Question

Question 4 (15%)

The AirJet Service Company’s bonds have four years remaining to maturity. Interest is paid semiannually; the bonds has a $1000 face value and the coupon interest rate is 9% compounded semiannually. Knowing that the next payment is due today and you want to make 10% compounded monthly, how much would you be willing to pay for this bond?

Answer 1

Effective Annual Interest Rate =(1+i/n)^n-1 =(1+10%/12)^12-1=(1+0.83%)^12-1 = 1.0083^12-1=1.1047-1=0.1047 or 10.47%

Effective Seminannual Rate = 10.47%/2 =5.235%

Seminannual Interest rate = 9%/2 =4.5%

Hence Semi Annual Coupon Amount = 4.5%*1000=$45

PV of coupon payments over 4 years (4*2 =8 periods)= A*(1-(1+r)^-n)/r

=45*(1-(1+5.235%)^-8)/5.235%

=45*(1-1.05235^-8)/0.05235

=45*(1-0.6648)/0.05235

=45*0.3352/0.05245

=$281.94

PV of coupon payments including today's payment = 281.94+45 = $326.45

PV of Face value = 1000/(1+10.47%)^4 = 1000/1.1047^4=1000/1.4893=$671.46

Hence Total Bond Value = 326.94+671.46=$998.40