XYZ Ltd is engaged in the business of manufacturing product "A". The material required for the manufacture of Product A is Material “B”. Each unit…

(i) Economic Order Quantity Working Notes: 1. Calculation of Production of Product A: Projected sales of product A for the period = 10,000 unitsAdd: Closing stock of product A (10,000 units * 10% as per general practice) = 1,000 unitsLess: Opening stock of product A = 948 units Product A to be produced = 10,052 units 2. Calculation of Material B required for production: Each unit of Product A requires 2 Kgs of Material B.Yield of Material B is 80% of the input.So, for 1 unit of Product A, Material B required = 2 Kgs / 0.80 = 2.5 Kgs Material B Required for 10,052 units of Product A = 10,052 units * 2.5 Kgs/unit = 25,130 Kgs 3. Calculation of Purchase Requirement of Material B: Material B Required = 25,130 KgsAdd: Closing stock of Material B (10% of Material B required) = 2,513 KgsLess: Opening stock of Material B = 2,630 Kgs Purchase Requirement (A) of Material B = 25,013 Kgs 4. Carrying Cost (C): Purchase price per unit = 20Rate of Overdraft = 12.5%Obsolescence Rate = 12.5%Carrying Cost = (12.5% + 12.5%) of 20 = 25% of 20 = 5 per Kg Calculation of EOQ: EOQ = √(2AO/C) Where: A = Annual Requirement = 25,013 Kgs (approx. 25,000 Kgs for calculation simplicity)O = Ordering cost per order = 500C = Carrying Cost per unit per annum = 5 EOQ = √(2 * 25,000 * 500 / 5) = √(25,00,000) = 1,581.14 Kgs (ii) Re-Order Quantity (ROQ) Current purchase policy is Quarterly. This means 4 orders per year. Annual Requirement = 25,013 Kgs ROQ = Annual Requirement / Number of orders = 25,013 Kgs / 4 = 6,253.25 Kgs (iii) Re-Order Level (ROL) Max usage is more than minimum usage by 100 Kgs.Lead time – 4 to 8 days. Assuming average usage is (Max usage + Min usage) / 2. Let Min usage be X, then Max usage is X+100. Average usage = (X + X + 100) / 2 = X + 50. Annual Requirement = 25,013 Kgs. Assuming 365 days in a year. Average daily usage = 25,013 Kgs / 365 days = 68.53 Kgs/day. So, X + 50 = 68.53 => X = 18.53 Kgs/day (Min usage) Max daily usage = 18.53 + 100 = 118.53 Kgs/day. Max Lead Time = 8 days. ROL = Maximum Usage × Maximum Lead Time ROL = 118.53 Kgs/day × 8 days = 948.24 Kgs (iv) Maximum Stock Level Maximum Stock Level = Re-order Level + Re-order Quantity – (Minimum Usage × Minimum Lead Time) Maximum Stock Level = 948.24 Kgs + 6,253.25 Kgs – (18.53 Kgs/day × 4 days) Maximum Stock Level = 948.24 + 6,253.25 – 74.12 = 7,127.37 Kgs (v) Minimum Stock Level Minimum Stock Level = Re-order Level – (Average Usage × Average Lead Time) Average Lead Time = (4 + 8) / 2 = 6 days Minimum Stock Level = 948.24 Kgs – (68.53 Kgs/day × 6 days) Minimum Stock Level = 948.24 – 411.18 = 537.06 Kgs (vi) Profitability analysis on EOQ v. ROQ Particulars EOQ (1,581 Kgs) ROQ (6,253 Kgs) Annual Requirement (A) 25,013 Kgs 25,013 Kgs Quantity Ordered (B) 1,581 Kgs 6,253 Kgs No. of Orders (C) = (A)/(B) 15.82 ≈ 16 orders 4 orders Order cost @500 16 * 500 = 8,000 4 * 500 = 2,000 Average Inventory (B/2) 1,581 / 2 = 790.5 Kgs 6,253 / 2 = 3,126.5 Kgs Carrying Cost @5 790.5 * 5 = 3,952.50 3,126.5 * 5 = 15,632.50 Total Relevant Cost 11,952.50 17,632.50 Savings in EOQ over ROQ 17,632.50 -11,952.50 = 5,680 (vii) If a volume discount of 5% is provided for a quarterly purchase by the supplier, will your answer to (vi) above change? If a 5% discount is provided for quarterly purchases (ROQ), the purchase price per Kg would be - 20 * (1 - 0.05) = 19. New Carrying Cost for ROQ = 25% of 19 = 4.75 per Kg. Particulars EOQ (1,581 Kgs) ROQ (6,253 Kgs) Annual Requirement (A) 25,013 Kgs 25,013 Kgs Quantity Ordered (B) 1,581 Kgs 6,253 Kgs No. of Orders (C) = (A)/(B) 16 orders 4 orders Order cost @500 8,000 2,000 Average Inventory (B/2) 790.5 Kgs 3,126.5 Kgs Carrying Cost (EOQ @5, ROQ @4.75) 3,952.50 3,126.5 * 4.75 = 14,850.88 Total Relevant Cost (excluding purchase price) 11,952.50 16,850.88 Total Purchase Price (25,013 Kgs) 25,013 * 20 = 5,00,260 25,013 * 19 = 4,75,247 Total Cost (Relevant Cost + Purchase Price) 5,12,212.50 4,92,097.88 With a 5% discount, the total cost for ROQ (₹ 4,92,097.88) is lower than EOQ (₹ 5,12,212.50). Therefore, the company should opt for quarterly purchases to avail the discount, as it results in a higher profitability.