Question

Aligram Software Ltd has five million shares outstanding and its market price is $61 per share. The company has only two bonds outstanding. Bond A is a 15-year bond issued four years ago, which has a face value of $100 million and a coupon rate of 5%, and is selling for 95% of the par value. Bond B is a five-year bond issued one year ago, which has a face value of $60 million and a coupon rate of 6.5%, and is sel ling for 103% of the par value. Both bonds pay coupon semiannually.

a What are the company’s capital structure weights (both equity and debt) on a market value basis?

b If the cost of equity is 11%, and the tax rate is 15%, what is the company’s Weighted Average Cost of Capital (WACC)?

Answer 1

a

MV of equity=Price of equity*number of shares outstanding

MV of equity=61*5000000

=305000000

MV of Bond1=Par value*bonds outstanding*%age of par

MV of Bond1=1000*100000*0.95

=95000000

MV of Bond2=Par value*bonds outstanding*%age of par

MV of Bond2=1000*60000*1.03

=61800000

MV of firm = MV of Equity + MV of Bond1+ MV of Bond 2

=305000000+95000000+61800000

=461800000

Weight of equity = MV of Equity/MV of firm

Weight of equity = 305000000/461800000

W(E)=0.6605

Weight of debt = MV of Bond/MV of firm

Weight of debt = 156800000/461800000

W(D)=0.3395

b

Cost of debt

Bond1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =11x2

950 =∑ [(5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^11x2

k=1

YTM1 = 5.6154496239

Bond2

K = Nx2

Bond Price   =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =4x2

1030 =∑ [(6.5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^4x2

k=1

YTM2 = 5.65

Firm cost of debt=YTM1*(MV bond1)/(MV bond1+MV bond2)+YTM2*(MV bond2)/(MV bond1+MV bond2)

Firm cost of debt=5.6154496239*(95000000)/(95000000+61800000)+5.65*(95000000)/(95000000+61800000)

Firm cost of debt=5.63%

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 5.63*(1-0.15)

= 4.7855

WACC=after tax cost of debt*W(D)+cost of equity*W(E)

WACC=4.79*0.3395+11*0.6605

WACC =8.89%