Question

On 4 February 2010 a company issued a bond with a face value of $500,000 that matures exactly 25 years later. The coupon rate is 5% p.a. compounded half-yearly. What is the bond's value on 4 February 2018 assuming the market yield is 8% p.a. compounded half-yearly.

a. $230,139.97

b. $670,428.40

c. $408,757.48

d. $361,916.02

e. $363,175.43

Answer 1

The value of the bond is computed as shown below:

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

The coupon payment is computed as shown below:

= Face value x Coupon rate / 2

= $ 500,000 x 0.05 / 2 (Since the interest is compounded half-yearly, hence divided by 2)

= $ 12,500

The interest rate is computed as shown below:

= 8% / 2 (Since the interest is compounded half-yearly, hence divided by 2)

= 4% or 0.04

n is computed as follows:

= (25 - 8) x 2 (Since the interest is compounded half yearly, hence multiplied by 2. Further since 8 years have already elapsed, hence deducted)

= 34

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

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

= $ 12,500 x [ [ (1 - 1 / (1 + 0.04)³⁴ ] / 0.04 ] + $ 500,000 / (1 + 0.04)³⁴

= $ 12,500 x 18.41119776 + $ 131,776.0448

= $ 230,139.972 + $ 131,776.0448

= $ 361,916.02 Approximately

So, the correct answer is option d.

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