Each extra unit sold would, therefore, generate an extra $10 contribution (selling price direct costs). Hence, accepting the order would actually add to the overall profits for the firm by $3,000*(300*$10 contribution). Providing the selling price exceeds the additional cost of making the product, and then this contribution on each unit will add to profits.Other issues concerned with accepting the order: It will also help the firm to utilize any spare capacity that is currently lying idle. For example, if a firm is renting a factory, then this will represent an indirect cost for the firm. It does not matter how much of the factory is used, the rent will remain the same. By accepting this order the firm may also generate sales with new customers or, via word-of-mouth, with other customers. The firm will have to decide whether the attractions of extra orders and higher sales outweigh the fact that these sales are at a lower selling price than normal. It will want to avoid having too many of its sales at this discounted price, as this lower price may start to be seen as normal. Customers already paying the higher price may be unhappy and demand to be allowed to buy at this lower price.Although the lower price is above the marginal cost of production, it may be that the firm does not cover its indirect and direct costs if too many are sold at the low price. Tough the contribution sold on these discounted units is positive; sales still have to be high enough to allow for enough unit contributions to cover the indirect costs. Orders at Below Cost Price Click on the image to enlarge it and THEN print it Buying in products: Increasing profit can be achieved either by increasing the selling price, which depends on the impact on sales, or reducing costs can increase profits. One possible way to reduce costs for a firm that uses manufactured goods would be if an alternative supplier could be found who can manufacture and sell products (or part of the products, such as components) for a lower price than the present costs of the firm producing these for it self. If this is the case then the firm will have a choice of whether to continue making the products or to buy them in from a supplier.Considerations: When making this decision a firm would probably consider the possible impact on its workforce. If production is being reduced there is likely to be a reduction in the size of the workforce needed. Unless the firm can retrain the workers for other functions within the firm, such as sales, redundancies are likely to occur. This could lead to industrial action or reduction in productivity as seeing co-workers their jobs may demotivate employees.The firm will also have to ensure that the supplier of the product is reliable. If they are located some distance away then the lead-time for delivery will become an important factor. Problems with delivery could lead to production bottlenecks, whereby overall production is halted or orders cannot be met due to unreliable suppliers. This is a particular problem if the firm is adopting just-in-time (JIT) production techniques.The quality of the products will also have to be monitored closely. Depending on the size of the order, the firm may be able to demand their own specifications for the order. On the other hand, if the firm is only a small customer of the supplier, it may have to accept the suppliers own specifications.If the firm does decide to buy in components or products from another supplier, it may close down all or part of the production facilities, unless alternative uses can be found, such as producing goods for other firms. If closures do take place this will save the firm fixed costs in the long-term, although the firm may be committed to paying some of these for the next few months. For example, rent or insurance may be payable annually without rebate if the service is no longer required.Contribution and full costing: When costing, a firm can use either contribution (marginal) costing, whereby the fixed costs are kept separate, or it can apportion overheads and use full costing. If the firm uses full costing then it has to decide how the overheads are to be apportioned or allocated to the different cost centers.Methods of allocating indirect costs: One of the easiest ways to allocate indirect costs is to split the overheads equally between the different cost centers. However, although easier to decide, splitting the indirect cost equally may not be as fair as it initially appears. Methods of allocating indirect costs: Chase Ltd. produces office furniture. It has decided to classify its different products as profit centers. The direct costs incurred in the production of each product are as follows: COMPUTER WORKSTATION SWIVEL CHAIR STANDARD DESK Material costs $20 $15 $10 Labor Costs $25 $8 $12 Packaging and finishing $5 $7 $3 TOTAL DIRECT COSTS $50 $30 $25 Along with the direct costs of production there are also indirect costs that are not specifically related to the production procedure. These total $90,000. Further data relating to Chase Ltd. is as follows: