Cost Concept, Cost Behaviour and Cost - Volume-Profit Analysis
Lesson 2: Cost Concept, Cost Behaviour and Cost - Volume-Profit Analysis
(a) Cost:
Cost is the cash or cash-equivalent value sacrificed for goods and services that are expected to bring a current or future benefit to the organization. We say cash equivalent because non-cash resources can be exchanged for the desired goods or services. For example, it may be possible to exchange equipment for materials used in production. In effect, we can think of cost as a dollar measure of the resources used to achieve a given benefit. In striving to produce a current or future benefit, managers should make every effort to minimize the cost required to achieve this benefit. Reducing the cost required to achieve a given benefit means that a firm is becoming more efficient. Costs, however, not only must be reduced but they should also be managed strategically. For example, managers should have the objective of providing the same (or greater) customer value for lower cost than their competitors. In this way, the strategic position of the firm is increased and a competitive advantage is created.
For example, a firm may invest $100,000 in inventory for a year instead of investing the capital in a productive investment that would yield a 12 percent rate of return. The opportunity cost of capital tied up in inventory is $12,000(0.12 *$100,000) and is part of the cost of carrying inventory.
Costs are incurred to produce future benefits. In a profit-making firm, future benefits usually mean revenues. As costs are used up in the production of revenues, they are said to expire. Expired costs are expenses. In each period, expenses are deducted from revenues in the income statement to determine the period's profit. For company to remain in business revenues must consistently exceed expenses; moreover, the income earned must be large enough to satisfy the owners of the firm. Thus, cost and price are related in the sense that price must exceed cost such that sufficient income is earned.
Furthermore, lowering price increases customer value by lowering customer sacrifice and the ability to lower prices is connected to the ability to lower costs. Hence, managers need to know the cost and trends in cost. Usually, however, knowing cost really means knowing what something or some object costs. Assigning costs to determine the cost of this object is therefore critical in providing this information to managers.
(b) Cost Objects:
Management accounting systems are structured to measure and assign costs to entities, called cost objects. A cost object is any item such as products, customers, departments, projects, and activities and so on, for which costs are measured and assigned. For example, if a bank wants to determine the cost of a platinum card, then the cost object is the platinum card. If a hospital wants to determine the cost of an operating department, then the cost object is the operating department. If a toy manufacturer wants to determine the cost of developing a new toy, then the cost object is the new toy development project.
In recent years, activities have emerged as important cost objects. Activities are people and/or equipment doing work for other people. Thus, an activity is a basic unit of work performed within an organization and can also be described as an aggregation of actions within an organization useful to managers for purposes of planning, controlling, and decision-making. Activities not only act as cost objects but also play a prominent role in assigning costs to other objects. Examples of activities include setting up equipment for production, moving materials and goods, purchasing parts, billing customers, paying bills, maintaining equipment, expediting orders, designing products, and inspecting products.
(c) Accuracy of Cost Assignments:
Assigning costs accurately to cost objects is crucial. The notion of accuracy is not evaluated based on knowledge of some underlying "true" cost. Rather, it is the relative concept and has to do with the reasonableness and logic of cost assignment methods used. The objective is to measure and assign as well as possible the cost of the resources consumed by cost object. The intuitive and somewhat tongue-in-cheek guideline is expressed as follows: "It is better to be approximately correct than precisely inaccurate." Some cost assignment methods are clearly more accurate than others. For example, suppose you want to determine the cost of lunch for Ryan Chaser, a student that frequents Hideaway, an off-campus pizza parlour. One cost assignment approach is to count the number of customers Hideaway has between 12:00 p.m. and 1:00 p.m. and then divide the total receipts earned during this period by this number of customers. Suppose that this comes out to $5.175 per lunchtime customer. Thus, based on this approach, we would conclude that Ryan spends $5.175 per day for lunch. Another approach is to go with Ryan and observe how much he spends. Suppose that he has a small pizza, salad, and a medium drink each day, costing $6.50. It is not difficult to see which cost assignment is more accurate. The $5.175 cost assignment is distorted by consumption patterns of other customers (cost objects). As it turns out, most lunchtime clients order the luncheon special for $4.99(a minipizza, salad, and medium drink).
