Intro to Finance: Working Capital Management - Inventory Management, EOQ Just-In-Time Safety Stock

What This Is

Inventory management is a crucial aspect of supply chain management that involves controlling the level of inventory to minimize costs and maximize efficiency. Companies like Apple and Tesla need to manage their inventory levels to ensure timely delivery of products to customers while minimizing storage costs. For example, if Apple wants to maintain an inventory level of 10,000 units of its latest iPhone model, it needs to calculate the optimal order quantity to minimize costs.

Key Formulas & Symbols

• EOQ = ?(2DS/C) where EOQ = Economic Order Quantity, D = annual demand, S = ordering cost per order, C = holding cost per unit per year.
• D = annual demand (units/year)
• S = ordering cost per order (dollars)
• C = holding cost per unit per year (dollars/year)
• TC = (EOQ/2) × C + (D/EOQ) × S where TC = total cost.
• TC = total cost (dollars/year)
• TC_min = ?(2DS/C) where TC_min = minimum total cost.
• Safety Stock = z ×-× ?(D × T) where Safety Stock = additional inventory to account for uncertainty.
• z = z-score (standard deviation)
• ? = standard deviation of demand
• D = annual demand (units/year)
• T = lead time (days)
• Just-In-Time (JIT) = D × T where JIT = optimal inventory level for JIT system.
• D = annual demand (units/year)
• T = lead time (days)

Step-by-Step Calculation

1. Calculate the annual demand (D) for the product. For example, if Apple sells 1 million units of its latest iPhone model per year, D = 1,000,000 units/year.
2. Determine the ordering cost per order (S) and the holding cost per unit per year (C). For example, if the ordering cost per order is $100 and the holding cost per unit per year is $10, S = $100 and C = $10.
3. Calculate the Economic Order Quantity (EOQ) using the formula EOQ = ?(2DS/C).
4. Calculate the total cost (TC) using the formula TC = (EOQ/2) × C + (D/EOQ) × S.
5. Determine the minimum total cost (TC_min) using the formula TC_min = ?(2DS/C).
6. Calculate the safety stock using the formula Safety Stock = z ×-× ?(D × T), where z is the z-score,-is the standard deviation of demand, D is the annual demand, and T is the lead time.

Common Mistakes

• Mistake: Using the wrong formula for calculating the Economic Order Quantity (EOQ).
• Correction: Use the correct formula EOQ = ?(2DS/C), where D is the annual demand, S is the ordering cost per order, and C is the holding cost per unit per year.
• Mistake: Not considering the lead time when calculating the safety stock.
• Correction: Include the lead time (T) in the safety stock formula Safety Stock = z ×-× ?(D × T).
• Mistake: Confusing the Economic Order Quantity (EOQ) with the Just-In-Time (JIT) inventory level.
• Correction: The EOQ is the optimal order quantity to minimize costs, while the JIT inventory level is the optimal inventory level for a JIT system, which is calculated as JIT = D × T.

Exam / CFA Tips

• Tip: Be careful with the units when calculating the Economic Order Quantity (EOQ) and the safety stock.
• Tip: Make sure to include the lead time when calculating the safety stock.
• Tip: Be able to distinguish between the Economic Order Quantity (EOQ) and the Just-In-Time (JIT) inventory level.

Quick Practice Problem

Apple wants to maintain an inventory level of 10,000 units of its latest iPhone model. The annual demand is 1 million units, the ordering cost per order is $100, and the holding cost per unit per year is $10. What is the Economic Order Quantity (EOQ)?

Answer: EOQ = ?(2 × 1,000,000 × $100 / $10) = 447.21 units

Explanation: The EOQ is the optimal order quantity to minimize costs, which is calculated as EOQ = ?(2DS/C).

Last-Minute Cram Sheet

• The Economic Order Quantity (EOQ) is calculated as EOQ = ?(2DS/C).
• The Just-In-Time (JIT) inventory level is calculated as JIT = D × T.
• The safety stock is calculated as Safety Stock = z ×-× ?(D × T).
• The lead time (T) must be included when calculating the safety stock.
• The units must be carefully considered when calculating the EOQ and the safety stock.
• The minimum total cost (TC_min) is calculated as TC_min = ?(2DS/C).
• The total cost (TC) is calculated as TC = (EOQ/2) × C + (D/EOQ) × S.