Question

USING EXCEL IF NEEDED FOR CALCULATIONS

You are working in a Paper Company and the company needs to loan money from a bank to cover for the daily expenses. By analyzing the previous data, you come to the conclusion that the daily expenses are pretty stable at $17,000 per day, and the company works for 305 days a year. A bank has agreed to give you the loan, at an annual interest rate of 9% (i.e. for every dollar that you borrow, you will pay 9 cents) which will be collected at the end of the year. Any time you take a loan, the bank charges you a loan origination fee of $1,200 plus 2.25% of the amount borrowed.

a. Use an EOQ model to determine the optimal borrowing policy. This includes (1) the amount of loans you should borrow from the bank (i.e. borrow $300,000 loans at a time), (2) the total cost of your borrowing policy, and (3) the number of loans you should borrow in a year. The company would also like to know, if it takes the bank 15 days to process a loan, what is the level of cash on hand at which you should apply for a new loan?

b. Suppose the bank offers you a discount as follows: On any loan amount greater than $500,000, the bank will lower the origination fee to $1,200 plus 2% of the amount borrowed. What is the new optimal borrowing policy, considering the discount?

NOTES- Eventually you have to cover all daily expenses ($17,000/day x 305 days) using the money borrowed from the bank. The question is not how much to borrow in total, but how much to borrow at a time.

- You will always need $17,000 daily expenses on the day of the expense, so don’t think of all the interest that you’ll need to pay, but instead think of the interest as a holding cost associated with the extra money in your account.

- Write down the yearly total cost, and label each component as either the ordering cost, carrying cost, or the purchasing cost.

Answer 1

a) Demand rate, d = $ 17,000 per day

Fixed Origination fee, S = $ 1,200

Variable Origination fee, C = 2.25%

Interest rate, h = 9%/305 = 0.0002951 per day

Optimal borrowing amount as per EOQ model = SQRT(2dS/h) = SQRT(2*17000*1200/0.0002951) = $ 371,831

(1) Borrow $ 371,831 from the bank

(2) Total cost of borrowing policy = purchasing cost + ordering cost + carrying cost

= d*C + (d/Q)*S + (Q/2)*h

= 17000*2.25% + (17000/371831)*1200 + (371831/2)*0.0002951

= $ 492.23 per day

(3) Number of loans to borrow in a year = 305*d/Q = 305*17000/371831 = 13.94

(4) Lead time, L = 15 days

Level of cash on hand at which loan should be applied = d*L = 17000*15 = $ 255,000

b) Total cost of discount policy

= d*C + (d/Q)*S + (Q/2)*h

= 17000*2% + (17000/500000)*1200 + (500000/2)*0.0002951

= $ 454.58 per day

Total cost of discount policy is lower. Therefore, optimal borrowing policy is to borrow $ 500,000 at a time.