Question

Consider a bond with the following characteristics. Par: $1,000 Two coupon payments per year (i.e., coupons are paid semi-annually) Coupon rate: 6.00% Years to maturity: 10 Bond price: $1,000 Suppose that the annual market interest rate for this bond jumps up by 1%. What is the new bond price?

Answer 1

Answer:

The new price of the bond is $928.94

Explanation:

Initially the bond's price is equal to its par value which means the coupon rate on bond and the market interest rates are the same i.e. 6%.

Th bond's price is calculated as the sum of the present value of the annuity of interest payments by the bond and the present value of the face value of the bond that will be received at maturity. The discount rate used to calculate the present values is the market interest rate.

As the bond is a semiannual bond, we will use the semi annual coupon payment, the semi annual percentage of the annual rate of interest on market and the number of semi annual periods outstanding.

Semi annual coupon payment = 1000 * 0.06 * 6/12 = $30

Number of semiannual periods till maturity = 10 * 2 = 20 periods

New market interest rate = 6 + 1 = 7% annual

New semi annual market interest rate = 7% / 2 = 3.5%

Price of bond =  30 * [ (1 - (1+0.035)^-20) / 0.035 ] + 1000 / (1+0.035)^20

Price of bond = $928.938 rounded off to $928.94

We used the present value of annuity ordinary formula for preset value of interest payments and the normal present value of principal formula for the face value.