A company issued 6%, 15-year bonds with a face amount of $75 million. The market yield for bonds of similar risk and maturity is 6%. 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) (Enter your answers in whole dollars. Round final answers to nearest whole dollar.)
Answer)
Calculation of issue price of bonds
Issue price of bonds is the aggregate of present value of intermediate interest payments and the present value of maturity amount.
Issue price of bonds = (Face value X Present value of $ 1 at 3% for 30th period) + (Semi Annual interest payment X Present value of annuity of $ 1 at 3% for 30 periods)
= ($ 75,000,000 X 0.41199) + ($ 2,250,000 X 19.60044)
= $ 75,000,000 (Approximately)
The bonds will sell at $ 75,000,000 (75 million).
Note:
· Since interest is payable semi-annually, the market rate of interest used as discounting factor is halved (i.e. 6%/2 = 3%) and the number of periods is doubled (i.e. 15 years X 2 = 30 semi-annual periods)
· If market rate of interest is equal to the rate of interest offered on bonds, the bonds will sell at par value.
Working Note:
Calculation of semi-annual interest payment
Semi-annual interest = Face amount of bonds X annual rate of interest on bonds X ½
=$ 75,000,000 X 6% X ½
=$ 2,250,000
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