Question

Doisneau 25​-year bonds have an annual coupon interest of 8 ​percent, make interest payments on a semiannual​ basis, and have a ​$1,000 par value. If the bonds are trading with a​ market's required yield to maturity of 17 percent, are these premium or discount​ bonds? Explain your answer. What is the price of the​ bonds?

The price of the bonds is ​?

. (Round to the nearest​ cent.)

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

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

= $ 40

The YTM will be as follows:

= 17% / 2 (Since the payments are semi annually, hence divided by 2)

= 8.5% or 0.085

N will be as follows:

= 25 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 50

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

= $ 40 x [ [ (1 - 1 / (1 + 0.085)⁵⁰ ] / 0.085 ] + $ 1,000 / 1.085⁵⁰

= $ 40 x 11.56559538 + $ 16.92439258

= $ 479.55

Since the bond is trading at less than its par value of $ 1,000, hence it is a discount bond.

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