Question

The Sisyphean Company has a bond outstanding with a face value of $1,000 that reaches maturity in 5 years. The bond certificate indicates that the stated coupon rate for this bond is 8.6% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 12%, then the price that this bond trades for will be closest to:

Answer 1

The price of the bond is computed as shown below:

The coupon payment is computed as follows:

= Coupon rate / 2 x $ 1,000 (Since the payments are semi annual hence divided by 2)

= 8.6% / 2 x $ 1,000

= $ 43

The YTM is computed as follows:

= 12% / 2 (Since the payments are semi annual hence divided by 2)

= 6% or 0.06

The n is computed as follows:

= 5 x 2 (Since the payments are semi annual hence multiplied by 2)

= 10

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

= $ 43 / 1.06¹ + $ 43 / 1.06² + $ 43 / 1.06³ + $ 43 / 1.06⁴ + $ 43 / 1.06⁵ + $ 43 / 1.06⁶ + $ 43 / 1.06⁷ + $ 43 / 1.06⁸ + $ 43 / 1.06⁹ + $ 43 / 1.06¹⁰ + $ 1,000 / 1.06¹⁰

= $ 874.88 Approximately

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