Manufacturing Accounts Manufacturing Accounts Classification of Costs Classification of Costs 2 Ir. Haery Sihombing (IP). Pensyarah Fakulti Kejuruteraan Pembuatan Universiti Teknologi Malaysia Melaka MANUFACTURING ACCOUNTS MANUFACTURING ACCOUNTS The following passage is: The following passage is: a brief introduction to manufacturing a brief introduction to manufacturing accounts and accounts and how manufacturing costs are how manufacturing costs are classified. classified. Classification of Costs Classification of Costs (1) A manufacturing account is prepared to A manufacturing account is prepared to find out: find out: the the cost of goods manufactured cost of goods manufactured. Costs of manufacturing include: Costs of manufacturing include: all resources used, directly or indirectly, all resources used, directly or indirectly, in the manufacture of goods. in the manufacture of goods. The manufacturing costs can be The manufacturing costs can be classified into classified into direct costs direct costs and and indirect indirect costs costs Direct costs can be identified specifically Direct costs can be identified specifically and exclusively with a given cost and exclusively with a given cost objective in an economically feasible way. objective in an economically feasible way. What are direct costs? What are direct costs? Classification of Costs Classification of Costs (2)
Transcript
Manufacturing AccountsManufacturing AccountsClassification of CostsClassification of Costs
of plant and machinery, etc. of plant and machinery, etc.
Indirect costs are also known as Indirect costs are also known as factoryfactoryoverheadsoverheads..
•• AA manufacturing accountmanufacturing account is prepared to find out the is prepared to find out the cost of goods manufactured. Costs of manufacturing cost of goods manufactured. Costs of manufacturing include all resources used, directly or indirectly, in the include all resources used, directly or indirectly, in the manufacture of goods. The manufacturing costs can be manufacture of goods. The manufacturing costs can be classified into direct costs and indirect costs. classified into direct costs and indirect costs.
•• Direct costsDirect costs are those costs directly involved in the are those costs directly involved in the manufacture of goods. Examples of direct costs are direct manufacture of goods. Examples of direct costs are direct materials, direct labor and direct expenses. All the direct materials, direct labor and direct expenses. All the direct costs are collectively known as prime cost. costs are collectively known as prime cost.
•• Indirect costsIndirect costs are not directly related to production. are not directly related to production. They are all the remaining production expenses. Examples They are all the remaining production expenses. Examples of indirect costs include factory rent, factory power, of indirect costs include factory rent, factory power, depreciation of plant and machinery, etc. Indirect costs depreciation of plant and machinery, etc. Indirect costs are also known as factory overheads. are also known as factory overheads.
What Distinguishes What Distinguishes
Direct and Indirect Costs?Direct and Indirect Costs?
Managers prefer to classify costs as direct
rather than indirect whenever it is
“economically feasible” or “cost effective.”
Other factors also influence whether a cost is
considered direct or indirect.
The key is the particular cost objective.
Categories of Categories of
Manufacturing CostsManufacturing Costs
Any raw material, labor, or other inputAny raw material, labor, or other input
used by any organization could, in theory, used by any organization could, in theory,
be identified as a direct or indirect costbe identified as a direct or indirect cost
depending on the cost objective.depending on the cost objective.
Flow of Product Costs in AccountsFlow of Product Costs in Accounts
Product costs flow from the Product costs flow from the DirectDirect
MaterialsMaterials,, Direct LaborDirect Labor andand MManufacturinganufacturing
OverheadOverhead through through Work in ProcessWork in Process toto
Finished Goods InventoryFinished Goods Inventory and finally to and finally to
Cost of Goods SoldCost of Goods Sold..
Flow of Product Costs in AccountsFlow of Product Costs in AccountsIncome Statement Presentation Income Statement Presentation
of Product Costsof Product Costs
When finished goods are sold they are When finished goods are sold they are
moved from moved from Finished GoodsFinished Goods to to CCost of ost of
Goods SoldGoods Sold..
Cost of Goods ManufacturedCost of Goods Manufactured
Cost of Goods Manufactured Cost of Goods Manufactured includes all includes all costs of goods completed during the period.costs of goods completed during the period.
Cost of Goods SoldCost of Goods Sold
Cost of Goods Sold.Cost of Goods Sold.
Types of Costing SystemsTypes of Costing Systems
Companies use product costing systems Companies use product costing systems
to measure and record the cost of to measure and record the cost of
manufactured products. Two types:manufactured products. Two types:
d.d. Cost of goods manufactured.Cost of goods manufactured.
Quick Review Quick Review Question #4Question #4
4.4. Cost of Goods Sold is $200,000, Cost of Goods Sold is $200,000, beginning Finished Goods is $50,000, beginning Finished Goods is $50,000, ending Finished Goods is $100,000 ending Finished Goods is $100,000 and ending Work in Process is and ending Work in Process is $10,000. What is the Cost of Goods $10,000. What is the Cost of Goods Manufactured?Manufactured?
a.a. $100,000$100,000
b.b. $250,000$250,000
c.c. $50,000$50,000
d.d. $150,000$150,000
THE ENDTHE END
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WHAT ARE THE COSTS?
The Meaning of “Cost” and “Loss” Whilst the expression “all direct costs and directly incurred losses” is not used in any of the standard forms of building contract, the judge noted that it nonetheless bears some similarity to the words “direct loss and/or expense" found in the JCT forms of contract. In each case the expression contains two elements; costs and losses in the letter of intent, and loss and expense in the JCT forms.
The judge said that the words “ cost" and “ expense" are regularly used as synonyms-Both denote sums expended or outlays, and underpin the idea that a claimant is entitled to recover money that he has been compelled to pay in consequence of an event with contractual significance.
Of the words “loss" and “ losses", the judge was also of the view that they correspond to each other. The judge explained the general significance of the word “ loss" as being the idea that a person does not have something that he had or would otherwise have had but for an event with legal significance. In cases involving breach of contract, the general principle is that the innocent party is entitled to be put in the same position as he would have been in if the contract had been performed. The judge said it was obvious that a loss of that nature may include both loss of profit and a contribution to general overheads:
“..it is of the nature of a contract that the party who supplies the goods or services expects, or at least hopes, to make a profit. The intention to make a profit lies at the heart of all, or nearly all commercial activity and the law must recognize that elementary economic fact. l am accordingly of the opinion that the failure of a contractor to make a profit should be accounted a “loss: not only in calculating damages for breach of contract, but also in construing contractual terms relating to payment or goods and services. The same is true of earning a contribution to general corporate overheads; indeed, until such a contribution has been earned it probably cannot be said that any profit has been generated”
The Use of the Words “Direct” or “Directly” The judge observed that the meaning of “ cost" and “ loss"(discussed above) are qualified by the use of the words “direct" or “ directly”
His lordship explained that the significance of the word “ direct" as used in the JCT forms of contract has been the subject of numerous judicial decisions and that two legal propositions can be drawn from the cases:
1. t is concerned with remoteness of loss, not with causation 2. lt denotes that the loss or expense in question must now naturally from the contractual event relied on by the claimant (in accordance with the first rule in Hadley V Biennale [1854]9Ex 341).
in the judge's opinion, that same meaning must be accorded to the words “ direct" and “ directly" which appear in the letter of intent. There was nothing in the letter of intent or the surrounding circumstances to persuade the judge that any other meaning was intended.
Direct cost is a cost that can be directly traced to a cost object such as a product or a department or to producing specific goods or services. In other words, direct costs do not have to be allocated to a product, department, or other cost object. For example, the cost of meat in a hamburger can be attributed directly to the cost of manufacturing that product. Other costs, such as depreciation or administrative expenses, are more difficult to assign to a specific product, and so are not considered direct costs
A direct cost is a cost that is directly attributable to the manufacture of a product (or provision of a service). A good example of a direct cost is the cost of the materials needed to make a product. The
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usage of the materials is directly related to the manufacture of the product. Direct costs are very often variable costs and vice-versa, but the two are not synonymous: For example, the costs of running machinery used in manufacturing are not direct costs, but they are likely to be variable or semi-variable.
If a company produces artisan furniture, the cost of the wood and the cost of the craftsperson are direct costs—they are clearly traceable to the production department and to each item produced—no allocation was needed. On the other hand, the rent of the building that houses the production area, warehouse, and office is not a direct cost of either the production department or the items produced. The rent is an indirect cost—an indirect cost of operating the production department and an indirect cost of crafting the product.
To calculate the total cost of the production department or to calculate each product’s total cost, it is necessary to allocate some of the rent (and other indirect costs) to the department and to the product.
There are three types of direct cost:
direct materials, direct labour, and Direct expenses.
Direct Material (Inventory Transactions) All items such as raw materials, standard and specialized parts, and sub-assemblies required to assemble or manufacture a complete product. Direct material costs are assignable to a specific product, cost center, or work-order. Direct material costs is Part of raw material cost that can be specifically and consistently associated with or assigned to the manufacture of a product, a particular work order, or provision of a service.
Let us now discuss how the accounting transactions that are related to Direct Material will be recorded in this new External and Internal structure.
Today in the External (Financial) Accounting we do not have any Expenditure account that will show management how much Direct Material we have purchased during this month (accounting period). The purchased amount will be debited directly to the Direct Material Inventory account. If we develop an External and Internal Accounting structure, we will be able to create special Expenditure accounts that will report to management how much Direct Material we have purchased this month. In the following Exhibit we will analyze this new procedure step by step.
Exhibit 1 In the upper part of this exhibit we are showing the transactions realized in the External Accounting. Every time we purchase some Direct Material (or any other Inventory item) we should debit this amount in the corresponding Expenditure account. Here we can see that during this month (accounting period) our company realized three different purchases. The total amount of these purchases we record in the debit of this account. In this example we credit this Stores Purchase account with our return of 300 Dollars. At the end of this month, we have a debit balance, which we will credit the Stores Purchase account and transfer to the debit of the Inventory Stores - Raw Material. In this Asset account we have a beginning balance - to which we add the net purchase.
The Stores Withdrawal (Raw Material, Supplies, Parts) correspond to Internal Accounting. We have created this account under the denomination of Cost Elements. All Raw Material withdrawal must be credited this account - and debited directly to the Production Cost Account. Here it is indicated, that the stores withdrawal correspond to the Product A. And there have been 3 different withdrawals (A, B and C). To the debit of this Stores Withdrawal, we have to record the return of some material. The credit of this return will be recorded in the Production Cost account of Product A. In this exhibit the credit of this return is not shown.
