Question

Two bonds make semi annual interest payments of R40. One matures in 2 years and the other matures in 10 years. Both bonds currently sell at par (R1000), meaning that they offer YTM of 8%.

Calculate the price of each bond if the YTM drops to 6%

Calculate the price of each bond if the YTM rises to 10%

Comment on obsereved patterns

Answer 1

when YTM is 6% then ytm semi annual is 3% and coupon rate semi annual is 8%/2 = 4% i.e. 4% * R1000 = R40

So price of bond when ytm semi annual is 3% = coupon * PVAF( r%, n periods) + Face value * PVF (r%, n periods)

prcie = R40 * PVAF( 3%, 4 periods) + R1000 * PVF (3%, 4 periods) = R1037.17

when YTM is 10% then ytm semi annual is 5% and coupon rate semi annual is 8%/2 = 4% i.e. 4% * R1000 = R40

So price of bond when ytm semi annual is 5% = coupon * PVAF( r%, n periods) + Face value * PVF (r%, n periods)

prcie = R40 * PVAF( 5%, 20 periods) + R1000 * PVF (5%, 20 periods) = R875.38

From above pattern of price of bond in two different ytm , we can conclude that if ytm is greator than coupon rate then price of bond will fall below face value

and when ytm is less than coupon rate then price of bond will be higher than face value.