Material Cost and Employee Cost — Practice

Question 1

A company has annual demand of 24,000 units, ordering cost of Rs.150 per order, and carrying cost of Rs.4 per unit per annum. Compute EOQ and the number of orders to be placed per year.

Accepted Answer

EOQ is computed as the square root of two times annual demand times ordering cost per order, divided by carrying cost per unit per annum: square root of (2 times 24,000 times 150) divided by 4, that is square root of 72,00,000 divided by 4, giving square root of 18,00,000, which is approximately 1,342 units. The number of orders to be placed per year is annual demand divided by EOQ, that is 24,000 divided by 1,342, giving approximately 17.9 orders, in practice rounded to a whole number of orders per year as the company's ordering policy requires. The intuition behind why this specific quantity is optimal is worth stating in any answer: ordering a smaller quantity each time would require more frequent orders, raising total ordering cost, while reducing average inventory held and therefore total carrying cost; ordering a larger quantity would do the reverse, reducing ordering cost but raising carrying cost through higher average inventory. EOQ is the specific order quantity at which these two opposing cost effects are balanced so that their combined total is at its lowest point, not the quantity that minimises either cost individually.

Question 2

A material has: maximum consumption 600 units per day, minimum consumption 300 units per day, normal consumption 450 units per day, reorder period 8 to 12 days (normal 10 days), and reorder quantity 6,000 units. Compute reorder level, minimum stock level, maximum stock level and average stock level.

Accepted Answer

Reorder Level is maximum consumption rate multiplied by maximum reorder period: 600 units per day times 12 days, giving 7,200 units, the level at which fresh ordering must be triggered to cover the worst combination of high usage and slow delivery. Minimum Stock Level is Reorder Level less the product of normal consumption rate and normal reorder period: 7,200 less (450 times 10), that is 7,200 less 4,500, giving 2,700 units, representing the buffer stock the company expects to still hold even under normal, non-worst-case conditions when the reordered material actually arrives. Maximum Stock Level is Reorder Level plus Reorder Quantity, less the product of minimum consumption rate and minimum reorder period: 7,200 plus 6,000, less (300 times 8), that is 13,200 less 2,400, giving 10,800 units, representing the highest stock level expected if consumption during the reorder period is at its lowest and delivery arrives at its fastest, so the newly ordered stock arrives before existing stock has been drawn down as much as the worst case would suggest. Average Stock Level is Minimum Stock Level plus half the Reorder Quantity: 2,700 plus half of 6,000, that is 2,700 plus 3,000, giving 5,700 units, representing the typical stock level held on average across an ordering cycle, useful for estimating average carrying cost.

Question 3

A company received materials as follows: 100 units at Rs.20, then 150 units at Rs.24, then 200 units at Rs.28. It issues 300 units for production. Compute the cost of materials issued and closing stock value under FIFO and under LIFO, and state which method produces the higher reported profit in this period of rising prices.

Accepted Answer

Under FIFO, issues are priced at the cost of the oldest batch first: the first 100 units issued are costed at Rs.20, the next 150 units at Rs.24, and the remaining 50 units of the 300 issued are costed from the third batch at Rs.28. Cost of materials issued is (100 times 20) plus (150 times 24) plus (50 times 28), that is 2,000 plus 3,600 plus 1,400, giving 7,000. Closing stock is the remaining 150 units from the third batch, valued at 28 each, giving 4,200, which is the most recent price, consistent with FIFO leaving the newest-priced stock on hand. Under LIFO, issues are priced starting from the most recently received batch: the first 200 units issued are costed at Rs.28 from the third batch, and the remaining 100 units of the 300 issued are costed from the second batch at Rs.24. Cost of materials issued is (200 times 28) plus (100 times 24), that is 5,600 plus 2,400, giving 8,000. Closing stock is the remaining 50 units from the second batch at 24, plus all 100 units from the first batch at 20, giving (50 times 24) plus (100 times 20), that is 1,200 plus 2,000, giving 3,200. Comparing the two, FIFO produces a lower cost of materials issued, 7,000 against LIFO's 8,000, and a correspondingly higher closing stock value, 4,200 against LIFO's 3,200, which in a period of rising prices means FIFO reports the higher profit, since a lower cost of production directly increases reported profit for the period, while LIFO, by charging the most recently, and in a rising price environment most expensively, purchased material to production first, reports the lower profit and correspondingly understates closing stock relative to current replacement cost.

