Calculate a Break-Even Point in Units and Dollars
The calculation of the break-even point (BEP) does not account for the cost of capital, interest rates, or projections on a return on this investment. After you read, you should be able to point out how the BEP is used.
Calculate a Break-Even Point in Units and Dollars
Examples of the Effects of Variable and Fixed Costs in Determining the Break-Even Point
Companies typically do not want to simply break even, as they are in business to make a profit. Break-even analysis also can help companies determine the level of sales (in dollars or in units) that is needed to make a desired profit. The process for
factoring a desired level of profit into a break-even analysis is to add the desired level of profit to the fixed costs and then calculate a new break-even point. We know that Hicks Manufacturing breaks even at 225 Blue Jay birdbaths, but what if they
have a target profit for the month of July? They can simply add that target to their fixed costs. By calculating a target profit, they will produce and (hopefully) sell enough bird baths to cover both fixed costs and the target profit.
If Hicks wants to earn $16,000 in profit in the month of May, we can calculate their new break-even point as follows:
Note that the example calculations ignored income taxes, which implies we were finding target operating income. However, companies may want to determine what level of sales would generate a desired after-tax profit. To find the break-even point at a desired after-tax profit, we simply need to convert the desired after-tax profit to the desired pre-tax profit, also referred to as operating income, and then follow through as in the example. Suppose Hicks wants to earn $24,000 after-taxes, what level of sales (units and dollars) would be needed to meet that goal? First, the after-tax profit needs to be converted to a pre-tax desired profit:
If the tax rate for Hicks is 40%, then the $24,000 after-tax profit is equal to a pre-tax profit of $40,000:
Taxes and profit work in a similar fashion. If we know the profit before tax is $100,000 and the tax rate is 30%, then tax expenses are $100,000 × 30% = $30,000. This means the after-tax income is $100,000 – $30,000 = $70,000. However, in most break-even situations, as well as other decision-making areas, the desired after-tax profit is known, and the pre-tax profit must be determined by dividing the after-tax profit by 1 – tax rate.
Thus, to calculate break-even point at a particular after-tax income, the only additional step is to convert after-tax income to pre-tax income prior to utilizing the break-even formula. It is good to understand the impact of taxes on break-even analysis as companies will often want to plan based on the after-tax effects of a decision as the after-tax portion of income is the only part of income that will be available for future use.
If Hicks wants to earn $16,000 in profit in the month of May, we can calculate their new break-even point as follows:
| Sales (425 units at $100 per unit) | $42,500 |
| Variable Costs (425 units ata $20 per unit) | 8,500 |
| Contribution Margin | 34,000 |
| Fixed Costs | 18,000 |
| Operating Income (loss) | $16,000 |
Note that the example calculations ignored income taxes, which implies we were finding target operating income. However, companies may want to determine what level of sales would generate a desired after-tax profit. To find the break-even point at a desired after-tax profit, we simply need to convert the desired after-tax profit to the desired pre-tax profit, also referred to as operating income, and then follow through as in the example. Suppose Hicks wants to earn $24,000 after-taxes, what level of sales (units and dollars) would be needed to meet that goal? First, the after-tax profit needs to be converted to a pre-tax desired profit:
If the tax rate for Hicks is 40%, then the $24,000 after-tax profit is equal to a pre-tax profit of $40,000:
Taxes and profit work in a similar fashion. If we know the profit before tax is $100,000 and the tax rate is 30%, then tax expenses are $100,000 × 30% = $30,000. This means the after-tax income is $100,000 – $30,000 = $70,000. However, in most break-even situations, as well as other decision-making areas, the desired after-tax profit is known, and the pre-tax profit must be determined by dividing the after-tax profit by 1 – tax rate.
To demonstrate the combination of both a profit and the after-tax effects and subsequent calculations, let's return to the Hicks Manufacturing example. Let's assume that we want to calculate the target volume in units and revenue that Hicks must sell to generate an after-tax return of $24,000, assuming the same fixed costs of $18,000.
Since we earlier determined $24,000 after-tax equals $40,000 before-tax if the tax rate is 40%, we simply use the break-even at a desired profit formula to determine the target sales.
This calculation demonstrates that Hicks would need to sell 725 units at $100 a unit to generate $72,500 in sales to earn $24,000 in after-tax profits.
Alternatively, target sales in sales dollars could have been calculated using the contribution margin ratio:
| sales(725 units × $100 per unit) | $72,500 |
| Variable costs (725 units × $20 per unit) | (14,500) |
| Contribution Margin | $58,000 |
| Fixed Costs | (18,000) |
| Pre-tax profit | $40,000 |
| Income tax expense (40%) | (16,000) |
| After-tax profit | $24,000 |
Thus, to calculate break-even point at a particular after-tax income, the only additional step is to convert after-tax income to pre-tax income prior to utilizing the break-even formula. It is good to understand the impact of taxes on break-even analysis as companies will often want to plan based on the after-tax effects of a decision as the after-tax portion of income is the only part of income that will be available for future use.