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During the month-end closing procedure, the net amount of the Stores Withdrawal will be transferred from debit of this account to the credit of the Asset account: Inventory Stores Raw Material. In this account, are also recorded any type of inventory adjustments. As we can observe, the new procedure provides much more clarity than what can be obtained using only Financial Accounting. The benefits of separating Financial from Internal Accounting are immense.
Raw Material Standard Costing On the subject of raw material that is withdraw from Stores Inventory to use for production - let us here clarify how we could express this withdrawal in some Standard Cost measurement. Exhibit 2 shows this type of procedure.
Exhibit 2 - The Stores Withdrawal - Raw Material will be credited with the actual amount that we are taking out of this store and expressed with the actual price. This amount will be taken to the Price Variance account - and we will compare this amount with the value of the actual Raw Material used at the Standard Price that we have established in advance. The variance between the debit and credit amount on this account, will refer to the Price Variance of Raw Material used in production.
The credit amount from this account, we transfer to the debit of the next variance account: the Efficiency Variance. The credit amount on this account will be representing the Standard quantity that we should have used for this production, multiplied with the Standard Price per unit of Raw Material. Finally, this amount ( Sq x Sp ) will be charged to the Production Cost account of this product realized and controlled by a Job Order system.
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Direct Labour Employees or workers who are directly involved in the production of goods or services. Direct labor costs are assignable to a specific product, cost center, or work order. Direct labor cost is Part of wage-bill or payroll that can be specifically and consistently assigned to or associated with the manufacture of a product, a particular work order, or provision of a service.
It is important for our understanding of Internal Accounting, that we recognize that the payment of hourly wage is also a Fixed Cost - just as we are referring to the Salary paid. As you will accept, the only difference between the Salary and the Wages - is the time period to which each payment refers.
The company does not have any agreement to pay the worker less or more per hour, if the production increased or decreased per hour of work (higher or lower efficiency). It is true, that we agreed not to charge to a smaller than normal production during a day, the total wages earned during this same day. That was the reason, why the accounting profession agreed to identify the Direct Labor payment as a variable cost, same way as the amount of Raw Material is used. However, you will have to accept, that the actual amount of Wages paid, must be recorded somewhere in our Internal Accounting system.
The actual amount of Direct Labor Wage paid, should be charged to the Direct Production Department where the worker is assigned. This procedure will give management accurate information referring to its Responsibility Accounting System. In the budget of each Direct Production Department should be included the gross payment for the Direct Labor wages of the accounting period. In the following graphic, we identify the recording procedures in the traditional way, and with the Internal Accounting method.
Exhibit 1 In the traditional way - we credit the Accrued Payroll account with the grand total of the wages for the period. A part of this amount ($ 5000 in our exhibit) will be charged to the Direct Production Department as indirect labor wages.
Direct Labor wages will be taken directly to the debit of the Work in Process account, (terminology used in today's accounting). In our exhibit the amount of 39,000. If during this accounting period, we did not use all Direct Labor wages in the production process, because of some machine was out of service or for some other reason, we would have to debit the Work in Process account with some smaller amount, compared with the total value of $ 39,000. The
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difference between 39,000 and 36,000 (as an example) we would need to debit to some specific account. We would need to create such special account.
If we work with our new Internal Accounting - the total Accrued Payroll of wages would be taken directly to the Direct Production Department. We would need to specify in the departments information, how much would correspond to the Indirect Labor and how much to the Direct Labor.
To: Factory Dept. - we have charged the actual value of Direct and Indirect Wages paid. From: Factory Dept. - we have to charge to the Production Cost Account only the amount of
Direct Wages that correspond to the production of this time period. The difference will stay as a departmental operating cost of this Direct Production Department. This procedure is very important to remember - otherwise we would charge to the production a Direct Labor Wage that does not correspond to this production volume. The next two exhibits are related to the discussion of Direct Wages payments.
Let us study them in detail.
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Exhibit 2 Step 1 - identifies the Class of Accounts that we use for this recording. Class 2 will have all Cost Elements accounts. This Class 2 is the very beginning of the Internal Accounting structure. We will credit Payroll Wages account with the Direct Payroll amount that we have received from the Payroll information - and this information refers to the Actual Hours worked (Ah) times the Actual Payment realized (AP), From credit of this Class 2 account -we will debit this amount to our Direct Production Departments in Class 3. This Class is identified with the name: To: Departments. This exhibit is also showing the possible departmental code that we could give this account.
Now let us study the next exhibit:
Exhibit 3 The best way to express the production cost is to charge to the Production Cost account the Standard amount of the corresponding Direct Labor Wages. As we have debited Class 3 Direct Production Department account with the amount that we have received by multiplying the Actual hours with Actual Payment ( Ah x Ap), we have to credit this Direct Production Department account in Class 4, with this same amount. However, we do not debit the production with the actual Direct Labor value. We express the Direct Labor Wages in STANDARD values. Based upon this requirement, we need to create within Class 4 From: Departments, two very specific accounts:
First to show the Payment Variance and Second to show the Efficiency Variance. The Payment Variance account requires an accounting code that would correspond to the accounting code of the Direct Production Department. In our case, we could establish following code: 4-1-95-008. In same way, we would give the Efficiency Variance following code: 4-1-96-008.
You will be able to understand the different amounts that we would transfer from Class 4 Direct Production department to the Payment Variance and to the Efficiency Variance accounts. The letter abbreviations are recorded in this exhibit. From the Efficiency Variance account - we transfer the Direct Labor Wage to the corresponding Production Cost account in Class 5. This Direct Labor Wage is now expressed in Standard hours and Standard Payment.
Direct Expense Alternative term for direct cost. Direct expense is in the Accounting & Auditing and Banking, Commerce & Finance subjects. Direct expense appears in the definition of the following term: prime
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cost all items of expense directly incurred by or attributable to a specific project, assignment, or task.
The last is anything that does not fall into the other two (commoner) categories. A method for tracking the cost of materials needs to be chosen: usually FIFO or LIFO, sometimes average cost or replacement cost.
In the early industrial age, most of the costs incurred by a business were what modern accountants call "variable costs" because they varied directly with the amount of production. Money was spent on labor, raw materials, power to run a factory, etc. in direct proportion to production. Managers could simply total the variable costs for a product and use this as a rough guide for decision-making processes.
Some costs tend to remain the same even during busy periods, unlike variable costs which rise and fall with volume of work. Over time, the importance of these "fixed costs" has become more important to managers. Examples of fixed costs include the depreciation of plant and equipment, and the cost of departments such as maintenance, tooling, production control, purchasing, quality control, storage and handling, plant supervision and engineering. In the early twentieth century, these costs were of little importance to most businesses. However, in the twenty-first century, these costs are often more important than the variable cost of a product, and allocating them to a broad range of products can lead to bad decision making. Managers must understand fixed costs in order to make decisions about products and pricing.
For example: A company produced railway coaches and had only one product. To make each coach, the company needed to purchase $60 of raw materials and components, and pay 6 laborers $40 each. Therefore, total variable cost for each coach was $300. Knowing that making a coach required spending $300, managers knew they couldn't sell below that price without losing money on each coach. Any price above $300 became a contribution to the fixed costs of the company. If the fixed costs were, say, $1000 per month for rent, insurance and owner's salary, the company could therefore sell 5 coaches per month for a total of $3000 (priced at $600 each), or 10 coaches for a total of $4500 (priced at $450 each), and make a profit of $500 in both cases.
The sum of all three types of direct costs is called the prime cost. Any cost that is not a direct cost is an indirect cost.
Variable costs Costs that change in proportion to sales are variable costs. Common variable costs include raw materials, shipping and depletion. The opposite of variable costs are fixed costs. In between are semi-variable costs that have fixed and variable elements. A high level of variable costs means a low level of operational gearing.
Materials and purchased parts Direct labour, quality control staff Maintenance costs Power/energy and utilities Packaging and storage costs Royalty/licensing payments
Semi-variable costs Semi-variable costs are those that have both fixed cost and variable cost elements. For example, a manufacturer's electricity bill may include elements that are fixed (such as lighting that is required regardless of the level of production) and elements that are variable (such as the electricity used by machinery directly involved in manufacturing).
Fixed costs Fixed costs are those that do not change with the level of sales. If sales increase or decrease but nothing else changes then fixed costs remain the same. Common examples of fixed costs include rents, salaries of permanent employees and depreciation. A high level of fixed costs increases operational gearing.
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Investment costs (interests and depreciation on capital investment – tooling, property tax, insurance)
Overhead costs (technical services/engineering, non-technical services/office personnel, general supplies)
Management expenses 9corporate management, legal staff, R&D staff) Selling expenses (sales force, delivery and warehouse costs, technical service staff)
Cost Classification The selling price may be twice the manufacturing cost. Manufacturing cost can be classified into fixed cost and variable costs; manufacturing cost can be also divided into direct costs and indirect costs.
Manufacturing Cost = Fixed Costs + Variable Costs
Cost Categories
Actual costs refer to real transactions, whereas opportunity costs refer to the alternative taken into consideration by decision makers who might want to choose the line of activity which minimize the costs. From an external point of view, it is difficult to ascertain which are the alternative considered.
Discretionary costs are not strictly necessary for current production but correspond to strategic goals (e.g. improving the firm's image through an advertising institutional campaign).
Production costsGiven a specific product version, production costs are usually classified according to their responsiveness to different levels of production attained. In addition to separating costs into categories such as direct and indirect and manufacturing and non-manufacturing, costs are also frequently identified by their behavior in relation to changes in an activity level. This separation is helpful for planning and budgeting purposes. The major types of costs, in terms of cost behavior, are: 1) variable costs, and 2) fixed costs, 3) semi-variable costs and 4) semi-fixed costs. These concepts are illustrated graphically in figure 1 and discussed individually below.
a) Fixed Costs Fixed costs are defined as those costs that do not vary with changes in the activity level. Some horizontal cost functions are presented in the top right panel of figure 1 to illustrate the idea. However, this does not mean that fixed costs remain constant. If a production volume based measure is used as the activity, a cost that changes for some reason other than a change in production activity is considered fixed. This simply means that the cost is driven by a non-production volume related phenomenon. For example, property taxes are considered fixed in traditional cost accounting systems that are typically based on production volume related activities. However, property taxes change when the taxing authority changes the tax rate or reassesses the property. The idea to grasp is that the designation of a particular cost as fixed or variable can change when it is analyzed in relation to a different activity. It is also important to understand that the notion of fixed and variable costs is a short run concept. All costs tend to be variable in the long run.
