Question

Quirk Drugs sold an issue of 30-year,$1000 par value bonds to the public that carry a 10.85% coupon rate , payable semiannually. it is now 10 years later, and the current market rate of interest is 9.00% if interest rates remain at 9.00% until Quirks bonds mature , what will happen to the value of the bonds over time ?

Answer 1

Coupon per period = (Coupon rate / No of coupon payments per year) * Par value

Coupon per period = (10.85% / 2) * $1000

Coupon per period = $54.25

Bond price 10 years later at YTM = 9%. There are 40 semi-annual coupon payments remaining.

Bond Price = Coupon / (1 +YTM / 2)^period + Par value / (1 + YTM / 2)^period

Bond Price = $54.25 / (1 + 9% / 2)¹ + $54.25 / (1 + 9% / 2)² + ...+ $54.25 / (1 + 9% / 2)⁴⁰ + $1000 / (1 + 9% / 2)⁴⁰

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $54.25 * (1 - (1 + 9% / 2)^-40) / (9% / 2) + $1000 / (1 + 9% / 2)⁴⁰

Bond Price = $1170.21

The bond is curretly selling at a premium to Par value. If the interest rates remain the same at 9%, the premium over the par value that the bond is selling for will be amortized over a time. It will continue the amortization untill it pays the par value i.e. $1000 at maturity. The bond value will decrease over time to $1000 at maturity as it nears the maturity date.