Company Projected TV Sales For December 2012
A Company Projected Sales Of Televisions For December 2012 Is 515 Unit
A company projected sales of televisions for December 2012 is 515 units. The costs of processing a purchase order for the televisions is $2.75. The demand for televisions for December 2012 is shown above at 515 units. It is estimated that the costs of stocking one television in the warehouse plus insurance costs totaled $2.20. The terms for this purchase is 2/10, n30.
Required: 1. What is the EOQ? 2. Based on the terms of the purchase, what is the annual percentage cost of not paying within the discount period?
Paper For Above instruction
The calculation of the Economic Order Quantity (EOQ) and the analysis of the cost implications of early payment discounts are fundamental components of inventory management and procurement strategy. This paper discusses the methodologies used to determine EOQ, applies the EOQ formula to the given data, and examines the cost implications of the purchase discount terms provided.
The EOQ model is designed to identify the optimal order quantity that minimizes total inventory costs, which include ordering costs and holding costs. The classic EOQ formula is expressed as:
EOQ = √(2DS / H)
where D is the annual demand, S is the ordering cost per order, and H is the holding or carrying cost per unit per year. With the provided data, the demand D is 515 units; the ordering cost S is $2.75; and the holding cost per unit, H, is $2.20.
Calculating EOQ:
EOQ = √(2 515 2.75 / 2.20) = √(2832.5 / 2.20) = √1287.5 ≈ 35.87 units
Therefore, the EOQ is approximately 36 units. This means the company should order around 36 units each time they place an order to minimize the combined costs associated with ordering and holding inventory.
Moving to the second part of the problem, the purchase terms offer a 2% discount if payment is made within 10 days, with a net period of 30 days. The question asks for the annual percentage cost of not paying within the discount period—that is, the implied cost of missing the discount.
To determine this, we calculate the cost of forgoing the discount, which is equivalent to the additional cost incurred by paying the full price instead of the discounted price. This is often expressed as the "cost of credit" or "cost of not taking the discount," calculated as follows:
Cost of not taking discount = Discount % / (1 - Discount %)
In this case, the discount is 2%, or 0.02:
Cost = 0.02 / (1 - 0.02) = 0.02 / 0.98 ≈ 0.02041
This cost represents the equivalent interest rate for the period between the end of the discount window (10 days) and the full payment period (30 days). The difference in days is 20 days:
Period length = 30 - 10 = 20 days
To annualize this cost, we calculate how many such periods fit into a year. Assuming 365 days in a year, the number of periods per year is:
Number of periods per year = 365 / 20 ≈ 18.25
Thus, the annual percentage cost of not paying within the discount period is:
Annual cost = 0.02041 * 18.25 ≈ 0.3724 or 37.24%
In conclusion, the EOQ for the televisions is approximately 36 units, which helps balance ordering and holding costs efficiently. Additionally, the cost of not paying within the discount period translates to an annual interest rate of roughly 37.24%, underscoring the importance of taking advantage of early payment discounts to reduce overall procurement costs.
References
- Coyle, J. J., Bardi, E. J., & Langley, C. J. (2016). The Management of Business Logistics: A Supply Chain Perspective. Cengage Learning.
- Supply Chain Management: Strategy, Planning, and Operation. Pearson.
- Gaskins, L. (2021). "Analyzing Supplier Payment Terms and Cash Discount Strategies". Supply Chain Economics Journal.