Question

Cost of commercial paper Commercial paper is usually sold at a discount. Fan Corporation has just sold an issue of 107-day commercial paper with a face value of $1.1 million. The firm has received initial proceeds of $1,063,129. (Note: Assume a 365-day year.) a. What effective annual rate will the firm pay for financing with commercial paper, assuming that it is rolled over every 107 days throughout the year? b. If a brokerage fee of $10,834 was paid from the initial proceeds to an investment banker for selling the issue, what effective annual rate will the firm pay, assuming that the paper is rolled over every 107 days throughout the year? a. The effective annual rate the firm will pay for financing with commercial paper, assuming that it is rolled over every 107 days throughout the year, is %. (Round to two decimal places.) b. The effective annual rate the firm will pay with the brokerage fee, assuming that the paper is rolled over every 107 days throughout the year, is %. (Round to two decimal places.)

Answer 1

a). Periodic rate for 107-days = [Amount Borrowed - Initial Proceed Received] / Initial Proceed Received

= [$1,100,000 - $1,063,129] / $1,063,129 = $36,871 / $1,063,129 = 0.0347

EAR = [1 + Periodic Rate]^{No. of compounding periods in a year} - 1

= [1 + 0.0347]^[365/107] - 1

= 1.1233 - 1 = 0.1233, or 12.33%

b). Periodic rate for 107-days = [Amount Borrowed - Initial Proceed Received + Brokerage Fee] / [Initial Proceed Received - Brokerage Fee]

= [$1,100,000 - $1,063,129 + $10,834] / [$1,063,129 - $10,834] = $47,705 / $1,052,295 = 0.0453

EAR = [1 + Periodic Rate]^{No. of compounding periods in a year} - 1

= [1 + 0.0453]^[365/107] - 1

= 1.1633 - 1 = 0.1633, or 16.33%