Check Marginal Unit Quantity Discount Exercise 11 16

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: Quantity Price per phone 20,000 $ 190.00 Initial Order Quantity = 1,000 Increment in Order Quantity = 1,000 Order Average Annual Annual Annual Total Quantity Unit Cost Holding Cost Order Cost Material Cost Annual Cost 1000.0 $ 200.000 $ 25,000 $ 30,000 $ 12,000,000 $ 12,055,.0 $ 200.000 $ 50,000 $ 15,000 $ 12,000,000 $ 12,065,.0 $ 200.000 $ 75,000 $ 10,000 $ 12,000,000 $ 12,085,.0 $ 200.000 $ 100,000 $ 7,500 $ 12,000,000 $ 12,107,.0 $ 200.000 $ 125,000 $ 6,000 $ 12,000,000 $ 12,131,.0 $ 200.000 $ 150,000 $ 5,000 $ 12,000,000 $ 12,155,.0 $ 200.000 $ 175,000 $ 4,286 $ 12,000,000 $ 12,179,.0 $ 200.000 $ 200,000 $ 3,750 $ 12,000,000 $ 12,203,.0 $ 200.000 $ 225,000 $ 3,333 $ 12,000,000 $ 12,228,.0 $ 200.000 $ 250,000 $ 3,000 $ 12,000,000 $ 12,253,.0 $ 199.545 $ 274,375 $ 2,727 $ 11,972,727 $ 12,249,.0 $ 199.167 $ 298,750 $ 2,500 $ 11,950,000 $ 12,251,.0 $ 198.846 $ 323,125 $ 2,308 $ 11,930,769 $ 12,256,.0 $ 198.571 $ 347,500 $ 2,143 $ 11,914,286 $ 12,263,.0 $ 198.333 $ 371,875 $ 2,000 $ 11,900,000 $ 12,273,.0 $ 198.125 $ 396,250 $ 1,875 $ 11,887,500 $ 12,285,.0 $ 197.941 $ 420,625 $ 1,765 $ 11,876,471 $ 12,298,.0 $ 197.778 $ 445,000 $ 1,667 $ 11,866,667 $ 12,313,.0 $ 197.632 $ 469,375 $ 1,579 $ 11,857,895 $ 12,328,.0 $ 197.500 $ 493,750 $ 1,500 $ 11,850,000 $ 12,345,.0 $ 197.143 $ 517,500 $ 1,429 $ 11,828,571 $ 12,347,.0 $ 196.818 $ 541,250 $ 1,364 $ 11,809,091 $ 12,351,.0 $ 196.522 $ 565,000 $ 1,304 $ 11,791,304 $ 12,357,.0 $ 196.250 $ 588,750 $ 1,250 $ 11,775,000 $ 12,365,.0 $ 196.000 $ 612,500 $ 1,200 $ 11,760,000 $ 12,373,.0 $ 195.769 $ 636,250 $ 1,154 $ 11,746,154 $ 12,383,.0 $ 195.556 $ 660,000 $ 1,111 $ 11,733,333 $ 12,394,.0 $ 195.357 $ 683,750 $ 1,071 $ 11,721,429 $ 12,406,.0 $ 195.172 $ 707,500 $ 1,034 $ 11,710,345 $ 12,418,.0 $ 195.000 $ 731,250 $ 1,000 $ 11,700,000 $ 12,432,.0 $ 194.839 $ 755,000 $ 968 $ 11,690,323 $ 12,446,.0 $ 194.688 $ 778,750 $ 938 $ 11,681,250 $ 12,460,.0 $ 194.545 $ 802,500 $ 909 $ 11,672,727 $ 12,476,.0 $ 194.412 $ 826,250 $ 882 $ 11,664,706 $ 12,491,.0 $ 194.286 $ 850,000 $ 857 $ 11,657,143 $ 12,508,.0 $ 194.167 $ 873,750 $ 833 $ 11,650,000 $ 12,524,.0 $ 194.054 $ 897,500 $ 811 $ 11,643,243 $ 12,541,.0 $ 193.947 $ 921,250 $ 789 $ 11,636,842 $ 12,558,.0 $ 193.846 $ 945,000 $ 769 $ 11,630,769 $ 12,576,.0 $ 193.750 $ 968,750 $ 750 $ 11,625,000 $ 12,594,.0 $ 193.659 $ 992,500 $ 732 $ 11,619,512 $ 12,612,.0 $ 193.571 $ 1,016,250 $ 714 $ 11,614,286 $ 12,631,.0 $ 193.488 $ 1,040,000 $ 698 $ 11,609,302 $ 12,650,.0 $ 193.409 $ 1,063,750 $ 682 $ 11,604,545 $ 12,668,.0 $ 193.333 $ 1,087,500 $ 667 $ 11,600,000 $ 12,688,.0 $ 193.261 $ 1,111,250 $ 652 $ 11,595,652 $ 12,707,.0 $ 193.191 $ 1,135,000 $ 638 $ 11,591,489 $ 12,727,.0 $ 193.125 $ 1,158,750 $ 625 $ 11,587,500 $ 12,746,.0 $ 193.061 $ 1,182,500 $ 612 $ 11,583,673 $ 12,766,.0 $ 193.000 $ 1,206,250 $ 600 $ 11,580,000 $ 12,786,.0 $ 192.941 $ 1,230,000 $ 588 $ 11,576,471 $ 12,807,.0 $ 192.885 $ 1,253,750 $ 577 $ 11,573,077 $ 12,827,.0 $ 192.830 $ 1,277,500 $ 566 $ 11,569,811 $ 12,847,.0 $ 192.778 $ 1,301,250 $ 556 $ 11,566,667 $ 12,868,.0 $ 192.727 $ 1,325,000 $ 545 $ 11,563,636 $ 12,889,.0 $ 192.679 $ 1,348,750 $ 536 $ 11,560,714 $ 12,910,.0 $ 192.632 $ 1,372,500 $ 526 $ 11,557,895 $ 12,930,.0 $ 192.586 $ 1,396,250 $ 517 $ 11,555,172 $ 12,951,.0 $ 192.542 $ 1,420,000 $ 508 $ 11,552,542 $ 12,973,.0 $ 192.500 $ 1,443,750 $ 500 $ 11,550,000 $ 12,994,.0 $ 192.459 $ 1,467,500 $ 492 $ 11,547,541 $ 13,015,.0 $ 192.419 $ 1,491,250 $ 484 $ 11,545,161 $ 13,036,.0

