# How much must be sold to break even or to realize a target profit?

While every company needs to know the answer to this question, the answer is even more vital for start-ups that do not have much margin for error. This is because the revenues will exactly equal the expenses at the breakeven point. In other words, the company does not incur a loss nor does it realize a profit.

Breakeven analysis or CVP (cost-volume-profit) analysis is the type of analysis that answers these important questions. It is an accounting tool to understand the relationship between revenues, variable costs, and fixed costs. The purpose of this article is to illustrate how you can perform a breakeven analysis and calculate the breakeven point of your business in different scenarios.

## What activity level is required to break even or realize a target income level?

The financial results of a business are heavily dependent on the total number of sales. In the short run, a company can estimate fairly accurately the sales price per unit, the variable costs per unit, and the fixed costs. However, the demand for the company’s goods and/or services is unknown. As a result, the company does not know in advance whether it will be profitable or not. CVP analysis allows you to determine the quantity, irrespective of whether it is a good or service, that needs to be sold to avoid a loss.

### Breakeven analysis: The basics

The basic version of the break-even formula is a 2-step approach to calculate the breakeven point. The first step is to determine the contribution margin and the second step is to calculate the breakeven point.

Throughout the rest of this article, we will make use of the below case study. A prerequisite is that you split your expenses between fixed expenses and variable expenses.

Smartphone Cover Inc., a fictitious company, is a manufacturer of smartphone covers. The company is a single product company. The following assumptions are made:

Management of Smartphone Cover Inc. would like to know its breakeven point.

Step 1: Calculate the contribution margin

First, the unit contribution margin (UCM), and the contribution margin ratio (CMR) need to be calculated. The contribution margin per unit is \$5.0 and the contribution margin ratio is 40%.

Unit Contribution Margin (UCM) = Unit Sales Price (USP) – Unit Variable Costs (UVC)

Contribution Margin Ratio (CMR) = Unit Contribution Margin (UCM) / Unit Sales Price (USP)

Step 2: Calculate the break even point

Subsequently, the breakeven point for Smartphone Cover Inc can be calculated. The breakeven point is 50,000 units or \$625,000. In both cases, the numerator is the fixed costs of \$250,000. To calculate the breakeven point in units, you need to divide the fixed costs by the Unit Contribution Margin. If you divide the fixed costs by the Contribution Margin Ratio, you obtain the breakeven point in dollars.

Breakeven point in units = Fixed Costs (FC) / Unit Contribution Margin (UCM)

Breakeven point in dollars = Fixed Costs (FC) / Contribution Margin Ratio (CMR)

Beyond the breakeven point, the company’s operating income is increased by the unit contribution margin for every additional unit sold. This is explained by the fact that all the variable expenses and fixed costs are covered at the breakeven point. So, Smartphone Cover Inc’s operating profit will increase by the unit contribution margin of \$5.0 for every additional unit sold beyond 50,000 units.

### Breakeven analysis: The break even formula expanded

The basic break even formula can be tweaked in several ways. In the next sections, you will learn how to:

1. calculate the number of units that you need to sell to achieve a target operating income level
2. incorporate a safety margin
3. calculate the contribution margin for a multiproduct company

#### Key assumptions & limitations

Before we can expand on the break even formula, it is important to highlight the underlying assumptions and limitations of breakeven analysis. CVP analysis is simple to apply and provides powerful insights, but it relies on some major simplifications.

1. Costs and revenues behave linearly over the relevant range of activity and period. The results can become unreliable beyond this relevant range.
• ‘Relevant range of activity’ means that the business has experience in the field and can therefore make accurate estimates.
• ‘Relevant range of period’: The classification of fixed and variable expenses is constant over the relevant period. Over the long-term all costs are variable.
2. Costs are split between variable expenses and fixed expenses. In practice, some costs might be semi-fixed, such as a lease agreement that has a fixed component and a variable component that is dependent on the sales amount. Fixed expenses are also variable in the long run.
3. Volume is the only variable that has an impact on revenues and expenses. All other variables, such as selling price per unit, unit variable costs, sales mix, and fixed costs are constant. In CVP analysis economies of scale, volume discounts, productivity and efficiency gains, etc. are not considered.
• Total variable costs change with the level of output, but unit variable cost remains constant.
• Fixed costs are constant, but unit fixed costs decrease (increase) when output increases (decreases).
4. Inventory levels are constant. The number of units produced is equal to the number of units sold.