Distorted cost assignments can produce erroneous decisions and bad evaluations. For example, if a plant manager is trying to decide whether to continue producing internally or to buy it from a local utility company, then an accurate assessment of how much it is costing to produce the power is fundamental to the analysis. An overstatement of the cost of power production could suggest to the manager that the internal power department should be shut down in favour of external purchase, whereas a more accurate cost assignment might reveal the opposite. It is easy to see that bad cost assignments can prove to be costly. As the pizza example suggests, establishing a cause-and -effect relationship between the cost to be assigned and the cost object is the key to creating a reasonably accurate cost assignment.
General Cost Classifications
Our initial focus in this lesson is on manufacturing companies, since their basic activities include most of the activities found in other types of business organizations. Manufacturing companies such as Texas Instruments, Ford and Kodak are involved in acquiring raw materials, producing finished goods, marketing, distributing, billing, and almost every business activity. Therefore, an understanding of costs in a manufacturing company can be very helpful in understanding costs in other types of organizations.
Manufacturing Costs:
Most manufacturing companies divide manufacturing costs into three broad categories: direct materials, direct labour, and manufacturing overhead.
Direct Materials:
The materials that go into the final product are called raw materials. This term is somewhat misleading, since it seems to imply unprocessed natural resources like wood pulp or iron ore. Actually, raw materials refer to any materials that are used in the final product; and the finished product of one company can become the raw materials of another company. For example, the plastics produced by Du Pont are raw material used by Compaq Computer in its personal computers.
Direct materials are those materials that become an integral part of the finished product and that can be physically and conveniently traced to it. This would include, for example, the seats Boeing purchases from subcontractors to install in its commercial aircraft. Also included is the tiny electric motor Panasonic uses in its CD players to make the CD spin.
Sometimes it is not worth the effort to trace the costs of relatively insignificant materials to the end products. Such minor items would include the solder used to make electrical connections in a Sony TV or the glue used to assemble an Ethan Allen chair. Materials such as solder and glue are called indirect materials and are included as part of manufacturing overhead.
Direct Labour:
The term direct labour is reserved for those labour costs that can be easily traced to individual units of the product. Direct labour is sometimes called touch labour, since direct labour workers typically touch the product while it is being made. The labour costs of assembly -line workers, for example, would be direct labour costs, as would be the labour costs of carpenters, bricklayers, and machine operators.
Labour costs that cannot be physically traced to the creation of products, or that can be traced only at great cost and inconvenience, are termed indirect labour and treated as part of manufacturing overhead, along with indirect materials. Indirect labour includes the labour costs of janitors, supervisors, materials handlers, and night security guards. Although the efforts of these workers are essential to production, it would be either impractical or impossible to accurately trace their costs to specific units of product. Hence such labour costs are treated as indirect labour.
In some industries, major shifts are taking place in the structure of labour costs. Sophisticated automated equipment, run and maintained by skilled indirect workers, is increasingly replacing direct labour. In few companies, direct labour has become such a minor element of cost that it has disappeared altogether as a separate cost category. However, vast majority of manufacturing and service companies throughout the world continue to recognize direct labour as a separate category.
Manufacturing Overhead:
Manufacturing Overhead includes all costs of manufacturing except direct materials and direct labour. Manufacturing overhead includes items such as indirect materials; indirect ...
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In some industries, major shifts are taking place in the structure of labour costs. Sophisticated automated equipment, run and maintained by skilled indirect workers, is increasingly replacing direct labour. In few companies, direct labour has become such a minor element of cost that it has disappeared altogether as a separate cost category. However, vast majority of manufacturing and service companies throughout the world continue to recognize direct labour as a separate category.
Manufacturing Overhead:
Manufacturing Overhead includes all costs of manufacturing except direct materials and direct labour. Manufacturing overhead includes items such as indirect materials; indirect labour; maintenance and repairs on production equipment; and heat and light, property taxes, depreciation, and insurance on manufacturing facilities. A company also incurs costs for heat and light, property taxes, insurance, depreciation, and so forth, associated with its selling and administrative functions, but these costs are not included as part of manufacturing overhead. Only those costs associated with operating the factory are included in the manufacturing overhead category.
