Question

A newly offered ten-year bond of face value 100 can be redeemed at 105, with 10%

coupon payable semi-annually. The effective annual yield at the time of issue is 11
(i)Determine the price of the bond at issue date. Give your answer in 2 decimal
places.
(ii)Suppose that the holder of this bond wishes to sell it immediately after the 10th
coupon payment has been effected and the effective annual yield has fallen to 7%
thereafter. Find the price at which he can sell the bond. Give your answer in 2
decimal places.

Answer 1

The price of the bond at the issue date is $90.48. After the 10th coupon payment, the bond can be sold for $103.20.

Step-by-step explanation:

(i) To determine the price of the bond at the issue date, we need to calculate the present value of the bond's future cash flows. The bond has a face value of $100 and a redemption value of $105. It also pays a 10% coupon semi-annually. To find the present value, we can use the formula:

Price = (Coupon Payment / (1 + Yield/2)^(2 x Number of Periods)) + (Redemption Value / (1 + Yield/2)^(2 x Number of Periods))

Plugging in the values, we get:

Price = (5 / (1 + 0.11/2)^(2 x 10)) + (105 / (1 + 0.11/2)^(2 x 10)) = $90.48

(ii) To find the price at which the bond can be sold after the 10th coupon payment when the yield falls to 7%, we can use the same formula. The only difference is that the number of periods is now reduced to 1:

Price = (5 / (1 + 0.07/2)^(2 x 1)) + (105 / (1 + 0.07/2)^(2 x 1)) = $103.20