# Learn Break Even Analysis (Ultimate Guide)

Break even analysis is a management imperative analysis. The analysis focuses in interplay of pricing, variable costs, volume and product mix. Hence sales and units helps in making decision on which products to offer, how much products will be priced and how organizations cost will be managed. It’s effective and efficient financial reporting system. As your prices go down, so does the gross profit margin, while the break even shoot up rapidly. Though Break even analysis doesn’t force decisions, it provides you additional insight on the effect of important business decisions that are on the bottom line.

As you know, profit is the main purpose of any business existence. Profit is the remainder from revenue after expenses has been covered.  Break even analysis helps businesses and owners in determining the level of sales or units which will lead to a zero profit. Zero profit here means a point where there is neither profit nor loss.

For break even analysis to occur there must be a balance between income and expenditure. It is a concept which managers and entrepreneurs use in different situations. The benefit of break even analysis is based on fact that both profits and risks are combined.

Profit= Revenue –Expenses

And since break even is point where revenue equals expenses, the base formula will be:

Expenses=Revenue

Revenue: This is the income from sales. It’s determined by multiplying selling price and the quantity sold. In most cases, Revenue increases the linear manner from zero, point where there is no sale, and stays directly proportional to the sales unless quantity discounts are given.

Revenue=Price per unit x Quantity

=P X Q

Expenses: There are 3 categories of expenses;

• Fixed costs
• Variable costs
• Mix of fixed and variable costs

Expenses do not start at zero point, unless you were out of business. There are expenses that are incurred when there are no sales to make. All such expenses with no production are referred to as fixed costs.

Fixed and variable costs: There is a basic assumption that costs can be separated as fixed and variable costs. A change in cost leads to proportionate change in volume. This is referred to as variable cost..

Variable costs are expenses that changes proportionately to the activity of business. Variable costs are made up of direct costs-which are costs attributable to preparation of each unit of sale, indirect costs-such as an overhead that varies with number of units prepared for sale.

Variable costs vary in parallel and proportionate manner with volume. Mathematically, a linear relationship exists between costs and volume. If volume increases or decreases by 10%, variable costs should also increased/decreased by 10%. A typical example is Raw materials.

It should be noted that unit Variable Cost remains uniform, it’s the total variable costs that changes proportionally to volume. When a cost doesn’t change with changes in volume, it’s referred to as fixed cost. This cost remains constant irrespective of change in volume. Examples of fixed costs are salaries, depreciation, repairs, insurance, maintenance and factory rent.

Total fixed costs remains constant while unit fixed costs decreases with increase in volume. Hence, the unit fixed costs and volume are inversely related. Since unit fixed cost decreases with unit and total increase in volume, per unit cost of production (including both fixed and variable costs) also decrease.

For a break even to occur, its necessary that a firm has both fixed and variable costs. If all costs of the firm are variable, no profit-no loss situation would arise at zero loss situation would arise at zero sales volume and profit would arise at zero sales volume and profit would vary proportionately with sales.

On the other hand, if all costs become fixed, the break even would occur where revenues equals the total fixed costs and afterwards, profits would be equal to sales revenue.

Ways of analyzing break even: Break even analysis can be done using two different methods;

• Mathematical approach
• Break-even chart

In this course, we shall only focus on mathematical approach of break even analysis. Break even can be computed in terms of units or products. Break even point in terms of units will be reached when the units sold create sufficient revenue to cover total cost (Fixed and Variable). Each of the products sold will cover its own variable cost and leave the remainder, known as contribution or marginal income to over the fixed costs.

Break even will occur where enough units have been sold so that total contribution is equal to total fixed costs.

NB: Contribution per unit is the difference between selling price per unit and variable cost per unit.

At Break Even Point (BEP) profit is at zero and hence total contribution will just cover the total fixed costs.

• Unit contribution=unit selling price-Unit variable cost
• Total contribution=total fixed cost + Profit

BEP can also be calculated by dividing the Total Fixed Cost (TFC) by the contribution per unit

TFC
BEP =       ___________________________________
Selling price –Variable cost per unit

Mathematically, if selling Price is less than Variable Cost per unit solution for BEP in terms of negative sales volume doesn’t exist; but a negative sales volume in practice is not an acceptable solution.

In case the selling price equals Variable cost per unit, then the BEP can exist unless the firm has zero fixed cost. In a situation where fixed cost is at zero, the sales volume point will be a BEP because revenue would be exactly equal to the Total cost at any volume of sale.

Contribution ratio: When the variable cost (per unit or total) is divided by sales (per unit or total) gives you variable cost ratio. The contribution ratio would calculate how much a product would earn from every sale generated

contribution per unit
Contribution ratio = __________________________
Sales per unit

Margin of safety: This measures sensitivity of budgeted sales volume as compared to the break-even sales volume.

