Short-Term Financing Questions

1) Calculate the Interest, Commitment Fees, and EAR on the following credit line:
– \$500,000 credit line
– 12% interest rate
– \$200,000 borrowed on average for year
– 1.0% commitment fee

2) TTDS is offered a \$750,000 loan for nine months at an APR of 8%. This loan has a loan origination fee of 2%. What is the EAR on the loan?

3) TTDS is offered a \$1,000,000 loan for six months at an APR of 9%. This loan requires TTDS to keep 20% of the loan principal in a non-interest-bearing account with the bank as a compensating balance. What is the EAR on the loan?

4) A firm has a \$4 million credit line to borrow at the prime rate (9%). Terms require a 10% compensating balance on borrowed funds and a 0.5% commitment fee on the unused balance. Average borrowings during the year are expected to be \$2 million. The firm has \$100,000 on deposit at the bank. Calculate the EAR.

5) A firm issues nine-month commercial paper with a \$50,000 face value and receives \$45,000. What effective annual rate (EAR) is the firm paying for its funds?

1).

Calculate the Interest = Used credit line * Interest rate

= \$200,000 * 0.12

= \$24,000

Commitment fees = Unused credit line * Commitment rate

= (\$500,000 – \$200,000) *0.01

= \$3,000

Calculation of EAR = (Interest + Commitment fees / Used Credit line) *100

= (\$24,000 + \$3,000 / \$200,000) *100

= 13.50%

Note = As sum provide average borrowing I have used annual rate directly.

2).

The Loan = \$ 750000

APR = 8%

Interest = 750000*8%*9/12 = \$45,000

Loan originating fee = 750000*2%= \$15,000

Total cost of loan = 45000+15000 = 60000

EAR on loan = (60000/750000)*12/9 = 10.67%

3).

Calculate the Total Amount to be Paid Back

The total amount to be paid on the loan will be calculated as follows:

Total Amount to be Paid Back = Loan Amount*(1+APR/2) – Compensating Balance Percentage*Loan Amount

Using the information provided in the question, we get,

Total Amount to be Paid Back = 1,000,000*(1+9%/2) – 1,000,000*20% = \$845,000

Calculate EAR

The 6 month rate can be calculated as follows:

6 Month Rate = Total Amount to be Paid Back/Amount of Loan after Adjustment for Compensating Balance – 1

= (845,000/(1,000,000 – 20%*1,000,000)) – 1 = 5.625%

The EAR is calculated with the use of following formula:

EAR = (1+6 Month Rate)^(n) – 1 = (1+5.625%)^2 – 1 = 11.57%

4).

EAR=[(2,000000*9%)+((4,000000-2,000000)*0.5%)]/(2000000+(2000000*10%)

=(190000/2200000)*100

=8.64%

5).

Calculation of Effective Annual Rate (EAR)

Face Value = \$50000

Present Value = \$45000

n = 1

Interest Rate = 11.11% ( Rate (1,0,-45000,50000)

Effective Annual Rate = (1+Rate)^n -1

= ((1+11.11%)^1)-1

= 11.11%

where n is the number of 9 month periods in a year

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