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Fixed costs are simply not responsive to production levels. If there are only fixed costs, the total costs follow this rule:
For instance, the cost of renting an office is a fixed cost, since usually the contract fixes it for a certain period of time (say one year), without any reference to the income produced by the operations that take place in the same office.
The firm deciding to rent this office, however, will have usually expected to be able to afford it as well as to be reasonably sure that it will not be too small for the kind of operation it intends to carry out.
This brings us to an important conclusion: a very common situation is that of quasi-fixed costs.They are flat in a certain range of (expected) production but they are forced to jump to higher levels if certain thresholds are overcome. Near these thresholds, in fact, quality deterioration of output and other negative phenomena take place.
Symmetrically, below other minimum thresholds in level of activities, the same costs become unaffordable and will probably be reduced. Here you have the graph of total costs when there are only quasi-fixed costs:
b) Variable Costs Variable costs are those costs that vary with changes in the level of activity. Variable costs tend to increase at various rates that generate linear (straight line) or a variety of non-linear cost functions when the costs are plotted on a graph. Some examples are illustrated in the top left panel of figure 1 The major activity that affects manufacturing costs is production volume, i.e., producing output. Production volume is frequently measured in terms of units produced, direct labor hours used, machine hours used, materials costs or some other production volume related measure. However, other activities that are not related to production volume might also be important in analyzing cost behavior. The recognition that non-production volume related activities also cause, or drive costs is a fundamental idea associated with activity based costing (ABC).
Variable costs grow with higher levels of production (proportionally or not). If there are only variable costs, at zero production the total costs will be zero. Total costs will follow for instance this rule:
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b.1) In particular, economies of scale describe situation when the total costs rise less than proportionally to production increases, as you see in the following diagram:
b.2) Dis-economies of scale represent the opposite situation:
b.3) Constant return to scale is the intermediate situation in which the growth in production is exactly matched by the same percentage increase in total costs, i.e. elasticity of costs to production levels is 1:
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In this case, productivity is constant. To understand the sources of economies of scale is helpful to consider that total costs for production inputs depends on two components: the quantity and the price of the inputs. Accordingly, it is often useful to distinguish two broad reasons for cost to rise: an increase of the input quantity or a soaring price for input. This allows for distinguishing different reasons for costs behaviors in reaction to changes in production levels.
In particular, economies of scale can be due:
a) to savings in average physical quantity of input when the production is higher (e.g. electricity dispersion is lower in percentage when the electricity throughput is high); b) to reduction in prices paid when buying larger quantities (e.g. because of stronger power in purchase negotiation). To make experiments with different situations, you can use the free Costs software, distributed by the Economics Web Institute.
c) Semi-Variable and Semi-Fixed Costs Semi-variable costs are part fixed and part variable. There is a minimum cost (the fixed portion) and a variable portion that increases as activity increases. Some examples of these mixed costs appear in the lower left panel of Exhibit 1-3.The point where the cost function intersects the vertical axis represents the fixed portion of the cost. There are also semi-fixed costs that do not change continuously as the level of activity changes, but do increase in steps as activity increases beyond various levels. These costs are sometimes referred to as step cost and step functions. For example, a single production supervisor (who's salary normally represents a fixed cost) might be adequate until production reaches a certain level, then a second supervisor would need to be hired. Supervisory costs might be driven by the number of production shifts. Step functions can take on many forms as illustrated in the lower right panel of Figure 1..
Total and average costs
Total costs are the sum of all costs. By dividing the total costs by the quantity produces, one gets the average costs: how much a unit of production costs ("unit cost").
Average costs can be directly compared with price to compute profitability: if the price is higher than average cost, the production is profitable.
Total profits will be given by multiplying the average profit with the quantity produced and sold.
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Identically, total profits can be obtained as total revenues less total costs. The relationship between total revenue and total costs depending on the production level is analyzed by the so-called "break-even analysis".
Let's see mathematically what component crucially influences average costs at two widely different levels of production.
In the simplified situation of a production process characterized by a fixed cost (F) plus aproportionally-growing variable cost (VC), total costs (TC) are described by the easy formulas below:
TC = F + VC×q
Where q is the quantity of good.
Average costs (AC) are thus the following:
AC= TC/q = F/q + VC
The first term of the right side (F/q) decreases systematically the higher the production level (q). At low production levels, this reduction is quantitatively relevant whereas for a high q it is not. In fact, for high q, the average cost is practically equal to variable cost VC.
A numerical example of fixed, variable and total costs:
F = 100
VC = 5
First case: q = 10
TC = 100 + 5x10 = 150
AC = 150/10 = 15 = 100/10 + 5
Second case: q = 100
TC = 100 + 5x100 = 600
AC = 600/100 = 6
For low levels of production, fixed costs are major determinants of average costs whereas for high levels of production, variable costs dominate.
The percentage composition of total cost is, in our example, the following:
Cost component q = 10 q = 100
F 66% 16%
VC 34% 84%
Total 100% 100%
Marginal costs
Marginal costs indicate by how much the total costs changes because of modification in the production level by one unit.
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When there are only fixed costs, marginal cost will be zero: any increase of production does not change costs.
If there are only proportionally-growing variable costs, marginal costs will be equal to variable costs.
A manufacturer's perspectiveThe main costs that a manufacturer faces can be summarized in the following table:
Cost item Cost category Justification
Raw materials to be processed
Variable (proportionally)
Production recipe: any un-proportional change would impact the features of the product
Constant productivity of people directly involved in production. Particularly flexibility-oriented legal contracts with the labor force
Personnel (indirect labor) Quasi-fixed
The size of necessary administrative personnel (and of other indirect labor) doesn't change so much if production incrementally changes. Discrete jump will happen when the overall scale of production drastically changes.
Plant rent Fixed The typical contract of rent makes no reference to effective production levels
Amortization of capital goods
Fixed Fiscal and accountancy rules
Policy costs (advertising, R&D,...)
Fixed or quasi-fixed
Discretionary costs
The above-mentioned table is just a rough and conditional description. It is only meant for easy introduction to the problem - often implicitly assuming many specific hypotheses.
For instance, the labor costs can be fixed costs, quasi-fixed costs or variable costs depending on the legal contracts of employment and the rules governing wages.
General firm strategies have deep impact on costs. For instance, if a firm in a high-wage country exports a lot in a low-wage country, it may consider a Foreign Direct Investment to setup a factory there where to carry out the final - or most labor-intensive - phases (e.g. assembly or labeling).
A retailer's perspectiveThe basic costs that a family-run small shop pays are the following:
Cost item Cost category Justification
Goods in sales Variable (proportionally)
Price list of wholesaler or producer
Shop space (if rented) Fixed Proportional to square meters, not to items sold
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Shop space (if in ownership)
None There is the opportunity cost to use this space otherwise but this does not lead to transactions
Lighting Fixed Proportional to the number of light bulbs in the shop, not to items sold
Total revenues less all these costs constitute a gross profit, comprehensive, however, of the time the owner and the family spend working there and of the shop space (if in ownership). This logically heterogeneous aggregate is in fact indivisible because it is received by the same people and does not vary according to the external markets of labor and commercial spaces. The market of a good where seller and buyer is the same person is not perfectly competitive, nor linked to others.
The temporal profile of costs: investment, cost of operations, sunk costsIn most cases, a firm has first to sustain certain costs (investment) before any production takes place (e.g. R&D, machinery investment). These costs are called investment costs.
These costs should be recovered within a reasonable period of operative activity (production). In certain cases, after the full exploitation of production opportunities there is further una-tantum revenue for asset sale. For instance, when a firm buys an office, it invests a certain amount of money. It will use it for a certain period, say 10 years, during which it saves the rent it would have paid if it didn't own the office, thus (totally or partially) recovering the initial cost. At the end of the 10-years period, it can decide to shut down operations and it will be able to sell the office (una-tantum revenue).
Sunk costs are investment costs incurred before a certain activity takes place which cannot be recovered by the possible sale of the asset they produced. Highly specific investment (e.g. R&D) are usually sunk costs.
Sunk costs represent barriers to exit. A firm which has incurred in high sunk costs will have difficulties in deciding to exit the market even if it sees good opportunities outside.
Conversely, a firm that is deciding whether to enter into a certain business will have to consider with a particular attention the sunk costs and the risk that during the operations period they might not be recovered. Sunk costs, in this perspective, represent barriers to entry.
In the case of an exporter, an example of sunk costs could be the costs of analyzing the market and of exploring opportunities and seeking commercial partners.
High sunk costs makes an investment irreversible, what, couple with uncertainty about the future, impacts the level of investment by industry, as this empirical analysis points out.
Profitability and shut down rulesIn one period of time, total profits are given by total revenue less total costs. If they are negative, the firm will look into the future and see whether there is a possible reversal of this situation. Perhaps it is carrying out investments that are large now but that can produce effects later on. But it can also take into consideration the possibility of shut down operations and exit the market. It will, for instance, evaluate the average variable costs and the current price. If the price is lower, then for every units of production the price doesn't recover even the direct costs. A very critical situation.
But exiting a market is a strategic decision that cannot be taken wholehearted and it should be put into the more larger picture of industrial dynamics, where exit dynamics is related to more than just cost considerations.
What is the difference between product costs and period costs?
A manufacturer’s product costs are the direct materials, direct labor, and manufacturing overhead used in making its products. (Manufacturing overhead is also referred to as factory overhead, indirect manufacturing costs, and burden.) The product costs of direct materials, direct labor, and
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manufacturing overhead are also “inventoriable” costs, since these are the necessary costs of manufacturing the products.
Period costs are not a necessary part of the manufacturing process. As a result, period costs cannot be assigned to the products or to the cost of inventory. The period costs are usually associated with the selling function of the business or its general administration. The period costs are reported as expenses in the accounting period in which they 1) best match with revenues, 2) when they expire, or 3) in the current accounting period. In addition to the selling and general administrative expenses, most interest expense is a period expense
What is absorption costing?
