Bond A and bond B both pay ann
Bond A and bond B both pay annual coupons, mature in 8 years,have a face value of $1000, pay their next coupon in 12 months, andhave the same yield-to-maturity. Bond A has a coupon rate of 6.5percent and is priced at $1,056.78. Bond B has a coupon rate of 7.4percent. What is the price of bond B?
a. $1,113.56 (plus or minus $4)
b. $1,001.91 (plus or minus $4)
c. $1,056.78 (plus or minus $4)
d. $1,000.00 (plus or minus $4)
e. None of the above is within $4 of the correct answer
Answer:
Solution
First the YTM for bond A will be calculated
For Bond A
Price of bond=Present value of coupon payments+Present value offace value
Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Facevalue/(1+r)^n
Face value =1000
n=number of periods to maturity=8
r-YTM
Coupon payment=Coupon rate*face value=6.5%*1000=65
Current price of bond=1056.78
Putting values in formula
1056.78=65*((1-(1/(1+r)^8))/r)+1000/(1+r)^8
Solving we get
r=YTM=5.600%
Now YTM of bond B is same as that oF Bond A=5.600%
Again using the formula for bond B
Price of bond=Present value of coupon payments+Present value offace value
Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Facevalue/(1+r)^n
Face value =1000
n=number of periods to maturity=8
r-YTM=5.600%
Coupon payment=Coupon rate*face value=7.4%*1000=74
Current price of bond=?
Putting values in formula
Price ofbond=74*((1-(1/(1+5.600%)^8))/5.600%)+1000/(1+5.600%)^8
Solving we get
Price od Bond B-1113.5675
Thus the correct answer is $1,113.56 (plus or minus$4)
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