MATERIALS COST CHAPTER2 PRACTICAL PROBLEMS

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1 HAPTER MATERIALS OST PRATIAL PROBLEMS Q4: A company manufactures a product from a raw material, which is purchased at `60 per kg. The company incurs a handling cost of `360 plus freight of `390 per order. The incremental carrying cost of inventory of raw material is `0.50 per kg. per month. In addition, the cost of working capital finance on the investment in inventory of raw material is `9 per kg. per annum. The annual production of the product is 1,00,000 units and.5 units are obtained from one kg of raw material. Required: (i) alculate the Economic Quantity of raw materials. (ii) Advise, how frequently should orders for procurement be placed. (iii) If the company proposes to rationalise placement of orders on quarterly basis, what percentage of discount in the price of raw materials should be negotiated? (A Inter Nov 001, A IP May 014) Solution: (i) A = 1,00,000 units x 1 kg = 40,000 kg.5 units O = `360 + `390 = `750 = (`0.50 x 1) + `9 = `15 EOQ = x A x O = x 40,000 kg x `750 =,000 kg `15 (ii) No. of orders p.a. = Requirement = 40,000 kg = 0 orders EOQ,000 kg Time between orders = 360 days = 18 days 0 orders (iii) No. of orders to be placed p.a. = 4 orders If orders are placed on quarterly basis size proposed = 40,000 = 10,000 kg 4 orders Statement showing determination of minimum percentage discount to be negotiated: ing ost 40,000kg x `750 (4 orders x `750),000kg,000 Kg 10,000 Kg 15,000 `3,000

2 . MATERIALS OST arrying ost,000kg x `15 10,000kg x `15 By: A Ashish Kalra `15,000 `75,000 Total Relevant ost `30,000 `78,000 Extra ost to be incurred `48,000 Requirement of Raw Material 40,000 Kg Extra ost p.a./ Min. disc. p.u. to be negotiated `1.0 Purchase price per Kg `60 Min. %age to be negotiated % Q5: Novelty Ltd. carries wide items for its customers. One item, Gaylook, is very popular. Desirous is keeping its inventory under control; a decision is taken to order only the optimal economic quantity for this item, each item. You have the following information. Make your recommendations: Demand 1,60,000 units Price per unit `0 arrying ost `1 per unit or 5% per rupee of inventory value. ost `50 Determine the Optimal Economic Quantity by developing the following table: Size of No. of s Average Inventory arrying osts osts Total osts Solution: Determination of Optimal Economic Quantity: Size of s (Units) 1,60,000 16,000 8,000 4,000,000 1,600 No. of s Avg. Inventory (Units) 80,000 8,000 4,000,000 1, arrying osts (`) 80,000 8,000 4,000,000 1, osts (`) ,000,000 4,000 5,000 Total osts 80,050 8,500 5,000 4,000 5,000 5,800 The least Total ost is at 4,000 units, hence, EOQ = 4,000 units Q6: A company, for one of the A-class items placed 6 orders each of size 00 in a year. Given ing ost = `600, Holding ost = 40 %, ost per unit = `40, find out the loss to the company in not operating scientific inventory policy? What are your recommendations for the future? Solution: EOQ = x A x O = x 1,00 x 600 = 300 units 16 A = 00 units x 6 orders = 1,00 units O = `600 per order = `40 x 40% = `16 Statement showing omputation of loss for not operating Scientific Inventory Policy: 300 units 00 units ing ost [ 1,00 x 600/300],400 [1,00 x 600/00] 3,600 arrying ost [300/ x 16],400

