Working capital Task 1. Determine the period of the turnover of working capital with the following data: quarterly output O = 100 bln BYN, standard of working capital WCs = 50 bln BYN. Solution: 1. Determine the turnover rate of working capital: 𝑂 𝑘𝑡u = 𝑊𝐶 = 𝑆 100 50 = 2 turnover rate (2 per quarter) 2. Period of turnover of working capital: 𝑇𝑡𝑢 = 𝑇 𝑘𝑡𝑢 = 90 𝑑𝑎𝑦𝑠 2 𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟 = 45 days Task 2. Establish a working capital standard for work-in-progress with the following data: annual output of Na=72,000 DC, production cycle duration Tc = 10 days, production cost per unit C = 1 mln. BYN, material costs M = 0.6 mln BYN. Solution: 1. Determine the incremental factor: 𝑘𝑖𝑓 = М + С 0,6 + 1 = = 0,8 2С 2⋅1 2. Establish a working capital standard for work in progress: 72000 𝑂𝑤𝑖𝑝 = 𝑁𝑎𝑣. 𝑑𝑎𝑖𝑙𝑦 ⋅ 𝑇𝐶 ⋅ С ⋅ 𝑘𝑖𝑓 = 360 ⋅ 10 ⋅ 1 ⋅ 0,8 = 1600 mln BYN. Task 3. Establish a working capital standard for the stock of finished goods in the warehouse with the following data: annual output of Ng = 18,000 pct., unit cost C = $20,000, preparation time for Trag production = 2 days. Solution: 𝑂 = 𝑑 ⋅ С ⋅ 𝑇𝑟𝑎𝑔 = 18000 360 ⋅ 20000 ⋅ 2 = $2 mln. Task 4. Determine the working capital standard for the production stock of materials, thous. BYN.: Production manufacturnovere 100 thous. pct. Material consumption rate per article 200 kg. Price per ton of material 800 thous. BYN. Time between two regular shipments 30 days Solution: 1. We shall determine the level of production stocks in physical terms: 𝑇 𝑁р ⋅𝑁𝑦𝑒𝑎𝑟 𝑇𝑠𝑢𝑝𝑝𝑙𝑦 0,2⋅100000 30 𝑁𝑝𝑠 = 𝑁𝑎𝑣. 𝑑𝑎𝑖𝑙𝑦 ⋅ 𝑠𝑢𝑝𝑝𝑙𝑦 = ⋅ = ⋅ 2 = 833,33 thous. kg. 2 𝑇 2 360 𝑟𝑎𝑔 2. Let us define the value of production stocks in terms of: 𝑁𝑣𝑎𝑙.𝑝𝑟𝑜𝑑. = 𝑁𝑝𝑠 ⋅ 𝐶м = 833,33 ⋅ 800000 = 666664000 BYN. Task 5. Establish a working capital standard for work-in-progress, if the production cost of the product according to the planned calculation of 200 thous. BYN. (The costs of raw materials, basic materials and purchased semi-processed goods - 120 000 BYN), production cycle duration 20 working days and annual production plan 8 thousand. Solution: 1. Establish a working capital standard for work-in-progress: 𝑂𝑤𝑖𝑝 = 𝑁𝑎𝑣. 