When the company issues the commercial paper they will receive $100,000. Since they have to repay $110,000, they have $10,000 of interest. However, the term of the commercial paper is only 6 months, so this needs to be done twice a year. Therefore, the annual cost of borrowing $100,000 will be $20,000, so the effective annual interest rate is 20% ($20,000 divided by the $100,000 net proceeds available to the company all year).
This is the effective rate for one of the issuances of commercial paper, but since it is only 6 months, this needs to be doubled.
This is $10,000 × 2 / $110,000. The cost in terms of an annual rate is the amount of interest paid during the course of a year ($10,000 × 2) divided by the amount of cash the company receives from the issuance of the commercial paper. The amount of cash the company will receive from issuing the commercial paper is only $100,000, not $110,000. (It will receive $100,000 and in 6 months it will have to repay $110,000, representing the principal received of $100,000 plus interest for 6 months of $10,000.) So to calculate the cost as an annual percentage, we need to divide the $20,000 annual interest expense by $100,000 instead of by $110,000.
This is $10,000 (interest for 6 months) divided by $110,000. This is incorrect for two reasons. One, the interest for one full year will be 2 × $10,000, since the commercial paper matures in six months. And two, the funds available will be only $100,000, not $110,000. For each commercial paper issue, the company will receive $100,000 and in 6 months it will have to repay $110,000, representing the principal received of $100,000 plus interest for 6 months of $10,000.
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