Question

ABC Inc.’s bonds have a 10% coupon rate and $1000 face value. Interest is paid semi-annually, and the bonds have a maturity of ten years. If the appropriate discount rate is 8%/year compounded semi-annually on similar bonds, what is the price of ABC’s bonds?

Answer 1

The price of the bond is computed as shown below:

The coupon payment is computed as follows:

= 10% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 50

The YTM is computed as follows:

= 8% / 2 (Since the payments are semi annually, hence divided by 2)

= 4% or 0.04

N is computed as follows:

= 10 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 20

So, the price of the bond will be as follows:

= $ 50 / 1.04¹ + $ 50 / 1.04² + $ 50 / 1.04³ + $ 50 / 1.04⁴ + $ 50 / 1.04⁵ + $ 50 / 1.04⁶ + $ 50 / 1.04⁷ + $ 50 / 1.04⁸ + $ 50 / 1.04⁹ + $ 50 / 1.04¹⁰ + $ 50 / 1.04¹¹ + $ 50 / 1.04¹² + $ 50 / 1.04¹³ + $ 50 / 1.04¹⁴ + $ 50 / 1.04¹⁵ + $ 50 / 1.04¹⁶ + $ 50 / 1.04¹⁷ + $ 50 / 1.04¹⁸ + $ 50 / 1.04¹⁹ + $ 50 / 1.04²⁰ + $ 1,000 / 1.04²⁰

= $ 1,135.90 Approximately

Feel free to ask in case of any query relating to this question