Various names are used for manufacturing overhead, such as indirect manufacturing cost, factory overhead and factory burden. All of these terms are synonymous with manufacturing overhead.
Manufacturing overhead combined with direct labour is called conversion cost. This term stems from the fact that direct labour costs and overhead costs are incurred in the conversion of materials into finished products. Direct labour combined with direct materials is called prime cost.
Non-manufacturing costs:
Generally non-manufacturing costs are subclassified into two categories:
. Marketing or selling costs.
2. Administrative costs.
Marketing or selling costs include all costs necessary to secure customer orders and get the finished product or service into the hands of the customer. These costs are often called order- getting and order - filling costs. Examples of marketing costs include advertising, shipping, sales travel, sales commissions, sales salaries, and costs of finished goods warehouses.
Administrative costs include all executive, organizational, and clerical costs associated with the general management of an organization rather than with manufacturing, marketing, or selling. Examples of administrative costs include executive compensation, general accounting, secretarial, public relations, and similar costs involved in the overall, general administration of the organization.
Product Costs versus Period Costs
In addition to the distinction between manufacturing and non-manufacturing costs, there are other ways to look at costs. For instance, they can also be classified as either product costs or period costs. To understand the differences between product costs and period costs, we must refresh our understanding of the matching principle from financial accounting.
Generally, costs are recognized as expenses on the income statement in the period that benefits from the cost. For example, if a company pays for liability insurance in advance for two years, the entire amount is not considered an expense of the year in which payment is made. Instead, one -half of the cost would be recognized as an expense each year. The reason is that both years-not just the first year -benefit from the insurance payment. The unexpensed portion of the insurance payment is carried on the balance sheet as an asset called prepaid insurance.
The matching principle is based on the accrual concept and states that costs incurred to generate particular revenue should be recognized as expenses in the same period that the revenue is recognized. This means that if a cost is incurred to acquire or make something that will eventually be sold, then the cost should be recognized as an expense only when the sale takes place- that is, when the benefit occurs. Such costs are called product costs.
Product Costs
For financial accounting purposes, product costs include all the costs that are involved in acquiring or making a product. In the case of manufacturing goods, these costs consist of direct materials, direct labour, and manufacturing overhead. Product costs are viewed as costs "attached" to units of product as the goods are purchased or manufactured and they remain attached as the goods go into inventory awaiting sale. So initially, product costs are assigned to an inventory account on the balance sheet. When the goods are sold, the costs are released from inventory as expenses (typically called cost of goods sold) and matched against sales revenue. Since product costs are initially assigned to inventories, they are also known as inventoriable costs.
We want to emphasize that product costs are not necessarily treated as expenses in the period in which they are incurred. Rather, as explained above, they are treated as expenses in the period in which the related products are sold. This means that a product cost such as direct materials or direct labour might be incurred during one period but not treated as an expense until during the following period when the completed product is sold.
Period Costs
Period costs are all the costs that are not included in product costs. These costs are expensed on the income statement in the period in which they are incurred, using the usual rules of accrual accounting you have already learned in financial accounting. Period costs are not included as part of the cost of either purchased or manufactured goods. Sales commissions and office rent are good examples of the kind of costs we are talking about. Neither commissions nor office rent are included as part of the cost of purchase or manufactured goods. Rather, both items are treated as expenses on the income statement in the period in which they are incurred. Thus, they are said to be period costs.
All selling and administrative expenses are considered to be period costs. Therefore, advertising, executive salaries, sales commissions, public relations, and other non manufacturing costs would all be period costs. They will appear on the income statement as expenses in the period in which they are incurred.
Cost Classifications for Predicting Cost Behaviour
Frequently, it is necessary to predict how a certain cost will behave in response to change in activity. For example, a manager at A T & T may want to estimate the impact of a 5% increase in long-distance calls would have on the company's total electric bill or on the total wages the company pays its long-distance operators. Cost behaviour means how a cost will react or respond to changes in the level of business activity. As the activity level rises and falls, a particular cost may rise and fall as well - or it may remain constant. For planning purposes, a manager must be able to anticipate which of these will happen; and if a cost can be expected to change, the manager must know by how much it will change. To help make such distinctions, costs are often categorized as variable or fixed.
