To determine whether it is worthwhile to avail of the discount offer, we need to calculate the total cost of ordering inventory. The total cost consists of two components: the carrying cost and the ordering cost.



The carrying cost is the cost of holding inventory in stock. It is calculated as a percentage of the unit cost of the item multiplied by the annual demand. In this case, the carrying cost is 20% of the unit cost and the annual demand is 250,000 units.

Carrying Cost = Carrying Cost % * Unit Cost * Annual Demand
Carrying Cost = 0.20 * ₹4 * 250,000
Carrying Cost = ₹2,000,000



The ordering cost is the cost of placing an order with the supplier. It is a fixed cost per order. In this case, the ordering cost is ₹40 per order.



To calculate the total cost without the discount, we need to consider how many orders will be placed. Since the annual demand is 250,000 units and the order quantity is not given, we will assume that the order quantity is equal to the annual demand.

Number of Orders = Annual Demand / Order Quantity
Number of Orders = 250,000 / 250,000
Number of Orders = 1

Total Cost without Discount = Carrying Cost + Ordering Cost
Total Cost without Discount = ₹2,000,000 + ₹40
Total Cost without Discount = ₹2,000,040



To calculate the total cost with the discount, we need to consider the order quantity required to avail of the discount. In this case, the discount is given for an order of 7,500 units or more.

If we place an order of 7,500 units, the number of orders will be:

Number of Orders = Annual Demand / Order Quantity
Number of Orders = 250,000 / 7,500
Number of Orders = 33.33

Since the number of orders cannot be a decimal, we will round it up to 34.

Total Cost with Discount = Carrying Cost + Ordering Cost
Total Cost with Discount = ₹2,000,000 + (₹40 * 34)
Total Cost with Discount = ₹2,000,000 + ₹1,360
Total Cost with Discount = ₹2,001,360



Total Cost without Discount = ₹2,000,040
Total Cost with Discount = ₹2,001,360

From the calculation, we can see that even with the discount, the total cost with the discount is slightly higher than the total cost without the discount.

Therefore, it is not worthwhile to avail of the discount offer as it will result in a higher total cost. The company should continue to order the item without availing of the discount.