# Break Even Analysis Problems And Solutions Pdf

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*CVP analysis looks at the effect of sales volume variations on costs and operating profit.*

*Exercise D Barney Company makes and sells stuffed animals. How many Michael Bears must be produced and sold each month to break even?*

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## Break-Even Analysis (With Diagram)

The below mentioned article provides a complete overview on Break-Even Analysis. The break-even point refers to the level of output at which total revenue equals total cost. Management is no doubt interested in this level of output. Therefore, the primary objective of using break-even charts as an analytical device is to study the effects of changes in output and sales on total revenue, total cost, and ultimately on total profit. The following list seeks to highlight some of the more practical applications of break-even analysis:.

What level of sales is needed to cover all costs and earn, say, Rs. Figure The horizontal axis measures the rate of output, and revenues and costs, measured in rupees, are shown on the vertical axis. The law of diminishing returns accounts for the curvilinear shape of the total cost curve. To the left of Q a and to the right of Q b total costs exceed total revenues, and there are losses. So there are two break-even points. The generalized model in Figure Conversely, linearity in the case of the total cost curve implies that the firm can expand output without changing its variable cost per unit very much.

For a relatively narrow output range, this is no doubt a reasonable assumption. These qualifications apart, there is much to -be said for using the linear break-even model in the real commercial world.

In Figure At both the points there is neither profit nor loss. But in Figure If the price of the product exceeds variable cost, the firm would attempt to expand production with a view to covering fixed cost and make profit subsequently. The difference between the two i. This shows the contribution of the product toward the recovery of fixed cost and toward net profit.

For example, if a product sells for Rs. The difference between the revenue produced from sale of a product, and its production and selling cost, is the contribution towards fixed costs and to the ultimate net profit. This contribution concept is often used for decision-making purposes. There is hardly any reason, however, why every product-line made and marketed by the firm should be expected to make the same contribution. By contrast, there is a case for assuming that preference should be given to those product-lines which offer the possibility of making the largest contribution.

Initially, it approaches the problem by way of full cost and produces some such statement as the following:. It may apparently seem, from this example, that both products yield the same percentage profit on sales and that there is nothing to choose between them. Now we get a completely different picture. The relationship is illustrated in Figure In order to adopt this type of approach, one must relate the costs directly to the production and marketing of the product—the costs which could be avoided by not producing the item.

In a multi-product firm, it is not enough merely to determine the product mix with a view to the maximization of contribution. As a guide to the solution of this problem it may appear necessary to evolve some yardstick to enable a decision to be made as to which product-line or order is to be discarded, when particular production facilities are overburdened.

The order B contributes Rs. But its claim on production facilities if 25 times as great. The result is that the contribution per facility hour is Rs. Thus, if the volume of production which the firm can sell exceeds the existing capacity, the optimal results will be obtained by producing those orders which make the maximum contribution per facility hour in the area where the bottleneck occurs.

Since the production hour is the limiting factor, product X, which makes greater contribution per hour, will be accorded priority. The remaining hours will be utilised for the production of Y, i. We know that average net profit, i. See Figure We may now define the symbols usually used in break-even analysis:. To illustrate, assume that we have a factory that can produce a maximum of 20, units of output per month.

These 20, units can be sold at a price of Rs. Variable costs are Rs. By a direct application of Eq. The denominator in equation 3a provide a measure of the contribution made by the product to recover fixed costs. For our example, the breakeven level in rupee sales is which is the same result that can be obtained by multiplying the break-even quantity by unit price. In equation 3 , the contribution margin is calculated on a per unit basis from the ratio of AVC to price.

In equation 3a , the contribution margin is calculated on a total sales revenue basis from the ratio of TVC to TR. The ratio is the same in each case and in both the situations the calculated ratio is subtracted from 1 to yield the percentage of revenue that contributes to recovery of fixed costs or overhead. How many passengers should be carried per month to break even?

What load factor i. Then, by equation 7 or 7a we get. We may then proceed to construct our model. But the major problem with this approach is that sufficient data may not be available to enable us to estimate either the cost or revenue functions. The break-even analysis can throw light on a number of real commercial world problems. We may now see how break-even analysis can be used as a tool to assist management in making decisions.