Question 4

A company purchases 1,000 kg of a chemical at Rs.50 per kg. Normal evaporation loss during storage is expected at 2%. Due to a container failure, an additional 30 kg is lost, which is well beyond the normal expectation. Compute the effective cost per kg of the usable material, and state the treatment of the abnormal portion.

Accepted Answer

Total cost of the purchase is 1,000 kg times 50, that is 50,000. Normal loss, expected as an inherent part of storing this chemical, is 2% of 1,000 kg, that is 20 kg, and this quantity is simply absorbed into the cost of the remaining good material, since the cost of what was actually purchased must still be recovered in full from whatever survives the expected wastage; no separate charge is made for it. The abnormal loss of 30 kg, arising from the container failure and well beyond the normal expectation, is treated entirely differently: it is costed separately at the material's cost, 30 kg times 50, that is 1,500, and this amount is charged to the costing profit and loss account rather than being absorbed into the cost of the remaining good material. After removing both the normal loss of 20 kg, absorbed rather than separately costed, and the abnormal loss of 30 kg, costed and charged out, the good usable material remaining is 1,000 less 20 less 30, that is 950 kg. Since the normal loss's cost is absorbed into the remaining material rather than separately charged, and the abnormal loss's cost has been removed entirely from the material cost pool and charged elsewhere, the effective cost of the 950 kg of good material is 50,000 less 1,500, that is 48,500, divided by 950 kg, giving an effective cost per kg of approximately 51.05, higher than the original 50 per kg purchase price, reflecting that the normal loss's cost has been spread across the surviving good material.

Question 5

Under Taylor's differential piece rate system, the standard output is 40 units per day, the low rate is Rs.4 per unit and the high rate is Rs.5 per unit for reaching or exceeding standard. Compute the earnings of a worker producing 35 units and a worker producing 45 units in a day, and explain the incentive logic of the scheme.

Accepted Answer

Taylor's differential piece rate system applies one of two sharply different rates depending on whether the worker reaches the standard output level, with no graduation between them: a lower rate applies to output below standard, and a substantially higher rate applies at or above standard, and the higher rate typically applies to the entire output produced that day, not merely to the units above standard, which is what makes the scheme so sharply incentivising. The worker producing 35 units, below the standard of 40, is paid at the low rate of Rs.4 per unit for the full 35 units produced, giving earnings of 35 times 4, that is 140. The worker producing 45 units, at or above the standard of 40, is paid at the high rate of Rs.5 per unit for the full 45 units produced, giving earnings of 45 times 5, that is 225. The incentive logic is deliberately blunt: the scheme is designed to create a strong, immediate financial reward for reaching the standard and a correspondingly sharp penalty for falling short of it, so that a worker just below standard has a very strong incentive to find the extra output needed to cross the threshold, since doing so does not merely add a few more units at the ordinary rate but retroactively raises the rate on every unit already produced that day. This all-or-nothing structure is more aggressive than an ordinary piece rate and is intended to drive efficient workers firmly towards, and ideally beyond, the standard rather than tolerating output that merely approaches it.

Question 6

A worker's standard time for a job is 10 hours, and the time rate is Rs.60 per hour. Compute total earnings, including bonus, under the Halsey plan (50% share) and the Rowan plan, for actual time of 8 hours and separately for actual time of 2 hours, and comment on which scheme pays more in each case.

