Question

A borrower arranged a 250,000,000 credit line with a bank. It drew down: 20% for the first quarter of the year An additional 20% for the second quarter The remaining for the second half. Assume the interest rate was 3% for the first quarter, and 3.2% for the rest of the year. The unused credit line fee was 0.2%. Ignore day counts for this question; that is, just use ¼ for each three month period. What is the interest amount and fee amount for each quarter? What is the effective “all in” cost of the borrowing? Do this by tallying up the average amount actually borrowed over the course of the year. Then calculate the total amount paid to the bank, and divide.

Answer 1

Given

Amount arranged by borrower = 250,000,000

Interest rate for 1st quarter = 3%

Interest for rest of year = 3.2%

unused credit line fee = 0.2%

Average expenditure actually borrowed

Amount spent	Weighting factor	Average expenditure
250,000,000 $\small \times$ 20/100 = 50,000,000	12/12	50,000,000
250,000,000 $\small \times$ 20/100 = 50,000,000	9/12	37,500,000
250,000,000 - 100,000,000 = 150,000,000	6/12	75,000,000

Average expenditure = 162,500,000

Computation of expenditure

Amount borrowed	Interest rate	Interest amount
50,000,000	3%	50,000,000 $\small \times$ 3/100 = 1,500,000
50,000,000	3.2%	50,000,000 $\small \times$ 3.2/100 $\small \times$ 9/12 = 1,200,000
150,000,000	3.2%	150,000,000 $\small \times$ 3.2/100 $\small \times$ 6/12 = 2,400,000

Calculation of unused credit fee

200,000,000 is unused in 1st quarter

unused credit fee for 1st quarter = 200,000,000 $\small \times$ 0.2% $\small \times$3/12 = 100,000

150,000,000 is unused in 2nd quarter

unused credit fee for 1st quarter = 150,000,000 $\small \times$ 0.2% $\small \times$6/12 = 150,000

Effective "all in" cost of the borrowing

Total amount of interest = 1,500,000 + 1,200,000 + 2,400,000 = 5100,000

Total amount of unused credit fee = 100,000 + 150,000 = 250,000

Effective all in cost of the borrowing = (5100,000 + 250,000)/162,500,000 = 3.29%