3 MATERIALS OST By: A Ashish Kalra.3 [00/ x 16] 1,600 Total Relevant osts 4,800 5,00 Loss to the company = `5,00 `4,800 = `400 Recommendation for future is to order EOQ = 300 units Q7: A firm is using EOQ system of inventory replenishment for one of its purchased items, which has a known annual demand of 48,000 units with a near uniform rate of consumption. The cost of placing an order is `50. The cost of the item is `5 per unit. The firm uses an inventory carrying rate of 30% p.a. 1. Find the optimum order quantity, the number of orders per year, and the systems cost.. If the lead time (i.e. the time between the placement of order and delivery) is 10 days no safety stock is kept and the year is taken as 300 days, find the re- order point. 3. If for administrative reasons the firm wishes to place orders only once in three months, how much extra cost will the firm incur on this policy? Solution: 1. (a) EOQ = x A x O = x 48,000 x 50 = 4,000 units `5 x 30% A = 48,000 units O = `50 per order = 30% x `5 = `1.50 per unit p.a. (b) Optimal Number of s per year = Requirement = 48,000 units = 1 orders EOQ 4,000 units (c) ost of Operating the Inventory System: ost of ing = 1 orders x `50 = `3,000 ost of Holding = 1/ x 4,000 x 5 x 0.30 = `3,000 Total Systems ost = 3, ,000 = `6,000. The daily demand rate is 48,000/300 = 160 units. Hence lead time demand = 160 units x 10 days = 1,600 units which is the Re- Point. 3. If order is placed once in a Quarter, then Q = 1,000 units [48,000 / 4] Average Stock in this case = 1,000 units x 1/ = 6,000 units ost of ing = `50 x 4 orders = `1,000 ost of Holding = 6,000 units x `5 x 0.30 = `9,000 Total ost = `1,000 + `9,000 = `10,000 So, this policy will involve an extra cost of ` (10,000 6,000) = `4,000 p.a. Q8: A ompany manufactures a special product which requires a component Alpha. The following particulars are collected for the year 008: (i) demand of Alpha 8,000 units (ii) ost of placing an order `00 per order (iii) ost per unit of Alpha `400 (iv) arrying cost % p.a. 0% The company has been offered a quantity discount of 4% on the purchase of Alpha, provided the order size is 4,000 components at a time. Required: (i) ompute the Economic Quantity. (ii) Advise whether the quantity discount offer can be accepted. (A PE II Nov 007) Solution: (i) EOQ = x A x O = x 8,000 units x 00 = 00 units `80 A = 8,000 units

4 .4 MATERIALS OST O = `00 = `400 per unit x 0% = `80 By: A Ashish Kalra (ii) Statement showing Evaluation of Proposal: Amount in (`) 00 Units 4,000 Units Purchase ost (`400/384 p.u.) 3,00,000 30,7,000 ing ost (`00 per order) 8, arrying ost (`80/ per unit) 8,000 1,53,600 Total osts 3,16,000 3,6,000 Advice: It is advised not to accept the quantity discount offer. Q9: JP Limited manufactures of a special product, follows the policy of EOQ (Economic Quantity) for one of its components. The component s details are as follows: Amount in (`) Purchase Price per component 00 ost of an 100 ost of arrying one unit in Inventory 10% of Purchase Price Total arrying ost of Inventory and ing per Annum 4,000 The company has been offered a discount of % on the price of the component provided the lot size is,000 components at a time. You are required to: (a) ompute the EOQ. (b) Advise whether the quantity offer can be accepted. (Assume that the inventory carrying cost does not carry according to discount policy) (c) Would your advice differ if the company is offered 5% discount on a single order? (A Inter Nov 1994) Solution: arrying & ing ost = 4,000 O = `100 per order = `00 x 10% = `0 (a) Total ost of ing & arrying = x A x O x `4,000 = x A x `100 x `0 4,000 = A x 4,000 A = 4,000 units EOQ = x A x O = x 4,000 units x 100 = 00 units `0 (b) Statement showing evaluation of Proposal Amount in (`) 00 units,000 units Purchase ost (4,000 units x `00); (4,000 units x `196) 8,00,000 7,84,000 Add: ing ost (`100 x 0 orders) ; (`100 x orders), Add: arrying ost,000 0, units x 0 ;,000 units x 0 Total osts 8,04,000 8,04,00 Advise: Reject the proposal

