Question

1. A Sprint bond has a face value of $1,000, a coupon rate of 7.75%, with coupons paid semi-annually, and 15 years to maturity. If the effective annual return for bonds of comparable risk is 7.75%, the price that you should be willing to pay for this bond is

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 7.75% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 38.75

The YTM will be as follows:

= 7.75% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.875% or 0.03875

N will be as follows:

= 15 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 30

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

= $ 38.75 x [ [ (1 - 1 / (1 + 0.03875)30 ] / 0.03875 ] + $ 1,000 / 1.0387530

= $ 38.75 x 17.55752976  + $ 319.6457219

= $ 1,000

We can also apply the concept that whenever the coupon rate and yield to maturity is same, then the bond always trades at par value.

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