Check Marginal Unit Quantity Discount Exercise 11-16 938906

Ex 1116 Checkmarginal Unit Quantity Discount Exercise 11 16fixed C

Ex 1116 Checkmarginal Unit Quantity Discount Exercise 11 16fixed C

Ex. 11.16 check Marginal Unit Quantity Discount (Exercise 11-16) Fixed cost per order = $500.00 Monthly demand = 5,000 Holding percentage = 25% Pricing: Min Qty Max Qty Price per phone 0 10,000 $200,000 $195,000 $190.00 Range Q Adjust to Q Total Cost Without Quantity Discount Price per phone Q Total Cost $200,954 $12,005,477

Exercise 11.16 involves analyzing the impact of different order quantities and pricing strategies on total costs within a scenario of fixed order costs, demand, and holding costs. The goal is to determine the optimal order quantity considering quantity discounts to minimize total costs, incorporating economic order quantity (EOQ) principles and the effects of volume-based pricing.

Paper For Above instruction

In the contemporary business environment, inventory management and procurement strategies significantly influence a company’s overall profitability and operational efficiency. Exercise 11.16 provides an opportunity to explore the application of economic order quantity (EOQ) models combined with quantity discounts—a common scenario in supply chain management. This case assesses how integrating cost analysis with volume-based pricing can optimize ordering policies and reduce total costs.

Introduction

The core of inventory management involves determining the optimal order size that minimizes total costs, which include ordering costs, holding costs, and purchase costs. Quantitative models, particularly EOQ, serve as valuable tools in this process. In Exercise 11.16, the focus is on a scenario involving a fixed order cost, demand rate, holding percentage, and tiered pricing structure based on order quantity thresholds. This setup mirrors real-world supply chain decisions where bulk purchasing discounts motivate larger order sizes, yet increased inventory incurs higher holding costs.

Understanding EOQ and Quantity Discounts

The EOQ model aims to identify the order quantity that minimizes the sum of ordering and holding costs without considering purchase price reductions. However, when quantity discounts are available, businesses face a more complex decision: should they increase order quantities to benefit from lower unit prices, or keep smaller, more frequent orders to reduce holding costs? Integrating EOQ with quantity discounts involves calculating the cost implications at various purchase levels and selecting the size that offers the lowest total cost.

Analysis of the Scenario

The scenario presented involves fixed costs per order, demand rate, and tiered pricing based on order quantities—less than 10,000 units at a certain price, between 10,000 and 20,000 at a reduced price, and above 20,000 at the lowest price. Applying the EOQ formula: Q* = sqrt(2DS/hC), where D is demand, S is fixed ordering cost, h is holding cost rate, and C is unit cost, allows the calculation of optimal batch sizes at different price points.

At the base level—without considering discounts—the EOQ would be straightforward. Given demand (D) = 5,000 units/month or 60,000 annually, fixed cost (S) = $500, and an annual holding cost rate of 25%, the EOQ can be estimated as follows:

EOQ = sqrt(2 60,000 500 / (0.25 * unit cost)).

Since unit costs vary with order size based on tiered pricing, calculations must be performed at each discount level to determine the most economical order quantity.

Cost Analysis at Different Price Points

For the lowest price—$190 per unit—more substantial order sizes are financially advantageous because the unit price decreases, reducing material costs. Calculating the total cost involves summing order costs, holding costs, and material costs; adjustments are also needed for the volume discounts.

When order quantities exceed 10,000 or 20,000 units, discounts of $195 or $190 per phone are applicable, respectively. At each level, total costs are calculated:

• Order cost: S * D / Q
• Holding cost: (Q / 2) h unit cost
• Material cost: D * unit cost

By comparing these total costs for incremental order quantities, the analysis identifies the order size with the minimum total cost, accounting for discounts and inventory holding implications.

Implications for Business Strategy

Determining the optimal order size in this context embodies a strategic balance: larger orders benefit from discounts but increase holding costs. The decision relies on calculations that reveal at which volume the savings from lower unit prices outweigh the additional costs of holding inventory. This exercise highlights the importance of integrating quantitative analysis into procurement decisions, especially when multiple pricing tiers are present.

Application to Broader Business Practices

Practically, managers overseeing supply chain operations can leverage this analysis to negotiate better terms with suppliers, plan inventory levels, and reduce total costs. For instance, companies might strategically time bulk orders to coincide with periods of lower demand or capitalize on discount thresholds, thus optimizing cash flow and inventory turnover.

Furthermore, understanding these models fosters better decision-making beyond inventory — such as budgeting, resource allocation, and production planning. The ability to quantify trade-offs ensures that decisions align with financial objectives and operational constraints, reinforcing the core values of efficiency, responsibility, and strategic foresight.

Conclusion

Exercise 11.16 exemplifies the application of EOQ combined with volume discounts, underscoring the significance of cost minimization in inventory management. By systematically analyzing how different order quantities impact total costs—including purchase prices, holding, and ordering expenses—businesses can make informed procurement decisions that enhance profitability and operational agility. This analytical approach also underpins sustainable and responsible business practices, aligning with broader core values of efficiency and strategic resource utilization.

References

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