Example Of Case Study On We Know That:

Varying Coupons

The ABC Corporation issues a very unusual type of bond on July 1, 2010. It is issued in units where the face amount is $1000 and the redemption amount is $1500 at July 1, 2020. Semi-annual coupons are payable January 1 and July 1 an are as follows:
What should the initial offering price per unit be if the yield to maturity is to be 10% per annum compound semi-annually?

Hence:
YTM=10*21000x-1=0.12=0.05x≈$376.89

The initial offering price per unit must be $376.89

b) Is this a premium or a discount? Specify the amount.
Since the payments for semi-annual coupons are started from $60 (which is 6% of the face amount, and this is bigger than YTM), hence this is premium.
c) If a purchaser on July 1, 2014, buys a bond at a price as calculated in a), then sells one unit of the bond at July 1, 2016, for $1300, what interest rate j2 would be realized?

PV of the redemption value on July 1, 2014, is:

PV=15001+0.126*2≈835.26

PV of all coupons on July, 2014, is:

PV=72+761+0.051+761+0.052+801+0.053+801+0.054+841+0.055+841+0.056+881+0.057+881+0.058+921+0.059+921+0.0510+961+0.0511+961+0.0512≈824.21

Then PP on July, 1, 2014, us:

PP=835.26+824.21=$1,659.47
1,659.47-376.89=1282.58

PV of the redemption value on July 1, 2016, is:

PV=15001+0.124*2≈1015.26

PV of all coupons on July, 2016, is:

PV=80+841+0.051+841+0.052+881+0.053+881+0.054+921+0.055+921+0.056+961+0.057+961+0.058≈658.54
PP=1015.26+658.54=1,673.8
1,673.8+13001+0.054*2=2553.69
2553.691282.58-1≈0.9911
j2=0.99112=.49555=49.56%