Question

Price and yield A 6% semiannual coupon bond matures in 4 years. The bond has a face value of $1,000 and a current yield of 6.6223%. What is the bond's price? Round your answer to the nearest cent. $ What is the bond's YTM? Round your answers to two decimal places. %

Answer 1

Part 1:

The formula used to calculate current yield=Annual Coupon payment/Current market value of the bond
Given that:
Coupon rate (annual)=6%
Face value=$1000
Annual coupon payment=Coupon rate*Face value=6%*$1000=$60
Given that the current yield of the bond=6.6223%
So, 6.6223%=$60/Current market value of the bond
=>Current market value of the bond=$60/6.6223%=$906.0296272 or $906 (Rounded the value to the nearest cent)

Part 2:

Now, as the coupon interest payment is calculated in a semiannual basis, semiannual coupon payment=Semiannual coupon rate*Face value=Annual coupon rate/2*Face value
=6%/2*$1000=3%*$1000=$30

Face value=$1000
Present value of the bond=$906
Semiannual coupon payment=$30
Time to maturity =4 years, as the coupon interest payment is calculated in a semiannual basis, number of periods=4*2=8
Now, we will use these values and calculate the value of yield to maturity using excel.
We get the value of semiannual yield to maturity as 4.42%

Annual yield to maturity or YTM=4.42%*2=8.84%