Question

A Rs. 100 par value bond bears a coupon rate of 14% and matures after 5 years. Interest in payable semi-annually. Compute the value of the bond if the required rate of return is 16%. Also calculate the price change in the bond if yield decreases by 1%. (make necessary assumptions if required)

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 14% / 2 x $ 100 (Since the payments are semi annually, hence divided by 2)

= 7

The YTM will be as follows:

= 16% / 2 (Since the payments are semi annually, hence divided by 2)

= 8% or 0.08

N will be as follows:

= 5 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 10

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

= $ 7 x [ [ (1 - 1 / (1 + 0.08)¹⁰ ] / 0.08 ] + $ 100 / 1.08¹⁰

= $ 7 x 5.368065119 + $ 46.31934881

= $ 93.29 Approximately

The value of the bond if yield decreases by 1% is computed as shown below:

The coupon payment is computed as follows:

= 14% / 2 x $ 100 (Since the payments are semi annually, hence divided by 2)

= 7

The YTM will be as follows:

= 15% / 2 (Since the payments are semi annually, hence divided by 2)

= 7.5% or 0.075

N will be as follows:

= 5 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 10

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

= $ 7 x [ [ (1 - 1 / (1 + 0.075)¹⁰ ] / 0.075 ] + $ 100 / 1.075¹⁰

= $ 7 x 6.864080956 + $ 48.51939283

= $ 96.57 Approximately

So, the change in price will be as follows:

= $ 96.57 - $ 93.29

= $ 3.28