SOLUTIONS TO ASSIGNMENT PROBLEMS. Problem No. 1

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1 . MATERIALS a) Total Annual Cost in Existing Inventory Policy SOLUTIONS TO ASSIGNMENT PROBLEMS Problem No. 1 Ordering cost (6 Rs. 5) 150 Carrying cost of average inventory (36,000 6) = 6,000 units per order Average inventory = 3,000 units Carrying cost = 0% of Rs. 1 3,000 = 3, Total cost A 750 b) Total Annual Cost in E.O.Q EOQ X36,000 X5 1X0% = 3000 units No. of orders = 36,000 3,000 units = 1 orders Ordering cost (1 Rs. 5) = 300 Carrying cost of average inventory (3, ) = 300 Total Cost B 600 Savings due to EOQ Rs. ( ) (A B) 150 Note: As the units purchase cost of Rs. 1 does not change in both the computation, the same has not been considered to arrive at total cost of inventory for the purpose of savings. Problem No. (i) Given 1kg of M requires 3 kgs of X and quarterly demand = 8000 units of M. Annual requirement of X = 8000 X 4 X 3kgs S ordering Cost = kgs of X = 1,000 per order Carrying Cost C = 0 X 15% = 3 EOQ = (1000)(96000) = 8000 kgs. 3 Associated cost = (96000)X1000X3 = 4000 Raw Material Cost = X 0 per kg = 19,0,000 Total Cost = 19,44, (ii) If Company accepts discount then order size = = 4000 units 4orders Then purchase price = 70 % = 19.6 Carrying cost = 19.6 X 15% =.94 Ordering Cost = 4 orders X 1000 = 4000 Carrying Cost = 4000 X 1 X.94 = 35,80 Raw Material Cost = 96,000 kgs X 19.6 per kg = 18,81,600 Total Cost at Discount = 19,0,880 Discount should be accepted by the company as it results in savings of (19,44,000-19,0,880) = 3,10 IPCC_34.5e_Costing _ Materials_ Assignment Solutions 1

2 Ph: /6 Problem No. 3 Problem No. 4 IPCC_34.5e_Costing _ Materials_ Assignment Solutions

3 Problem No. 5 a) The question is asked about to calculate most economical purchase level, since the information given in the Question is vague, i.e. because, Question is not asking about different levels of order size. Hence as per the Information available in the Question, we will try to final out economical order size at different order sizes of different price ranges. 1. at Less than 50 Say 40. at at at at No. Of Raw orders Material Carrying Cost (Annual cost (Price O.S Ordering Cost XC.C ( x 5) Demand / per tone x O.S) A) Size of the order ,00, (500X9600) ,80, (500X9360) ,60, (500X910) 48, X 9,600 X0.5 58, X 9,360 X0.5 1,14, X 9,10 X0.5 1,56,50 (1.5X1500) 1,5,000 (10X1500) 5,500 (5X1500) Total Cost (3+4+5) 50,04,50 48,63,500 47,36,500 IPCC_34.5e_Costing _ Materials_ Assignment Solutions 3

4 Ph: / (500X8880) (500X8640),, X 8,880 X0.5 3,4, X 8,640 X0.5 31,50 (.5X1500) 0,875 (1.67X1500) 46,93,50 46,64,875 From the above calculations it is crystal clear that, if company places an order of 300 or more order size, then it is most economical to company. b) EOQ, if, there are no quantity discounts and purchase price per tonne = Rs. 10,500/- Carrying Cost = 10,500 X 5% = 65 EOQ = X500 X1,500 = 69 tonnes,65 Working Notes: Problem No EOQ without discount EOQ = = AS C X50Units X`0 `4 =, 500 = 50 units. Prices with discount for different order size 5% Discount = 30 5% = Rs % Discount = 30 10% = Rs % Discount = 30 1%= Rs Statement of Computing Total cost at various order sizes Orders size (units) No. of Orders in a year Ordering Cost Carrying cost of average inventory Purchase cost Total cost (1) () (3) (4) (5) (3+4+5)= (6) 50 50Units Units 7,15 7,35 5 (5 100 X 4 (50 50Units orders Rs.0) Rs.8.50) Units Units 6,750 7,000 (.5 00 X 4 (50 Rs.7) 100 Units oders Rs.0) Units 40 15Units 6,750 7,040 ( 50 X 4 (50 Rs.7) 15 Units oders Rs.0) 00 50Units 5 00Units 6,600 7,05 1.5* ( X 4 (50 00Units oders Rs.0) Rs.6.4) Units 1 50 Units 0 50Units 6,600 (1oder Rs.0) 500 X 4 (50 Rs.6.4) 7,10 Optimal order quantity = 100 units Minimum total cost of inventory and purchasing cost = Rs. 7,000. IPCC_34.5e_Costing _ Materials_ Assignment Solutions 4

