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A 5-year bond has a face value of £100. The bond pays coupons semi-annually at a rate of 4%. The bond currently yields 5% p.a. effective in the market. Calculate the price of the bond £_____. Enter your answer as a decimal correct to 2 decimal places

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Final answer:

To find the price of a 5-year bond with semi-annual 4% coupon payments and a market yield of 5%, one must calculate and sum the present values of each semi-annual coupon payment and the face value payment at maturity, discounted at a semi-annual yield of 2.5%.

Step-by-step explanation:

To calculate the current price of the bond, we need to calculate the present value of the future cash flows, which consist of the semi-annual coupon payments and the face value payment at maturity. The bond pays a 4% annual coupon rate, so with semi-annual payments, each payment will be 2% of the £100 face value, which is £2. There are a total of ten coupon payments for a 5-year bond with semi-annual payments.

The yield of 5% per annum compounded semi-annually gives us a semi-annual yield of 2.5%. Now, calculate the present value (PV) of each payment. Then sum up these present values to get the total price of the bond:

PV = £2 / (1 + 0.025) + £2 / (1 + 0.025)2 + ... + £2 / (1 + 0.025)10 + £100 / (1 + 0.025)10

By summing up these terms, we obtain the current price of the bond.