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# Comprehensive Economic Order Quantity (EOQ) Calculation

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15. (Comprehensive EOQ calculations) Knutson Products Inc. is involved in the production of airplane parts and has the following inventory, carrying, and storage costs:

1. Orders must be placed in round lots of 100 units.
2. Annual unit usage is 250,000. (Assume a 50-week year in your calculations.)
3. The carrying cost is 10 percent of the purchase price.
4. The purchase price is \$10 per unit.
5. The ordering cost is \$100 per order.
6. The desired safety stock is 5,000 units. (This does not include delivery-time stock.)
7. The delivery time is 1 week.

Given the forgoing information:
a. Determine the optimal EOQ level. EoQ=?[(2x25000x100)/(10x.1)]= 2236.068
b. How many orders will be placed annually?
c. What is the inventory order point? (That is, at what level of inventory should a new order be placed?)
d. What is the average inventory level?
e. What would happen to the EOQ if annual unit sales doubled (all other unit costs and safety stocks remaining constant)? What is the elasticity of EOQ with respect to sales? (That is, what is the percentage change in EOQ divided by the percentage change in sales?)
f. If carrying costs double, what will happen to the EOQ level? (Assume the original sales level of 250,000 units.) What is the elasticity of EOQ with respect to carrying costs?
g. If the ordering costs double, what will happen to the level of EOQ? (Again assume original levels of sales and carrying costs.) What is the elasticity of EOQ with respect to ordering costs?
h. If the selling price doubles, what will happen to EOQ? What is the elasticity of EOQ with respect to selling price?

#### Solution Preview

Please see the attachment for full solutions.

a. Optimal EOQ is 7,071.
b. 35 orders will be placed annually.
c. The inventory order point is 10,000 units. ...

#### Solution Summary

Comprehensive economic order quantity calculations are examined. Safety stock units are discussed.

\$2.19

## Cash receipts acceleration system

Peggy Pierce Designs Inc. is a vertically integrated, national manufacturer and retailer of women's clothing. Currently, the firm has no coordinated cas management system. A proposal, however, from the first Pennsylvania Bank aimed at speeding up cash collections is being examined by several of Pierce's corproate executives.

The firm currently uses a centralized billing procedure, which requires that all checks be mailed to the Philadelphia head office for processing and eventual deposit. Under this arrengement all the customers' remittance checks take an average of 5 business days to reach the head office. Once in Philadelphia, another 2 days are required to process the checks for ultimate deposit at the First Pennsylvania Bank.

The firm's daily remittances average \$1 million. The average check size is 42,000. Pierce Designs currently earns 6 percent annully on its marketable-securities protfolio.

The cash acceleration plan proposed by officers of First Pennsylvania invloves both a lockbox system and concentration banking. First Pennsylvania would be the firm's only concentration bank. Lockboxes would be established in (1) San Francisco, (2) Dallas, (3) Chicago, and (4) Philadelphia. This would reduce funds tied up by mail flaot to 3 days, and processing float will be eliminated. Funds would then be tranferred twice each business day by menas of automated depoositiry transfer checks from local banks in San Francisco, Dallas, and Chicago to the First Pennsylvania Bank. Each DTC costs \$15. These transfers will occur all 270 business days of the year. Each check processed through the lockbox system will cost \$0.18.

A.) What amount of cash balances will be freed up if Peggy Pierce Designs Inc. adopts the system suggested by First Pennsylvania?

B.) What is the opportunity cost of maintaining the current banking setup?

C.) What is the projected annual cost of operating the proposed system?

D.) Should Pierce adopt the new system? Compute the net annual gain or loss associated with adopting the system.

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