Question

American Bank has given you a line of credit of $20,000. Interest on the borrowed amount is 20% per year. You must maintain a 25% compensating balance on outstanding loans and pay a commitment fee (paid at the end of the period) of 2 % of the unused portion of the credit line.

1. Calculate the AFC if the amount borrowed is $5,000 for 6 months.

2. Calculate the AFC if the amount borrowed for 6 months is the full credit limit of $12,000.

3. You plan on borrowing $5,000 (as in Part a), but you want the AFC to be what is in Part b. All other things equal, what must be the new value for the stated interest rate?

Answer 1

AFC =(Interest cost + Commitment Fees) / Usable funds x 365 / Maturity (days)

Part (1)

All financials below are in $.

Amount borrowed = $ 5,000 for 6 months which is equivalent to $ 5,000 / 2 = $ 2,500 borrowed for 1 year.

We will do all our computation using this equivalent amount of $ 2,500

Compensating balance = 25% on outstanding = 25% x 2,500 = $ 625

Usable funds = $ 2,500 - 625 = $ 1,875

Commitment fees = 2% of the unused portion of the credit line = 2% x (20,000 - 2,500) = 350

Interest cost = 20% x 2,500 = 500

Hence, AFC = (500 + 350) / 1,875 x (365 / 365) = 45.33%

Part (2)

Calculate the AFC if the amount borrowed for 6 months is the full credit limit of $12,000.

Please note that there is a discrepancy in question itself. Full credit limit is $ 20,000 as stated in the first line of question and not $ 12,000 as stated in part (2) of the question.

I am solving this question based on the figure of $ 12,000 as given in part (b)

Amount borrowed = $ 12,000 for 6 months which is equivalent to $ 12,000 / 2 = $ 6,000 borrowed for 1 year.

We will do all our computation using this equivalent amount of $ 6,000

Compensating balance = 25% on outstanding = 25% x 6,000 = $ 1,500

Usable funds = $ 6,000 - 1,500 = $ 4,500

Commitment fees = 2% of the unused portion of the credit line = 2% x (20,000 - 6,000) = 280

Interest cost = 20% x 6,000 = 1,200

Hence, AFC = (1,200 + 280) / 4,500 x (365 / 365) = 32.89%

Part (3)

AFC = (Interest + 350) / 1,875 x (365 / 365) = 32.89%

Hence, Interest = 32.89% x 1,875 - 350 =  266.67 = interest rate x 2,500

Interest rate = 266.67 / 2,500 = 10.67% per annum