Final answer:
To calculate the current price of the bond, the present value of its future cash flows (semi-annual coupon payments and the principal repayment) must be determined using the current market yield of 6.2%. The price of the bond should reflect the sum of the present value of the annuity of coupon payments and the present value of the face value at maturity, both discounted at the yield to maturity.
Step-by-step explanation:
The question at hand involves a calculation of the current price of a 10-year, 5.0% coupon bond that was issued 2 years ago and now carries a market yield of 6.2% with semi-annual coupon payments. To calculate the current price of the bond, we need to determine the present value of the bond's future cash flows, which include the semi-annual coupon payments and the principal repayment at maturity.
Bond pricing is determined by the present value of these future cash flows, discounted back at the bond's yield to maturity (YTM), which in this case is 6.2%. Since the bond has 8 years remaining (16 semi-annual periods), and the semi-annual coupon payment is $25 (5% divided by 2, multiplied by the $1,000 face value), we can use the present value formula for annuities to calculate the present value of the coupon payments. Additionally, we calculate the present value of the $1,000 principal amount that will be returned at the end of the bond's life. The sum of these two present values is the current price of the bond. Implementing these calculations requires using the present value for an annuity formula and a single cash flow.
Example: Calculation of the Price of a 5.0% Semi-Annual Coupon Bond
• Semi-annual coupon payment present value: This is calculated using the present value of an annuity formula.
• Principal repayment present value: This is calculated by discounting the face value back at the YTM over the remaining life of the bond.
• Current bond price: This is the sum of the previous two present values.
By calculating these present values, we can determine the price of the bond under the current market yield, which will likely be lower than the face value due to the higher market interest rate as compared to the coupon rate of the bond.