# Get PDF A2 Company Accounts and Contribution/Break Even Analysis Questions

In management accounting, costs are usually classified according to the cost and its relationship with the level of output of the business. The following costs are therefore defined in how they change in value, as the level of output changes. These costs are those that remain unchanged as the output level of firm changes. It does not matter what level of output the firm produces even zero output makes no difference , any costs which is a fixed costs will remain the same.

Common examples of fixed costs are as follows:.

## A2 Accounting Unit 1 Lesson 1 Classification of Costs. - ppt download

A common mistake that is made is to state that fixed costs will always remain constant. This is not the case, all we are saying is that these cost are fixed with respect to short - term changes in the level of output only. Any cost which varies directly with the level of output would be classified as a variable cost.

Varying directly means that the total variable cost will be totally dependent on the level of output. If output doubles, then the variable cost would double. If halved, the variable costs would halve. If output were zero, then no variable costs would be incurred. In reality, nearly all costs would not easily be classified into either fixed or variable. Most costs will fall somewhere between the two classifications. In this case, we can classify these costs as semi-variable costs.

For example, although the wages of the production staff may appear to be variable costs. In reality, they will vary with the level of output but not in a direct manner. The direct relationship is unlikely to hold over a long period of time. Similarly, many costs will have a fixed element but also a variable element for example, most bills for gas and electricity will consist of a standing charge which is fixed and a variable element which depend on the usage. Because there is a link between the cost and the level of output, we would expect the semi-variable; cost curve to be upward sloping.

However, there is no real 'textbook' appearance for this curve. It will normally slope upwards in a non-linear i. A direct cost is similar to a variable cost in that it compares the cost with the level of output. However, a direct cost is any cost which is directly related to the output level of a particular product. Direct cost is more appropriate for a firm that makes more than type of product. For example, if a firm is producing furniture and the chairs produced use a certain type of wood, but the tables use another type of wood, then both types of wood would be direct costs because they are directly related to the level of output of a particular product not to the level of output in general.

An indirect cost is any cost which cannot be linked with the output of any particular product. These costs are sometimes known as overheads. They are related to the level of output of the firm but not in a direct manner and not for any one product.

## A2 Accounting Unit 1 Lesson 1 Classification of Costs.

For example, the cost of powering machinery will be related to the level of output but not to a particular product. Generally, the terms indirect and direct are more likely to be used when the firm produces a range of products. In break-even analysis, the firm will only producing a certain product type.

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This means that the terms fixed and variable are more likely to be used. Total cost would be calculated as all the costs totalled together for any particular level of output. If the output level were zero, then total costs would just consist of fixed costs. In nearly cases, total costs will be the addition of fixed costs and total variable costs where total variable cost is the variable cost per unit multiplied by the level of output. The term 'marginal cost' refers to the cost of producing one extra unit of output.

The cost of producing an additional unit of output will be the variable costs and any other costs that are directly related to the level of output. Marginal costing is a costing method that can be used by managers when making business decisions. This method considers how a product is to be 'costed' and will only use data relating to the variable or direct cost of production.

Any fixed or indirect costs are ignored. The cost of a product will be the cost of actually producing this extra unit and no more. However, marginal costs will not prove as useful when attempting to set a selling price of a product. Consider the following example. B Pitt has just opened up a small restaurant.

The following has been estimated for the cost of producing the typical meal:. How much should he charge for a meal? Try to work this out and follow the link below once you have had a go to see how you got on. Revenue is the money earned from selling output. It is based on both the level of output and the selling price of this output. It is calculated as follows:. Notice that in the above formula we assume that a buyer can be found for all units produced. This is viewed as a limitation of some of the costing scenarios that you may face. The total revenue is also based on the assumption that the selling price remains constant.

If this is the case then we illustrate total revenue graphically. This would appear as follows:. Linked closely with marginal costs and marginal costing is the concept of contribution. Contribution is defined as the difference between the selling price of one unit of output and the variable cost of producing this extra unit of output. Total contribution would be the same as the contribution per unit, but with each component would be multiplied by the level of output.

