Question

Logan Distributing Company of Atlanta sells fans and heaters to retail outlets throughout the Southeast. Joe Logan, the president of the company, is thinking about changing the firm’s credit policy to attract customers away from competitors. The present policy calls for a 1/10, net 30 cash discount. The new policy would call for a 3/10, net 50 cash discount. Currently, 30 percent of Logan customers are taking the discount, and it is anticipated that this number would go up to 50 percent with the new discount policy. It is further anticipated that annual sales would increase from a level of \(400,000 to \)600,000 as a result of the change in the cash discount policy. The increased sales would also affect the inventory level. The average inventory carried by Logan is based on a determination of an EOQ. Assume sales of fans and heaters increase from 15,000 to 22,500 units. The ordering cost for each order is \(200, and the carrying cost per unit is \)1.50 (these values will not change with the discount). The average inventory is based on EOQ/2. Each unit in inventory has an average cost of $12. Cost of goods sold is equal to 65 percent of net sales; general and administrative expenses are 15 percent of net sales; and interest payments of 14 percent will only be necessary for the increase in the accounts receivable and inventory balances. Taxes will be 40 percent of before-tax income.

b. Determine the EOQ before and after the change in the cash discount policy. Translate this into average inventory (in units and dollars) before and after the change in the cash discount policy.

Short answer

The EOQ before policy change is 2,000 units and after policy change is 2,449 units. The average inventory before policy change is 1,000 units and after policy change is 1,224.50 units. The average inventory before the policy change is $12,000 and $14,694 after the policy change.

Step-by-step solution

Calculation of EOQ before the policy change

The EOQ before policy change is 2,000 units.

$\begin{array}{rcl}\mathrm{EOQ}& =& \sqrt{\frac{2\times \mathrm{Sales}\times \mathrm{Ordering}\mathrm{cost}}{\mathrm{Carrying}\mathrm{cost}}}\\ & =& \sqrt{\frac{2\times 15,000\times \$200}{\$1.50}}\\ & =& \sqrt{\frac{\$6,000,000}{\$1.50}}\\ & =& 2,000\mathrm{units}\end{array}$

Calculation of average inventory before policy change

The average inventory is 1,000 units and $12,000.

$\begin{array}{rcl}\mathrm{Average}\mathrm{inventory}& =& \frac{\mathrm{EOQ}}{2}\\ & =& \frac{2,000}{2}\\ & =& 1,000\mathrm{units}\end{array}$

$\begin{array}{rcl}\mathrm{Average}\mathrm{inventory}& =& \frac{\mathrm{EOQ}}{2}\times \mathrm{Per}\mathrm{unit}\mathrm{average}\mathrm{cost}\\ & =& \frac{2,000}{2}\times \$12\\ & =& \$12,000\end{array}$

Calculation of EOQ after the policy change

The EOQ after policy change is 2,449 units.

$\begin{array}{rcl}\mathrm{EOQ}& =& \sqrt{\frac{2\times \mathrm{Sales}\times \mathrm{Ordering}\mathrm{cost}}{\mathrm{Carrying}\mathrm{cost}}}\\ & =& \sqrt{\frac{2\times 22,500\times \$200}{\$1.50}}\\ & =& \sqrt{\frac{\$9,000,000}{\$1.50}}\\ & =& 2,449\mathrm{units}\end{array}$

Calculation of average inventory after policy change

The average inventory is 1,224.50 units and $14,694.

$\begin{array}{rcl}\mathrm{Average}\mathrm{inventory}& =& \frac{\mathrm{EOQ}}{2}\\ & =& \frac{2,449}{2}\\ & =& 1,224.50\mathrm{units}\\ \mathrm{Average}\mathrm{inventory}& =& \frac{\mathrm{EOQ}}{2}\times \mathrm{Per}\mathrm{unit}\mathrm{average}\mathrm{cost}\\ & =& \frac{2,449}{2}\times \$12\\ & =& \$14,694\end{array}$