Absorption costing means that all of the manufacturing costs are absorbed by the units produced. In other words, the cost of a finished unit in inventory will include direct materials, direct labor, and both variable and fixed manufacturing overhead. As a result, absorption costing is also referred to as full costing or the full absorption method.
Absorption costing is often contrasted with variable costing or direct costing. Under variable or direct costing, the fixed manufacturing overhead costs are not allocated or assigned to (not absorbed by) the products manufactured. Variable costing is often useful for management’s decision-making. However, absorption costing is required for external financial reporting and for income tax reporting.
What is a burden rate in inventory?
The burden rate in inventory refers to a manufacturer’s indirect manufacturing costs, which are also referred to as factory overhead, indirect production costs, and burden. In the U.S., a manufactured product’s cost consists of direct materials, direct labor, and manufacturing overhead. Since manufacturing overhead is an indirect cost, it is usually assigned or allocated through an overhead rate or burden rate. Two examples of an overhead or burden rate are 1) a percentage of direct labor, and 2) an hourly cost rate assigned on the basis of machine hours.
A product’s manufacturing cost, consisting of direct materials, direct labor and manufacturing overhead, is used to report the cost of goods sold and also the cost of units in inventory. Therefore, if you look at the detail of a product’s inventory cost, you may see the manufacturing overhead being assigned or applied to the unit through a burden rate.
What is manufacturing overhead and what does it include?
Manufacturing overhead (also known as factory overhead, factory burden, production overhead) involves a company’s factory operations. It includes the costs incurred in the factory other than the costs of direct materials and direct labor. This is the reason that manufacturing overhead is often classified as an indirect product cost.
Generally accepted accounting principles require that cost of direct material cost, direct labor, and manufacturing overhead be considered as the cost of products for valuing inventory and for determining the cost of goods sold. (Expenses that are outside of the factory, such as selling, general and administrative expenses, are not product costs and are not inventoriable. They are reported as expenses on the income statement in the accounting period in which they occur.)
Examples of manufacturing overhead include the depreciation or the rent on the factory building, depreciation on the factory equipment, supervisors in the factory, the factory quality control department, factory maintenance employees, electricity and gas for the factory, indirect factory supplies, etc.
Because manufacturing overhead is an indirect cost, accountants are faced with the task of assigning or allocating overhead costs to each of the units produced. This is a challenging task because there may be no direct relationship. (For example, the property tax on the factory building
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is based on its assessed value and not on the number of units produced. Yet the property tax must be assigned to the units manufactured.)
In the world of manufacturing–as competition becomes more intense and customers demand more services–it is important that management not only control its overhead but also understand how it is assigned to products and ultimately reported on the company's financial statements. We view overhead as two types of costs and define them as follows:
a) Manufacturing overhead (also referred to as factory overhead, factory burden, and manufacturing support costs) refers to indirect factory-related costs that are incurred when a product is manufactured. Along with costs such as direct material and direct labor, the cost of manufacturing overhead must be assigned to each unit produced so that Inventory and Cost of Goods Sold are valued and reported according to generally accepted accounting principles (GAAP).
Manufacturing overhead includes such things as the electricity used to operate the factory equipment, depreciation on the factory equipment and building, factory supplies and factory personnel (other than direct labor). How these costs are assigned to products has in impact on the measurement of an individual product's profitability.
b) Non-manufacturing costs (sometimes referred to as “administrative overhead”) represent a manufacturer’s expenses that occur apart from the actual manufacturing function. In accounting and financial terminology, the non-manufacturing costs include Selling, General and Administrative (SG&A) expenses, and Interest Expense. Since accounting principles do not consider these expenses as product costs, they are not assigned to inventory or to the cost of goods sold. Instead, non-manufacturing costs are simply reported as expenses on the income statement at the time they are incurred.
Non-manufacturing costs include activities associated with the Selling and General Administrative functions. Examples include the compensation of non-manufacturing personnel; occupancy expenses for non-manufacturing facilities (rent, light, heat, property taxes, maintenance, etc.); depreciation of non-manufacturing equipment; expenses for automobiles and trucks used to sell and deliver products; and interest expenses. (Note that factory administration expenses are considered part of manufacturing overhead.)
Although non-manufacturing costs are not assigned to products for purposes of reporting inventory and the cost of goods sold on a company’s financial statements, they should always be considered as part of the total cost of providing a specific product to a specific customer. For a product to be profitable, its selling price must be greater than the sum of the product cost (direct material, direct labor, and manufacturing overhead) plus the non-manufacturing costs and expenses.
1. Manufacturing Overhead Costs
On financial statements, each product must include the costs of the following: Direct material Direct labor Manufacturing (or factory) overhead
According to generally accepted accounting principles (GAAP), manufacturing overhead must be included in the cost of Work in Process Inventory and Finished Goods Inventory on a manufacturer’s balance sheet, as well as in the Cost of Goods Sold on its income statement.
As their names indicate, direct material and direct labor costs are directly traceable to the products being manufactured. Manufacturing overhead, however, consists of indirect factory-related costs and as such must be divided up and allocated to each unit produced. For example, the property tax on a factory building is part of manufacturing overhead. Although the property tax covers an entire year and appears as one large amount on just one tax bill, GAAP requires that a portion of this amount be allocated or assigned to each product manufactured during that year.
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Some of the costs that would typically be included in manufacturing overhead include:
1. Material handlers (forklift operators who move materials and units). 2. People who set up the manufacturing equipment to the required specifications. 3. People who inspect products as they are being produced. 4. People who perform maintenance on the equipment. 5. People who clean the manufacturing area. 6. People who perform record keeping for the manufacturing processes. 7. Factory management team.
(Note: For the seven items above, the company will incur costs for salaries, wages, Social Security and Medicare taxes, unemployment compensation tax, worker compensation insurance, health insurance, holiday pay, vacation pay, sick pay, pension or retirement plan, seminars and training, and perhaps more.)
8. Electricity, natural gas, water, and sewer for operating the manufacturing facilities and equipment.
9. Computer and communication systems for the manufacturing function. 10. Repair parts for the manufacturing equipment and facilities. 11. Supplies for operating the manufacturing process. 12. Depreciation on the manufacturing equipment and facilities. 13. Insurance and property taxes on the manufacturing equipment and facilities. 14. Safety and environmental costs.
Note that all of the items in the list above pertain to the manufacturing function of the business. Since the costs and expenses relating to a company’s administrative, selling, and financing functions are not considered to be part of manufacturing overhead, they are not reported as part of the final product cost on financial statements. Rather, non-manufacturing expenses are reported separately (as SG&A and interest expense) on the income statement during the accounting period in which they are incurred.
2. Non-Manufacturing Overhead Costs
The term "non-manufacturing overhead costs" or "non-manufacturing costs" to mean the Selling, Administrative & General (SG&A) expenses and Interest Expense. Under generally accepted accounting principles (GAAP), these expenses are not product costs. (Product costs only include direct material, direct labor, and manufacturing overhead.) Non-manufacturing costs are reported on a company’s income statement as expenses in the accounting period in which they are incurred. Expressed another way, non-manufacturing costs are not allocated to products via overhead rates since they are not included in the amounts reported as inventory on the balance sheet or in the cost of goods sold that is reported on the income statement.
Even though non-manufacturing overhead costs are not product costs according to GAAP, these expenses (along with product costs and profit) must be covered by the selling prices of a company’s products. In other words, selling prices must be large enough to cover SG&A expenses, interest expense, manufacturing overhead, direct labor, direct materials, and profit.
Some of the costs that would typically be included in non-manufacturing costs include: Salaries and fringe benefits of selling, general and administrative personnel. This would include the company president, vice presidents, managers, and other employees in the non-manufacturing functions of the company. Rent, property taxes, utilities for the space used by the non-manufacturing functions of the company. Insurance for areas outside of the factory. Interest on business loans. Marketing and advertising. Depreciation and maintenance of equipment and buildings outside of manufacturing. Supplies for the offices.
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2.a Financial Reporting vs. Individual Products and Customers
As mentioned above, non-manufacturing costs cannot be included in inventory or the cost of goods sold; rather, non-manufacturing costs are reported as SG&A expenses and Interest Expense in the accounting period in which they occur.
However, if management wants to determine the profitability of a specific product or customer, it is necessary to allocate or assign non-manufacturing costs to the products and/or customers outside of the financial statements. This information stays within the company—it is only used internally to assist management with decisions such as pricing; choosing which products to promote or to phase out; choosing which products to review for possible production processing changes; etc. In the end, management should know whether each product’s selling price is adequate to cover the product’s manufacturing costs, non-manufacturing costs, and required profit.
If management does not allocate the non-manufacturing costs to specific products, a product that requires a significant amount of sales support and administrative costs may actually be unprofitable even though its gross profit (sales minus manufacturing costs) indicates that it is very profitable. On the other hand, a product with a low gross profit may actually be very profitable, since it uses only a minimal amount of administrative and selling expense.
2.b Methods of Allocating Non-manufacturing Overhead Costs As mentioned previously, non-manufacturing costs are allocated internally to products and customers for the purpose of giving management information that is useful for decision-making, and not for the purpose of financial reporting. When doing the internal allocation of non-manufacturing costs it is logical to follow these four steps: (1) identify the activities that cause the non-manufacturing costs, (2) measure the cost of those activities, (3) identify the products and customers requiring the activities, and (4) assign the cost of the activities to those products and customers. In short, the best way to allocate non-manufacturing costs is to use activity based costing (ABC).
Some activities involving non-manufacturing expenses include:
1. Servicing existing accounts (product designs and other needs) 2. Invoicing customers for shipments of products 3. Processing payments from customers 4. Maintaining the company’s computer information system 5. Financing the inventories and other business assets 6. Prospecting for new accounts 7. Preparing financial statements and reports to government agencies 8. Overall management of the company
It is likely that you will have to estimate the cost of these activities. Next, you will need to allocate the cost of the activities to the individual products. Estimates and allocations based on logical assumptions are better than precise amounts based on faulty assumptions.
3.0 Cost Behavior Techniques There are a variety of techniques for analyzing cost behavior.
Assumptions of conventional linear CVP analysis Conventional linear cost volume profit analysis is based on five assumptions as follows:
Constant sales price.
Constant variable cost per unit.
Constant total fixed cost.
Constant sales mix.
Units sold equal units produced.