The formula for this is as follows:. Contribution can also be thought of as the profit ignoring fixed costs. Although it cannot 'officially' be termed profit until all costs have been deducted. Contribution really refers to the amount each extra unit sold will contribute towards paying the fixed costs of the firm. Most firms will want to maximise their profits. Being profitable is not always possible. New firms, small firms and firms facing an economic slowdown may find that they cannot generate profits at all.

In this situation, it may be a more realistic objective for firms to aim to simply break-even. Break-even implies that the firm does not make any profit, but it also does not make any losses either. All the costs incurred by the firm are exactly matched by their revenues earned over a period of time. The break-even point is measured by the level of output where total costs equals total revenue but in can also be measured in terms of sales value.

The break-even model is based on some simplifying assumptions, which does make the model less realistic, but can also make it easier for us to use and to manipulate for changing circumstances. These assumptions are as follows:. Based on the simplifying assumptions outlined earlier - that there are only two types of costs: As long as the firm generates a positive contribution on each extra unit of output that is sold, then profits will always be higher or its losses will be lower if it sells an extra unit of output.

If a firm had no fixed costs to worry about at all, then any units sold would lead to the firm making a profit. However, nearly all firms will have fixed costs that will be paid regardless of the level of output. In this case, for the firm to earn a profit, the contribution earned on the units of output actually sold must be higher than the overall level of fixed costs. The break-even point must therefore be at the level of output where the contribution generated from these sales is exactly equal to the total level of fixed costs. This gives rise to the following formula:. A sole trader runs a sandwich shop.

How many sandwiches need to be sold on an average week to break-even? Have a go at working this out and then follow the link below to see how you've got on. We can also measure the break-even point in sales revenue. We still use the formula to calculate the output level for break-even, but then we multiply the break-even output level by the selling price. The break-even model can also be expressed in a graphical format on a break-even chart.

This will bring together the graphical representation of both costs and revenue curves that have been developed earlier. The chart is based on the simple relationships between costs, revenues and output. As output increases, there will be an increase in costs and also in revenues. This can be summarised as follows:. This will be drawn from the vertical axis at the level of fixed costs and will be plotted across the chart. Therefore, as output increases, the total cost will also increase.

What are the total costs for the firm at the output levels of zero, , and bookcases? Have a go at working them out and then follow the link below to see how you got on. We know that at zero output the total costs and the fixed costs will be the same. This will be the first point on the total cost curve. As output increases, we know that total costs will increase in linear i.

If we simply find that end point of the total cost curve, then we can join up the end and the starting point to give us the full total costs curve. The total costs at the end point will simply be as follows:. Maximum output multiplied by the variable unit cost plus the fixed costs. Of course, if we make a mistake then the whole curve will be inaccurate. It may be wise to plot a third point on the curve just as a back up. Choose any output level and calculate the total costs at this point and simply plot this on the chart. This is because if no output is sold, then no revenue will be received.

The revenue curve will also rise in a liner, straight-line, manner. Plotting the total revenue curve will involve calculating revenue at various levels of output. Total revenue will be calculated as follows:. The quick method here would be to calculate total revenue at the maximum output level by multiplying this output level by the selling price and then joining this point up with the origin.

What is the total revenue received by the firm at the output levels of zero, , and chairs? Have a go at working this out and drawing the total revenue curve and then follow the link below to see how you got on. If we combine the data relating to the cost and the revenue situations of chairs as outline in the previous examples, we would arrive at the following:. If we assume that the maximum level of output that can be produced per week is chairs, then the data relating to costs and revenue at different output levels can be represented as follows:. It may help to think of the output levels as the horizontal co-ordinates on the chart and the money values as the vertical co-ordinates.

For example, the total revenue curve will always start at 0, 0.