Fixed Costs
A cost that stays the same as output changes is a fixed cost. More formally, a fixed cost is a cost that, in total, remains constant within a relevant range as the level of activity output changes. We will look at a company, Mould Technology, which produces casing for computers. One of the processes required for the production of casing is injection moulding. Consider the injection moulding machines: they are leased for $80,000 per year and have the capacity to produce up to 320, 000 casings. The cost of leasing the moulding machines is a fixed cost, since it stays at $80,000 total cost per year no matter how many casings are moulded.
Lease of Moulding Number of Casings Unit Cost
Machines
$ 80, 000 0 N/A
80,000 20, 000 $4.00
80,000 100,000 0.80
80,000 160,000 0.50
80,000 320,000 0.25
Two parts of the fixed-cost definition need further discussion: relevant range and the phrase "in total." Relevant range is the range of output over which the assumed cost/output relationship is valid. For the injection moulding activity, the moulding machines currently leased can produce upto 320,000 units of casings. Thus, the relevant range is from zero to 320,000 units - the output for which the total cost of leasing remains constant. Mould Technology pays $80,000 per year for leasing the equipment, regardless of whether it produces 0, 80,000, 100, 000 or 320, 000 units.
Cost
Fixed Cost = $80,000
20,000 100,000 160,000 320,000
Units Produced
Variable Costs
While fixed costs remain unchanged as output varies, variable costs do change as output changes. A variable cost is a cost that, in total, varies in direct proportion to changes in output. That is, a variable cost goes up as output goes up and goes down as output goes down.
Let's expand the Mould Technology example to include other resource used by the moulding machine: power. Power cost, however, behaves differently from the cost of the cutting machines. Power is consumed only if output is produced, as more output is produced, more power is used. Assume that each time a casing is moulded, the machines use 0.1kilowat -hour. The cost of power per casing is $0.20. The cost of power for various levels of activity/ output is as follows:
Cost of Power Number of Casings Unit Cost
$ 0 0 $ 0
4,000 20,000 0.20
20,000 100,000 0.20
32,000 160,000 0.20
64,000 320,000 0.20
As more casings are produced, the total cost of power increases in direct proportion. For example, as output doubles from 160,000 to 320,000 units, total cost of power doubles from $32,000 to $64,000.
Cost
64,000
32,000 Y =0.20X
20,000
4,000
20,000 100,000 160,000 320,000
Number of units produced
Mixed Cost
A mixed cost is a cost that has both a fixed and a variable component. For example, sales representatives are often paid a salary plus commission on sales. Suppose Mould Technology has three sales representatives, each earning a salary of $10,000 per year plus a commission of $0.50 for every casing they sell. The activity is selling casing, and the driver is units sold. If 100,000 casings are sold, then the total selling cost is $80,000 - the sum of the fixed salary cost of $ 30,000 (3* $10,000) and variable cost of $50,000($0.50* 100,000). The linear equation is given by:
Total cost = Fixed cost + Total variable cost
For Mould Technology, the selling cost is represented by the following equation:
Total cost = $30,000 + ($0.50 * Units sold)
The following table shows the selling cost for different levels of sales activity:
Casings Variable Cost Fixed Cost Total Selling Cost
Sold of Selling of Selling Selling Cost Per unit
20,000 $10,000 $30,000 $40,000 $ 2.00
00,000 50,000 30,000 80,000 0.80
60,000 80,000 30,000 110,000 0.69
320,000 160,000 30,000 190,000 0.59
Cost
90,000
10,000
40,000
30,000
20,000 100,000 160,000 320,000
Number of Casings produced
Classifying Costs According to Behaviour
To assess cost behaviour, we must first consider the time horizon. Then, we must identify the resources needed and output of the activity. Finally, we must measure the inputs and outputs and determine the impact of output changes on the activity cost.