𝑑𝑎𝑖𝑙𝑦. ⋅ 𝑇𝑐 ⋅ С ⋅ 𝑘𝑖𝑓 = 𝑁𝑎𝑣. 101,59 thous. BYN. М+С 𝑑𝑎𝑖𝑙𝑦. ⋅ 𝑇𝑐 ⋅ С ⋅ ( 2С 8 120+200 ) = 252 ⋅ 20 ⋅ 200 ⋅ ( 2⋅200 )= Task 6. During the reporting year, production was sold on 800 mln. BYN, for the next year, it is planned to increase sales to 1000 mln. BYN. The working capital standard is increased from 10 mln to 12 mln. RUN. Determine the intended reduction in turnover time and the amount of revolving funds released. Solution: 1. Determine the turnover factor for the reporting period: 𝑟𝑒𝑝 𝑄𝑝 𝑟𝑒𝑝 𝑘𝑡𝑢𝑟 = 𝑂С𝑟𝑒𝑝 = 𝑝 800 10 = 80 turnover 2. Determine the turnover factor for the plan period: 𝑝𝑙 𝑘𝑡𝑢 = 𝑝𝑙 𝑄𝑝 𝑝𝑙 𝑂С𝑝 = 1000 12 = 83,3 turnover 3. Determine the duration of one turnover in the reporting period: 𝑇 𝑟𝑒𝑝 𝑝𝑙 𝑇𝑡𝑢𝑟 = 𝑘 𝑟𝑒𝑝 = 𝑡𝑢𝑟 360 80 = 4,5 days 4. Define the duration of one turnover in the planned period: 𝑝𝑙 𝑇𝑡𝑢𝑟 = 𝑇𝑝𝑙 𝑝𝑙 𝑘𝑡𝑢𝑟 360 = 83,3 = 4,3 days 5. Determine the intended rotation acceleration: 𝑟𝑒𝑝 𝑝𝑙 𝛥𝑇𝑎𝑐 = 𝑇𝑎𝑐 − 𝑇𝑎𝑐 = 4,5 − 4,3 = 0,2 days 6. Value of working capital released: 𝑟𝑒𝑝 𝑊𝐶𝑟𝑒𝑙 = 𝑁𝑎𝑣. 𝑑𝑎𝑖𝑙𝑦 ⋅ 𝛥𝑇𝑟𝑒𝑙 = 𝑟𝑒𝑝 𝑄𝑝 𝑇𝑝𝑙 800 ⋅ 𝛥𝑇𝑟𝑒𝑙 = 360 ⋅ 0,2 = 0,44 thous. BYN. Material Resources Task 1. Mass of steel part 96 kg, steel consumption rate 108 kg. It produces 3,000 products per year. The supply of steel is quarterly. Transport stock – 2 day. Determine production stock; calculate the steel utilization rate. Solution: 1. Average daily consumption (consumption) in physical terms: 𝑁𝑦 3000 𝑃𝑎𝑣.𝑑𝑎𝑖𝑙𝑙𝑦 = 𝑁𝑎𝑣. 𝑑𝑎𝑖𝑙𝑙𝑦 ⋅ 𝑁𝑐 = 360 ⋅ 𝑁р = 360 ⋅ 108 = 900 kg 2. Current reserves: 𝑁𝐶𝑅 = 𝑃𝑎𝑣.𝑑𝑎𝑖𝑙𝑙𝑦 ⋅ 𝑇𝑝 = 0,9 ⋅ 90 = 81 t 3. Safety stock: 𝑁𝑆𝑆 = 0,5 ⋅ 𝑇𝑆 = 0,5 ⋅ 81 = 40,5 t 4. Transport stock: 𝑁𝑇𝑟.𝑆 = 𝑃𝑎𝑣.𝑑𝑎𝑖𝑙𝑙𝑦 ⋅ 𝑇𝑇𝑟.𝑆 = 0,9 ⋅ 2 = 1,8 t 5. Production stock: 𝑁𝑃𝑆 = 𝑁𝑆𝑆 + 𝑁𝐶𝑅 + 𝑁𝑇𝑟.𝑆 = 81 + 40,5 + 1,8 = 123,3 t 6. Utilization rates material: 𝑘𝑈𝑀 = 𝑡 𝑚 𝑚𝑎𝑡 96 = 108 = 0,89 Task 2. Weight detail - 350 kg. The value of the actual waste in the processing of harvests is 92 kg. Thanks to improvements in component manufacturnovering technology, it is planned to reduce waste by 10%. Calculate the metal utilization factor and the proportion of waste before and after technology change. Solution: 1. Actual waste after technology change: 𝑁 𝑚𝑤 = 92⋅(100%−10%) 100% = 82,8 kg 2. Utilization rate metal - before the change technology: 𝑏 𝑘𝑐𝑡 = 𝑚𝑑𝑏 350 = = 0,79 𝑏 𝑏 𝑚𝑑 + 𝑚𝑤 350 + 92 - after the change technology: 𝑎 𝑘𝑐𝑡 𝑚𝑑𝑏 350 = 𝑎 = = 0,81 𝑎 𝑚𝑑 + 𝑚𝑤 350 + 82,8 3. Share of waste - before the change technology: 𝑏 𝑘𝑤 𝑏 𝑚𝑤 92 = 𝑏 = = 0,21 𝑏 350 + 92 𝑚𝑑 + 𝑚𝑤 - after the change technology: 𝑎 𝑘𝑤 𝑎 𝑚𝑤 82,8 = 𝑎 = = 0,19 𝑎 𝑚𝑑 + 𝑚𝑤 350 + 82,8 Personnel of a company Task 1. Standard labour intensity of maintenance - 270,000. Standard hours; Compliance rate 1.15; the annual working time balance of 1,830 hours. Determine the