On December 31, 2021, Interlink Communications issued 5% stated rate bonds with a face amount of $113 million. The bonds mature on December 31, 2051. Interest is payable annually on each December 31, beginning in 2022. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $). Determine the price of the bonds on December 31, 2021, assuming that the market rate of interest for similar bonds was 6%. Table values are based on:
n = 30
i = 6%
Cash Flow Amount Present Value
Interest $111,300,000 $74,454,240
Principal $100,000,000 $13,137,000
Price of bonds $87,591,240

Bond Price = $97.4457408 million rounded off to $97.45 million

Explanation:

To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is an annual bond, the coupon payment, number of periods and annual YTM will be,

Coupon Payment (C) = 113 million * 0.05 = 5.65 million

Total periods (n) = 30

r or YTM = 0.06 or 6%

The formula to calculate the price of the bonds today is attached.

Bond Price =5.65 * [( 1 - (1+0.06)^-30) / 0.06]  +  113 / (1+0.06)^30

Bond Price = $97.4457408 million rounded off to $97.45 million

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