Question

Michelangelo’s craft center issues 7%, 9-year bonds with a face amount of $200,000. the market interest rate for bonds of similar risk and maturity is 8%. interest is paid semiannually. required: at what price will the bonds be issued?

Answer 1

The bonds will be issued at a price less than the face value due to the market interest rate being higher than the bond's coupon rate. The semiannual payments and principal are discounted at the market rate to determine the present value, which gives us the bond's issue price.

Step-by-step explanation:

The price at which the bonds will be issued can be determined by discounting the future cash flows (interest payments and the principal at maturity) at the market interest rate. Since the bond's coupon rate is 7%, but the market interest rate is 8%, the bond must be issued at a discount to attract buyers.

First, we should calculate the semiannual interest payment, which is 7% of $200,000 divided by 2, giving us $7,000 every six months. Then we discount those payments, as well as the principal, back to the present at the semiannual market rate, which is 4% (half of the 8% annual rate).

To find the present value, we sum the present values of all future cash flows. Using the present value formula for an annuity (for the interest payments) and a lump sum (for the principal), we get two present value factors which we will multiply by the respective cash flows:

PV of interest payments = Interest Payment x Annuity Factor
PV of principal = Principal x Lump Sum Factor

Adding these two amounts together gives us the bond's issue price.