required number of metalworking. Solution: 1. The required number of subjects is determined (calculated on the basis of the labour intensity of the production programme): ∑𝑛 Р𝑟𝑠 = 𝐹 𝑖=1 ⋅𝑘 𝑠𝑡 𝑁𝑖 ⋅𝑡𝑠𝑡 𝑐𝑜𝑚𝑝𝑙 =𝐹 ∑𝑡 𝑠𝑡 ⋅𝑘𝑐𝑜𝑚𝑝𝑙 270000 = 1830⋅1,15 = 128,3 ≈ 128 man. Task 2. To list the number of employees according to the following data: Operating hours of the enterprise are continuous (365 days per year); Effective (planned) fund for one worker - 220 days; Number of units served - 60; Each unit is served by a 3-member unit; Work schedule 3-shift (shift 8 hours). Solution: 1. The number of employees is determined on the basis of the following numbers: Р𝑛𝑢𝑚𝑏 = 𝑚𝑝𝑙𝑎𝑛𝑡 ⋅ 𝑁𝑛 ⋅ 𝑘𝑠ℎ𝑖𝑓𝑡 = 60 ⋅ 3 ⋅ 3 = 540 man. 2. Determine the rate of returnovern of the number of personnel to the list of: 𝑘𝑟𝑒𝑑 = 𝑇𝑛 365 = = 1,66 𝑇𝑓 220 3. List the number of staff: Р𝑙𝑖𝑠𝑡 = Р𝑛𝑢𝑚𝑏 ⋅ 𝑘𝑟𝑒𝑑 = 540 ⋅ 1,66 = 896,4 man. Task 3. To produce 54,000 parts within a year. The replacement output rate for one working person is 25 parts; the N is met on average by 120%. The section works in 2 shifts. Determine the number of workers on the site if 225 workdays are planned. Solution: 1. Determine the number of employees: Р𝑙𝑖𝑠𝑡 = [𝑁 𝑁г ÷𝑇𝑝𝑙𝑎𝑛 ÷𝑘𝑟𝑒𝑑 𝑑𝑒𝑡𝑒𝑟𝑚 ⋅𝑘𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒 ] ⋅ 𝑘𝑟𝑒𝑑 = [ 54000÷225÷2 25⋅1,2 ] ⋅ 2 = 8 man. Task 4. The workshop has 70 automatic machine tools and a double-shift operating mode; Maintenance rate - 7 machines per adjuster, planned working time balance of one employee - 220 days, nominal fund of enterprise - 255 days. Determine the number of attendants and the number of attendants. Solution: 1. Determine the number of attendants by service standards: Р𝑙𝑖𝑠𝑡 = 𝑚𝑓𝑜𝑢𝑛𝑑 ⋅𝑘𝑟𝑒𝑑 𝑁𝑂 = 70⋅2 7 = 20 man. 2. Determine the rate of returnovern of the number of personnel to the list of: 𝑘𝑟𝑒𝑑 = 𝑇𝑁 255 = = 1,16 𝑇𝐹 220 3. List the number of staff: Р𝑙𝑖𝑠𝑡 = Р𝑙𝑖𝑠𝑡 ⋅ 𝑘𝑟𝑒𝑑 = 20 ⋅ 1,16 = 23,2man. Task 5. Calculate the monthly wage of the worker according to the timed pay system. The worker has the 4th tariff category, the tariff coefficient of which is 1.57. The rate of the first category, taking into account the increasing coefficient, is set in the enterprise at 1200 BYN. in month 168 hours worked. Solution: 1. Determine the RFP on the basis of a simple timescale pay system: 𝑅𝐹𝑃 = 𝐶ℎ𝑇𝐶 ⋅ 𝑘𝑡 ⋅ 𝑡 = 1200 ⋅ 1,57 ⋅ 168 = 316512 BYN. Task 6. Determine the price per detail. The production time limit is 40 minutes. The work is