There's two principles at play here.
The first and most basic is the proceeds the company receives from selling the face value of the bonds at a discount.
= 2,000 * $1,000 bonds @ 94% = $1,880,000
Secondly, (which makes this a bit tricky) is the fact that they sold the bonds in the middle of an interest paying period. The problem states that interest is paid quarterly, so: 2,000,000 * 8% = 160,000 of yearly interest is paid to the bond holders.
Converting that to quarterly, it's 40,000 per quarter.
However, the bond was issued on SEPTEMBER 1st, which is the middle of the 3rd quarter.
3rd quarter months are: July, August and September. This means that bondholders will receive a full quarter's interest payment of $40,000 at the end of September, but will have really only earned September's (because that's when the bonds became outstanding). So the bondholders will prepay interest for July and August, and will get it back at as part of that $40,000 quarterly payment.
So they will prepay ( 40,000 * 2/3 = 26,667 ) in interest. Two-thirds because 2 months out of the 3-month quarter haven't been “earned”, only September will be.
So in total they will receive: 1,880,000 + 26,667 = 1,906,667
If you like journal entries to understand it a bit better like me, then it would be as follows:
DR Cash 1,880,000
DR Discount 120,000
CR Bonds Payable 2,000,000
Prepayment of interest:
DR Cash 26,667
CR Interest Payable 26,667
And on September 30th, when they make the interest payment:
DR Interest Payable 26,667
DR Interest Expense 13,333
CR Cash 40,000
Here they expense only 1 month of interest, since that's how long the bond has been outstanding, and give back the prepayment plus the 1 month's interest.
I hope that makes sense.
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