Final answer:
The present value of a bond is calculated by discounting its future cash flows, which consist of annual coupon payments and the face value repayment at maturity, using the given interest rate.
Step-by-step explanation:
To compute the present value (PV) of a 14-year German government bond (bund) with a face value of €300 and a coupon rate of 5% paid annually, we need to discount the future cash flows of the bond at the given interest rate of 6.40% per year. The bond's annual payment, or coupon, can be calculated as 5% of its face value, which amounts to €15 (300 x 0.05). Subsequently, these annual payments will be received for the next 14 years, and the face value of the bond will be returned at the end of the 14th year.
To determine the bond's PV, we use the formula for the present value of an annuity for the coupon payments, and the present value formula for a single sum for the face value repayment:
- For the coupon payments: PV = C * [(1 - (1 + r)^-n) / r], where C is the annual coupon payment, r is the discount rate, and n is the number of years.
- For the face value repayment: PV = F / (1 + r)^n, where F is the face value.
After calculating these two components, we combine them to get the total present value of the bond.