Carborundum Metals issues commercial paper with a face value of $1,000,000 and a maturity of three months. Carborundum receives net proceeds of $992,000 when it sells the paper. If the prime rate is 8% APR compounded quarterly, how much savings in interest did Carborundum realize by accessing the commercial paper market?
To calculate the savings in interest that Carborundum realized by accessing the commercial paper market, we need to compare the interest expense from using commercial paper with the interest expense from borrowing at the prime rate.
First, let's determine the interest expense for borrowing at the prime rate. The annual percentage rate (APR) of 8% compounded quarterly means that the interest is compounded four times in a year, with each compounding period being a quarter.
We can use the formula for compound interest to calculate the future value (FV) of the borrowing amount after three months:
FV = Principal * (1 + (interest rate / compounding periods)) ^ (compounding periods * time)
The principal amount is $1,000,000, the interest rate is 8% (0.08 in decimal form), compounding periods are 4, and the time is 3 months (or 0.25 years).
FV = $1,000,000 * (1 + (0.08 / 4)) ^ (4 * 0.25)
FV = $1,000,000 * (1 + 0.02) ^ 1
FV = $1,000,000 * (1.02)
FV = $1,020,000
Therefore, by borrowing $1,000,000 at the prime rate, Carborundum would have to pay back $1,020,000 after three months.
Now let's calculate the interest expense for using commercial paper. Carborundum received net proceeds of $992,000 when it sold the commercial paper, and it will have to pay back the face value of $1,000,000 after three months.
The interest expense for using commercial paper is the difference between the face value and the net proceeds:
Interest Expense = Face Value - Net Proceeds
Interest Expense = $1,000,000 - $992,000
Interest Expense = $8,000
Therefore, Carborundum saved $8,000 in interest expenses by accessing the commercial paper market instead of borrowing at the prime rate.