Accepted Answer

Time saved in the first scenario is standard time of 10 hours less actual time of 8 hours, that is 2 hours. Under Halsey, bonus is 50% of time saved valued at the time rate: 50% times 2 hours times 60, that is 60. Basic pay for actual time worked is 8 hours times 60, that is 480, so total Halsey earnings are 480 plus 60, giving 540. Under Rowan, bonus is time saved divided by standard time, multiplied by actual time, multiplied by the time rate: (2 divided by 10) times 8 times 60, that is 0.2 times 8 times 60, giving 96. Total Rowan earnings are 480 plus 96, giving 576. In this first scenario, with a comparatively modest 2 hours saved out of a 10-hour standard, Rowan pays more than Halsey, 576 against 540. In the second scenario, actual time is 2 hours, so time saved is 10 less 2, that is 8 hours, a substantial saving representing very high efficiency. Under Halsey, bonus is 50% times 8 hours times 60, that is 240; basic pay for 2 hours actual time is 2 times 60, that is 120; total Halsey earnings are 120 plus 240, giving 360. Under Rowan, bonus is (8 divided by 10) times 2 times 60, that is 0.8 times 2 times 60, giving 96; total Rowan earnings are 120 plus 96, giving 216. In this second scenario, with a very large 8 hours saved, Halsey pays substantially more than Rowan, 360 against 216. The pattern illustrated is exactly the general behaviour of the two schemes: at low levels of time saved Rowan pays more, while at high levels of time saved Halsey pays more, with the two schemes intersecting at the point where time saved equals half the standard time, here at 5 hours saved; Rowan's bonus formula, containing time saved in the numerator and standard time in the denominator, causes its bonus to rise and then fall as a proportion of the job as time saved increases towards the full standard time, moderating the reward at extreme efficiency levels in a way Halsey's flat percentage-of-time-saved formula does not.

Question 7

A factory had an average of 500 employees during the year. During the year, 60 employees left, and 45 new employees were hired to replace some of them, with the remaining departures reflecting a deliberate reduction in headcount. Compute the separation rate, replacement rate and flux rate, and explain what the gap between the separation and replacement figures indicates.

Accepted Answer

Separation Rate is the number of employees separated during the period divided by the average number of employees during the period, multiplied by 100: 60 divided by 500, times 100, giving 12%. Replacement Rate is the number of employees replaced during the period divided by the average number of employees, multiplied by 100: 45 divided by 500, times 100, giving 9%. Flux Rate combines both movements, being the number separated plus the number replaced, divided by the average number of employees, multiplied by 100: (60 plus 45) divided by 500, times 100, that is 105 divided by 500 times 100, giving 21%. The gap between the separation rate of 12% and the replacement rate of 9% reflects that 15 of the 60 departures, that is 60 less 45, were not matched by a new hire, indicating a genuine, deliberate reduction in headcount of 15 employees over the year rather than the full turnover simply being routine churn where every departure is replaced. Reading this gap correctly is important: a company reporting only a separation rate without a corresponding replacement rate might look, on the separation figure alone, exactly like a company experiencing high routine churn with full replacement, when in fact part of its workforce reduction was structural rather than a like-for-like substitution of leavers with new joiners; the three rates together, rather than any single one in isolation, are needed to distinguish genuine downsizing from ordinary turnover with full replacement.

Question 8

A factory's workers are idle for 2 hours during a scheduled machine changeover, and separately idle for 6 hours when the plant loses power in an unexpected outage. In a different situation, a worker is asked to work 3 hours of overtime to meet a specific, urgent order a customer has requested be expedited. State the treatment of each, and the general principle distinguishing them.

