The firm issued $720 million principal amount of 3.1% fixed-rate notes in Januar

Question

The firm issued $720 million principal amount of 3.1% fixed-rate notes in January, 2017 that will come due February, 2027. Interest is payable semi-annually in the rears. Assume that the notes were issued to yield 3.5%, i.e. the market interest rate on the day the notes were issued was 3.5%. What amount did the firm receive when the notes were issued?

I think this question is asking for the present value of $720 million, is that correct? PLEASE help me get started on how to solve this problem.

Thanks!

Explanation / Answer

Yes, what is required is the PV; but not of the 720 alone but also of the semi-annual interest. Since the interest payment is semiannual, the half yearly discount rate is 3.50/2 = 1.75%. # of periods = 10*2 = 20 The PV is the sum of the following: PV of the principal amount = 720000000/1.0175^20 = $    508,913,696 PV of the semi-annual interest payments = 720,000,000*1.55%*(1.0175^20-1)/(0.0175*1.0175^20) = $    186,962,155 Amount received on the note $    695,875,851

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