Time Horizon
Determining whether a cost is fixed or variable depends on the time horizon. According to economists, in the long run, all costs are variable; in the short run, at least one cost is fixed. But how long is the short run? In the Mould Technology example, the leasing cost of the moulding machines was fixed for the year, so a year was the length of the short run for that cost. The length of the short run may differ from one cost to another.
Resources and Output Measures
Every activity needs resources to accomplish the task it has to do. Resources might include materials, energy or fuel, labour, and capital. These inputs are combined to produce an output. For example, if the activity is moving materials, the inputs could include crates (materials), fuel (energy), a forklift operator (labour), and a forklift (capital). The output would be "MOVED MATERIALS". But how do we measure the output? One measure is the number of times the activity is performed. For example, suppose that the activity is moving raw materials from the storeroom to the assembly line. A good measure of output is the number of moves. The more moves that are made, the higher the cost of moving. Therefore, we could say that the number of moves is a good output measure for the activity of moving materials.
Another term for output measure is driver. Activity drivers are observable causal factors that measure the amount of resources a cost object uses. Activity drivers explain changes in activity costs by measuring changes in activity use or output. Thus, driver for material handling may be number of moves; the driver for shipping goods may be units sold; and the measure for laundering hospital bedding may be pounds of laundry. The choice of driver is tailored not only to the particular firm but also to the particular activity or cost being measured. Therefore, in order to understand the behaviour of costs, we must first determine the underlying activities and the associated drivers that measure activity capacity and usage. The need to understand this cost-activity relationship leads us to the determination of appropriate measure of activity output and activity driver.
There are two general categories of activity drivers: production (or unit-level) drivers and non-unit level drivers. Pounds of direct materials, kilowatt-hours used to run production machinery, and direct labour hours are examples of production drivers. In other words, as pounds of materials used, kilowatt-hours, and direct labour hours increase, output also increases.
Non Unit -Level Drivers
Non Unit -level drivers explain changes in cost as factors other than units change. For example, set ups are non unit-level activity. Every time the factory has to stop producing one product in order to set up the production line to produce another product, set up costs are incurred. No matter how many units are in the new batch, the cost to set up remains the same. Let us consider a common household production activity- making chocolate chip cookies. Suppose that you decide to make two dozen cookies. First, you will have to set up for the cookie baking by taking out a bowl, spoon, baking sheet, and the relevant ingredients. On another occasion, you might decide to make four dozen cookies. You still have to set up, and it will probably take the same amount of time as it took you to set up for two dozen cookies. Setting up is therefore not related to the number of units. Instead, it is a non unit -level activity. Other examples of non-unit level costs include depreciation on the factory, the salary of the factory manager, and the cost of running the purchasing department.
In a functional -based cost system, cost behaviour is assumed to be described by unit-based drivers only. In an activity-based system, both unit and non-unit drivers are used. Thus, the ABS system produces a much richer view of cost behaviour than a functional -based system.
Activities, Resource Usage, and Cost Behaviour
Short-run costs often do not adequately reflect all the costs necessary to design, produce, market, distribute, and support a product. In the early 1990's, there were some new insights into the nature of long run and short-run cost behaviour. These insights related to activities and the resources needed to perform them.
Capacity is simply the actual or potential ability to do something. So, when we talk about capacity for an activity, we are describing the amount of activity the company can perform. How much capacity is needed depends on the level of performance required. Usually, we can assume that the capacity needed corresponds to the level where the activity is performed efficiently. This efficient level of activity performance is called practical capacity. Occasionally, there is excess capacity. To see how that happens and how it affects cost behaviour, we need to look at flexible and committed resources.
Flexible Resources
It would be nice if a company could purchase only those resources it needed and precisely at the time the resources were needed. Sometimes that happens. For example, direct materials are frequently purchased at the time and in the amount needed. This kind of resource is called flexible resource. Flexible resources are supplied as used and needed; they are acquired from outside resources, where the terms of acquisition do not require any long-term commitment for any given amount of the resource. Thus, the organization is free to buy only the amount needed. As a result, the quantity of the resource supplied equals the quantity demanded. Materials and energy are examples. There is no unused capacity for this category of resources, since the amount of resource used just equals the amount purchased.