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Fixed cost and total cost curve both begin at 0, Using a table as shown above may help you to eliminate any chance of errors being made. However, in an examination situation, the construction of such a table may take up valuable time, which you cannot afford to give up. Hint - until you are confident in drawing break-even charts, use a full table as shown above. When drawing a chart, it is sensible to first of all calculate the break-even point using the formula. This way, we can have a rough idea of what the chart should look like before we draw the chart. It always makes sense to round up the answer to the nearest whole.

Number unless output can be broken up into fractions. At any output level, the profit or loss can be calculated by simply drawing up a vertical line from the output level of the horizontal axis in this case from 30 units. Sooner or later, this line will pass through both the total cost and the total revenue curve. As it intersects both of these curves, you should draw a horizontal line i. The two lines one from the total cost intersection and one from the total revenue intersection will eventually hit the vertical axis.

Now, all you have to do is measure the vertical gap between these lines in money terms be careful of the scale you are using to measure money. This gap will be the profit or loss. On the diagram above, the profit will be the distance ab. With the same example of selling chairs, we can estimate the profit levels at different levels of output.

If a firm is generating a profit, then its output level will be higher than the break-even output level. A firm may wish to know how far output can fall safely, before the firm begins to experience losses. This idea is summarised in the concept of the margin of safety. The margin of safety measure how far output can fall before the firm begins to make a loss. It is measured by the number of units of output between the current level of production and the break-even level of production.

It can also be expressed as a percentage of the current output level. Continuing with the maker of chairs. If the actual output level were chairs, then the margin of safety would be:. In other words, output and sales can safely fall by chairs before the firm stops making profits. If it falls by chairs, then the firm would begin to make losses. Expressed as a percentage this would be: It is possible to show the effects of price changes, changes in both the fixed costs of the firm and also the unit costs of the firm on the break-even chart.

The break-even level of output will always change if any of the following three items change:. Any changes in one or more of these will also change the curves as shown on the break-even chart. If any of the initial conditions changes, then it is possible to re-plot a new curve on top of the old chart, to all comparisons over different scenarios. For example, a firm may have an option of investing in new machinery, which would increase the fixed costs, but would also lower the variable cost per unit.

The overall effect on profits can be seen by drawing a break-even chart. Figure 9 Increase in selling price - change in break-even. Here, any change in the selling price of each unit will simply 'swing' the total revenue curve either upwards or downwards. If the selling price is increased, then the curve will pivot around the origin in an upwards manner - this will lead to the firm breaking even at a lower output level than before. For example, the answers to the questions above can be verified as follows:. Yes, since total contribution margin is equal to total fixed cost of ,, i. For an alternative check A summary of the cost volume profit equations for solving single product problems in dollars is presented in Exhibit 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. 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. Then subtracting variable cost from both sides of the equation provides the basic break-even point equation in sales dollars. 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.

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. This provides Equation 3. 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. When the desired net income is stated as an after tax rate R , the equation needed is developed by simply dividing R S in Equation 4 by 1-T.

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. 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. 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? To answer these questions, we need the contribution margin ratio. A graphic analysis of this example is also illustrated in Figure since we are simply solving the problem in dollars rather than units. The graph is also useful for comparing the two approaches.

Example places emphasis on the horizontal axis units while Example places emphasis on the vertical axis dollars. 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:. 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. 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.

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. Suppose 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. Using the margin of safety we can answer this question quickly. To show that the margin of safety calculations work on either side of the break-even point, consider another example.

Some additional symbols are needed to illustrate the algebraic techniques applicable to multiple product problems. A summary of the cost volume profit relationships for multiproduct problems is presented in Exhibit The five equations are comparable to the single product equations presented in Exhibit , but are somewhat more involved. Each equation is developed and illustrated below. 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. 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. 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. Using R to represent the target rate of return on sale dollars before taxes, i. 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.

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. The appropriate equation for after tax net income is found by dividing the term [ R YX], in Equation 4, by 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 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.

