Question

1) Shelby Inc. negotiates a 1-year, $10 million revolving line of credit with Union Bank under the following terms:

- Commitment fee = 0.30% of unused portion of the line, payable monthly in arrears.

- Interest rate = 1.25% over Union Bank’s Prime Rate (interest paid monthly in arrears).

- Assume a 360-day year (?12 months of 30 days each).

- Union Bank’s Prime Rate is currently at 3.5% and is not expected to change during the

next 12 months.

What is the Effective borrowing rate (expressed as an Effective Annualized Rate of interest - EAR) for Shelby under the following 2 scenarios?

1. It borrows $6,000,000 on Day 1 and reimburses the full amount at the end of the year (at the close of Day 360).

2. It borrows $6,000,000 on Day 1, reimburses the full amount after 3 months (Day 90), and does not use the facility for the remainder of the year?

Answer 1

Total Interest Rate on the Loan = Prime rate + Premium = 3.5 + 1.25 = 4.75 % per annum or 0.395833 5 per month

(1) Borrowing = $ 6 million, Monthly Interest = 6 x 0.00395833 = $ 0.02375 million and Monthly Committment Fee = 0.003 x (10 -6) = $ 0.012 million

Total Payable (after an year) = initial Borrowing + Total Interest + Total Committment Fee = 6 + 0.285+ 0.144 = 4 6.429 million

Inetrest Rate = [(6.429 - 6) / 6] = 0.0715 or 7.15 %

EAR = [{1+ (0.715/12)}^(12) - 1] = 0.07389 or 7.389 %

(2) Borrowing = $ 6 million, Tenure = 90 days , Monthly Interest = 0.00395833 x 6 = $ 0.02375 million

Total Monthly Committment Fee = 4 x 3 x 0.003 + 10 x 9 x 0.003 = $ 0.306 million

Total Interest = 0.02375 x 12 = $ 0.285 million

Total Payable = 6 + 0.285 + 0.306 = $ 6.591 million

Nominal Interest Rate = [(6.591-6) / 6] = 0.0985 or 9.85 %

EAR = [{1+(0.0985/12)}^(12) - 1] = 0.103071 or 10,3071 %