Since the cost of the resources supplied as needed equals the cost of resources used, the total cost of the resource increases as demand for the resource increases. Thus, the cost of flexible resource is a variable cost.
Committed Resources
Other resources must be purchased before they are needed. A factory building is a good example. The building must be planned and built before production takes place. Committed resources are resources that are supplied in advance of usage; they are acquired by the use of either an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the amount of the resource available is fully used or not. Committed resources may have unused capacity, since more may be available than is actually used.
Let's look further at committed resources. Many resources are acquired before the actual demands for the resource are realized. For example, organizations acquire many multiperiod service capacities by paying cash up front or by entering into an explicit contract that requires periodic cash payments. Buying or leasing buildings and equipment is an example of this form of advance resource acquisition. The annual expense associated with the multiperiod category is independent of actual usage of the resource; thus, these expenses can be defined as committed fixed expenses and they provide long-term activity capacity.
A second and more important example of committed resources concerns organizations that acquire resources in advance through implicit contracts, usually with their salaried and hourly employees. The implicit understanding is that the organization will maintain employment levels even though there may be temporary downturns in the quantity of activity used. As a result, the expense associated with this category of resources is independent of the quantity used - at least in the short run. Thus, in the short run, the amount of resource expense remains unchanged even though the quantity used may vary, and this resource cost category can be treated as fixed expense. We may call these shorter-term committed resources discretionary fixed expenses. They are costs incurred for the acquisition of short-term activity capacity.
Hiring three receiving clerks for $90,000 who can supply the capacity of processing 9,000 receiving orders is an example of implicit contracting (" receiving orders" is the driver used to measure the receiving activity' capacity and usage). Certainly, none of the three clerks would expect to be laid off if only 6,000 orders were actually processed, unless, of course, the downturn in demand is viewed as permanent. This implicit contracting raises ethical issues. Many companies today are turning to contingent employment to handle variation in demand for labor services. A key reason for the increase in contingent employment includes "buffering core workers against job loss." Apparently, many companies attempt to shield long-time workers from market fluctuations. Suppose that the drop is permanent. In this case, we have an activity with too much capacity, and until we reduce the capacity, resource spending will not be reduced. Thus, resource spending changes lag changes in permanent activity output demands.
Step-Cost Behaviour
In our discussions of cost behaviour, we have assumed that the cost function is continuous. In reality, some cost functions are discontinuous. This type of cost function is known as a step function. A step cost displays a constant level of cost for a range of output and then jumps to a higher level of cost at some point, where it remains for similar range of output.
Items that display step-cost behaviour, must be purchased in chunks. The width of the step defines the range of output for which that amount of resource must be acquired. Suppose, for example, that a company hires three sustaining engineers; these are engineers responsible for redesigning existing products to meet changing customer needs. Each engineer is paid $50,000 per year and is capable of processing 2,500 engineering change orders per year. Then the company could process as many as 7,500 (3*2500) per year at a total cost of $150,000(3*$50,000). The nature of the resource requires that the capacity be acquired in chunks ((one engineer hired at a time).
Step costs with wide steps are assigned to the fixed cost category. Most of these costs are fixed over the normal operating range of a firm. If that range is 5,000 to 7,500 change orders then the firm will spend $150,000 on engineering resources. Only if the firm wants to increase its capacity for engineering above the 7,500 level, will it increase spending on engineers. Of course, if the use of engineering services is not at the maximum of 7,500 orders, perhaps 6,000 orders are actually being processed per year- then there is excess capacity for this service. Frequently, there is excess capacity for activities that are characterized by this type of step behaviour.
For example, during the year the company may not actually process 7,500 change orders; that is, all of the available change order-processing capacity may not be used. Assume that 6,000 change orders were processed during the year.
Implications for Control and Decision Making
The activity-based model just described can improve both managerial control and decision-making. Operational control systems encourage managers to pay more attention to controlling resource use and spending. For example, a well-designed operational control system allows managers to assess the changes in resource demands that will occur from new product-mix decisions. Adding new, customized products may increase the demands for various overhead activities. If sufficient unused activity capacity does not exist, then resource spending must increase. Similarly, if activity management brings about excess capacity, managers must carefully consider what is to be done with the excess capacity. Eliminating the excess capacity may decrease resource spending and thus improve overall profits. Alternatively, the excess capacity could be used to increase the number and type of products, thereby increasing revenues without increasing spending.
