Question

What happens to the price of a three-year annual coupon paying bond with an 8% coupon when interest rates change from 8% to 6.85%? Answer in dollar terms to the nearest decimals without the $ sign. Use a "-" sign to denote a price decrease. Do not use a "+" sign.

Answer 1

Face Value of bond = $1000

Annual Coupon Payment = $1000*8%

= $80

No of years to maturity(n) = 3 years

When the Market Interest rate was 8%, the Price of the bond will be the same as the Par value which is $1000 because when the Coupon rate and Market Interest rate are the same the Bond sells at par Value.

So, At an 8% Interest rate price is $1000

- Interest rate(YTM) changed to 8.86%

Calculating the Price of Bond:-

Price = \frac{CouponPayment}{(1+YTM)^{1}}+\frac{CouponPayment}{(1+YTM)^{2}}+...+\frac{CouponPayment}{(1+YTM)^{n}}+\frac{FaceValue}{(1+YTM)^{n}}

Price = \frac{80}{(1+0.0886)^{1}}+\frac{80}{(1+0.0886)^{2}}+\frac{80}{(1+0.0886)^{3}}+\frac{1000}{(1+0.0886)^{3}}

Price =$203.008 + $775.166

Price = $978.17

So, when the Interest rate changed to 8.86% the price falls to $978.17

Change in Price due to increase in Interest rate = $978.17 - $1000

= -$21.83

Hence, the price decreased by $21.83

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