Note that these are the same assumptions that are applicable to the master budget, with the exception of number five. Now we will examine the implications of each assumption.
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Constant Sales Price To assume that the sales price is constant implies that the company is facing a horizontal demand function as illustrated in Figure 11-1. The implications of a horizontal demand function are that the company can sell any number of units at a constant sales price. Another way to describe this is to say that consumers are willing and able to buy any quantity the company offers for sale at a constant price. Average revenue (AR) is constant and equal to the sales price, (i.e., AR = PX÷X = P) as illustrated in Figure 2.
Figure 2.
The slope of the total revenue function (see Figure 3) is equal to the sales price. When the company sells one additional unit, total revenue increases by an amount equal to the sales price of that unit. The fact that the sales price is constant causes the slope of the total revenue function to be constant which results in a linear total revenue function. Another way to describe this is to say that total revenue increases at a constant rate as additional units are sold.
Figure 3.
A more realistic down sloping demand function (see Figure 4) illustrates what economists refer to as the law of demand. This law describes the fundamental idea that consumers are willing and able to buy more at a lower price than a higher price. When the price is decreased from P1 to P2, the quantity purchased, or demanded, increases from X1 to X2. The total revenue function based on the law of demand is nonlinear as illustrated in Figure 5. Total revenue increases at a decreasing rate as additional units are sold. This is because the sale of additional units requires that the company reduce the sales price. Each price corresponds to a specific sales quantity. Thus, average revenue (AR) will be decreasing, rather than constant.
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Figure 4.
Figure 5.
Although the assumption of a constant sales price is not realistic, it is defended as a practical way to expedite the planning process within a fairly narrow range of sales activity. The idea that most products are subject to a down sloping demand curve is intuitively obvious, but applying the concept is simply not practical. Most companies sell too many products in a constantly changing economic environment. Today’s demand curve is very likely to be obsolete tomorrow.
Constant Variable cost per unit The second assumption of the conventional linear cost-volume-profit approach is that the variable cost per unit of output is constant. This includes two important underlying assumptions: a) input prices are assumed to be constant for all variable inputs such as direct material, direct labor, and the various types of indirect resources represented by variable factory overhead costs and variable selling and administrative expenses, and b) the firm experiences constant productivity, i.e., constant output per variable input. Constant productivity is illustrated in Figure 6. When productivity is constant, each new unit of output requires an equal amount of input and thus each unit of output will
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cost the same amount. This causes both the production function to be linear (see Figure 6) and the average variable cost function to be horizontal (see Figure 7). Output (X) is placed on the vertical axis in Figure 6 because output is the dependent variable, i.e., inputs drive outputs. Output is on the horizontal axis in the other graphs because cost is the dependent variable, i.e., output drives cost.
Figure 6.
Figure 7.
Although it is convenient to assume constant productivity for short run planning purposes, other types of production functions are more realistic when the whole range of production possibilities is considered. When a company begins to expand output from a low volume startup level to a medium volume level, productivity might be expected to increase due to the effects of increased specialization, experience and learning. When productivity is increasing, output increases at an increasing rate (see Figure 8) . As variable inputs are added to production, each input generates more output than the previous input. When productivity is increasing, average variable cost per unit will be decreasing as in Figure 9.
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Figure 8 Figure 9.
If the company increased production from a medium volume level to a high volume level by continuing to add variable inputs to a fixed size facility, productivity would be expected to decrease as indicated in Figure10. This is because at high volume production levels, the inputs (labor, materials etc.) would become excessive relative to the size of the fixed facility. In the case of decreasing productivity, average variable cost per unit will be increasing as illustrated in Figure 11.
Each unit will cost more because it requires more inputs to produce.
Figure 10. Figure 11.
Theoretically, the production and average variable cost functions for the entire range of short run production possibilities will be similar to those illustrated in Figures 12 and 13. The point where the production function changes directions from increasing to decreasing productivity and the average variable cost function changes from decreasing to increasing cost per unit is referred to as the point of diminishing returns. Output continues to increase beyond this point, but at a decreasing rate.
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Figure 12.Figure 13.
Constant Fixed Costs and The Families of Total Cost Functions A family of total cost functions for the conventional linear model is presented in Figure 14. The total variable cost and total cost functions are linear, i.e., they increase at a constant rate, because productivity is assumed to be constant. The total fixed cost function is represented by a horizontal line because of assumption three which eliminates the possibility of a non-output related change in fixed costs during the planning period. No changes in the company’s fixed factors of production can occur. The total cost and total variable cost functions are vertically parallel and separated by the amount of total fixed costs.
A comparable family of total cost functions for the theoretical economic model appears in Figure 15. The total variable cost and total cost functions increase at a decreasing rate at first in response to increasing productivity. When the inputs are becoming more productive, additional outputs cost less per unit because they require less input. However, when productivity begins to decrease, the total cost and total variable cost functions begin to increase at an increasing rate. In the case of decreasing productivity, the inputs are generating less output per input, thus the unit cost of additional outputs is increasing. The total cost functions in Figure 15 are also parallel and separated vertically by the amount of total fixed costs.
Figure 14.Figure 15.
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Constant Sales Mix and Inventory Level The last two assumptions of the conventional linear cost-volume-profit model are more easily understood than the previous assumptions. The fourth assumption is that the sales mix will remain constant during the planning period for a multiproduct company. Sales mix proportions may be stated in terms of either units or dollars as explained in the illustrations below.
The fifth and last assumption is that units produced are equal to units sold. This means that there will be no changes in beginning or ending inventory levels to complicate the analysis. This assumption along with the assumption concerning constant fixed cost will be relaxed in the following chapter where we will use the conventional linear CVP model to consider the differences between direct costing and full absorption costing.
SUMMARY OF THE CONVENTIONAL LINEAR AND THEORETICAL MODELS Graphic summaries of the two models are presented in Figures 16 and 17. In the linear model there is one break-even point (BEP) where total revenue is equal to total cost. Since the total revenue and total cost functions are linear, the profit function is also linear. This is because the slope of the profit function is equal to contribution margin per unit which is automatically constant when the sales price and variable cost per unit are constant.
Figure 17. Figure 18.
The theoretical model summarized in Figure 17 conveys a very different picture. There are two break-even points where total revenue and total cost are equal. The theoretical profit function intersects the horizonal axis at the two break-even points and reaches a maximum level at the point where the vertical distance between TR and TC is the greatest. In the linear model illustrated in Figure 16, the area to the left of the break-even point represents a loss area and the area to the right of this point represents a profit area that continuously grows larger as additional units are produced and sold. In the linear model the company maximizes profit where production and sales are at maximum capacity. However, in the theoretical model , there are two loss areas, one to the left of the first BEP and one to the right of the second BEP. The profit area is between the two break-even points, thus trying to achieve the maximum level of production and sales will produce losses rather than increased profits.3 For this reason, some critics of the conventional linear model argue that it represents a naive and dangerous view of a firm's economic environment. On the other hand, advocates of the linear model contend that short term planning does not require a theoretical model of the entire range of production possibilities. Although the concepts underlying the theoretical model are important, the model does not provide a practical approach for short term planning. However, the linear model is a practical and adequate alternative for planning within the normal relevant range of production and sales alternatives.
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"What-If" Analysis Versus Changing the Model For any given linear CVP analysis, we can ask a whole set of "what-if" questions about how increases and decreases in the sales price, unit variable costs, sales mix and fixed costs would affect the outcome. However, when we do that we are simply changing from one set of static assumptions to another set. This means that we are changing from one conventional linear problem to a somewhat different conventional linear problem. If the first two assumptions are relaxed to allow the sales price and unit variable costs to change continuously in response to the forces of supply and demand, we are not asking a "what if" question, we are changing the analysis from the practical linear approach to the theoretical nonlinear approach.
TECHNIQUES FOR SOLVING CVP PROBLEMS
The following symbols are used below to illustrate the various techniques used in cost-volume-profit
analysis.
P = Sales price.
V = Variable costs per unit.Note: This is not inventory cost because it includes both variable manufacturing costs as well as variable selling and administrative expenses.
X = The number of units produced and sold. A unit is a common way to describe an output, but an output may be expressed in pounds, gallons, board feet, cubic feet, etc.
TR = S = Total revenue, or sales dollars.
TVC = Total variable costs = VX
TFC = Total fixed costs.
TC = Total costs = TFC + TVC.
P-V = Contribution margin per unit. This is the amount of sales revenue that each unit provides towards covering the fixed costs and providing a profit, i.e., what's left over after the variable costs associated with the unit have been covered.
These are just different ways to define the contribution margin ratio. They all work because the functions are linear. There are many algebraic equations illustrated on the next several pages that may appear to require memorization. However, every equation is simply a variation of the following basic concepts:
Total revenue, or sales dollars, less total variable costs equals total contribution margin. Contribution margin is the revenue over and above the variable costs that contributes towards covering the fixed costs and also towards providing a profit after the fixed costs have been covered. Practically any cost-volume-profit problem can be solved with the last equation stated above and an understanding of the concepts involved.
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SOLVING SINGLE PRODUCT CVP PROBLEMS IN UNITS A summary of the cost volume profit equations for single product problems is presented in Table 1. All five equations are variations of the basic conceptual equation stated above. To reinforce the concept, each equation is developed and illustrated below.
TABLE 1 SUMMARY EQUATIONS FOR SOLVING
SINGLE PRODUCT CVP PROBLEMS IN UNITS
NUMBER EQUATION USED TO DETERMINE
[1] (P-V)X = TFC Units needed to break-even.
[2] (P-V)X = TFC + NIBT Units needed to generate a target net income before taxes.
[3] (P-V)X = TFC + [NIAT ÷ (1-T)] Units needed to generate a target net income after taxes.
[4] (P-V)X = TFC + (R)(PX) Units needed to generate a target NIBT stated as a proportion (R) of sales dollars (PX).
[5] (P-V)X = TFC + [(R)(PX) ÷ (1-T)] Units needed to generate a target NIAT stated as a proportion (R) of sales dollars (PX).
UNITS NEEDED TO BREAK-EVEN We can derive the break-even equation by starting with the fact that total revenue equals total cost at the break-even point. Then the equation is restated in terms of unit sales, unit prices and unit cost and then rearranged into the more convenient format presented in Equation 1.
Equation 1 shows that the break-even point is where total contribution margin (P-V)(X) is equal to total fixed costs, i.e., this level of production and sales provides just enough revenue to cover all the cost.
