Question

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, and have the same yield-to-maturity. Bond A has a coupon rate of 6.5 percent and is priced at $1,056.78. Bond B has a coupon rate of 7.4 percent. 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 1

Solution

First the YTM for bond A will be calculated

For Bond A

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(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 of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(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 of bond=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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