Determining Annual Inventory Expenses, Reorder Point, and Stockout Costs You have been engaged to install an accounting system for the Kaufman Corporation. Among the inventory control features Kaufman desires as a part of the system are indicators of "how much" to order and "when" to order. The following information is furnished for one item, called a komtronic, which is carried in inventory:

a. Komtronics are sold by the gross (twelve dozen) at a list price of \(\$ 800\) per gross F.O.B. shipper. Kaufman receives a \(40 \%\) trade discount off list price on purchases in gross lots.

b. Freight cost is \(\$ 20\) per gross from the shipping point to Kaufman's plant.

c. Kaufman uses about 5,000 komtronics during a 259 -day production year and must purchase a total of thirty-six gross per year to allow for normal breakage and usage. Minimum and maximum usages are 12 and 28 komtronics per day, respectively.

d. Normal delivery time to receive an order is twenty working days from the date a purchase request is initiated. A rush order in full gross lots can be received by air freight in five working days at an extra cost of \(\$ 52\) per gross. A stockout (complete exhaustion of the inventory) of komtronics would stop production, and Kaufman would purchase komtronics locally at list price rather than shut down.

e. The cost of placing an order is \(\$ 10\); the cost of receiving an order is \(\$ 20\).

f. Space storage cost is \(\$ 12\) per year per gross stored.
g. Insurance and taxes are approximately \(12 \%\) of the net delivered cost of average inventory and Kaufman expects a return of at least \(8 \%\) on its average investment (ignore return on order and carrying cost for simplicity).
{Required:}
(1) Prepare a schedule computing the total annual cost of komtronics based on uniform order lot sizes of one, two, three, four, five and six gross of komtronics. (The schedule should show the total annual cost according to each lot size.) Indicate the economic order quantity (economic lot size to order).
(2) Prepare a schedule computing the minimum stock reorder point for komtronics. The komtronics inventory should not fall below this point without reordering, so as to guard against a stockout. Factors to be considered include average lead-period usage and safety stock requirements.
(3) Prepare a schedule computing the cost of a stockout of komtronics.
Factors to be considered include the excess costs for local purchases and for rush orders.