The activity -based resource usage model also allows managers to calculate the changes in resource supply and demand resulting from implementing such decisions as to whether to make or buy a part, to accept or reject special orders, and to keep or drop product lines. Additionally, the model increases the power of a number of traditional management accounting decision-making models.
Cost- Volume-Profit Analysis
The income statement is a useful tool for organizing the firm's costs into fixed and variable categories. The income statement can be expressed as a narrative equation:
Operating income = Sales revenues - Variable expenses - Fixed expenses
The controller of a company, Super Mowers, which manufactures lawn mowers, has prepared the following income statement:
Sales (1,000 units @ $400) $400,000
Less: Variable expenses 325,000
--------------
Contribution margin $ 75,000
Less: Fixed expenses 45,000
------------
Operating income $ 30,000
------------
We see that for Super Mower, the price of a lawn mower is $ 400 each, and the variable cost per unit is $325.Fixed cost is $45,000.At the break-even point, then, the operating income equation would be the following form:
0= ($400*units) - ($325*units) - $45,000
0= ($75*units) - $45,000
$75*units = $45,000
Units = 600
Therefore, Super Mower must sell 600 lawn mowers to just cover all fixed and variable expenses.
A good way to check this answer is to formulate an income statement based on 600 units sold.
Sales (600 units at $400) $ 240,000
Less: Variable expenses 195,000
------------
Contribution margin $ 45,000
Less: Fixed expenses 45,000
-----------
Operating income $ 0
-----------
Shortcut to Calculating Break-Even Units
Number of units = Fixed cost/Unit contribution margin
Unit Sales Needed to Achieve Targeted Profit
While the break-even point is useful information, most firms would like to earn operating income greater than zero. CVP analysis gives a way to determine how many units must be sold to earn a particular targeted income. Targeted operating income can be expressed as a dollar amount (for example, $20,000) or as a percentage of sales revenue (for example, 15% of revenue). Both the operating -income approach and the contribution margin approach can be easily adjusted to allow for targeted income.
Targeted Income as a Dollar Amount:
Assume that Super Mower wants to earn operating income of $60,000.How many mowers must be sold to achieve this result?
$60,000 = ($400*Units) - ($325* Units) - $45,000
$105,000 = $75* Units
Units =1400
Targeted Income as a % of Sales Revenue
Assume that Super Mower wants to know the number of lawn mowers that must be sold in order to earn a profit equal to 15% of sales revenue. Sales revenue is price multiplied by the quantity sold Thus, the targeted operating income is 15% of price times quanity.Using the income statement:
0.15*$400*Units = $400 * Units - $325*Units - $45,000
After Tax Profit Targets:
Net income = Operating income- Taxes
= Operating income- (Tax rate* Operating income)
= Operating income (1- Tax rate)
Operating income = Net income/(1 -Tax rate)
Suppose Super Mower wants to achieve net income of $48,750 and its tax rate is 35%
$48,750 = Operating income - (0.35 *Operating income)
$48,750 = 0.65(Operating income)
$75,000 = Operating income
Number of units to be sold = ($45,000+ $75,000)/$75 = 1,600
Break-Even Point in Sales Dollars
Dollars % of Sales
Sales $400,000 100.00
Less: Variable costs 325,000 81.25
Contribution margin $ 75,000 18.75
Less: Fixed Costs 45,000
Operating income $ 30,000
Break-Even sales Value = $45,000/0.1875
Profit Targets and Sales Revenue
How much sales revenue must Super Mower generate to earn a before tax profit of $60,000-
Sales = ( $45,000+ $60,000)/0.1875
= $105,000/0.1875
= $ 560,000
Multiple -Product Analysis
Super Mower has decided to offer two models of lawn mowers: Model A and Model B. The marketing department is convinced that 1, 200 of model A(at $400) and 800 of Model B(at $800) can be sold during the year.
