On September 30, 2018, the San Fillipo Corporation issued 8% stated rate bonds with a face amount of $480 million. The bonds mature on September 30, 2038 (20 years). The market rate of interest for similar bonds was 10%. Interest is paid semiannually on March 31 and September 30. Required:
Determine the price of the bonds on September 30, 2018.

The price of the bonds today is $397.64 million (rounded off to two decimal places)

Explanation:

The price of a bond is calculated as the present value of the face value of the bond discounted at the market interest rate plus the present value of the annuity of interest payments related to the bond discounted at the market interest rate or the Yield to Maturity (YTM).

The formula for the price of the bond is attached hereby.

Semi annual coupon rate = 8%/2  = 4%

Semi annual market interest rate = 10% / 2 = 5%

Number of semi annual interest periods = 20 * 2 = 40 periods

The interest paid by the bond semi annually is = 480 * 0.04 = $19.2 million

Price of the bond = 19.2 * [(1 - (1+0.05)^-40) / 0.05] + 480 / (1+0.05)^40

Price of the bond = $397.6363855 million rounded off to $397.64 million

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