COMPUTER WORKSTATION SWIVEL CHAIR STANDARD DESK Annual Output 5,000 3,000 4,000 Selling price $75 $45 $35 We can produce a costing statement that highlights the costs and revenues that arise out of each profit center: COMPUTER WORKSTATION ($) SWIVEL CHAIR ($) STANDARD DESK ($) Sales Revenue Materials Labor Packaging ang finishing Total direct costs Contribution 375,000 100,000 125,000 25,000 250,000 125,000 135,000 45,000 24,000 21,000 90,000 45,000 140,000 40,000 48,000 12,000 100,000 40,000 If a firm wishes to work out the profit made by each profit center then the overheads will have to be allocated to each one. In the example below, overheads are allocated equally: COMPUTER WORKSTATION ($) SWIVEL CHAIR ($) STANDARD DESK ($) Sales Revenue Materials Labor Packaging and finishing Indirect costs Total costs Profit 375,000 100,000 125,000 25,000 30,000 280,000 95,000 135,000 45,000 24,000 21,000 30,000 120,000 15,000 140,000 40,000 48,000 12,000 30,000 130,000 10,000 It is worth noting that the firms overall profit should not be any different whether it uses contribution of full costing. All that changes is how it deals with the costs-either apportioning them out to the cost or profit centers for full costing or deducting them in total from the total contribution of the centers for contribution costing. If the indirect costs are allocated, the decision about how to allocate them will affect the profit or loss of each profit center, but it will not affect the overall profit of the firm.Allocation rules: Allocating overheads equally is the simplest and quicker means of apportioning indirect costs, but many managers do use other allocation rules. In some cases they also use different allocation rules for different types of indirect costs-this is known as absorption costing. Although these do not attempt to allocate the indirect costs accurately (in the sense that indirect costs cannot clearly be allocated to different cost centers), they attempt to take account of relevant factors that might affect the extent to which different cost centers incur the indirect costs. For example, overall heating costs might be allocated according to the floor space of different departments.Typical Allocation Rules include:Typical indirect costs are connected with the staff of the firm, and then allocating overheads on the basis of labor costs may be suitable. Example of staff costs would include canteen expenses or the costs associated with running the human resources department.For manufacturing firms, the basis of allocating indirect costs may be related to the materials costs incurred by each cost center. This will depend on the costs centers within the organizationIf a firm is operating in an industrial sector using expensive equipment, then the overheads may be allocated on the basis of the value of machinery in each cost center. This is because maintenance, training and insurance costs may be related to the value of machinery in a loose way. In some ways these rules are no more or less accurate than dividing their indirect costs equally although they may appear to be intuitively appealing and in some sense feel fairer.Consequences of unfair overhead allocation: We can rationalize over the reason chosen for the basis of overhead allocation; however, we must realize that no method is perfect. Costs being apportioned require a method to be chosen independently, precisely because there is no direct link between the cost and the cost center. The method chosen can have unfortunate effects on the organization as a whole. If the firm uses departments as cost centers then it is possible that using absorption costing could lead to resentment by staff. This can be illustrated through the following example. Hopkinson Ltd. has decided to allocate fixed overheads using labor costs as the basis of allocation. Fixed overheads for the organization total $360,000 and will be allocated on the basis of labor costs (i.e. in the ratio 2:3:4) between the three branches. A ($) B ($) C ($) Sales Revenue Labor Costs Materials Costs Other Direct Costs 165,000 40,000 20,000 10,000 240,000 60,000 30,000 10,000 300,000 80,000 40,000 10,000 Fixed overheads Profit/loss 80,000 15,000 120,000 20,000 160,000 10,000 Allocating overheads in this way gives the result that branch B generates the highest profit and branch C is the least profitable. The staff at branch C may be labeled as poor performers. This could lead to demotivation, rivalry between branches and lower productivity. Staff at branch C may also be worried that promotions or bonuses may not be available to them due to rating lowest out of three branches. However, this result is arrived at only because the high fixed overheads were allocated in these ways. If we ignored the fixed costs and considered contribution only, the following results occur: A ($) B ($) C ($) Sales Revenue Labor Costs Materials Costs 165,000 40,000 20,000 240,000 60,000 30,000 300,000 80,000 40,000 Other direct costs Contribution 10,000 95,000 10,000 140,000 10,000 170,000 Based on contribution costing, branch C provides the