Question

An 8% coupon, 30-year maturity bond has a par value of $1,000. Suppose the interest rate is 6% annually. What is the bond value if it pays annual coupon payments? What is the bond value if it pays semi-annual coupon payments?

Answer 1

The bond value is computed as follows:

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

Coupon payment will be:

= 8% x $ 1,000

= $ 80

So, the price will be as follows:

= $ 80 x [ [ (1 - 1 / (1 + 0.06)³⁰ ] / 0.06 ] + $ 1,000 / 1.06³⁰

= $ 80 x 13.76483115 + $ 174.1101309

= $ 1,275.30 Approximately

The bond value is computed as follows:

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

Coupon payment will be:

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

= $ 40

r will be as follows:

= 6% / 2 (As the payments are semi annual, hence divided by 2)

= 3%

n will be as follows:

= 30 x 2 (As the payments are semi annual, hence multiplied by 2)

= 60

So, the price will be as follows:

= $ 40 x [ [ (1 - 1 / (1 + 0.03)⁶⁰ ] / 0.03 ] + $ 1,000 / 1.03⁶⁰

= $ 40 x 27.67556637 + $ 169.73309

= $ 1,276.76 Approximately

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