Accepted Answer

The 2 hours of idle time during the scheduled machine changeover is normal idle time, since a changeover of this kind is a routine, expected part of running the machine and recurs as an inherent feature of the production process; it is treated as a factory overhead and absorbed generally into production cost, since it is not attributable to any specific abnormal event and simply reflects the ordinary cost of operating this way. The 6 hours of idle time from the unexpected power outage is abnormal idle time, since a power failure of this kind is not an expected, routine part of production and represents a genuinely unusual disruption; it is costed separately, at the wages paid for those idle hours, and charged directly to the costing profit and loss account rather than being absorbed into the general cost of production, following the same normal-versus-abnormal logic that governs the treatment of material losses elsewhere in this chapter. The overtime worked to meet the specific urgent customer order is treated differently from general overtime: where overtime premium arises from general pressure of work across the factory as a whole, it is treated as an overhead and spread across production generally, but where it is worked specifically at a customer's request to expedite a particular job, the premium may be charged directly to that job, since in that situation the extra cost is directly attributable to fulfilling that one customer's specific requirement rather than being a general cost of running the factory that happens to fall on whichever jobs are in production at the time. The general principle distinguishing all three situations is the same one that governs normal and abnormal losses throughout this paper: costs that are routine, expected and inherent to the process are absorbed generally, while costs that are unusual, unexpected, or specifically attributable to an identifiable cause are traced and charged separately to reflect their true origin.

Question 9

A company received materials as follows: 100 units at Rs.20 (opening), then 150 units at Rs.24, then 200 units at Rs.28. It issues 300 units for production. Compute the cost of materials issued and closing stock value under the weighted average method.

Accepted Answer

Under the weighted average method, a new weighted average cost is computed after each receipt, and all issues until the next receipt are valued at that current average. After the first receipt, opening stock, 100 units at 20, total 2,000; after the second receipt of 150 units at 24, total received value 3,600, total units on hand 250, total value 5,600, giving a weighted average of 5,600 divided by 250, that is 22.40 per unit. After the third receipt of 200 units at 28, total received value 5,600, total units on hand 450 (assuming no issues occurred between receipts, as the question does not specify any), total value 5,600 plus 5,600, that is 11,200, giving a weighted average of 11,200 divided by 450, that is 24.89 per unit approximately. The 300 units issued are valued at this final weighted average rate of 24.89, giving a total cost of materials issued of approximately 7,467. Closing stock is the remaining 450 less 300, that is 150 units, valued at the same weighted average rate of 24.89, giving approximately 3,733. The two figures, 7,467 plus 3,733, sum to approximately 11,200, reconciling with total material cost, and the weighted average method's characteristic feature is visible here: rather than tracking any specific batch through to issue or closing stock as FIFO and LIFO do, it smooths price fluctuations by blending all receipts into a single running average, producing a cost of materials issued and a closing stock value that sit between the FIFO and LIFO figures that would be computed from the same underlying receipts.

Question 10

Under Merrick's differential piece rate system, ordinary piece rate is Rs.5 per unit, with 110% of ordinary rate applied at 83% to 100% efficiency, and 120% of ordinary rate applied above 100% efficiency. Standard output is 50 units per day. Compute earnings for a worker producing 38 units, one producing 44 units, and one producing 55 units in a day.

Accepted Answer

Merrick's system applies one of three graduated rates depending on which efficiency band a worker's output falls into, unlike Taylor's two-rate system, giving a less sharply punitive structure for output that falls somewhat, but not drastically, below standard. Efficiency is actual output divided by standard output. The worker producing 38 units has efficiency of 38 divided by 50, that is 76%, below the 83% threshold for any enhanced rate, so ordinary piece rate applies to the full output: 38 times 5, giving 190. The worker producing 44 units has efficiency of 44 divided by 50, that is 88%, within the 83% to 100% band, so 110% of ordinary rate applies to the full output produced: 44 times 5 times 1.10, that is 44 times 5.50, giving 242. The worker producing 55 units has efficiency of 55 divided by 50, that is 110%, above the 100% threshold, so 120% of ordinary rate applies to the full output: 55 times 5 times 1.20, that is 55 times 6, giving 330. The graduated structure is visible in the outcomes: the worker at 76% efficiency earns strictly at the base rate with no enhancement at all, the worker at 88% efficiency earns a moderate 10% enhancement across the whole of their output, and the worker at 110% efficiency earns the full 20% enhancement, illustrating how Merrick's three bands create intermediate incentive levels that Taylor's cruder two-rate, all-or-nothing structure does not provide.