5 Note: Theoretically it may be.5 orders, (50 100), however practically 3 orders are required. Therefore ordering cost would be Rs. 60 (3 0) and total cost Rs. 7,010 ( ). (* Theoretically orders may be in fraction but in practicality orders shall be in a whole number.) Working notes: Problem No Annual demand (30,000 units per quarter 4 quarters) = 1,0,000 units. Raw material required for 1,0,000 units (1,0,000 units 1.5 kg.) = 1,80,000 kg. 3. EOQ = X1,80,000kgs. X1,000 = 13,416 kgs.(appx) 4. Total cost of procurement and storage when the order size is equal to EOQ or 13,416 kg. (i) No. of orders (1,80,000 kg. 13,416 kg.) = 13.4 times or 14 times Ordering cost (14 orders Rs.1,000) = Rs. 14,000 Carrying cost (½ 13,416 kg. Rs. ) = Rs. 13,416 Total cost = Rs. 7,416 Re-order point = Safety stock + Lead time consumption 1,80,000kg. = 8,000kg. X4days 360 days = 8,000 kg. + 1,000 kg. = 0,000 kg. (ii) Statement showing the total cost of procurement and storage of raw materials (after considering the discount) Order size No. of orders Total cost of procurement Average stock Total cost of storage of raw materials Discount Total Cost Kg. Kg. (1) () (3)=() Rs.1,000 (4)=½ (1) (5)=(4) Rs. (6) (7)=[(3)+(5) (6)] 1,80, ,000 90,000 1,80,000 3,000 1,49,000 90,000,000 45,000 90,000 0,000 7,000 45, ,000,500 45,000-49,000 30, ,000 15,000 30,000-36,000 (iii) Number of orders which the company should place to minimize the costs after taking EOQ also into consideration is 14 orders. Total cost of procurement and storage in this case comes to Rs. 7,416 (please refer working note-4 above), which is minimum. Problem No. 8 Given that, Ordering cost per order (S) = Rs.45 Carrying Cost is 15% of average inventory i.e. (C) =.40 15% = Rs Given for 3 months supply no. of lots (1 quarter) = 6,50 lots. Supply for 1 months (4 quarters) (A) = 6,50 X 4 = 5,000 lots. Therefore, EOQ = AS 5, = c 0.36 =,500 units. IPCC_34.5e_Costing _ Materials_ Assignment Solutions 5

6 Ph: /6 Calculation of annual cost No. of orders Qty /order Avg. Inventory O.C C.C T.C a) ,15 (4 45 ) ( ) 1,305 b) (10 45 ) ( ) 900 Savings in cost 405 c) Reorder point = Lead time consumption + Safety stock = 5, days 50 Maximum level = EOQ + Safety stock =, = 3000 units. Minimum level = Safety stock = 500 units Given Average inventory level = Maximum Minimum = Problem No. 9 3, = 1750 units. A B Max usage (weekly) Average Usage Minimum Usage 5 5 R.O.Q Lead time Maximum Minimum A B Average Minimum Maximum 5 3 a) R.O.L = Maximum usage X Maximum Lead time (A) = 75 X 6 = 450 (B) = 75 X 4 = 300 b) Minimum Stock level = R.O.L (Average Usage X Average Lead Time) (A) = 450 (50 X 5) = 00 (B) = 300 (50 X 3) = 150 c) Maximum Stock Level = R.O.L + R.O.Q (Minimum Usage X Minimum L.T) (A) = (5 X 4) = 650 (B) = (5 X ) = 750 Minimum Stock Level Maximum Stock Level d) Average Stock level = (A) = = (B) = = 450 Problem No. 10 i) Economic order Quantity(EOQ) = ii) AS C X36,000X35,000 = 17.5 = 1000 Litres 10% of risk of being out of stock indicates 90% of having stock. which will take 14days lead time Safety stock = A x (14 days-1 days) 360 days IPCC_34.5e_Costing _ Materials_ Assignment Solutions 6