UNITS NEEDED FOR TARGET NET INCOME BEFORE TAXES This equation can be derived from scratch in the same manner used to develop Equation 1. Notice however that Equation 2 may be obtained by simply adding the desired amount of net income to the right hand side of Equation 1.
Equation 2 simply indicates that total contribution margin is equal to the total fixed costs plus the desired net income before taxes. These relationships are illustrated graphically in Figure 18 which is similar to Figure 16 presented in the previous section.
Figure 18 shows that the break-even point is where the two lines representing total revenue and total cost intersect. To the left of this intersection, the vertical difference between the total revenue and total cost functions represents a net loss. To the right of the break-even point, the vertical difference between the two functions represents net income before taxes. The lower part of the graph shows that the break-even point can also be found by plotting the before tax profit function. When the number of units produced and sold equals zero, the loss is equal to total fixed costs. When the firm produces a positive number of units, the loss is reduced by an amount equal to the contribution margin per unit multiplied by the number of units produced and sold. The slope of NIBT is contribution margin per unit. When enough units are produced and sold to cover the fixed costs, the company reaches the break-even point. This is the point on the graph where the profit function intersects the horizontal axis and it is directly below the point where the total revenue and total cost functions intersect.
Figure 17.
UNITS NEEDED FOR TARGET NET INCOME AFTER TAXES
If T = the tax rate, and NIAT = desired net income after taxes, then
(1-T)(NIBT) = NIAT therefore NIBT = NIAT ÷ (1-T)
Substituting NIAT÷(1-T) for NIBT in Equation 2, provides Equation 3, which allows us to solve for units needed to generate a desired amount of net income after taxes.
The after tax relationships are also illustrated graphically in Figure 18. The after tax profit function
begins at a point equal to (1-T)(-TFC) assuming the tax benefits of a loss can be used in a prior period or perhaps in some other segment of the company. The slope of the after tax profit function
is (1-T)(P-V), therefore the function is not as steep as the before tax profit function. The break-even point is the same however, and the vertical difference between the two profit functions is equal to the amount of the tax involved.
WHEN TARGET NET INCOME BEFORE TAXES IS STATED AS A % OF SALES $
If we use R to define the desired rate of return on sales, i.e., R = NIBT/TR, then we can substitute R(PX) for the desired net income before taxes in Equation 3. This provides Equation 4.
Since PX equals sales dollars, then R multiplied by PX will provide the desired profit before taxes. Although the desired profit is often stated as a percentage, R is a proportion, i.e, it ranges from 0 to 1.
WHEN TARGET NET INCOME AFTER TAXES IS STATED AS A PERCENTAGE OF
SALES $
If the target rate of return is stated as an after tax rate, i.e., R = NIAT/TR, then the following
approach is used. Substituting R(PX)÷(1-T) for R(PX) in Equation 4 provides Equation 5.
When solving CVP problems, it is less confusing visually and more convenient for computational purposes to leave (P-V) on the left-hand side of the equations initially as indicated in Exhibit 11-1. It is best to simplify the expressions on both sides of the equation first, rather than attempt to divide every element on the right-hand side by P-V.
EXAMPLE 1The Cal Company produces pocket size calculators that are sold for $10 per unit. The costs associated with each unit are as follows: Direct material = $3.00, Direct labor = $ .25, Variable overhead = $2.00, and Variable selling and administrative cost = $ .75. Total fixed costs are $100,000 for manufacturing and $20,000 for the selling and administrative functions. The company’s tax rate is 40%.
In a recent meeting, the board of directors asked the following questions. How many calculators do we need to produce and sell to accomplish each of the following requirements? 1. Break-even. 2. Earn net income before taxes of $40,000. 3. Earn net income after taxes of $24,000. 4. Earn a 20% return on sales before taxes. 5. Earn a 12% return on sales after taxes.
To answer these questions, we start by calculating the contribution per unit as follows: Contribution margin per unit = P - V = 10 - (3 + .25 + 2 + .75) = 10 - 6 = 4. Then, the five questions are answered by using the equations in Exhibit 2.
1. Break-even. Using Equation [1] 4X = 120,000 X = $120,000 ÷ 4 = 30,000 units.
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2. Earn net income before taxes of $40,000. Using Equation [2] 4X = 120,000 + 40,000 X = 160,000 ÷ 4 = 40,000 units.
3. Earn net income after taxes of $24,000. Using Equation [3] 4X = 120,000 + [24,000 ÷ (1-.4)] 4X = 120,000 + 40,000 X = 160,000 ÷ 4 = 40,000 unit.
A graphic solution to Example 2 is illustrated in Figure 19.
Figure 19.
4. Earn a 20% return on sales before taxes. Using Equation [4] 4X = 120,000 + .2(10X) 4X = 120,000 + 2X 2X = 120,000 X = 120,000 ÷ 2 = 60,000 units.
5. Earn a 12% return on sales after taxes. Using Equation [5] 4X = 120,000 + [.12(10X) ÷ (1-.4)] 4X = 120,000 + .2(10X) 4X = 120,000 + 2X 2X = 120,000 X = 120,000 ÷ 2 = 60,000 units.
Using The After Tax Equations As An Alternative The equation for NIAT that appears in the graph is found by multiplying the equation for NIBT by (1-T) , i.e., (1-.4)(-120,000 + 4X) = -72,000 + 2.4X. Rearranging this equation we have 2.4X = 72,000 + NIAT. This revised equation indicates that the contribution margin after taxes ($2.4X) is equal to
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fixed costs after taxes ($72,000) plus the desired after tax income. It provides an alternative way to find the answers to questions 3 and 5 as illustrated below.
3. Earn net income after taxes of $24,000. 2.4X = 72,000 + NIAT desired 2.4X = 72,000 + 24,000 2.4X = 96,000 X = 96,000 ÷ 2.4 = 40,000 units.
5. Earn a 12% return on sales after taxes. 2.4X = 72,000 + NIAT desired 2.4X = 72,000 + .12(10X) 2.4X = 72,000 + 1.2X 1.2X = 72,000 X = 72,000 ÷ 1.2 = 60,000 units.
Checking the Solutions The accuracy of linear cost-volume-profit calculations can be verified easily. For example, the answers to the questions above can be verified as follows:
1) Is 30,000 units the break-even point? Yes, since total contribution margin is equal to total fixed cost of 120,000, i.e., (4)(30,000) = $120,000.
2) Will 40,000 units generate a before tax profit of $40,000? Yes, because total contribution margin is (4)(40,000) = $160,000 and this amount is 160,000 - 120,000 = $40,000 above total fixed costs.
3) Will 40,000 units generate an after tax profit of $24,000? Yes, since (1-.4)($40,000 NIBT) = $24,000.
4) Will 60,000 units provide a 20% return on sales before taxes? Yes, since the NIBT is TCM - TFC or (4)(60,000) - 120,000 = $120,000. Sales equals PX or ($10)(60,000) = $600,000. R = 120,000 ÷ 600,000 = .20 or 20%.
5) Will 60,000 units provide a 12% return on sales after taxes. Yes, (1-.4)(.2) = .12 or 12%. For an alternative check (1-.4)(120,000) = $72,000 NIAT. Therefore, the after tax rate of return is 72,000 ÷ 600,000 = .12 or 12%.
SOLVING SINGLE PRODUCT CVP PROBLEMS IN DOLLARS A summary of the cost volume profit equations for solving single product problems in dollars is presented in Table-2. These five equations are also variations of the basic conceptual equation stated in the first part of this chapter. Each of these equations is developed and illustrated below.
[4] (CMR)(S) = TFC + (R)(S) Sales $ for target NIBT stated as a proportion (R) or sales $
[5] (CMR)(S) = TFC + [(R)(S) ÷ (1-T)] Sales $ for target NIAT stated as a proportion (R) of sales $
BREAK-EVEN POINT IN DOLLARS FOR A SINGLE PRODUCT The equation for the break-even point in sales dollars may also be derived by equating total revenue and total cost. It is more convenient to use the single symbol S for sales dollars, rather than TR for total revenue.
TR = TCS = TFC + TVC
Since the variable cost ratio (V÷P) multiplied by sales dollars (S) equals total variable cost, we can substitute (V÷P)(S) for variable cost in the equation above as follows.
S = TFC + (V÷P)(S)
Then subtracting variable cost from both sides of the equation provides the basic break-even point equation in sales dollars.
S - (V÷P)(S) = TFC
Stated in words, the equation indicates that total revenue, less total variable costs, equals total contribution margin, and the break even point is where total contribution margin is equal to total
fixed cost. Since the contribution margin ratio (CMR = 1- V÷P) multiplied by total revenue equals total contribution margin, it is more convenient for computational purposes to state the equation in the following manner.
(1- V÷P)(S) = TFC[1] (CMR)(S) = TFCS = TFC ÷ CMR
TOTAL REVENUE NEEDED FOR TARGET NET INCOME BEFORE TAXES Although we could derive this equation from scratch, the fact that total contribution margin must be equal to the total fixed costs plus the desired net income before taxes allows us to develop Equation 2 by simply adding the desired net income to Equation 1.
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[2] (CMR)(S) = TFC + NIBTS = (TFC+NIBT) ÷ CMR
TOTAL REVENUE NEEDED FOR TARGET NET INCOME AFTER TAXES Solving for total revenue needed to generate a target net income after taxes involves
substituting NIAT ÷ (1-T) for NIBT in the equation for Sales dollars needed before taxes (i.e., Equation 2). This provides Equation 3.
TOTAL REVENUE NEEDED WHEN TARGET NIBT IS STATED AS A PERCENTAGE
OF SALES $ To solve a problem in sales dollars, when the desired net income is stated as a percentage of sales dollars, substitute (R)(S) into Equation 2 for NIBT as follows.
To emphasize a point made earlier, it is less confusing visually and also more convenient for computational purposes to leave CMR on the left-hand side of each of the 5 equations initially. Simplify the expressions first, rather than attempting to divide every element on the right-hand side by CMR.