Paper For Above instruction

The exercise presented involves analyzing the impact of quantity discounts on inventory costs and ordering strategies for a company selling phones. Understanding the interplay between demand, costs, and discount brackets is crucial for optimizing order quantities and minimizing total costs. This paper discusses the concepts of marginal unit analysis, economic order quantity (EOQ), and the strategic implications of tiered pricing structures, illustrating how these tools support effective inventory management decisions.

Introduction

Efficient inventory management is vital for businesses to reduce costs and improve profitability. A critical component involves determining optimal order quantities considering ordering costs, holding costs, and pricing strategies. The case study emphasizes tiered pricing schemes, where unit prices decrease with larger order sizes, incentivizing bulk purchasing. Analyzing these models helps businesses decide on economical batch sizes that balance order costs, holding costs, and purchase prices.

Analysis of the Quantity Discount Model

The model begins with defining key parameters: fixed order cost ($500), demand rate (5,000 units/month), and inventory holding costs (25% of unit price). The tiered pricing structure incentivizes larger orders: under 10,000 units at $200 per phone, between 10,000 and 20,000 units at $195, and over 20,000 units at $190. These thresholds influence the economic order quantity (EOQ), which is calculated to minimize total costs, considering both ordering and holding costs.

The classical EOQ formula, Q* = sqrt(2DS / hC), where D is annual demand, S is order cost, h is holding cost per dollar of inventory, and C is unit cost, provides an initial estimate. Since the discount brackets reduce unit costs at certain order sizes, the analysis adjusts the EOQ to determine the most cost-effective order quantity that reaches a specific discount tier.

Through iterative calculations, it’s evident that ordering just enough to qualify for the next discount bracket can significantly reduce the total cost per unit, but this must be balanced against increased order frequency. For instance, ordering 10,000 units at $200 might be less cost-effective than ordering 20,000 units at $195, due to the past increased holding costs but decreased unit price. The comprehensive analysis involves calculating total costs for each order quantity bracket and choosing the minimum.

Cost Analysis and Results

The total annual cost combines ordering costs, holding costs, and material costs. The calculations show that larger order quantities reduce the unit purchase price but increase holding costs proportionally. Conversely, smaller orders have higher per-unit costs but lower inventory holding costs. The analysis indicates that an optimal order size exists within each discount tier, which minimizes the sum of ordering, holding, and material costs.

For example, with 10,000 units ordered at the $200 price, total costs are computed as follows: Annual ordering cost is (D/Q) S, while annual holding costs are (Q/2) h, where h considers the holding percentage (25%). Similarly, when ordering beyond 20,000 units, the lower unit price reduces material costs, but increased inventory holding needs to be factored in.

Strategic Recommendations

Businesses should leverage quantity discounts byordering just enough units to qualify for the best pricing tiers, provided the cost savings outweigh inventory holding costs. Dynamic inventory strategies, including safety stock considerations and lead times, should inform order quantities to optimize costs continually. Advanced modeling, like EOQ adjusted for discounts and real demand fluctuations, enhances decision-making precision.

Conclusion

Analyzing quantity discounts through economic order quantity models provides a valuable framework for minimizing total inventory costs. Companies must balance the benefits of lower per-unit costs with the increased holding costs of larger orders. Optimal ordering strategies should target discount thresholds while considering demand variability and holding capacities to ensure cost efficiency and supply reliability.

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