Question

Hamilton, Inc. bonds have a coupon rate of 13 percent. The interest is paid​ semiannually, and the bonds mature in 13 years. Their par value is ​$1,000. If your required rate of return is 8 percent, what is the value of the​ bond? What is the value if the interest is paid​ annually?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 13% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 65

The YTM will be as follows:

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

= 4% or 0.04

N will be as follows:

= 13 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 26

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 65 x [ [ (1 - 1 / (1 + 0.04)²⁶ ] / 0.04 ] + $ 1,000 / 1.04²⁶

= $ 65 x 15.98276918 + $ 360.6892329

= $ 1,399.57 Approximately

The value of the bond if the interest is paid annually is computed as shown below:

The coupon payment is computed as follows:

= 13% x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 130

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 130 x [ [ (1 - 1 / (1 + 0.08)¹³ ] / 0.08 ] + $ 1,000 / 1.08¹³

= $ 130 x 7.903775942 + $ 367.6979247

= $ 1,395.19 Approximately

Please ask in case of any query.