P16-15-Cost of commercial paper Commercial paper is usually sold at a discount.
ID: 2636627 • Letter: P
Question
P16-15-Cost of commercial paper Commercial paper is usually sold at a discount. Fan Corporation has just sold a issue of 90-day commercial paper with a face value of $1 million. The firm has received initial proceeds of $978,000. (Note; Assume a 365-dayyear)
a) What effective annual rate will the firm pay for financing with commercial paper, assuming that it is rolled over every 90 days throughout the year?
b) If a brokerage fee of $9,612 was paid from the initial process to the investment banker for selling the issue, what effective annual rate will the firm pay, assuming that the paper is rolled over every 90 days throughout the year?
Explanation / Answer
A. 90-DAY INVESTMENT A $978,000 investment yields $1M, an interest rate of 2.25% to the firm. But just as credit cards compound (monthly), you?ll be paying an additional 2.25% each quarter. At low interest rates like this, financial officers might call it a 9% effective annual rate, but it does compound a little. There are a couple of ways to figure it but this might be the easiest to understand. Q1: $22,000 Q2: $22,000 + 0.0225 * ($22,000) -- using the $22,000 extra cash you needed to pay back the bond Q3: $22,000 + 0.0225 * ($44,000) ? you?re funded 2 quarters of $22,000 extra now Q4: $22,000 + 0.0225 * ($66,000)?3 quarters where the company has covered extra cash TOTAL = $22,000 + $22,495 + $22,990 + $23,485 = $90,970 Interest rate = $90,970 / $978,000 = 9.30% B. BROKERAGE FEES Brokerage fees reduce the amount that the company receives ? so the company?s interest rate is higher than the effective rate paid to INVESTORS. I know that your question asks about the company ? it?s paying the SAME rate of 9.30%, as fees are included in its implied interest rate. The fees are a current expense. This problem is made simpler by the fact that the underwriting or brokerage fees are for the current year. Were they for a longer period, they?d have to be capitalized and spread over the expected life of the bond. (You have to do the same with points paid on a mortgage.) But the investors are paying $987,612 and receiving $1M back after 90 days. So the interest that they?re receiving is $12,388. 90-day rate: $12,388 / $987,612 = 1.25% Q1: $12,388 Q2: $12,388 + 0.0125 * ($12,388) -- using the $22,000 extra cash you needed to pay back the bond Q3: $12,388 + 0.0125 * ($24,776) ? you?re funded 2 quarters of $22,000 extra now Q4: $12,388 + 0.0125 * ($37,164)?3 quarters where the company has covered extra cash TOTAL = $12,388 + $12,543 + $12,698 + $12,853 = $50,482 Interest rate = $50,482 / $987,612 = 5.11%
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