Question

1. Suppose you buy a 30 year bond that pays a 6% coupon for the first 15 years and a 8% coupon for the last 15 years. The YTM of this bond is 7%. What is the price of the bond?

2. Suppose you buy a 6 year 12% bond that has a YTM of 9%. What is the price of the bond?

Answer 1

We know that,

Price of the bond = Present Value of all the annual coupons and face value discounted at ytm.

a.

Face Value = 1000

Number of payments = 30

YTM = 7%

Coupon Amount = 6%* 1000 = 60

Coupon Amount = 8%*1000 = 80

Price = 60/(1+0.07)^1 + 60/(1+0.07)^2 + 60/(1+0.07)^3 + 60/(1+0.07)^4 + 60/(1+0.07)^5 + 60/(1+0.07)^6 + 60/(1+0.07)^7 + 60/(1+0.07)^8 + .......... 60/(1+0.07)^14 + 60/(1+0.07)^15 + 80/(1+0.07)^16 + 80/(1+0.07)^17 +80/(1+0.07)^18 +80/(1+0.07)^19 +80/(1+0.07)^20 +80/(1+0.07)^21 +80/(1+0.07)^22 +80/(1+0.07)^23 + ............. 80/(1+0.07)^30 + 1000/(1+0.07)^30

= 941.93 Answer

b.

Face Value = 1000

Number of payments = 6

YTM = 9%

Coupon Amount = 12%* 1000 = 120

Price of the bond = 120/(1+0.09)^1 + 120/(1+0.09)^2 + 120/(1+0.09)^3 + 120/(1+0.09)^4 + 120/(1+0.09)^5 + 120/(1+0.09)^6 + 1000/(1+0.09)^6

= 1134.58 Answer