5 MATERIALS OST By: A Ashish Kalra.5 (c) Statement showing Evaluation of Proposal Amount in (`) 4,000 units Purchase ost (4,000 units x `190) 7,60,000 Add: ing ost 100 Add: arrying ost 4,000 Units x `0 40,000 Total osts 8,00,100 Advise: Accept the proposal. Q30: KL Limited produces product M which has a quarterly demand of 8,000 units. The product requires 3 kgs quantity of material X for every finished unit of product. The other information is: ost of material X `0 per kg. ost of placing an order `1,000 per order arrying ost 15% per annum of average inventory You are required: (i) alculate the Economic Quantity for material X. (ii) Should the company accept an offer of % discount by the supplier, if he wants to supply the annual requirement of material X in 4 equal quarterly installments? (A IP Nov 01) Solution: demand of Product M = 8,000 units x 4 = 3,000 units A or demand of Raw Material X = 3,000 units x 3kg = 96,000 kg O = `1,000 per order = 15% of `0 (i) EOQ = x A x O = x 96,000 kg x `1,000 = 8,000 kg `3 (ii) Statement Showing Evaluation of Supplier s proposal 8,000 kg 4,000 kg Purchase ost (96,000 kg x `0) 19,0,000 [96,000 kg x (`0 % of 0)] 18,81,600 ing ost 96,000 kg x `1,000 1,000 8,000 kg 96,000 kg x `1,000 4,000 4,000 kg arrying ost 8,000 kg x 15% x `0 1,000 4,000 kg x 15% x ` ,80 Total Relevant osts 19,44,000 19,0,880 Advise: The ompany should accept the proposal of supplier of % discount. Q31: Thampson Toolings has a contract from the Department of Defense for 1,50,000 bushings a year. Thampson Toolings orders the metals for the bushings in lots of 40,000 units from a supplier. It costs `400 to place an order and the estimated carrying charge is 0% of the unit cost which is `1.50. Thampson Toolings wants to know what percent their order quantity varies from optimal and what the variations is costing them, if any? Solution: A = 1,50,000 units, O = `400 per order = `1.50 per unit x 0% = `0.3

6 .6 MATERIALS OST EOQ = x A x O = x 1,50,000 units x `400 = 0,000 units `0.3 By: A Ashish Kalra 0,000 Units 40,000 Units No. of s ing ost `400 `3,000 `1,500 Average Stock 10,000 Units 0,000 Units arrying ost `0.30 per unit `3,000 `6,000 Total ing & arrying ost `6,000 `7,500 Variation of units in per order = 0,000 units Variation (% age) = 0,000 x 100 = 100% 0,000 ost of Variation = `7,500 `6,000 = `1,500 Q3: PQR Limited produces a product which has a monthly demand of 5,000 units. The product requires a component X which is purchased at `15 per unit. For every finished product, units of omponent X are required. The ing cost is `350 per order & arrying cost is 1% p.a. Required: (i) alculate the Economic Quantity for omponent X. (ii) If minimum lot size to be supplied is 5,000 units, what is the extra cost, the company has to incur? (iii) What is the Minimum arrying ost, the ompany has to incur? (A PE II May 006) Solution: (i) EOQ = x A x O A = 5,000 units x 1 months x units = 1,48,000 units O = `350 per order = 1% x `15 = `1.80 = x 1,48,000 units x `350 =,030 units of components `1.8 (ii) Extra ost incurred by the company Total ost (when order size is 5,000 units) = Total ing ost + Total arrying ost = 5,000 units x 1 months x units x ` ,000 units x `15 x 1% 5,000 units = `8,400 + `46,800 = `55,00 Total ost when order size is,030 units (i.e. EOQ) = x A x O x = x 1,48,000 units x `350 x `1.8 = `39,655 Extra cost incurred = `55,00 `39,655 = `15,545 (iii) Minimum arrying ost, the company has to incur = arrying ost of EOQ units =,030 x `1.80 = `19,87 Q33: G. Ltd. produces a product which has a monthly demand of 4,000 units. The product requires a component X which is purchased at `0. For every finished product, one unit of component is required. The ordering cost is `10 per order and the holding cost is 10% p.a. You are required to calculate: (i) Economic Quantity. (ii) If minimum lot size to be supplied is 4,000 units, what is the extra cost, the company has to incur? (iii) What is the Minimum arrying ost, the company has to incur?

7 MATERIALS OST By: A Ashish Kalra.7 Solution: A = 4,000 units x 1 months = 48,000 units O = `10 per order = `0 x 10% = ` per order per annum EOQ = x A x O = x 48,000 units x `10 =,400 units ` (ii) Statement Showing Determination of Relevant ost,400 units ing ost 48,000 units x `10 48,000 units x `10,400 units 4,000 units arrying ost,400 units x ` 4,000 units x ` 4,000 units,400 1,440,400 4,000 Total ost 4,800 5,440 Extra ost includes = `(5,440 4,800) = `640 (iii) Minimum arrying ost = arrying ost of EOQ units = `,400 which is possible at,400 units (EOQ). Q34: A hardware store procures and sells hardware items. Information on an item is given bellow: Expected Sales 8,000 units ing ost `180 per order Holding ost 10 % of the average inventory value The item can be purchased according to the following schedule: Lot size Unit price (`) `.00 1,000 1,499 `0.00 1,500 1,999 `19.50,000 and above `18.50 You are required to determine the best order size. Solution: Statement showing determination of Economic Quantity requirement size No. of s (A) (B) () ordering ost Purchase price per unit Purchase ost Avg. Units arrying ost per unit arrying ost Total ost (A) + (B) + () Units Units Nos. (`) (`) (`) Units (`) (`) (`) 8, ,000 1,500, ,880 1, ,76,000 1,60,000 1,56,000 1,48, , ,000 1, ,850 Best/ Economic Size =,000 units Q35: RST Limited has received an offer of quantity discount on its order of materials as under: Price per tonne Tonnes number `9,600 Less than 50 `9, and less than 100 `9, and less than 00 `8, and less than 300 1,79,430 1,6,440 1,58,41.5 1,50,570