Model A Model B Total
Sales $480,000 $640,000 $1,120,000
Less: Variable expenses 390,000 480,000 870,000
Contribution margin 90,000 160,000 250,000
Less: Direct fixed expenses 30,000 40,000 70,000
Product margin 60,000 120,000 $ 180,000
Less: Common fixed expenses $ 26,250
Operating income $ 153,750
BEP for Model A = $30,000/$75 = 400 units
BEP for Model B = $40,000/$200 = 200 units
Determining the Sales Mix
A number of different sales mixes can be used to define the break-even volume.For example, a sales mix of 2:1 will define a break even point of 550 Model A and 275 Model B. The total contribution margin produced by this mix is $96,250.Simlarly, if 350 Model A and 350 Model B are sold (corresponding to a 1:1 sales mix); the total contribution is $96,250.
However, according to marketing study, Super Mower expects a product mix of 3:2.
Sales Mix and CVP Analysis
Product Price Unit VC Unit CM Sales Mix Package Unit CM
Model A $400 $325 $ 75 3 $225
Model B 800 600 200 2 400
Package Total $625
Break-Even Package = Fixed Cost/Package Contribution Margin
= $96,250/$625
= 154 Packages (462 of A and 308 of B)
Sales Dollar Approach
With the sales mix of 3:2, the contribution margin ratio is 0.2232($250,000/$1,120,000)
Break-Even Sales = Fixed Cost/Contribution margin ratio
= $96,250/0.2232
= $431,228
Changes in CVP Variables
Super Mower recently conducted a market study of the Model A that revealed three different alternatives:
(1) Alternative 1: If advertising expenditures increase by $8,000 sales will increase from 1,600 units to 1, 725 units
(2) Alternative 2: A price decrease from $400 to $375 per lawn mower will increase sales from 1,600 units to 1,900 units.
(3) Alternative 3: Decreasing price to $375 and increasing advertising expenditures by $8,000 will increase sales from 1,600 units to 2,600 units.
Of the three alternatives identified by the marketing study, the one that promises the most benefit is the third. It increases total profits by $2,000.The first alternative increases profits by $1,375 and the second actually decreases profits by $25,000.
Introducing Risk and Uncertainty
An important assumption of CVP analysis is that prices and costs are known with certainty. This is seldom the case. Risk and uncertainty are part of a business decision-making and must be dealt with. Formally, risk differs from uncertainty in that under risk the probability distributions of the variables are known; under uncertainty, they are not known. For our purposes, however, the terms will be used interchangeably.
How do managers deal with risk and uncertainty? There are a variety of methods. First, of course, is that management must realize that the uncertain nature of future prices, costs, and quantities. Next, managers move from consideration of a break-even point to what might be called a " break-even band." In other words, given the uncertain nature of data, perhaps, a firm might break even when 1,800 to 2,000 units are sold instead of the point estimate of 1,900 units.
Margin of safety
The margin of safety is the units sold or expected to be sold or the revenue earned or expected to be earned above the break-even volume. For example, if the break -even volume of a company is 200 units and the company is currently selling 500 units, the margin of safety is 300 units (500-200). The margin of safety can be expressed in sales revenue as well. If the break-even volume is $200,000 and the current revenues are $350,000, then the margin of safety is $150,000.
Operating Leverage
In financial terms, operating leverage is concerned with the relative mix of fixed costs and variable costs in an organization.It is sometimes possible to trade off fixed costs for variable costs. As variable costs decrease, the unit contribution margin increases, making the contribution of each unit sold much greater. In such a case, fluctuations in sales have an increased effect on profitability.Thus, firms that have realized lower variable costs by increasing the proportion of fixed costs will benefit with greater increases in profits as sales increase than will firms with a lower proportion of fixed costs. Fixed costs are being used as leverage to increase profits. Unfortunately, it is also true that firms with a higher operating leverage will experience greater reductions in profits as sales decrease.Therefore, operating leverage is the use of fixed costs to extract higher percentage changes in profits as sales activity changes.
The greater the degree of operating leverage, the more that changes in the sales activity will affect profits. Because of this phenomenon, the mix of costs that an organization chooses can have a considerable influence on its operating risk and profit level.
Degree of operating leverage = Contribution margin/Profit