Question 11

Classify each as a preventive cost or a replacement cost of labour turnover, with reasons: (a) cost of a recruitment agency fee for a new hire; (b) cost of an employee wellness programme; (c) reduced output during a new employee's initial training period; (d) exit interview administration cost.

Accepted Answer

Item (a), the recruitment agency fee for a new hire, is a replacement cost, since it is incurred as a direct consequence of a vacancy having arisen from an employee leaving, and would not be incurred at all had the departure not occurred; replacement costs are, by definition, incurred because turnover has already happened. Item (b), the employee wellness programme, is a preventive cost, since it is incurred proactively, before any departure occurs, specifically to improve employee satisfaction and retention and thereby reduce the likelihood of turnover happening in the first place; preventive costs are incurred to keep turnover low, in anticipation of the problem rather than in response to it. Item (c), reduced output during a new employee's initial training and learning period, is a replacement cost, since this lost productivity is a direct consequence of the departure that created the vacancy the new employee is filling, and the loss would not have arisen without that prior departure. Item (d), exit interview administration cost, is also a replacement cost, being incurred specifically in connection with, and as a consequence of, an employee actually leaving; it has no preventive character at all, occurring only after the departure decision has already been made. The general test worth applying to any item is timing and causation relative to the departure itself: preventive costs are incurred to avoid a departure that has not yet happened, while replacement costs are incurred because a departure has already occurred and something must now be done about it.

Question 12

A company has annual demand of 20,000 units, ordering cost of Rs.200 per order, and carrying cost of 10% of unit price per annum. Unit price is Rs.50 for orders below 5,000 units, and Rs.48 for orders of 5,000 units or more. Compute EOQ ignoring the discount, then evaluate whether ordering in the discount quantity is more economical overall.

Accepted Answer

EOQ ignoring the discount, using the base price of 50 and carrying cost of 10% of 50, that is 5 per unit per annum: square root of (2 times 20,000 times 200) divided by 5, that is square root of 80,00,000 divided by 5, giving square root of 16,00,000, that is 1,265 units approximately, well below the 5,000 unit discount threshold. To evaluate whether the discount quantity is more economical overall, total annual cost must be compared at both the EOQ of 1,265 units and at the discount-qualifying quantity of 5,000 units, since total cost includes purchase cost, ordering cost and carrying cost together, not merely the ordering-and-carrying balance EOQ alone optimises. At EOQ of 1,265 units: purchase cost is 20,000 times 50, giving 10,00,000; ordering cost is (20,000 divided by 1,265) times 200, approximately 15.8 orders times 200, giving approximately 3,160; carrying cost is average inventory, half of 1,265, that is 632.5, times 5, giving approximately 3,163; total cost approximately 10,00,000 plus 3,160 plus 3,163, giving approximately 10,06,323. At the discount quantity of 5,000 units: purchase cost is 20,000 times 48, giving 9,60,000; ordering cost is (20,000 divided by 5,000) times 200, that is 4 orders times 200, giving 800; carrying cost is average inventory, half of 5,000, that is 2,500, times the new lower carrying rate of 10% of 48, that is 4.80, giving 2,500 times 4.80, that is 12,000; total cost 9,60,000 plus 800 plus 12,000, giving 9,72,800. Comparing the two, ordering at the discount quantity of 5,000 units gives a total cost of 9,72,800, substantially lower than the 10,06,323 at the EOQ of 1,265 units, driven overwhelmingly by the 40,000 saving in purchase cost from the lower unit price, which comfortably outweighs the modest increase in carrying cost from holding more average inventory; the company should order in quantities of 5,000 to capture the discount, despite this exceeding the EOQ computed without regard to the price break.

Question 13

A material has average consumption of 200 units per day, and emergency purchase lead time is 3 days. Compute the danger level, and explain its purpose relative to the reorder level.