biggest input into earning money for the firm.The problems that can occur when allocating overheads can lead arguments between managers over how they should be divided up. To boost their particular divisions performance, managers will eager to change a method that shifts some of their indirect costs onto another division.In some ways, however, it does not matter what rules are used to allocate indirect costs. Whichever rule is used is inaccurate (by definition indirect costs cannot be clearly be associated with a particular cost center) but the actual process of allocating overheads makes everyone aware of their importance and of the need to monitor and control them. Furthermore, provided the rules are not changed over time, managers will be able to analyze the trend profit figures for different departments, products or regions. A significant increase in indirect costs will decrease the profits of all business units to some degree, regardless of how these costs are allocated. If the indirect costs continue to rise, all the managers will be able to notice this trend in their accounts.If we use the full costing method of allocating indirect overheads then we can illustrate how this information may be used to make a strategic decision in terms of closing down an unprofitable business.In the following question, we will look at the costing data for Beynons Ltd., as small family chain of bakeries. The chain is owned and managed as a family concern, with the father, James Beynon, has been convinced of the merits of segmental reporting. He is worried because his youngest son, who he considers to be inexperienced in retail management, runs the branch. Consider the following breakdown of costs: HIGHFIELDS ($) BRWONDALE ($) NORTON ($) Sales Revenue Staffing costs Supplies Branch running Marketing Central admin. 22,000 7,000 5,000 1,000 2,000 4,000 17,000 8,000 4,000 1,000 2,000 4,000 26,000 9,000 6,000 1,000 2,000 4,000 Other direct costs Contribution 19,000 3,000 19,000 (2,000) 22,000 4,000 The marketing and central administration costs incorporate many of the overall costs associated with running the bakery chain. They are indirect and not related to any one branch in particular. These have been allocated equally across all three branches, as it seemed to be the fairest method of cost allocation.The data in the above appears to confirm the fathers belief that in the long-term interest of the firm, he may have to close down the Browndale branch and concentrate his efforts on the other two branches. If we use contribution costing, however, we see a different picture: HIGHFIELDS ($) BRWONDALE ($) NORTON ($) Sales Revenue Staffing costs Supplies Branch running 22,000 7,000 5,000 1,000 17,000 8,000 4,000 1,000 26,000 9,000 6,000 1,000 Total costs Profit (loss) 19,000 3,000 19,000 (2,000) 22,000 4,000 As we can see, all three branches make a positive contribution to the overall profits. The reason why the father wished to close down the branch was that it appeared to be making a loss. However, it is quite the reverse; if the branch was closed then, the positive contribution from the branch would be lost and overall profits would fall. This is because the indirect costs of production do not vary with output and, therefore, closure of a section of the firm would not lead to immediate savings. This may mean that closing the branch would be a mistake on financial grounds.This mistake is made due to a misunderstanding of nature of cost behavior. If the branch is closed then the only costs that would be saved are the costs directly related to the running of the branch: the staffing costs, the supplies and the branch running costs. The costs are indirect in nature, in this example the marketing and central administration costs, would still have to be paid as they are unaffected by output. For this decision to be made, we should use contribution as a guide for deciding whether or not to close a branch.The Beynons Ltd. example highlighted that contribution is a guide to keeping a branch open that, if we used full costing, could make a loss. This can also be applied to the production of certain product lines, or the cost effectiveness of departments. On financial grounds, contribution is therefore, a better guide in making decisions. Total ($) Overall Contribution Indirect Costs Profit 23,000 18,000 5,000 Continuing production even if the contribution is negative: It is possible that a section of a firm, be it a product line or branch, is kept open even though on financial grounds that particular section is making a negative contribution to the overall profit levels of organization. The reason for this is that closing down a section of a business is likely to lead a firm shedding labor that becomes surplus. The workers employed in that section may no longer be required.If alternative employment cannot be found within the firm then these workers may be redundant. This could impose redundancy costs upon the firm. It is likely that trade unions will be involved that may oppose any redundancies. This could lead to industrial action