Question

The Sisyphean company has a bond outstanding with a face value of $1,000 that reaches maturity in 15 years. The bond certificate indicates that the stated coupon rate for this bond is 8% and that the coupon payment are to be made semi-annually.

How much are each of the semi-annual coupon payments? Assuming the appropriate YTM on the Sisyphean bond is 8.8%, then at what price should this bond trade?

Answer 1

The semi annual coupon payment is computed as shown below:

= Coupon rate / 2 x face value

= 8% / 2 x $ 1,000 (Since the payments are semi annual, hence divided by 2)

= $ 40

The price of the bond is computed as shown below:

The coupon payment is computed as follows:

= Coupon rate / 2 x face value

= 8% / 2 x $ 1,000 (Since the payments are semi annual, hence divided by 2)

= $ 40

The YTM is computed as follows:

= 8.8% / 2

= 4.4% or 0.044

N is computed as follows:

= 15 x 2

= 30

So, the price of the bond will be:

= $ 40 / 1.044¹ + $ 40 / 1.044² + $ 40 / 1.044³ + $ 40 / 1.044⁴ + $ 40 / 1.044⁵ + $ 40 / 1.044⁶ + $ 40 / 1.044⁷ + $ 40 / 1.044⁸ + $ 40 / 1.044⁹ + $ 40 / 1.044¹⁰ + $ 40 / 1.044¹¹ + $ 40 / 1.044¹² + $ 40 / 1.044¹³ + $ 40 / 1.044¹⁴ + $ 40 / 1.044¹⁵ + $ 40 / 1.044¹⁶ + $ 40 / 1.044¹⁷ + $ 40 / 1.044¹⁸ + $ 40 / 1.044¹⁹ + $ 40 / 1.044²⁰ + $ 40 / 1.044²¹ + $ 40 / 1.044²² + $ 40 / 1.044²³ + $ 40 / 1.044²⁴ + $ 40 / 1.044²⁵ + $ 40 / 1.044²⁶ + $ 40 / 1.044²⁷ + $ 40 / 1.044²⁸ + $ 40 / 1.044²⁹ + $ 40 / 1.044³⁰ + $ 1,000 / 1.044³⁰

= $ 934.07 Approximately

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