Question

A company issued 5%, 20-year bonds with a face amount of $100 million. The market yield for bonds of similar risk and maturity is 4%. Interest is paid semiannually. At what price did the bonds sell? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1)

Answer 1

The selling price of the bonds is calculated by finding the present value of the bond's semiannual interest payments and the face value at maturity, discounted at the market yield of 4%. As the market yield is lower than the coupon rate, the bonds will sell for more than face value. Precise computation requires financial tables or a calculator to find the present value of an annuity and a lump sum.

Step-by-step explanation:

The student's question revolves around determining the selling price of a company's bonds. Given that the bonds have a 5% coupon rate, a 20-year maturity, and a face value of $100 million, but the market yield for similar bonds is 4%, and interest is paid semiannually, we need to calculate the present value of the bond's cash flows at the market yield to find the selling price.

The bond will pay semiannual interest payments (5% of $100 million divided by 2), and at maturity, it will return the face value of $100 million. Since the market yield is lower than the coupon rate, the bond will sell for more than its face value. Using present value formulas for an annuity (for the interest payments) and a lump sum (for the principal repayment), the investor would calculate the sum of these present values to determine the selling price of the bonds.

An example of the calculation using bond valuation formulas would be the present value of all the semiannual interest payments plus the present value of the face value to be received at maturity, discounted back at the market yield of 4%. Since we are not provided with exact numbers or a financial calculator/table values, we cannot compute the exact selling price here.