Final answer:
a. The effective annual rate the firm will pay for financing with commercial paper, assuming it is rolled over every 80 days, is approximately 16.97%. b. Taking into account the brokerage fee, the effective annual rate the firm will pay is approximately 16.61%.
Step-by-step explanation:
a. To calculate the effective annual rate (EAR) for financing with commercial paper, assuming it is rolled over every 80 days throughout the year, we can use the following formula:
EAR = (1 + r/n)^n - 1
where r is the nominal rate and n is the number of compounding periods in a year. In this case, the nominal rate is the same as the annual rate because the commercial paper is rolled over every 80 days. The number of compounding periods in a year can be calculated as 365 divided by 80 = 4.56. Substitute the values into the formula:
EAR = (1 + r/4.56)^4.56 - 1
Let's solve for r:
1 + r/4.56 = (1 + 0.0385)^4.56
r/4.56 = (1.0385)^4.56 - 1
r = (1.0385^4.56 - 1) * 4.56
r ≈ 0.1697
So, the effective annual rate the firm will pay for financing with commercial paper is approximately 16.97%.
b. If a brokerage fee of $13,108 was paid from the initial proceeds to an investment banker for selling the issue, we need to adjust the initial proceeds before calculating the effective annual rate. The adjusted proceeds would be $1,383,599 - $13,108 = $1,370,491. Using the same formula and process as in part a, we can calculate the effective annual rate:
EAR = (1 + r/4.56)^4.56 - 1
1 + r/4.56 = (1 + 0.0379)^4.56
r/4.56 = (1.0379)^4.56 - 1
r = (1.0379^4.56 - 1) * 4.56
r ≈ 0.1661
So, the effective annual rate the firm will pay, considering the brokerage fee, is approximately 16.61%.