Question

Bond A and bond B have the same maturity of 10 years and share identical risk features. Bond A has coupon rate of 7.5%, while bond B’s coupon rate is 6.5%. In each case the coupon is paid semi-annually. If bond B is currently selling for $800, what should be bond A’s current price?

Answer 1

As both the bonds are identical, so we can find the YTM of Bond B and use that YTM to compute the price of Bond A.

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Finding the YTM from Bond B:

N = 20 (The Bond is for 10 Years and making semi-annual payments so in total 20 payments)

PV = -800 (The present value of the bond is $800)

PMT => 6.5% of 1,000 => 65/2 = 32.5 ( The coupon 6.5% is on Face Value that is 1,000, but it will be paid semiannually, so divide by 2)

FV = 1,000 (The Face value of bond is $1,000)

CPT + I/Y = 4.832%

Calculate the price of Bond A by using YTM of 4.832%

N = 20 (The Bond is for 10 Years and making semi-annual payments so in total 20 payments)

PMT => 7.5% of 1,000 => 75/2 = 37.5 ( The coupon 7.5% is on Face Value that is 1,000, but it will be paid semiannually, so divide by 2)

FV = 1,000 (The Face value of bond is $1,000)

I/Y = 4.832

CPT + PV = 863.217

So the price of Bond A is 863.217

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