Question

an investor owns a $3,000 par-value 12% bond with semiannual coupons. the bond will mature at par at the end of fourteen years. the investor decides that a ten-year bond would be preferable. current yield rates are 6% convertible semiannually. the investor uses the proceeds from the sale of the 12% bond to purchase an 8% bond with semiannual coupons, maturing at par at the end of ten years. find the face value of the 8% bond.

Answer 1

The face value of the 8% bond is $7,000.

Step-by-step explanation:

To find the face value of the 8% bond, we need to understand the present value of the cash flows. The 12% bond with semiannual coupons will pay $120 every six months for fourteen years, in addition to the $3,000 par value at maturity. By discounting these cash flows using a 6% convertible semiannual rate, we can calculate their present value. To find the face value of the 8% bond, we set the present value of the cash flows equal to the proceeds obtained from selling the 12% bond. Solving for the face value of the 8% bond, we find that it is $7,000.