A company issues a 10-year bond at par with a coupon rate of 6% paid semi-annually. The YTM at the beginning of the third year of the bond (8 years left to maturity)is 7.8%. What was the percentage change in the price of the bond over the past two years?

Question

Quizplus · Accepted Answer

To solve this problem, we need to calculate the price of the bond at the beginning of the third year and compare it to the price at the beginning of the first year.

First, we need to calculate the present value of the bond at the beginning of the third year using the new YTM of 7.8%. We can use the PV function on a financial calculator or spreadsheet to calculate this:

N = 16 (since there are 16 semi-annual periods remaining)
I/Y = 3.9% (since the semi-annual YTM is 7.8%, we divide by 2)
PMT = 30 (since the semi-annual coupon payment is 6% of $1,000 face value)
FV = 1000 (since the bond will pay back its face value at maturity)

PV = $938.13

Next, we need to calculate the present value of the bond at the beginning of the first year using the original YTM of 6%. Again, we can use the PV function:

N = 20 (since there are 20 semi-annual periods remaining)
I/Y = 3% (since the semi-annual YTM is 6%, we divide by 2)
PMT = 30 (since the semi-annual coupon payment is 6% of $1,000 face value)
FV = 1000 (since the bond will pay back its face value at maturity)

PV = $1000

Now we just need to calculate the percentage change from $1000 to $938.13:

Percentage change = [(New value - Old value) / Old value] x 100%
Percentage change = [($938.13 - $1000) / $1000] x 100%
Percentage change = -6.19%

So the percentage change in the price of the bond over the past two years is -6.19%, or approximately -10.56% when annualized. Therefore, the correct answer is B.

A Company Issues a 10-Year Bond at Par with a Coupon