Question

1. A coupon bond which pays interest of $50 annually, has a par value of $1,000, matures in 10 years, and the interest rate is 12%, what will be the bond price?
2. A company issued a 15-year bond with $1,000 face value and 8 percent coupon rate.  If the required rate of return on this bond is 10 percent, what will be the bond price?

Without using a financial calculator

Answer 1

a. The bond price is computed as shown below:

= Present value of interest + Present value of par value

Present value is computed as follows:

= Future value / (1 + r)ⁿ

So, the bond price is computed as follows:

= $ 50 / 1.12¹ + $ 50 / 1.12² + $ 50 / 1.12³ + $ 50 / 1.12⁴ + $ 50 / 1.12⁵ + $ 50 / 1.12⁶ + $ 50 / 1.12⁷ + $ 50 / 1.12⁸ + $ 50 / 1.12⁹ + $ 50 / 1.12¹⁰ + $ 1,000 / 1.12¹⁰

= $ 604.48 Approximately

b. The bond price is computed as shown below:

= Present value of interest + Present value of par value

Present value is computed as follows:

= Future value / (1 + r)ⁿ

So, the bond price is computed as follows:

The coupon payment is computed as follows:

= Coupon rate x Par value

= 8% x $ 1,000

= $ 80

= $ 80 / 1.10¹ + $ 80 / 1.10² + $ 80 / 1.10³ + $ 80 / 1.10⁴ + $ 80 / 1.10⁵ + $ 80 / 1.10⁶ + $ 80 / 1.10⁷ + $ 80 / 1.10⁸ + $ 80 / 1.10⁹ + $ 80 / 1.10¹⁰ + $ 80 / 1.10¹¹ + $ 80 / 1.10¹² + $ 80 / 1.10¹³ + $ 80 / 1.10¹⁴ + $ 80 / 1.10¹⁵ + $ 1,000 / 1.10¹⁵

= $ 847.88 Approximately

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