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:

Target\ Profit\ = \frac{Fixed\ costs+desired\ profit}{Contribution\ margin\ per\ unit} = \frac{$18,000+$16,000}{$80} = 425units

We have already established that the $18,000 in fixed costs is covered at the 225 units mark, so an additional 200 units will cover the desired profit (200 units × $80 per unit contribution margin = $16,000). Alternatively, we can calculate this in terms of dollars by using the contribution margin ratio.

Target\ Profit\ = \frac{Fixed\ costs +desired\ profit}{Contribution\ margin\ ratio} = \frac{$18,000+$16,000}{0.80} = $42,500

As done previously, we can confirm this calculation using the contribution margin income statement:

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:

Pre-tax\ desired\ profit = \frac{After-tax\ profit}{(1 – tax\ rate)}


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:

$40,000=\frac{$24,000}{(1 – 0.40)}

The tax rate indicates the amount of tax expense that will result from any profits and 1 – tax rate indicates the amount remaining after taking out tax expense. The concept is similar to buying an item on sale. If an item costs $80 and is on sale for 40% off, then the amount being paid for the item is 60% of the sale price, or $48 ($80 × 60%). Another way to find this involves two steps. First find the discount ($80 × 40% = $32) and then subtract the discount from the sales price ($80 – $32 = $48).

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.

Target\ sales=\frac{(Fixed\ costs + Desired\ profit)}{Contribution\ margin\ per\ unit}=\frac{($18,000+$40,000)}{$80}=725units

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:

Target\ sales=\frac{(Fixed\ costs+Desired\ profit)}{Contribution\ margin\ per\ unit}=\frac{($18,000+$40,000)}{0.80}=$72,500

Once again, the contribution margin income statement proves the sales and profit relationships.

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.