tariffed in the 5th category with a tariff coefficient of 1.73. The rate of the first category, taking into account the increasing coefficient, is fixed at the enterprise in the amount of 1200 BYN. Solution: 1. We shall calculate the price per detail on the basis of the direct individual piece-rate system: 40 𝑅𝐹𝑃 = ∑ 𝑃𝑖 ⋅ 𝑞𝑖 = 𝐶ℎ𝑇𝐶 ⋅ 𝑘𝑡 ⋅ 𝑡𝑔𝑟𝑎𝑛𝑑 = 1200 ⋅ 1,73 ⋅ 60 = 1384 BYN. Task 7. Calculate the monthly wage of a worker on a piece-rate basis. The worker worked 168 hours in the month, made 280 parts. The N for one piece is 36 minutes. The work is tariffed according to the 4th tariff category, whose tariff coefficient is 1.57. The rate of the first category, taking into account the increasing coefficient, is fixed at the enterprise in the amount of 1200 BYN. Bonus conditions: 20% of the bonus; 0.8 per cent for each percentage. Solution: 1. We shall calculate the price per detail on the basis of the pay-bonus system: 𝑅𝐹𝑃 = 𝑅𝐹𝑃 ⋅ (1 + 36 Р+𝛼⋅𝑛 100% ) = ∑ 𝑃𝑖 ⋅ 𝑞𝑖 ⋅ (1 + 20%+0,8%⋅0% Р+𝛼⋅𝑛 100% ) = 𝐶ℎ𝑇𝐶 ⋅ 𝑘𝑡 ⋅ 𝑡𝑔𝑟𝑎𝑛𝑑 ⋅ (1 + = 1200 ⋅ 1,57 ⋅ 60 ⋅ (1 + ) = 1356,48 BYN. 100% Note: No percentage exceeds the plan, i.e. 168*60/36=280. 2. Monthly RFP value: 𝑅𝐹𝑃 = 𝑅𝐹𝑃 ⋅ 𝑁 = 1356,48 ⋅ 280 = 379814,4BYN. Р+𝛼⋅𝑛 100% )= Task 8. The total labour intensity of the work in the workshop was 180,000 N-hours. Of these, 30,000 N-hours are for work of the 2nd category, 70,000. N-hours for work of the 3rd category and 80,000. N-hours for work of the 4th category. Determine the average wage rate. Solution: 1. The average wage rate is determined by the formula: К𝑡.𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒. = ∑𝑛 𝑖=1 Кр𝑖 ⋅𝑇𝑖 = ∑𝑛 𝑖=1 𝑇𝑖 30⋅1,16+70⋅1,35+80⋅1,57 180 = 34,8+94,5+125,6 180 = 254,9 180 = 1,416, PRODUCTION CAPACITY Task 1. Determine the annual production capacity of the workshop with three specialized units according to the following data: Capacity of the unit - 150 kg/h; 6% of nominal time. Calculate for two-shift operation. 252 workdays and 7 pre-break days a year. Solution: 1. Determine the nominal working time fund: 𝐹𝑁 = 𝑘𝑤𝑜𝑟𝑘 𝑑𝑎𝑦𝑠 ⋅ 𝑡𝑤𝑜𝑟𝑘 𝑑𝑎𝑦𝑠 ⋅ 𝑘𝑟𝑒𝑑 − 𝑘ℎ𝑜𝑙𝑖𝑑𝑎𝑦 ⋅ 𝑡𝑠ℎ𝑜𝑟𝑡 ⋅ 𝑘𝑟𝑒𝑑 = 252 ⋅ 8 ⋅ 2 − 7 ⋅ 1 ⋅ 2 = 4018 hour. 2. Determine the true working time fund: 𝐹𝐷 = 𝐹𝑁 ⋅ [1 − (𝛼р + 𝛼𝑁 )] = 4018 ⋅ [1 − (0,06 + 0)] = 3776,92 hour. 3. Determine the annual capacity of the workshop: 𝑊𝐶 = 𝐹𝐷 ⋅ 𝑊 ⋅ 𝑛 = 3776,92 ⋅ 150 ⋅ 3 = 1699614 Problem 2. There are 40 machines installed in the mechanized workshop. Workshop operating mode - 2 shifts, equipment operating time fund - 4,000 hours. Production time per unit - 2 hours; The production plan for the year is 76,000 C. Determine the capacity of the workshop and the capacity utilization factor. Solution: 1. Determine the capacity of the workshop: 𝑁 𝐹𝐷 ⋅𝑛⋅𝑘𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒 4000⋅40⋅1 𝑡𝑔𝑟𝑎𝑛𝑑 2 𝑚𝑎𝑥 tb. 2. Determine the power utilization factor: 𝑁 𝑘𝑢𝑝 = 76000 𝑁𝑚𝑎𝑥 80000 either 𝑘𝑢𝑝 = 𝐹 𝑁⋅𝑡𝑔𝑟𝑎𝑛𝑑 𝐷 ⋅𝑛⋅𝑘𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒 76000⋅2 = 4000⋅40⋅1 = 0,95 Task 3. Determine the time load factor of the equipment. Number of units of equipment n=100 pc. Real annual fund of time Fd=4,000 hours, production program - 50,000 pieces. per year, unit time N 288 min. Rate of compliance 1.2. Solution: 𝑘з = 60⋅𝐹 𝑁⋅𝑡𝑔𝑟𝑎𝑛𝑑 50000⋅288 𝐷 ⋅𝑛⋅𝑘𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒 = 60⋅4000⋅100⋅1,2 = 0,5 Task 4. Determine the capacity utilization rate of the enterprise. At the beginning of the year, 100 items of equipment had been installed in the workshop, 20 additional items of equipment had been purchased in June and 20 items of equipment had been written off in November. 4,000 hours of operating time per year. Production programme 100,000 C.T. Unit time 288 min. Compliance rate 1.2. Solution: 1. Determine average annual number of working machines: 𝑛𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒.г = 𝑛𝑁.г + 𝑛𝑑𝑒𝑡𝑒𝑟𝑚 ⋅𝑡1 12 − 𝑛𝑑𝑒𝑡𝑒𝑟𝑚 ⋅𝑡2 12 = 100 + 20⋅6 12 − 10⋅1 12 = 109 tb. 2. Determine the equipment-loading factor (capacity utilization factor): 𝑘з = 𝑁 ⋅ 𝑡𝑔𝑟𝑎𝑛𝑑 100000 ⋅ 288 = = 0,92 60 ⋅ 𝐹𝐷 ⋅ 𝑛 ⋅ 𝑘𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒 60 ⋅ 4000 ⋅ 109 ⋅ 1,2 Task 5. Define the enterprise’s production programme on the basis of its production capacity. Number of pieces of equipment - 20 pieces. 5,700 hours per year, 72 min per unit time, 1.2% rate of compliance. Solution: 𝑁= 60⋅𝐹д ⋅𝑛⋅𝑘𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑔𝑟𝑎𝑛𝑑 = 60⋅5700⋅20⋅1,2 72 = 114000 tb. Task 6. Determine the equipment load factor if 114,000 parts were planned and 80,000 parts were produced. Solution: 𝑁𝐹 𝑘з = 𝑁 𝑝𝑙𝑎𝑛 80000 = 114000 = 0,7 tb. Task 7. Determine the amount of equipment required in the workshop. Actual annual Time Fund Fd=4,000 hours, production program - 100,000 pieces per year, unit time N 144 mines. Rate of compliance 1.2. Solution: 𝑡 𝑛 = 60⋅𝐹 𝑔𝑟𝑎𝑛𝑑 ⋅𝑘 𝐷 ⋅𝑁 𝑎𝑣𝑣𝑒𝑟𝑎𝑔𝑒 = 144⋅100000 60⋅4000⋅1,2 = 50 tb.
