Question

Great Lakes Packing has two bond issues outstanding. The first issue has a coupon rate of 3.78 percent, a par value of $1,000 per bond, matures in 4 years, has a total face value of $5.0 million, and is quoted at 105 percent of face value. The second issue has a coupon rate of 6.55 percent, a par value of $1,000 per bond, matures in 16 years, has a total face value of $9.3 million, and is quoted at 107 percent of face value. Both bonds pay interest semiannually. The company's tax rate is 39 percent. What is the firm's weighted average aftertax cost of debt?

Multiple Choice 2.70% 2.54% 4.69% 3.78% 2.94%

Answer 1

Yield – to – Maturity of the Bond (YTM)

YTM = {C+(F - P)/n} / {(F + P)/2}

Where C = Coupon amount

F = Face value

P = Market price

N= Maturity period

Bond I:

= {18.90 + (1000 – 1050)/8} / {1000 + 1050/2}

= (18.90 – 6.25) / 1025

= 1.23% semi annually i.e. 2.46%

Bond II:

= {32.75 + (1000 – 1070)/32} / {1000 + 1070/2}

= (32.75 – 2.19) / 1035

= 2.95% semi annually i.e. 5.90%

Market value of Bond I = $5 millions *1.05=$5.25 millions

Market value of Bond II = $9.3 millions *1.07=$9.95 millions

Weighted average cost of debt = Wd1*Kd1+Wd2*Kd2

Where Wd1=5.25/15.20 =0.35

Kd1 = 2.46%

Wd2=9.95/15.20 =0.65

Kd2 = 5.90%

Weighted average cost of debt = 0.35*2.46%+0.65*5.90%

= 4.69%