EXAMPLE 2
The Cal Company example can be restated in the following manner. Variable costs (including both manufacturing and selling and administrative costs) represent sixty percent of sales dollars. Total fixed costs are $120,000. Assume the board of directors wants the answers to their questions provided in sales dollars rather than units. What amount of sales in dollars does the company need to accomplish each of the following requirements? 1. Break-even. 2. Earn net income before taxes of $40,000. 3. Earn net income after taxes of $24,000. 4. Earn a 20% return on sales before taxes. 5. Earn a 12% return on sales after taxes. To answer these questions, we need the contribution margin ratio. The ratio is CMR = 1- V/P = 1-.6 = .4 Then, the answers to the five questions are easily obtained as follows:
1. Break even. Using Equation [1] .4S = 120,000 S = 120,000 ÷ .4 = $300,000
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2. Earn net income before taxes of $40,000. Using Equation [2] .4S = (120,000 + 40,000) S = 160,000 ÷ .4 = $400,000
3. Earn net income after taxes of $24,000. Using Equation [3] .4S = 120,000 + (24,000 ÷ .60) .4S = 120,000 + 40,000 S = 160,000 ÷ .4 = $400,000
4. Earn a 20% return on sales before taxes. Using equation [4] .4S = 120,000 + .2S .2S = 120,000 S = 120,000 ÷ .2 = $600,000
5. Earn a 12% return on sales after taxes. Using equation [5] .4S = 120,000 + (.12S ÷ .6) .4S = 120,000 + .2S .2S = 120,000 S = 120,000 ÷ .2 = $600,000
A graphic analysis of this example is also illustrated in Figure 19 since we are simply solving the problem in dollars rather than units. The graph is also useful for comparing the two approaches. Example 12 places emphasis on the horizontal axis (units) while Example 13 places emphasis on the vertical axis ( dollars).
THE MARGIN OF SAFETY Before we move on to multiproduct companies, there is a handy concept referred to as the margin of safety that you might find useful. The margin of safety (MS) for any sales level represents the amount of sales dollars above or below the break-even point. Mathematically, the margin of safety is:
MS = Sales$ - Break-even sales$
When sales are above the break-even point, the margin of safety is positive. When sales are below the break-even point, the margin of safety is negative. After determining the MS for a particular sales level, Equations 6 and 7 can be used to make some quick calculations.
[6] NIBT = (MS)(CMR)
Solving Equation 6 provides the amount of contribution margin above the break-even point (when MS is positive) and this amount represents the net income (or loss if the MS is negative) before taxes. Why? Because after the total fixed costs have been covered, additional contribution margin represents the before tax profit. Before the fixed cost have been covered the additional contribution needed represents the before tax loss. The equation for after tax profit is
[7] NIAT = (MS)(CMR)(1-T)
EXAMPLE 3Suppose we are in a board of directors meeting and a board member asks how much income would Cal Company generate at a particular sales level. For convenience let’s say $1,000,000. Using the margin of safety we can answer this question quickly. Since we already know the break-even point is $300,000, then the margin of safety is 1,000,000 - 300,000 = $700,000.
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Using Equation [6] NIBT = (700,000)(.4) = $280,000. Using Equation [7] NIAT = (700,000)(.4)(.6) = $168,000.
To show that the margin of safety calculations work on either side of the break-even point, consider another example. Suppose someone ask, how much income would Cal Company generate when total revenue is only $200,000? MS = 200,000 - 300,000 = -100,000, i.e., $100,000 below the BEP. Using Equation [6] NIBT = (-100,000)(.4) = -40,000 net loss before taxes, or Using Equation [7] NIAT = (-40,000)(.6) = -24,000 net loss after taxes.
SOLVING MULTIPLE PRODUCT CVP PROBLEMS IN UNITS Some additional symbols are needed to illustrate the algebraic techniques applicable to multiple product problems.
The following symbols are used below:
i = The number designating a particular product.
Pi = The price of product i.
Vi = The variable cost per unit of product i.
X = Total mixed units sold, i.e., includes all products.
Xi = Units of product i sold.
Mi = The mix ratio for product i, i.e., the proportion that product i represents out of the total number of units sold.
E = Sigma or summation sign which means "the sum of".
W = Weighted average contribution margin per unit = E [(Pi-Vi)(Mi)]Y = The weighted average price = E (Pi)(Mi)
A summary of the cost volume profit relationships for multiproduct problems is presented in Table 3. The five equations are comparable to the single product equations presented in Table 1, but are somewhat more involved. Each equation is developed and illustrated below
TABLE 3 SUMMARY EQUATIONS FOR SOLVING
MULTIPLE PRODUCT CVP PROBLEMS IN UNITS
NUMBER EQUATION USED TO DETERMINE
[1] WX = TFC Total mixed units at the BEP.
[2] WX = TFC + NIBT Total mixed units for target NIBT.
[3] WX = TFC + [NIAT ÷ (1-T)] Total mixed units for target NIAT.
[4] WX = TFC + (R)(YX) Total mixed units for target NIBT stated as a proportion (R) of
sales $.
[5] WX = TFC + [(R)(YX) ÷ (1-T)] Total mixed units for target NIAT stated as a proportion (R) of
sales $.
Xi = X(Mi) The number of units of each product after X is obtained.
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BREAK-EVEN POINT IN UNITS FOR MULTIPLE PRODUCTS The same logic used to solve single product problems is applicable to multiple product problems. At the break-even point, total contribution margin is equal to total fixed costs. However, in multiple product situations, total contribution margin is found by multiplying the weighted average contribution margin per unit by the total number of mixed units produced and sold. The weighted average contribution margin per unit is calculated by multiplying each product's contribution margin per unit (Pi-Vi) by the mix ratio applicable to that product (Mi) and then summing the results. The mix ratios (Mi's) represent the weights. The equation is,
W = E [(Pi-Vi)(Mi)]
The break-even equation for mixed units (X) is stated in the following manner.
[1] WX = TFC
After the total mixed units (X) have been determined, then the number of units of the individual products are found by multiplying the total mixed units by each product's mix ratio.
Xi = X(Mi)
UNITS NEEDED FOR TARGET NET INCOME BEFORE TAXES The equation for mixed units needed to generate a desired amount of net income before taxes is developed by simply adding NIBT to the right hand side of Equation 1.
[2] WX = TFC + NIBT
UNITS NEEDED FOR TARGET NET INCOME AFTER TAXES The equation for mixed units needed to generate a desired after tax profit is developed by
substituting NIAT ÷ (1-T) for NIBT in Equation 2.
[3] WX = TFC + [NIAT ÷ (1-T)]
WHEN TARGET NET INCOME BEFORE TAXES IS STATED AS A PERCENTAGE OF SALES $
Using R to represent the target rate of return on sale dollars before taxes, i.e., R = NIBT÷TR, the following equation can be used to find the mixed units needed.
[4] WX = TFC + (R)(YX)
Sales dollars are represented by the term YX. Since total sales dollars are mixed, we must multiply the total mixed units (X) by a weighted average price (Y) to find the total mixed sales dollars. Then, multiplying the term YX by R represents the desired NIBT. The weighted average price (Y) is found by multiplying the price of each product (Pi) by the product mix ratios (Mi) and then summing the
results, i.e., Y = E (Pi)(Mi).
WHEN TARGET NET INCOME AFTER TAXES IS STATED AS A PERCENTAGE OF SALES $
The appropriate equation for after tax net income is found by dividing the term [(R)(YX], inEquation 4, by 1-T.
[5] WX = TFC + [(R)(YX) ÷ (1-T)]
Remember that it is usually best for computational purposes to leave the amount represented by W on the left hand side in each of the equations until the expression on the right hand side has been
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simplified. Also remember that the units for individual products (Xi) are always found by multiplying the total mixed units (X) by the mix ratios (Mi) for each product.
EXAMPLE 4
The Sandlot Cap Company produces baseball caps in two categories referred to as regular logo and special logo. Caps in the regular logo category are high volume products that display familiar names of universities and professional sports teams. Caps in the special design category are typically created for a particular customer to promote special events such as the Olympics, or the opening of a unique museum exhibit. For convenience we will refer to the regular logo caps as product X1 and the special logo caps as product X2. Sales prices and variable costs are provided below.
Product Price Variable Cost Per Unit Mix Ratio
Based on Units
X1X2
$4
8
$3 5
.75
.25
The variable costs for each product include direct materials and conversion costs of $2. Marketing costs account for an additional $1 for regular logo caps and $3 for special logo caps. As indicated above, three quarters of the company’s unit sales are represented by regular logo caps, while the other one quarter represents special logo caps. The company’s total fixed costs are $300,000. Sandlot Cap Company management wants to know how many caps need to be produced and sold to accomplish the following:
1. Break even. 2. Earn desired net income before taxes of $60,000. 3. Earn desired net income after taxes of $36,000 given the tax rate is 40%. 4. Earn desired net income before taxes equal to 15% of sales dollars. 5. Earn a desired net income after taxes equal to 9% of sales dollars. To solve this problem we need to calculate the weighted average contribution margin per unit, i.e., the contribution margin per mixed unit.
W = (4-3)(.75) + (8-5)(.25) = 1.5
The mix ratios (.75 and .25) are used as the weights to reflect the fact that the company normally sells three times as many X1's as X2's. After obtaining the weighted average contribution of $1.50, then 1.5X represents the total contribution margin on the lefthand side of each equation.
1. To break-even. Using Equation [1] 1.5X = 300,000 X = 300,000 ÷ 1.5 = 200,000 Total mixed units. X1 = (200,000)(.75) = 150,000 units X2 = (200,000)(.25) = 50,000 units
2. To earn $60,000 net income before taxes. Using Equation [2] 1.5X = 300,000 + 60,000 1.5X = 360,000 X = 360,000 ÷1.5 = 240,000 mixed units X1 = (240,000)(.75) = 180,000 units X2 = (240,000)(.25) = 60,000 units
3. To earn $36,000 net income after taxes. Using Equation [3] 1.5X = 300,000 + (36,000 ÷ .6) 1.5X = 300,000 + 60,000 X = 360,000 ÷1.5 = 240,000 mixed units
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X1 = (240,000)(.75) = 180,000 units X2 = (240,000)(.25) = 60,000 units
In the last two requirements, income is stated as a percentage of sales dollars. Therefore, we need the YX measure of total mixed sales dollars to indicate the desired amount of income. Total mixed sales dollars is the weighted average price Y, multiplied by the mixed units X. To calculate Y we must use the unit mix ratios as weights to reflect the importance of each product in the price.
