Bond X is a premium bond making annual payments. The bond has a coupon rate of 8
ID: 2732925 • Letter: B
Question
Bond X is a premium bond making annual payments. The bond has a coupon rate of 8.1 percent, a YTM of 6.1 percent, and has 14 years to maturity. Bond Y is a discount bond making annual payments. This bond has a coupon rate of 6.1 percent, a YTM of 8.1 percent, and also has 14 years to maturity. Assume the interest rates remain unchanged.
Bond X is a premium bond making annual payments. The bond has a coupon rate of 8.1 percent, a YTM of 6.1 percent, and has 14 years to maturity. Bond Y is a discount bond making annual payments. This bond has a coupon rate of 6.1 percent, a YTM of 8.1 percent, and also has 14 years to maturity. Assume the interest rates remain unchanged.
Explanation / Answer
Solution:
Whenever the YTM is less than the coupon rate that indicates thaat the bond is at premium and when the coupon rate is less than the YTM rate then the bond is at discount. Since the year is same 14 years hence let us assume the face value to be 1000 hence the price would be
YTM = coupon +( 1000 - X)/n/( 1000+x)/2)
.061 = 81 + (1000- x)/14 / 1000+x/2
.061 = 2286 +2000 - 2X/14000 +14X
854 +.854X = 4286 -2X
2.854X = 3432
X = 1202 is the bond price
Now coupon is 6.1% and YTM 8.1%
.081 = 61 + (1000- x)/14 / 1000+x/2
.081 = 1708 +2000 - 2X/14000 +14X
1134 +1.134X = 3708 -2X
3.134 X = 2574
X = $821
Thank you.