Rodgers Corporation produces and sells football equipment. On July 1, 2016, Rodg

Question

Rodgers Corporation produces and sells football equipment. On July 1, 2016, Rodgers Corporation issued $65,000,000 of 10-year, 12% bonds at a market (effective) interest rate of 10%, receiving cash of $73,100,469. Interest on the bonds is payable semiannually on December 31 and June 30. The fiscal year of the company is the calendar year. 5. Compute the price of $73,100,469 received for the bonds by using the tables shown in Present Value Tables. (Round to the nearest dollar.) Present value of the face amount? Present value of the semiannual interest payments? Price received for the bonds

Explanation / Answer

The market price of a bond consists of both the PV of its Face value and the PV of the periodic interest payments (an Annuity), both at the market rate of 10%.

PV of 65.0 mil, N 20, R 5% = 24,497,816
PV of an Annuity of 3,900,000, N 20, R 5% = 48,602,619
Total PV and price of bonds when issued = 73,100,435 (difference due to rounding)

Remember that there are 20 payments, so the semiannual interest payment is based on the Face value of 65.0 mil x the Face or Coupon rate of 12% / 2, or 6% x 65.0 mil = 3,900,000.

But don't use the Coupon rate to get its PV. Instead, use the market rate of 10% / 5.

And the PV of the Face value is also based on 20 compounding periods, at the market rate.

The Coupon rate is ONLY used to get the periodic interest due.

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