7 Reorder point 36, 000 = xdays 360 = 00litres = Minimum stock level + (Average lead time x Average consumption) = 00 + (1x100) = 1400 litres iii) At 5% risk of being out stock represent 95% chance of having stock Safety stock days = 15 days -1 days = 3 days Total ordering cost = No of orders 36, 000 = X = Rs1,05,000 Total carrying cost of inventory A EOQ x s = (safety stock + Average inventory x carrying cost/pu/p.a) = x3days (1000x ) x 990 * x1.7676% 360 = Rs Total cost = = /- Material Turnover Ratio (In times) = Problem No. 11 Cost material consumed Average stock (In days) = 365 days No.of times Particulars Material A Material B Material Consumed (Opening Stock + Purchases Closing Stock) Material Turnover Ratio (In times) 8,000 10, ,000 6,000 = 56,000 units 9, ,000 11,000 = 5,000 units 56,000 5,000 = 7 times =.5 times 10,000 Material Turnover Ratio = 5 days = 146 days (In days) 7.5 Conclusion: Material A is fast moving item compared to Material B. Problem No. 1 IPCC_34.5e_Costing _ Materials_ Assignment Solutions 7

8 Ph: /6 Problem No. 13 Store Ledger of Aditya Ltd. (Weighted Average Method) Date Receipts Issues Balance of Stock Feb. Qty (kg.) Rate Amount Qty (kg.) Rate Amount Qty (kg.) Rate Amount , ,70, ,63, ,06, , ,10, , ,16, , ,06,175 1, ,10, ,18, , ,9, , ,64, , ,93, ,00 3, ,6, , ,93,133 1, ,33, * ,611 1, ,48,688 * 180 kgs. is abnormal loss, hence it will be transferred to Costing Profit & Loss A/c. Problem No. 14 a) Gross quantity of input material required to be procured. Output required - 4,800 tonne Add: Scrap: A: (4,800 5%) 40 tonne Total input required - b) Selection of supplier: Invoice price Less: Discount Add: Freight charges Cost per tone B: (4,800 10%) 480 tonne 5,50 tonne Particulars X Y Z 60,000 55, ,000 55,500,000 3,000 6,000 58,000 65,000 (3,50) 61,750 Nil 61,750 Option- I: Purchase the raw material from Y subject to his capacity of 4000 tonnes and purchase the balance from X Cost per tonne = 4,00058,000 1,506,000 5,50 = Rs.59,101 per tonne. Option-II: Purchase the total raw material in total from Rs. 61,750 per tonne. Decision: Option-I is to be selected. Note: Income resulting from scrap is to be ignored, since the same is common for all options. Problem No. 15 Classification of the items of inventory as per ABC analysis number of varieties of inventory items should be classified as A category items because of the following reasons: a) Constitute 0.375% of total number of varieties of inventory handled by stores of factory, which is minimum as per given classification in the table. IPCC_34.5e_Costing _ Materials_ Assignment Solutions 8

9 b) 50% of total use value of inventory holding (average) which is maximum according to the given table. c) Highest in consumption about 85% of inventory usage (in end-product) number of varieties of inventory items should be classified as B category items because of the following reasons : a) Constitute.750% of total number of varieties of inventory items handled by stores of factory. b) Requires moderate investment of about 30% of total use value of inventory holding (average). c) Moderate in consumption about 10% of inventory usage (in end product). 3. 3,875 number of varieties of inventory items should be classified as C category items because of the following reasons: a) Constitute % of total varieties of inventory items handled by stores of factory. b) Requires about 0% of total use value of inventory holding (average). c) Minimum inventory consumption i.e. about 5% of inventory usage (in end-product). THE END IPCC_34.5e_Costing _ Materials_ Assignment Solutions 9