In the first alternative, the university would incur a fixed costs of Rs. In the second alternative, Rs. The P. First, what must the enrolment be for the university to break even with either alternative, if the tuition fee is set at Rs. Substituting these values into Eq. That is, it requires a larger number of lecture hours to cover all of its costs. Output will have to reach lecture hours for project 1 to be as profitable as project 2. Beyond hours, the comparative profitability of project 1 becomes greater because of the greater contribution per unit.

With this information, the P. The break-even point represents the volume of sales at which revenues equal expenses; that is, at which profit is zero. This is done by dividing the fixed costs or overheads by the contribution margin-ratio contribution margin divided by selling price.

Generally, in these types of computations, the desired profit is added to the fixed costs in the numerator in order to ascertain the sales volume necessary for producing the target profit. If management plans for a certain profit, then revenues needed to cover all costs plus the desired profit is.

This information can be shown graphically, as in Figure In this example, fixed costs are Rs. The price charged is Rs. If management wants a profit of Rs. If this is the objective, the break- even equations have to be modified as follows:. Now suppose that management wants to earn a target profit of Rs.

Making the appropriate substitution into Eqns. If we add this target profit to the fixed costs we see that the break-even levels of all three factors get increased.

The information in this example could be extended so as to make provisions for such factors as payment of taxes or for payment of any other fixed obligations that might be associated with the fixed costs such as interest payments on bonds or debentures used to finance an investment.

Suppose the objective of Indian Airlines is to make a profit of Rs. One final question is: What is the maximum amount of profit that can be made by Indian Airlines? An after-tax profit of Rs. This figure of Rs. Essentially, the introduction of taxes or other fixed obligations will result in increasing the break-even levels of output in numbers, rupees sales, and capacity. The break-even quantity is not a fixed number. Management can alter the quantity by changing the controllable variables.

Herein lies an important application of break-even charts in profit planning, control, and forecasting. To illustrate this situation, suppose that we have collected the following information all tabulated on a per month basis :. Panel a illustrates the original situation where the break-even level of output is units and total revenue and cost equal Rs. Panel b depicts the impact of reducing fixed costs from Rs.

The shaded portion on the graph provides a measure of the original profits, and the crosshatched area provides a measure of the increase of profits. If the fixed costs can be reduced to Rs. The impact of reducing variable costs to Rs. In this situation, costs and revenue both fall to Rs. Panel d presents the final option of increasing the market price of the product to Rs.

When the price is increased, the slope of the total revenue curve changes, while the break-even level of output falls to 75 units. So long only one of the controllable variables price, or fixed or variable costs was changed, but in practice management may have the power to change all three of them simultaneously. In order to be able to assess the impact of changing more than one of the variables we often adopt a modified version of break-even analysis.

## Operations management

It often is used in conjunction with a sales forecast when developing a pricing strategy, either as part of a marketing plan or a business plan. The formula for a breakeven analysis is:. They are fixed over a specified period of time or range of production, and examples include:. Fixed costs are easy to calculate for existing businesses, but new businesses must do research to get the most accurate figures available. Unit costs vary depending on the number of products produced and other factors.

Calculate break even point. Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics. Formula for percentage. Finding the average. Basic math formulas Algebra word problems.

Next Lesson: Process Costing Problems. Assume that as an investor, you are planning to enter the construction industry as a panel formwork supplier. The potential number of forthcoming projects, you forecasted that within two years, your fixed cost for producing formworks is Rs. The variable unit cost for making one panel is Rs. The sale price for each panel will be Rs. If you charge Rs.

Break-Even Analysis: Problem with Solution # 1. From the following particulars, calculate: (i) Break-even point in terms of sales value and in units.

## How to Calculate the Break-Even Point

The below mentioned article provides a complete overview on Break-Even Analysis. The break-even point refers to the level of output at which total revenue equals total cost. Management is no doubt interested in this level of output. Therefore, the primary objective of using break-even charts as an analytical device is to study the effects of changes in output and sales on total revenue, total cost, and ultimately on total profit.

What Is the Break-Even Point? Break-Even Point Examples. NOTE: FreshBooks Support team members are not certified income tax or accounting professionals and cannot provide advice in these areas, outside of supporting questions about FreshBooks. If you need income tax advice please contact an accountant in your area.

*The maximum factory capacity is 20, units and it anticipates selling 15, units. Construct a break-even chart showing the break-even point and the margin of safety at present. Fully label your diagram.*

#### Break-even analysis - numerical questions

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