A 12-year,5% coupon bond pays interest annually. The bond has a face value of $1,000. What is the change in the price of this bond if the market yield rises to 6% from the current yield of 4.5%?

Question

Quizplus · Accepted Answer

First, we need to calculate the current price of the bond using the current yield of 4.5%.

PV = (coupon payment / interest rate) x [1 - 1 / (1 + interest rate) ^ n] + face value / (1 + interest rate) ^ n
where PV is the present value or current price, coupon payment is the annual interest payment ($50), interest rate is the current yield (0.045), n is the number of years until maturity (12).

PV = (50 / 0.045) x [1 - 1 / (1 + 0.045) ^ 12] + 1000 / (1 + 0.045) ^ 12
PV = $1,126.85

Next, we need to calculate the new price of the bond using the new market yield of 6%.

PV = (50 / 0.06) x [1 - 1 / (1 + 0.06) ^ 12] + 1000 / (1 + 0.06) ^ 12
PV = $1,002.47

The change in price is then calculated as:
Change in price = (New price - Current price) / Current price x 100%
Change in price = ($1,002.47 - $1,126.85) / $1,126.85 x 100%
Change in price = -0.1119 or -11.19%

Therefore, the bond price has decreased by 12.38% (rounded to the nearest hundredth) which is closest to option B.

A 12-Year,5% Coupon Bond Pays Interest Annually