#### Target Operating Income and Net Income

If Smartphone Cover Inc. wants to achieve a specific target profit (pre-tax), for example, \$150,000, they can simply include a target operating income in the numerator. In other words, you need to treat the target operating income as an additional fixed cost.

To realize a target operating income of \$150,000, the company must sell 80,000 units or \$1,000,000 (\$12.5 * 80,000 units). 80,000 units * \$5.0 unit contribution margin is equal to \$400,000. If you subtract \$250,000 fixed costs from this amount, you will also arrive at \$150,000 operating profit.

In our example, the target operating income is a pretax amount. The target income might also be defined as an after-tax amount. Beware that you need to convert target net income (an after-tax amount) to target net operating income (pretax amount). Target net income can easily be converted into the target operating income by dividing the target net income by the factor (1 – tax rate). For example, let us assume that Smartphone Cover Inc’s tax rate is 35%. Target net income of \$97,500 (97,500 / 0.65) is equal to target operating income of \$150,000.

Net Income / (1 – 0,35) = Target operating income

#### Safety Margin

The safety margin is the excess of budgeted sales over breakeven sales. It exhibits how much sales can decrease before the company reaches its breakeven point or worse breaches it! Thus, the safety margin provides a cushion against operating losses. The safety margin is calculated as follows:

Safety Margin (in units) = Budgeted Sales – Breakeven Sales

Safety Margin (in \$) = (Budgeted Sales – Breakeven Sales) * Unit Selling Price (USP)

Safety Margin (in %) = Safety Margin / Budgeted sales

For example, Smartphone Cover Inc. might have budgeted sales of 55,000 units while their breakeven sales were 50,000 units. Total revenues at the budgeted sales level amount to \$687,500. The margin of safety is 5,000 units (55,000 – 50,000). The safety margin is 9.1% (5,000 units divided by 55,000 units) and the safety margin in \$ is 5,000 units * 12.50 \$ per unit or \$62,500. You can also calculate the safety margin in % by dividing \$62,500 / \$687,500.

#### Sensitivity analysis

Sensitivity analysis allows you to quickly re-run your calculations under various circumstances. This method allows you to verify the impact of changes in input variables (changes in sales price per unit, unit variable costs, fixed costs, or sales mix) on the dependent variable. The dependent variable is usually the breakeven point, target profit, or net profit.

If you do not know how to create a data table in Excel, please check the following link. This guide will help you troubleshoot setting up your data tables.

In a single product company, the breakeven point in units is very dependent on a correct estimation of your selling price per unit and the unit variable cost. However, your actual unit selling price may deviate from the anticipated unit selling price, for example, because of volume discounts or competitive pressure. The actual unit variable cost might also differ from the expected unit variable cost because of changes in the commodity prices, freight rates, FX rates, etc. To model this uncertainty, we can make use of a data table to obtain an indication of the number of units that need to be sold in case these two variables change.

As can be seen in the table, the breakeven point will decrease to 35,714 units from 50,000 units in case the Unit Contribution Margin (UCM) would increase to \$13.5 from \$12.5 and the unit variable cost would decrease to \$6.5 from \$7.5. If the unit selling price would decrease to \$12 from \$12.5 and the unit variable cost would increase to \$8.0 from \$7.5, the breakeven point would increase by 12,500 units to 62,500 units from 50,000 units.

Another input variable that could have been sensitized in our breakeven analysis is the fixed expenses. However, this seems to be a poor choice considering that fixed expenses are fairly predictable, and they are fixed in the short term.

We also sensitized net income. The two input variables we sensitized are unit contribution margin and budgeted sales. Through the unit contribution margin, we can capture both changes in the unit selling price and the unit variable costs. Units sold are the major driver of net income in CVP calculations. As can be expected, Smartphone Cover Inc.’s net income would deteriorate in case of declining unit contribution margins or a decline in units sold.

#### Multi-product companies

In essence, the calculation of the multi-product breakeven point in units and in \$ is calculated in the same way as for a single product company. Instead of dividing total fixed costs by the unit contribution margin, respectively the contribution margin ratio, the weighted-average unit contribution margin, respectively weighted-average contribution margin ratio, is used.

#### Multi-product breakeven point in units

The breakeven point is calculated by dividing the total fixed costs by the weighted-average unit contribution margin (UCM). The weighted-average UCM can be found by calculating the weighted-average selling price and subtracting the weighted-average variable costs.

