Final answer:
The price of the bond is calculated by discounting the semi-annual coupon payments and the call premium back to the present using the market rate of return. Since the market rate is less than the coupon rate, the bond is priced at a premium. A financial calculator or software is needed to find the exact price paid.
Step-by-step explanation:
To calculate the price paid for a 30-year, 7.9% semi-annual coupon bond when the current market rate of return is 5.5%, we first need to determine the semi-annual coupon payments and then find the present value of these payments and the face value of the bond, taking into account that the bond is callable in 6 years with a $1,093 call premium.
The semi-annual coupon payment is calculated by taking 7.9% of the $1,000 face value, which gives us a yearly interest of $79. Since it is paid semi-annually, each payment will be $79/2 = $39.50. We expect these payments to continue for the next 6 years or until the bond is called.
Next, we discount these coupon payments and the call premium at the market rate of return of 5.5% per year, which is 2.75% per semi-annual period. The present value of the annuity of semi-annual payments is calculated using the present value of annuity formula, and the future value of the call premium is discounted back to the present.
We sum the present value of the coupons and the present value of the call premium to determine the price paid for the bond. This price will be higher than face value due to the higher coupon rate of 7.9% compared to the market rate of 5.5%, reflecting that the bond is priced at a premium.
Therefore, to determine the exact price paid, a financial calculator or software capable of present value calculations would be required.