Budget sales-break even sales
Margin of safety =        _____________________________
Budget sales

The margin of safety indicates the extent to which the sales may fall before the firm suffers a loss. The larger the margin of safety, the safer the firm. A low margin of safety may result from having a low contribution ratio.

When both margin of safety and P/V ratio are low, the management should think of the possibilities to increase the selling price, provided that it doesn’t adversely affect sales volume, or reduce variable cost for bringing improvement in manufacturing process.

Effects of Break Even

Profit is a function of a variety of factors as discussed earlier. The following are some of the effects on changes on volume, cost and prices.

• Effect of change in price Changes: An increase in selling price will increase the P/V ratio. As a result, it will lower the BEP. On the contrary, decrease in Selling Price will reduce the profit-volume ratio and hence bringing a higher BEP.
• Effect of Volume changes: Change in volume, without change in Selling Price an costs will not affect the P/V ratio. This will in turn lead to a no effect on the Break Even Point.
• Effect on changes on Profits: Profit may be affected by increase, change or decrease in the following factors:
1. Selling price
2. Volume
3. Variable cost
4. Fixed Cost
5. Combination of all the above

The selling price may change due to economic factors or the management itself may initiate change due to increase/decrease in competition or cost, or some other reason.

• Effects on price and volume changes: Changes in price affect volume invariably. Price reduction may increase the demand of a product and consequently increasing the volume. On the other side, increase in price may affect demand which can adversely reduce volume.
• Effect on changes in variable costs: Impact of changes in variable costs on profits is a straightforward case when it doesn’t cause any change in volume or selling price. An increase in the variable cost will lower P/E ratio, push up the BEP and reduce profits.
• Effect on changes in fixed costs: A change in fixed cost has no effect on the P/V ratio. However, other factors remaining constant, a fall in fixed costs will lower the BEP and raise profits. An increase in fixed cost is caused either by external factors or changes in management policy, which raises the BEP.

Uses of Break Even Analysis

• Understanding accounting data: Break even is a simple concept used to comprehend and interpret accounting data. Most executives and other people in the business who are unable to understand the accosting data contained in the financial statements and reports prefer using break even analysis. It becomes easy to grasp and interpret data when using break even analysis.
• Diagnostic tool: Break even analysis indicates to the management the cause of increasing falling profits and BEP. The analysis causes the management to deliberate on the cause of action for the business. Practically, knowing where BEP lies can be useful to the management in determining the need for action. Nevertheless, increase in BEP shouldn’t always be a matter to raise alarm to the management.
• Profit improvement: Break even analysis computes BEP and P/V ratio, P/V graphs and Break even charts, analyze and report the effect of changing the factors on profit plans and other budgets and forecasts prepared by the management. Beak even analysis hence provides basis information for improvement study.
• Risk evaluation: Desirability of an action should be considered on basis of its profit, and risk as well. The reason why break even considers more than profit because a firm may commit risky action if its only subjected to profit consideration. Break even analysis in an extent, is a useful method to consider the risk implications of the alternative actions. The problem of risk evaluation can be approached by considering effects of alternative action on the BEP. From one alternative, a firm may expect higher profit and also higher BEP.

Limitations of break even analysis

• Cost segregation:  One of the prerequisites of break even analysis is that cost can be easily classified into fixed or variable. While some costs can be easily identified as fixed, for example, rent of building; a large number of costs belong to the mixed category. These costs are known as semi-fixed costs. Semi-fixed costs consist of both fixed and variable elements which is difficult to separate. Furthermore, some costs are very difficult to determine, for example, where there are various ways to calculate depreciation; it’s not easy to determine which is the best one.
• Constancy of fixed cost: There is an assumption in break even analysis that fixed costs remain constant entirely. However, the concept is not valid. If a firm is operating at zero output, some fixed costs can certainly be eliminated or reduced, for example, termination of executives to reduce salaries. Otherwise, if a company uses the idle capacity, this would incur additional fixed cost. Conclusion is that fixed costs are only constant over relevant range of activities.
• Applicability to Multi product firm: Break even analysis is perhaps best suited for a single-product producing firm. In case of multi product firm, BEP of the firm can be calculated with an assumption of some product mix. The BEP would lower if product mix is weighed in favor of high profit product. If it’s desired to calculate break even point for each product then the firms fixed costs will have to be allocated to each product. Allocation of fixed cost on products is a problem in practice. Because of that difficulty in allocation, meaningful BEP can’t be calculated for each product in case of a multi-product firm.

Other limitations Includes:

• Break even analysis is only a forecast
• The break even analysis will only be accurate depending on the data which it is based