by workers in other sections of the firm. It may also lead to bad publicity in the media, which may affect the level of sales and profits. In this situation, a business may let natural wastage occur in staff involved, rather than make job cuts, or it may simply decide to keep the section going. Even if there is industrial unrest, the effect of closure on overall morale within the firm could be very important. It is likely that the remaining employees will be demotivated on seeing c0-workers being made redundant. This could lead to unrest, and declining productivity.In the case of a loss-making product, a firm may decide to keep this in production if it has been recently launched. In the early years of product life cycle, sales are likely to be lower than they are expected to be in later years and, as a result, the contribution may be negative. Sales will hopefully eventually rise and the revenues arising from sales will eventually outweigh the costs of running this new product.Complementary products: A loss-making product may also be kept in production because the firm produces complementary products. In this situation a firm may be willing to incur negative contribution in order to maintain or even boost the sales of its other products. Examples of complementary products include:Pottery firms dinner plates, saucers and cupsTextile firms bed sheets, pillowcases and duvet coversAn Example A firm is producing garden furniture, selling parasols, tables and chairs. These form the basis of different cost centers for the firm as they are produced in different sections. The firm has produced the following contribution costing statement: PARASOLS TABLES CHAIRS Sales Revenue Labor Costs Material Costs Other direct costs Contribution 7,000 2,000 2,000 1,000 5,000 2,000 5,000 1,000 500 2,000 3,500 1,500 4,000 1,000 2,000 1,500 4,500 (500) As you can see from the data in table 5.13, the chairs are making a negative contribution and would appear to be lowering the overall profits for the firm. Closing down production of the chairs would appear to lead to higher profits. The profits may be boosted further if the production of the chair producing facility saved some of the indirect costs.It is important to consider the impact on the sales of other products. With a firm selling garden equipment is likely that the three separate products will be purchased together as they form part of a matching set. If the production of one of these complementary products is halted, then it is likely to adversely affect the sales of the other products. This could mean that discontinuing the production of a product with a negative contribution leads to lower overall profits.You may like using the Break-Even Analysis and Costing Analysis JavaScript for performing some sensitivity analysis on the parameters for investigation of their impacts on your decision making.Further Reading:Schweitzer M., E. Trossmann, and G. Lawson, Break-Even Analyses: Basic Model, Variants, Extensions, Wiley, 1991.Modeling the Bidding Process in Competitive MarketsDue to deregulation in most market such as the electrical power markets, the cost minimization utilities used by electric utilities are being replaced by bidding algorithms. Every firm is trying to maximize their profit subject to the price determined by suppliers, consumers and other participants. Finding an optimized bidding policy in a competitive electricity market has become one of the main issues in electricity deregulation. There are many factors that can affect the behavior of marketparticipants, such as the size of players, market prices, technical constraints, inter-temporal linkages, etc. Several of these factors are purely technical and the others are strictlyeconomical. Thus there is a need to develop a methodology combining both issues in a structured way. Daily electricity markets can be classified according to the market power that oneor more players can exercise: monopolistic, oligopolistic, or perfectly competitive.The most competitive oligopolistic models can be categorized as follows: Nash-Cournot models, Bertrand models, Supply function equilibrium models, Quantity leadership models, and Price leadership models. Each one of these models uses different strategic variables, such as price and quantity, producing results that are sometimes close to a monopoly and other times close to perfect competition.Nash-Cournot models have been widely studied to model competitive markets. However, these models are based on certain assumptions, such as fixing the quantity offered by the competitors finding the equilibrium if all players hold this assumption.Further Reading:Varian H.R., Microeconomics Analysis, Norton, New York, 1992. Products Life Cycle Analysis and ForecastingThe stage in a product's life cycle conventionally, divided into four stages as depicted in the following figure: Products Life Cycle Click on the image to enlarge it and THEN print it Design and Introduction: This stage mainly concerns the development of a new product, from the time is was initially conceptualized to the point