Question

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

Answer 1

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