Final answer:
To calculate the new price of a bond when the market interest rate has risen above the bond's coupon rate, we need to find the present value of both the annuity of coupon payments and the future par value. The sum of these present values will give us the bond's current market price.
Step-by-step explanation:
The question asks to calculate the new price of a bond when the market interest rate is higher than the bond's coupon rate. The corporation issued 10-year, 11.06% annual coupon bonds at a par value of $1000 exactly one year ago. If the market interest rate has risen to 14.16% today, we need to find the present value of the remaining 9 years of coupon payments plus the present value of the par value at maturity. The coupon payments are $1,000 * 11.06% = $110.60 per year.
To find the present value of these payments, we use the formula for the present value of an annuity:
PV = C * [(1 - (1 + r)^-n) / r]
Where:
- PV is the present value of the bond
- C is the annual coupon payment
- r is the market interest rate per period
- n is the number of periods remaining until maturity
Additionally, we need to find the present value of the par value, which is a single future payment.
PV (par value) = FV / (1 + r)^n
Where:
- FV is the future value or par value of the bond
- r and n are defined as above
Calculating the present value of both the annuity (coupon payments) and the future par value, and summing them up, will give us the current price of the bond in the market.