Accepted Answer

Danger level is computed as average consumption rate multiplied by lead time for emergency purchase: 200 units per day times 3 days, giving 600 units. Its purpose is distinct from the reorder level, which triggers the start of ordinary, planned reordering; danger level instead signals that ordinary reordering has already failed to prevent stock from falling to a critically low level, and that emergency procurement, typically at a premium price and on an expedited basis, is now required to avoid an outright stockout before normal replenishment can arrive. In ordinary operation, stock should never actually fall as low as the danger level, since the reorder level is set specifically high enough, using maximum consumption and maximum reorder period, to ensure a fresh order is placed with a comfortable margin before stock would ever approach this critical point; danger level being reached is therefore a signal that something has gone wrong with the normal reordering process, whether a missed reorder trigger, an unusually severe consumption spike, or a supplier delay beyond what the reorder level's built-in buffer anticipated, and it calls for exceptional, rather than routine, action.

Question 14

A factory pays overtime premium of Rs.40,000 in a month because general order volume across all products has been unusually high. In a separate incident, it pays overtime premium of Rs.8,000 specifically to expedite one customer's order that the customer has requested be completed ahead of schedule for an additional fee. State the treatment of each, and the reasoning that distinguishes them.

Accepted Answer

The 40,000 of overtime premium arising from generally high order volume across all products is treated as a factory overhead, spread across production generally rather than charged to any specific job or product, because it arises from general pressure of work across the whole factory rather than from any single, identifiable order's specific requirements; no single job caused this overtime to be necessary, and it would be arbitrary and potentially misleading to load it entirely onto whichever jobs happened to be in production during the overtime hours. The 8,000 of overtime premium paid specifically to expedite one customer's order, at that customer's request and for an additional fee, is instead charged directly to that specific job, because in this case the overtime was incurred specifically and solely because of that one customer's requirement to have their order completed ahead of the normal schedule; the cost is directly attributable to fulfilling that particular customer's specific need, and charging it to that job, rather than spreading it across general overhead, correctly reflects that the cost was caused by, and should be borne by, that specific order. The reasoning distinguishing the two situations is causation: where an overtime cost is caused by a specific, identifiable job's specific requirement, it is charged directly to that job; where it arises from a general condition affecting the factory as a whole with no single identifiable cause, it is treated as a general overhead.

Question 15

A material has minimum stock level of 1,200 units and reorder quantity of 3,000 units. Compute average stock level using both the formula involving minimum stock and reorder quantity, and the alternative formula involving minimum and maximum stock levels, given maximum stock level is 5,700 units, and confirm the two approaches agree.

Accepted Answer

Using the first formula, average stock level is minimum stock level plus half the reorder quantity: 1,200 plus half of 3,000, that is 1,200 plus 1,500, giving 2,700 units. Using the alternative formula, average stock level is half the sum of minimum and maximum stock levels: half of (1,200 plus 5,700), that is half of 6,900, giving 3,450 units. These two figures do not agree, 2,700 against 3,450, which reveals that the two formulas are not always interchangeable and rest on slightly different assumptions about the pattern of stock movement between minimum and maximum. The minimum-plus-half-reorder-quantity formula assumes stock cycles between the minimum level and the minimum level plus the reorder quantity in a simple sawtooth pattern typical of a basic reorder cycle; the minimum-and-maximum-average formula assumes the true average sits midway between the two extreme observed levels, which can differ if maximum stock level, computed using the minimum consumption and minimum reorder period rather than simply minimum stock plus reorder quantity, reflects a different underlying scenario than the simple cycling assumption. In examination practice, the minimum-plus-half-reorder-quantity formula is the more commonly expected computation unless a question specifically directs otherwise, and a candidate encountering both should verify which formula the specific question or standard reference material in use actually prescribes, since the two are approximations built on different simplifying assumptions rather than mathematically identical restatements of the same fact.

Practice — Material Cost and Employee Cost

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