it is introduced on the market. The enterprise having first an innovative idea will often have a period of monopoly until competitors start to copy and/or improve the product (unless a patent is involved). Characteristics: cost high, very expensive no sales profit, all losses sales volume low Type of Decisions: amount of development effort product design business strategiesoptimal facility sizemarketing strategy including distribution and pricing Related Forecasting Techniques: Delphi method historical analysis of comparable products input-output analysispanel consensusconsumer surveymarket testsGrowth and Competitive Turbulence: If the new product is successful (many are not), sales will start to grow and new competitors will enter the market, slowly eroding the market share of the innovative firm. Characteristics: costs reduced due to economies of scale sales volume increases significantly profitability Type of Decisions: facilities expansion marketing strategies production planning Related Forecasting Techniques: statistical techniques for identifying turning points market surveys intention-to-buy surveyMaturity: At this stage, the product has been standardized, is widely accepted on the market and its distribution is well established. Characteristics: costs are very low sales volume peaks prices tend to drop due to the proliferation of competing products very profitable Type of Decisions: promotions, special pricing production planning inventory control and analysis Related Forecasting Techniques: time series analysis causal and econometric methods market surveylife cycle analysis Decline or Extinction: As the product is becoming obsolete, eventually, the product will be retired, event that marks the end of its life cycle. Characteristics: sales decline prices drop profits declineForecasting the Turning Points: To be able to forecast a major change in growth that is about to occur allows managers to develop plans without the pressure of having to immediately react to unforeseen changes. For example, the turning point is when growth will go from positive to negative. It is these turning points that help managers develop plans early.Consider the Mexican economy, since it is directly related to US economy, a dramatic changes in US economic climate can lead to a major turning point in Mexican economy, with some lagged-time (i.e., delay).Similarly, your time series might be compared to key national economic data to identify leading indicators that can give you advance warning -- before changes occur in consumer-buying behavior. Currently, the U.S. government publishes data for over ten leading indicators that change direction before general changes in the economy.They do not want to be taken by surprise and ruined. They are anxious to learn in time when the turning points will come because they plan to arrange their business activities early enough so as not to be hurt by, or even to profit from.Further Readings:Ross Sh., An Elementary Introduction to Mathematical Finance: Options and other Topics, Cambridge University Press, 2002. It presents the Black-Scholes theory of options as well as introducing such topics in finance as the time value of money, mean variance analysis, optimal portfolio selection, and the capital assets pricing model.Ulrich K., and S. Eppinger, Product Design and Development, McGraw-Hill, 2003.Urban G., and J. Hauser, Design and Marketing Of New Products, Prentice Hall, 1993.Zellner A., Statistics, Econometrics and Forecasting, Cambridge University Press, 2004.Learning and The Learning CurveIntroduction: The concept of the learning curve was introduced to the aircraft industry in 1936 when T. P. Wright published an article in the February 1936 Journal of the Aeronautical Science. Wright described a basic theory for obtaining cost estimates based on repetitive production of airplane assemblies. Since then, learning curves (also known as progress functions) have been applied to all types of work from simple tasks to complex jobs like manufacturing.The theory of learning recognizes that repetition of the same operation results in less time or effort expended on that operation. Its underlying concept is that, for example the direct laborman-hours necessary to complete a unit of production will decrease by a constant percentage each time the production quantity is doubled. If the rate of improvement is 20% betweendoubled quantities, then the learning percent would be 80% (100-20=80). While the learning curve emphasizes time, it can be easily extended to cost as well.Psychology of Learning: Based on the theory of learning it is easier to learn things that are related to what you already know. The likelihood that new information will be retained is related to how much previous learning there is that provides "hooks" on which to hang the new information. In other words, to provide new connectivity in the learner's neural mental network. For example, it is a component of my teaching style to provide a preview of the course contents and review of necessary topics form prerequisites courses (if any) during the first couple of class meeting, before teaching them to course topics in detail. Clearly, change in one's mental model happens more readily when you have a mental model similar to the one you're trying to learn; and that it will be easier to change a mental model after you become more consciously aware.A steep learning curve is often referred to indicate that something is difficult to learn. In practice, a curve of the amount learned against the number of trials (in experiments) or over time (in reality) is just the opposite: if something is difficult, the line rises slowly or shallowly. So the steep curve refers to the demands of the task rather than a description of the process.The following figure is of a fairly typical of a learning curve. It depicts the fact that the learning curve does not proceed smoothly: the plateaus and troughs are normal features of the process. A Typical Learning Curve Click on the image to enlarge it and THEN print it The goal is to make the "valley of despair" as Shallow and as Narrow as possible.To make it narrow, you must give plenty of training, and follow it up with continuing floor support, help desk support, and other forms of just-in-time support so that people can quickly get back to the point of competence. If they stay in the valley of despair for too long, they will lose hope and hate the new software and the people who made them switch.Valley of Despair Characteristics:Who's dumb idea was this?I hate thisI could do better the old wayI cannot get my work doneSuccess Characteristic:How did I get along without this?To make it as shallow as possible, minimize the number of things you try to teach people at once. Build gradually, and only add more to learn once people have developed a level of competence with the basic things. In the acquisition of skills, a major issue is the reliability of the performance. Any novice can get it right occasionally, but it is consistency which counts, and the progress of learning is often assessed on this basis. Need to train workers in new method based on the facts that the longer a person performs a task, the quicker it takes him/her: Learn-on-the-job approach:learn wrong method bother other operators, lower production anxiety Simple written instructions: only good for very simple jobs Pictorial instructions: "good pictures worth 1000 words" Videotapes: dynamic rather than static Physical training: real equipment or simulators, valid does not interrupt production monitor performance simulate emergencies Factors that affect human learning: Job complexity - long cycle length, more training, amount of uncertainty in movements, more C-type motions, simultaneous motions Individual capabilities- age, rate of learning declines in older age, amount of prior training, physical capabilities, active, good circulation of oxygen to brain Because of the differences between individuals, their innate ability, their age, or their previous useful experience then each turner will have his/her own distinctive learning curve. Some possible, contrasting, curves are shown in the following figure: An Individuals Differences Classification Click on the image to enlarge it and THEN print it Individual C is a very slow learner but he improves little by little. Individual B is a quick learner and reaches his full capacity earlier than individuals A or C. But, although A is a slow learner, he eventually becomes more skilled than B. Measuring and Explaining Learning Effects of Modeling: It is already accepted that modeling triggers learning, this is to say the modeler's mental model changes as effect of the activity "modeling". In "systems thinking" it also includes the way people approach decision situations by studying attitude changes model building.Modeling the Learning Curve: Learning curves are all about ongoing improvement. Managers and researchers noticed, in field after field, from aerospace to mining to manufacturing to writing, that stable processes improve year after year rather than remain the same. Learning curves describe these patterns of long-term improvement. Learning curves help answer the following questions. How fast can you improve to a specific productivity level? What are the limitations to improvement? Are aggressive goals achievable?The learning curve was adapted from the historical observation that individuals who perform repetitive tasks exhibit an improvement in performance as the task is repeated a number of times.With proper instruction and repetition, workers learn to perform their jobs more efficiently and effectively and consequently, e.g., the direct labor hours per unit of a product are reduced. This learning effect could have resulted from better work methods, tools, product design, or supervision, as well as from an individuals learning the task. A Family of Learning Curves Funtions: Of the dozens of mathematic concepts of learning curves, the four most important equations are: Log-Linear: y(t) = k tb Stanford-B: y(t) = k (t + c)b DeJong: y(t) = a + k tb S-Curve: y(t) = a + k (t + c)bThe Log-Linear equation