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. Sandlot Cap Company management wants to know how many caps need to be produced and sold to accomplish the following:. To solve this problem we need to calculate the weighted average contribution margin per unit, i.

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. Rearranging this equation we have. We can use this equation as an alternative way to find the answers to question 3 and 5 as follows.

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.

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Note, these ratios are not equal to the mix ratio based on units. 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. Equation 2 is developed in the usual manner by simply adding the desired amount of NIBT to the right hand side of Equation 1.

If R is used as the before tax target rate of return on sales, i. If R is used as the after tax target rate of return on sales, i. Sandlot Cap Company management wants to know the amount of sales dollars needed for each product to accomplish the same five objectives. To find the answers we need to start by calculating the weighted average contribution margin ratio.

The mix ratios stated in dollars are used as the weights. Then the solutions are obtained as follows:. The solutions to these five questions are also illustrated in Figure since we simply changed our emphasis from the horizontal axis units to the vertical axis dollars. 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 , then the solutions must be obtained in units. If the mix ratios are stated in dollars, as in Example , then the solutions must be obtained in dollars.

To see why we cannot use the mix ratios interchangeably, suppose the Sandlot Cap Company data were stated in the following manner. Now, find the break-even point in units. Try this, at least mentally before you look at the solution in the footnote below. Now suppose Sandlot Cap Company management gave you following information and asks for the break-even point.

What would you do? Since some of the fixed costs do not require cash payments e. The 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. 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.

The 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:. For example, to recalculate taxes for a prior year, or to offset taxable income in some other segment of the Company.

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.

Breakeven Analysis: Contribution & Contribution per Unit

Just add the desired amount and solve for X. There are two issues that involve the contribution margin approach and the closely related direct or variable costing inventory valuation method. The first issue is a relatively old controversy over whether direct costing or full absorption costing is the most useful way to present accounting information.

The second issue questions the wisdom of separating costs into fixed and variable categories. We will return to the first issue in the next chapter. From the activity based costing perspective, critics of the contribution margin approach argue that the costs traditionally defined as fixed costs have been increasing faster than the costs traditionally defined as variable costs. As a result, the CVP model does not reflect the cost structure of complex, multiproduct organizations.

Although the CVP model may be useful for some short term forecasting and optimization decisions, it is misleading for decisions such as product introduction, product pricing, product mix and make versus buy. The so-called fixed costs are not explained by output volume, but by the diversity and complexity of the company's products, services, customers, distribution channels and product lines. The CVP approach is flawed because it assumes that the volume of production is the only cost driver. As a result, the model motivates managers to produce as much as possible to lower total unit cost 8.

It encourages managers to add new products and services ignoring the "overhead creep" that inevitably results. But this signal to constantly expand is a trap because the costs that are assumed to be constant, increase rapidly instead, in response to the greater demands that are placed on the various support activities. As the so-called fixed costs rise, the manager attempts to add more volume to lower unit cost again.

The process is somewhat analogous to a dog chasing it's tail. The contribution margin approach has the same basic defect as any other constrained optimization technique. However, from the viewpoint of the lean enterprise concepts of just-in-time and the theory of constraints, becoming competitive and maintaining competitiveness in the long run requires a dynamic learning organization.

The emphasis should be on relentlessly eliminating waste, removing constraints, re-engineering processes when necessary and increasing customer value, not on maximizing output in an attempt to minimize short run unit costs. Defenders of the contribution margin approach argue that the concepts of contribution margin and related techniques are useful for short term planning Chapter 11 and for performing a variety of special relevant cost studies Chapter Although production volume is not the only cost driver, it is still the major cost driver.

Production volume based systems and techniques such as direct costing and CVP analysis still provide reasonably accurate information for a fraction of the cost of elaborate ABC systems. Another advantage of these methods is that income statements based on the contribution margin approach i. We explore this idea in the next chapter.

