Market price of bond =MVd = $934.96 * 7,000 = $6,544,720

Market Price of Preference stock = MVp = 400,000 * $8 = $3,200,000

Market price of common stock = MVc = 500,000 * $2.39 = $1,195,000

Total market value =MV = MVd + MVp + MVc = $6,544,720 + $3,200,000 + $1,195,000 = $10,939,720

Weight of bond = Wd = MVd / MV = $6,544,720 / $10,939,720 = 0.598252972 = 0.598253

Weight of Preference stock = Wp = MVp / MV = $3,200,000 / $10,939,720 = 0.292512057 = 0.292512

Weight of Common stock = Wc = MVc / MV = $1,195,000 / $10,939,720 = 0.109234971 = 0.109235

t = tax rate = 30%

WACC = [Wd * rd * (1-t)] + [Wp * rp] + [Wc * ke]

= [0.598253 * 9% * (1-30%)] + [0.292512 * 12.5%] + [0.109235 * 13.8%]

= 3.7689939% + 3.6564% + 1.507443%

= 8.9329376%

Therefore, WACC is 8.93%