is the simplest and most common equation and it applies to a wide variety of processes. The Stanford-B equation is used to model processes where experience carries over from one production run to another, so workers start out more productively than the asymtote predicts. The Stanford-B equation has been used to model airframe production and mining. The DeJong equation is used to model processes where a portion of the process cannot improve. The DeJong equation is often used in factories where the assembly line ultimately limits improvement. The S-Curve equation combines the Stanford-B and DeJong equations to model processes where both experience carries over from one production run tothe next and a portion of the process cannot improve.An Application: Because of the learning effect, the time required to perform a task is reduced when the task is repeated. Applying this principle, the time required to perform a task will decrease at adeclining rate as cumulative number of repetitions increase. This reduction in time follows the function: y(t) = k t b, where b = log(r)/log (2), i.e., 2b = r, and r is the learning rate, a lower rate implies faster learning, a positive number less than 1, and k is a constant.For example, industrial engineers have observed that the learning rate ranges from 70% to 95% in the manufacturing industry. An r = 80% learning curve denotes a 20% reduction in thetime with each doubling of repetitions. An r = 100% curve would imply no improvement at all. For an r = 80% learning curve, b = log(0.8)/log(2) = -0.3219.Numerical Example: Consider the first (number if cycles) and the third (their cycle times) columns for the following data set: # Cycles Log # Cycles Cycle Time Log Cycle Time 1 0 12.00 1.08 2 0.301 9.60 0.982 4 0.602 7.68 0.885 8 0.903 6.14 0.788 16 1.204 4.92 0.692 32 1.505 3.93 0.594To estimate y = k tb one must use linear regression on the logarithmic scales, i.e., log y = log(k) + b log(t) using a data set, and then computing r = 2b. Using the Regression Analysis JavaScript, for the above data, we obtain:b = Slope = -0.32, y-Intercept = log(k) = 1.08log y = log(k) + b log(t)b = -0.32k = 101.08 = 12 y(t) = 12 t -0.32r = 2b = 2-0.32 = 80%Conclusions: As expected while number of cycles doubles, cycle time decreasesby a constant %, that is, the result is a 20% decrease or 80% learning ratio or 80% learning curve with a mathematical model y(t) = 12 t -0.32 Further Readings:Dilworth J., Production and Operations Management: Manufacturing and Non-manufacturing, Random House Business Division, 2003.Krajewski L., and L. Ritzman, Operations Management: Strategy and Analysis, Addison-Wesley Publishing Company, 2004.Economics and Financial Ratios and Price IndicesEconomics and finance use and analysis ratios for comparison and as a measuring tool and decision process for the purpose of evaluating certain aspects of company's operations. The following are among the widely used ratios:Liquidity Ratios: Liquidity ratios measure a firm's ability to meet its current obligations, for example:Acid Test or Quick Ratio = (Cash + Marketable Securities + Accounts Receivable) / Current LiabilitiesCash Ratio = (Cash Equivalents + Marketable Securities) /Current LiabilitiesProfitability Ratios: Profitability ratios profitability ratios measure management's ability to control expenses and to earn a return on the resources committed to the business, forexample:Operating Income Margin = Operating Income / Net SalesGross Profit Margin = Gross Profit / Net SalesLeverage Ratios: Leverage ratios measure the degree of protection of suppliers of long-term funds and can also aid in judging a firm's ability to raise additional debt and itscapacity to pay its liabilities on time, for example:Total Debts to Assets = Total Liabilities / Total AssetsCapitalization Ratio= Long-Term Debt /(Long-Term Debt + Owners' Equity)Efficiency: Efficiency activity or turnover ratios provide information about management's ability to control expenses and to earn a return on the resources committed to thebusiness, for example:Cash Turnover = Net Sales / CashInventory Turnover = Cost of Goods Sold / Average InventoryPrice IndicesIndex numbers are used when one is trying to compare series of numbers of vastly different size. It is a way to standardize the measurement of numbers so that they are directly comparable.The simplest and widely used measure of inflation is the Consumer Price Index (CPI). To compute the price index, the cost of the market basket in any period is divided by the cost ofthe market basket in the base period, and the result is multiplied by 100.If you want to forecast the economic future, you can do so without knowing anything about how the economy works. Further, your forecasts may turn out to be as good as those ofprofessional economists. The key to your success will be the Leading Indicators, an index of items that generally swing up or down before the economy as a whole does.
2,500 to 10,000 in two years: growth of veganism reflected in annual march
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