Question

# Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon...

Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of \$1,000, and it makes semiannual interest payments. If you require an 12.7% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

 a. \$901.80 b. \$674.76 c. \$1243.46 d. \$833.43 e. \$769.5

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 9.5% / 2 x \$ 1,000 (Since the payments are semi annually, hence divided by 2)

= \$ 47.50

The YTM will be as follows:

= 12.7% / 2 (Since the payments are semi annually, hence divided by 2)

= 6.35% or 0.0635

N will be as follows:

= 20 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 40

So, the price of the bond will be computed as follows:

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

= \$ 47.50 x [ [ (1 - 1 / (1 + 0.0635)40 ] / 0.0635 ] + \$ 1,000 / 1.063540

= \$ 47.50 x 14.40611187 + \$ 85.21189635

= \$ 769.50 Approximately

So, the correct answer is option e.

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