Total fixed costs / Weighted-average UCM

Assume Smartphone Cover inc. sells 2 products: Product X and Product Y. The following assumptions are made:

• Step 1: Get the product unit contribution margin by subtracting the variable costs per unit from the selling price. The unit contribution margin for product X is \$5 (\$12.5  – \$7.5) and the contribution margin for product Y is \$10 (\$20 – \$10).
• Step 2: Determine the sales mix. Smartphone Cover Inc. anticipates selling in total 45,715 units (11,429 product X and 34,286 product Y). The sales mix consists of 25% of product X and 75% of product Y.
• Step 3: Obtain the weighted-average unit contribution margin (UCM) by multiplying the unit contribution margins of product X and product Y by their respective weights. The weighted-average unit contribution margin is \$8.75 ((25% * \$5) + (75% * \$10)).
• Step 4: Lastly, calculate the multi-product breakeven point. You need to divide the total fixed expenses by the weighted-average UCM. The multi-product breakeven point is 28,572 total units (\$250,000 divided by \$8.75). Product X accounts for 7,143 units (25% of 28,572) and product Y accounts for 21,428 units (75% of 41,667).

#### Multi-product breakeven point in \$

To calculate the weighted-average CMR, the weighted-average UCM is divided by the weighted-average selling price. Next, we divide the total fixed costs by the weighted-average CMR to arrive at the multi-product breakeven point in USD.

Total fixed costs / Weighted-average CMR

• Step 1: Obtain the weighted-average unit contribution margin. The weighted-average contribution margin is \$8.75 as per our calculation above (see steps 1-3).
• Step 2: Get the weighted-average unit selling price by multiplying the selling price per unit of product X and Y by their respective weights. The result is \$18.13 ((\$12.5 * 0.25) + (\$20 * 0.75)).
• Step 3: Determine the weighted-average contribution margin ratio (CMR). The weighted-average contribution margin ratio can be obtained by dividing weighted-average UCM by the weighted-average unit selling price. The weighted-average CMR is 48.3% (\$8.75 divided by \$18.12).
• Step 4: Divide the fixed costs by the weighted-average CMR to obtain the multi-product breakeven point in dollars. The breakeven point in dollars is \$517,857.6 (\$250,000 divided by 0.483).

#### Target Income and Safety Margin in a multiproduct company

Target Income and Safety Margin in a multi-product company are calculated in the same way as a single product company. You only need to pay attention that you use the weighted-average UCM and CMR in the target income calculation. The safety margin in \$ makes use of the weighted-average unit selling price instead of the unit selling price.

In our example, the target income was set at \$150,000. If 45,714 units were sold, the company would realize an operating profit of \$150,000 on the condition that the sales mix remains constant. Changes in the sales mix would affect the weighted-average UCM and CMR.

#### Sensitivity analysis

Our model was sensitized to see the impact of changes in input variables on the breakeven point in units and net income. Recall that the breakeven point in units is found by dividing the fixed costs by the weighted-average UCM. The components of the weighted-average UCM are the weighted-average selling price and the weighted-average unit variable cost.

A key assumption of CVP analysis is that the sales mix remains constant. The variation in the USP and UVC are due to other reasons than changes in the sales mix. In our example, product X and product Y continue to account for 25% of the unit sales, respectively. 75%. The below table summarizes the various breakeven points for different combinations of weighted-average USP’s and weighted-average UVC’s.

Lastly, the weighted-average unit contribution margin and budgeted sales were sensitized to see the impact on net income. Through the unit contribution margin, we can capture both changes in the weighted-average unit selling price and the weighted-average unit variable costs. The other major driver of net income is the units sold. This resulted in the below matrix of net incomes.

Smartphone Cover Inc. would most likely be comfortable with this outcome because it shows that even in case of a substantial decline in units sold and a decline in the weighted-average contribution margin, the company would remain profitable. This is attributable to the fact that the weighted-average UCM was quite high at \$8.75 because of the chief contribution of product Y.

## Conclusion:

We have now reached the end of this guide on breakeven analysis. You should now be able to perform your own breakeven analysis for a single or multiproduct company. This allows you to answer a vital question: how much must be sold to be profitable? Before you can apply breakeven analysis, you need to (1) correctly distinguish between fixed costs and variable costs, and (2) determine the sales price of your good or services. These inputs determine the accuracy of the analysis. Last, you have learned how to use data tables to model uncertainty in your breakeven analysis.