In addition, direct costing reduces the full cost behavioral bias towards over production by eliminating the production volume variance and the inventory change effect that increases net income when production exceeds sales. The argument that the contribution margin approach promotes overproduction is not warranted. In fact, full absorption costing creates a much stronger motivation to overproduce and ABC is just an expanded form of that same methodology.

In addition, CVP analysis does not discourage continuous improvement. It is just a quantitative tool that can be used or misused like any other tool. The CVP approach can complement the plan-do-check-action PDCA continuous improvement cycle by providing a way to estimate the financial consequences of proposed changes in the system.

A possible reconciliation between ABC and the contribution margin approach is provided by Robin Cooper's levels of cost variability. This expanded information will indicate which products, distribution channels and customers really are profitable and perhaps help avoid the potential trap set by the contribution margin logic that keeps companies from ever dropping anything. See the Ali summary for more on this idea.

The classical economists e. Around , the neoclassical economist, Alfred Marshall argued that the interaction of supply and demand determines the price using his famous scissors analogy i. Later, around , Edward Chamberlin and others developed the theoretical model described in this chapter. Joel Dean presented the linear model as a practical alternative.

The Macmillan Company; Chamberlin, E. The Theory of Monopolistic Competition. Harvard University Press; and Dean, J. Solving for this point requires using calculus. Marginal revenue is the rate of change in total revenue and can be found by taking the first derivative of the total revenue function. Marginal cost is the rate of change in total cost and can be determined by taking the first derivative of the total cost function.

Upper level microeconomics textbooks show this in considerable detail using quadratic and cubic equations. We must solve the problem in dollars first and then convert to units. We calculate the weighted average contribution margin ratio, i. Then solve for mixed sales dollars at the break-even point, i. Then we divide by the sales prices to find the break-even point in units, i. Any attempt to use it will produce the wrong answer.

Since there is no way to find the contribution margin per unit for each product, or the mix ratios in dollars, you would need to ask for additional information to answer the question. What did we earn last month? Harris used the term direct costing rather than variable costing. Journal of Management Accounting Research Fall: This is because total unit cost decreases as the average fixed cost per unit decreases when additional units are produced, i. Although changes in productivity are considered in the model, the problem referred to as "overhead creep" is not considered. In other words, in the theoretical model, productivity affects the rate of change in variable costs, but fixed costs remain constant.

The economic order quantity and economic batch size models, linear programming and standard costing provide a few examples. Professors, customers and value: Bringing a global perspective to management accounting education. The inventory change effect is also illustrated in some of the master budget problems in Chapter 9. What are the assumptions underlying the conventional linear cost volume profit analysis?

What does a constant sales price mean? See Figures and What does constant variable cost per unit mean? What assumption causes the total variable cost function to be linear? See Figure for the linear functions, then Figures and How does total variable cost and total cost change under constant, decreasing and increasing productivity? In the conventional model, how is variable cost fixed and fixed cost variable? See Figure for unit variable cost and draw your own graph for unit fixed costs.

In the microeconomic model, what causes the average variable cost curve to be U-shaped? How do linear and non-linear CVP analysis differ in terms of in indicating how much to produce and what price to charge? How is the basic break-even equation for unit data developed or derived? What is the slope of the profit functions in Figure and Figure ?

Compare Exhibits and See Some Questions in Chapter What two weighted average calculations are needed in unit based multi-product CVP analysis? Why are they needed? In multi-product CVP calculations, are the mix proportions for units and dollars the same? What are the implications? See Note on Mix Ratios. Is the cash flow break-even point in sales dollars above or below the accrual accounting break-even point?

See Cash flow break-even and Figure What are some of the arguments against conventional linear CVP analysis? See the Controversy of CVP. Would converting to the theoretical CVP model solve the problems in question 17? See Figure for some ideas. Is the CVP model consistent with the concept of continuous improvement? Assume there are no constraints on the firm's capacity to produce or the demand for the firm's products.

What would be the maximum return on sales dollars for a multi-product firm before and after taxes? The link related to question 13 is helpful.