8 .8 MATERIALS OST By: A Ashish Kalra `8, and above The annual requirement for the material is 500 tonnes. The ordering cost per order is `1,500 and the stock holding cost is estimated at 5% of the material cost per annum. Required: (i) ompute the most economical purchase level. (ii) ompute EOQ if there are no quantity discounts and the price per tonne is `10,500. (A PE II Nov 004, A IP Nov 010 Adapted) Solution: (i) Statement showing Determination of EOQ: Demand Size No. of s ing ost (A) Purchase Price per unit Purchase ost (B) arryi ng ost per unit Average Units arrying ost () Total ost (A+B+) (tonnes) (Nos.) (`) (`) (`) (`) (tonnes) (`) (`) ,56,50 1,5,000 6,500 31,50 0,875 9,600 9,360 9,10 8,880 8,640 48,00,000 46,80,000 45,60,000 44,40,000 43,0,000,400,340,80,0, ,000 58,500 1,14,000,,000 3,4,000 50,04,50 48,63,500 47,36,500 46,93,50 46,64,875 The above table shows that the total cost of 500 tonnes including ordering and carrying cost is minimum (`46,64,875) where the order size is 300 tonnes. Hence the most economical purchase level is 300 tonnes. EOQ = x A x O = x 500 tonnes x `1,500 = 69 tonnes `,65 A = 500 tonnes O = `1,500 per order = `10,500 x 5% = `,65 Q36: X Ltd. is reviewing its stock policy, and has the following alternatives available for the evaluation of stock: (i) Purchase stock twice in a month, 400 units (ii) Purchase monthly, 800 units (iii) Purchase every three months,,400 units (iv) Purchase six monthly, 4,800 units (v) Purchase annually, 9,600 units It is ascertained that the purchase price per unit is `40 for deliveries upto,000 units. A 5% discount is offered by the supplier on the whole order where deliveries are,001 to 4,000 units and 10% reduction on the total order for deliveries in excess of 4,000 units. Each purchase order incurs administration costs of `50. Interest on capital and other storage costs are `1.50 per unit of average stock quantity held. alculate the optimum order size. (A PE II June 009)

9 MATERIALS OST By: A Ashish Kalra.9 Solution: Size of No. of s p.a. Statement showing Determination of EOQ Purchase ost arrying ing Amount (A) Rate ost ost (B) () Total osts (A) + (B) + () (Units) (Nos.) (`) (`) (`) (`) (`) 9, ,45, , ,05,850 4,800 3,45, , ,76,100, ,64, , ,80, ,84, , ,9, ,84, ,000 3,9,500 Purchasing of 4,800 units has lowest total cost `3,76,100. Therefore, it is optimum order size. Working Notes: (i) Purchase Price below or upto,000 units = `40 At order size,000 units `40 5% Discount = `38 At 4,800 units & 9,600 units it is 10% less i.e. `40 `4 = `36 (ii) Storage ost: `1.50 per unit of Average Stock size 400 Average stock 00 units x `1.50 = `,500 At 4,800 units =,400 units x `1.50 = `30,000

Capital Budgeting. Questions 4, 5, 8, 9, 12, 15, 16, 19, 22, 23, 24, 25, 27, 45, 61, 62, 63, 64, 65, 66

Capital Budgeting. Questions 4, 5, 8, 9, 12, 15, 16, 19, 22, 23, 24, 25, 27, 45, 61, 62, 63, 64, 65, 66 Financial Management 1 Capital Budgeting LIST OF IMPORTANT QUESTIONS MUST TO REVISE Questions 4, 5, 8, 9, 12, 15, 16, 19, 22, 23, 24, 25, 27, 45, 61, 62, 63, 64, 65, 66 Rest also to be done but list of