Final answer:
To determine the price of a $1,000 bond with a 12% coupon paid semi-annually and a required return of 10.58%, one must calculate the present value of the coupon payments and the principal. Since the bond's coupon rate exceeds the required return rate, the bond should be priced above par value. The correct answer is option d. $1,000.00.
Step-by-step explanation:
The question posed is about determining the fair price to pay for a bond with a $1,000 par value and a 12% coupon rate that is paid semi-annually, given a required rate of return of 10.58%. It's an exercise in calculating the present value of both the interest payments and the principal repayment to decide the maximum price at which the bond is a good investment.
When attempting to calculate the price you would be willing to pay for the bond, you take into account the coupon payments you will receive every six months and the principal you will receive at the end of the 10-year period. If the market interest rate is less than the coupon rate of the bond, the bond will be worth more than its face value.
After computing the present value of all future coupon payments and the face value using the required rate of return, we can determine the appropriate value of the bond. Using the formula for present value of an annuity and the present value of a lump sum, the calculations would confirm which answer choice is correct. Given the market interest rate is lower than the coupon rate; you would expect the price of the bond to be higher than its par value, thus eliminating choices b, d, and e right off the bat.
The yield or total return includes both the interest payments and capital gains (or losses) realized upon the sale or maturity of the bond. In this case, with the coupon rate being higher than the required rate of return, one can deduce that the bond should be sold at a premium, above its face value, to provide a yield equal to the required rate of return to the investor.