Q no.1. What will be the relationship among coupon rate, current yield, and yield to maturity for bonds selling at discounts from par? (Marks=2)
If bond is selling at discount then :
Coupon rate < Current Yield < Yield to maturity
You can convert this equation in your own wordings.
Q no.2. Illustrate the aforementioned relationship and provide supporting calculations using the 8% (semiannual payment) coupon, 30-year maturity bond with par value of Rs.1,000 paying 60 semiannual payments of Rs 40 each assuming it is selling at a yield to maturity of 10%. (Marks=8).
If we treat it as annuity then this formulas will be used:
Bond Price = C*{1-(1/1+r)2*n)/r} +par/(1+r)2*n
=40*{1-(1/1+.05)60/.05 +1000/(1+.05)60
= 40*(1-0.054/.05) +1000/ 18.68
=40*18.92 + 53.533
=756.80 =53.533
= 810.33
Current yield = par or face value*coupon rate/price
= 1000*.08/81.33
= 9.86
It was to prove that if bond is selling at discount then YTM is greater than current yield and current yield is greater than coupon yield , so it is proved from above calculations that:
Coupon rate < current yield < YTM
8% < 9.86% <10%
If bond is selling at discount then :
Coupon rate < Current Yield < Yield to maturity
You can convert this equation in your own wordings.
Q no.2. Illustrate the aforementioned relationship and provide supporting calculations using the 8% (semiannual payment) coupon, 30-year maturity bond with par value of Rs.1,000 paying 60 semiannual payments of Rs 40 each assuming it is selling at a yield to maturity of 10%. (Marks=8).
If we treat it as annuity then this formulas will be used:
Bond Price = C*{1-(1/1+r)2*n)/r} +par/(1+r)2*n
=40*{1-(1/1+.05)60/.05 +1000/(1+.05)60
= 40*(1-0.054/.05) +1000/ 18.68
=40*18.92 + 53.533
=756.80 =53.533
= 810.33
Current yield = par or face value*coupon rate/price
= 1000*.08/81.33
= 9.86
It was to prove that if bond is selling at discount then YTM is greater than current yield and current yield is greater than coupon yield , so it is proved from above calculations that:
Coupon rate < current yield < YTM
8% < 9.86% <10%
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