Y = 4(.75) + 8(.25) = $5
Then, $5 represents the weighted average price and 5X represents the total mixed sales dollars. 4. To earn before tax net income equal to 15% of sales dollars, we substitute .15(5X) in the equation for desired income, i.e., R(YX). Then using Equation [4] 1.5X = 300,000 + .15(5X) 1.5X = 300,000 + .75X .75X = 300,000 X = 300,000 ÷ .75 = 400,000 mixed units X1 = .75(400,000) = 300,000 units X2 = .25(400,000) = 100,000 units
5. To earn after tax net income equal to 9% of sales dollars, the desired income is (R)(YX) ÷ 1-T, or (.09)(5X) ÷ (1-.4). Then using Equation [5] 1.5X = 300,000 + [(.09)(5X) ÷ (1-.4)] 1.5X = 300,000 + [.45X ÷ .6] 1.5X = 300,000 + .75X .75X = 300,000 X = 300,000 ÷ .75 = 400,000 mixed units X1 = .75(400,000) = 300,000 units X2 = .25(400,000) = 100,000 units
Using The After Tax Equations As An Alternative A graphic analysis of the Sandlot Cap Company example appears in Figure 20.
Figure 20.
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The equation for NIAT illustrated in the graph is found by multiplying the equation for NIBT by (1-T), i.e., (1-.4)(-300,000) + (1-.4)(1.5X) = -180,000 + .9X. Rearranging this equation we have .9X = 180,000 + NIAT where .9X is the weighted average contribution margin after taxes. We can use this equation as an alternative way to find the answers to question 3 and 5 as follows. 3. Earn desired net income after taxes of $36,000. .9X = 180,000 + 36,000 .9X = 216,000 X = 216,000 ÷ .9 = 240,000 mixed units
5. Earn desired net income after taxes equal to 9 percent of sales dollars. .9X = 180,000 + .09(5X) .9X = 180,000 + .45X .45X = 180,000 X = 180,000 ÷ .45 = 400,000 mixed units We do not covert the desired income to a before tax amount (by dividing by 1-T) because we are using the after tax version of the equation, i.e., we need NIAT in the equation, not NIBT.
SOLVING MULTIPLE PRODUCT CVP PROBLEMS IN DOLLARS The following additional symbols are used to develop this section. S = Total mixed sales dollars. Si = Sales dollars for product i. CMRi = Contribution margin ratio for product i. M$i = The mix ratio for product i based on sales dollars. Note, these ratios are not equal to the mix ratio based on units. WCMR = The weighted average contribution margin ratio = E(CMRi)(M$i) A summary of the cost volume profit relationships for this section is presented in Table 4.
[4] WCMR(S) = TFC + (R)(S) Sales $ for target NIBT stated as a proportion (R) of sales $.
[5] WCMR(S) = TFC + [(R)(S) ÷ (1-T)] Sales $ for target NIAT stated as a proportion (R) of sales $.
Si = S(M$i) Sales dollars for each product after S is obtained.
BREAK-EVEN POINT IN SALES DOLLARS FOR MULTIPLE PRODUCTS The same basic conceptual logic used in the previous sections is used to develop the equations in this section. The firm breaks even when total contribution margin is equal to total fixed costs.
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[1] (WCMR)(S) = TFCThe difference between the equations for single product and multiproduct situations is that we must
use a weighted average contribution margin ratio, WCMR = E(CMRi)(M$I) to find the total
mixed sales dollars. Then sales dollars for the individual products are found by multiplying the total
mixed sales dollars (S) by the mix ratios for each product, Si = (S)(M$I)
TOTAL REVENUE NEEDED FOR TARGET NET INCOME BEFORE TAXES Equation 2 is developed in the usual manner by simply adding the desired amount of NIBT to the right hand side of Equation 1.
[2] (WCMR)(S) = TFC + NIBT
TOTAL REVENUE NEEDED FOR TARGET NET INCOME AFTER TAXES Revising the previous equation to include after tax profit we have:
[3] (WCMR)(S) = TFC + [NIAT ÷ (1-T)]
WHEN TARGET NET INCOME BEFORE TAXES IS STATED AS A PERCENTAGE OF SALES $
If R is used as the before tax target rate of return on sales, i.e., NIBT÷S, then the equation needed to achieve the target return before taxes is:
[4] (WCMR)(S) = TFC + (R)(S)
WHEN TARGET NET INCOME AFTER TAXES IS STATED AS A PERCENTAGE OF SALES $ If R is used as the after tax target rate of return on sales, i.e., NIAT÷S, the equation becomes,
[5] (WCMR)(S) = TFC + [(R)(S) ÷ (1-T)]
EXAMPLE 5Suppose the Sandlot Cap Company information is provided to you in the following format.
Product Contribution Margin Ratios Mix Ratios Based on sales dollars
X1
X2
.25
.375
.6
.4
TFC = $300,000. Sandlot Cap Company management wants to know the amount of sales dollars needed for each product to accomplish the same five objectives. 1. Break even. 2. Earn desired net income before taxes of $60,000. 3. Earn desired net income after taxes of $36,000. Assume the tax rate is 40%. 4. Earn desired net income before taxes equal to 15% of sales dollars. 5. Earn a desired net income after taxes equal to 9% of sales dollars.
To find the answers we need to start by calculating the weighted average contribution margin ratio. WCMR = (.25)(.60) + (.375)(.40) = .30
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The mix ratios stated in dollars are used as the weights. Then the solutions are obtained as follows: 1. To break even. Using Equation [1] .3S = 300,000 S = 300,000 ÷ .3 = $1,000,000 S1 = (1,000,000)(.6) = $600,000 S2 = (1,000,000)(.4) = 400,000
2. To earn $60,000 before taxes. Using Equation [2] .3S = 300,000 + 60,000 S = 360,000 ÷ .3 = $1,200,000 S1 = (1,200,000)(.6) = $720,000 S2 = (1,200,000)(.4) = 480,000
3. To earn $36,000 after taxes. Using Equation [3] .3S = 300,000 + (36,000 ÷ .6) S = 360,000 ÷.3 = $1,200,000 S1 = ($1,200,000)(.6) = $720,000 S2 = ($1,200,000)(.4) = 480,000
4. To earn desired NIBT of 15% of sales dollars. Using Equation [4] .3S = 300,000 + .15S .15S = 300,000 S = 300,000 ÷ .15 = $2,000,000 S1 = ($2,000,000)(.6) = $1,200,000 S2 = ($2,000,000)(.4) = 800,000
5. To earn desired NIAT of 9% of sales dollars. Using Equation [5] .3S = 300,000 + (.09S ÷ .6) .15S = 300,000 S = 300,000 ÷ .15 = $2,000,000 S1 = ($2,000,000)(.6) = $1,200,000 S2 = ($2,000,000)(.4) = 800,000
The solutions to these five questions are also illustrated in Figure 11-19 since we simply changed our emphasis from the horizontal axis (units) to the vertical axis (dollars).
A NOTE CONCERNING MIX RATIOS The mix ratios determine whether the emphasis is on units or dollars and the manner in which the answers must be obtained. If the mix ratios are stated in units, as in Example 4, then the solutions must be obtained in units. If the mix ratios are stated in dollars, as in Example5, then the solutions must be obtained in dollars. Why? To see why we cannot use the mix ratios interchangeably, suppose the Sandlot Cap Company data were stated in the following manner.
Product Price Variable Cost per Unit Mix Ratios Based on Sales Dollars
X1 X2
$4 8
$3 5
.6
.4
Total fixed costs = $300,000. Now, find the break-even point in units. Try this, at least mentally before you look at the solution in the footnote below. 4
Now suppose Sandlot Cap Company management gave you following information and asks for the break-even point. TFC is still $300,000. What would you do?
Product Contribution Margin Ratios Mix Ratios Based on Units
X1 X2
.25.375
.75
.25
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THE CASH FLOW BREAK-EVEN POINT Since some of the fixed costs do not require cash payments (e.g., depreciation), the cash flow break-even point will be below the conventional accrual accounting break-even point. The following technique is applicable:
CASH FLOW BREAK-EVEN BEFORE TAXESThe cash flow break-even point is where the cash inflows before taxes are equal to the cash outflows before taxes. This is presented in equation form below.
PX = TFC + VX - Non cash Fixed Costs PX - VX = TFC - Non cash Fixed Costs (P-V) X = TFC - Non cash Fixed Costs
The equation above is based on the assumption that all other costs are paid for during the period and that all sales dollars are collected during the period.
CASH FLOW BREAK-EVEN AFTER TAXESThe cash flow break-even point after taxes is where the cash inflows after taxes are equal to the cash outflows after taxes. We simply convert the contribution margin and total fixed costs to an after tax basis by multiplying by 1-T. The equation is as follows: (1-T)(P-V)X = (1-T)(TFC) - Non cash Fixed Costs
EXAMPLE 6
Cal Company’s specifics from Example 11-1 are P = $10, V = $6, total fixed costs = $120,000 and the tax rate is 40%. If depreciation is $24,000 and there are no other non cash fixed costs, then the cash flow break-even point after taxes is:
The solution is verified in Tabel 5 and Figure 21.
TABLE 5INCOME STATEMENT SHOWING CAL
COMPANY’S CASH FLOW BREAK-EVEN POINT
Sales (20,000)($10)
Variable Costs (20,000)($6)
Contribution Margin
Less Total Fixed Costs
Net Loss
Add Tax Reduction* (.4)(40,000)
Add back Depreciation**
Cash Flow after taxes
$200,000
120,000
80,000
120,000
(40,000)
16,000
24,000
0
======
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* The idea is that the tax reduction can be used to reduce cash payments for taxes in some way. For example, to recalculate taxes for a prior year, or to offset taxable income in some other segment of the Company.
** Depreciation is included in the $120,000 fixed costs, but it does not require a cash outflow. Therefore it must be added back to arrive at the cash flow result.
We can also use the equation above to calculate the number of units needed to generate a desired amount of net cash inflow after taxes. Just add the desired amount and solve for X. For example, suppose management desires a net cash inflow after taxes of $36,000.
2.4X = 48,000 + 36,000 X = 84,000 ÷ 2.4 = 35,000 units
Check: (35,000units)($4) = 140,000 contribution margin. Subtract fixed cost of $120,000, then multiply by .6 and we have $12,000 NIAT. Add back depreciation of 24,000 to obtain $36,000.
