Here are the steps an entrepreneur must take to compute the break-even point using an example of a typical small business, the Magic Shop:
Determine the expenses the business can expect to incur. Using the budgeting process described earlier, develop estimates of sales revenue, cost of goods sold and expenses for the upcoming accounting period. The Magic Shop expects net sale of $950,000 in the upcoming year, with a cost of goods sold of $646,000 and total expenses of $236,500.
Categorize the expenses estimated in step 1 into fixed expenses and variable expenses. Separate semi variable expenses into their component parts. From the budget, the owner anticipates variable expenses (including the cost of goods sold0 of $705,125 and fixed expenses of $177,375.
Calculate the ratio of variable expenses to net sales. For the Magic Shop this percentage is $705,125/$950,000 = 74 percent. So the Magic Shop uses $0.74 out of every sales dollar to cover variable expenses, leaving $0.26 as a contribution margin to cover fixed costs and make a profit.
Compute the break-even point by inserting this information into the following formula:
Break-even sales = Total fixed cost Contribution margin expressed as a percentage of sales Break-even sales = $177,375 0.26 = $682,212 The same break-even point will result from solving the following equation algebraically. Break-even sales = Fixed expense + Variable expenses expressed as a percentage of sales S = $177,375 + 0.74S 100S = 17,737,500 + 74S 26S = 17.737,500 S = $682,212
Thus, the Magic shop will break even with sales of $682,212. At this point sales revenue generated will just cover total fixed and variable expense. The Magic Shop will earn no point and will incur no loss. To verify this, make the following calculations:
Sales at break-even point $682,212
Variable expenses (74% of sales) -504,837
Contribution margin 177,375
Fixed expenses -177,375
Net profit (or net loss) $ 0
Adjustable Profit. But what if the Magic Shop's owner wants to do better than just break even? The analysis can be adjusted to consider such a possibility. Suppose the owner expects a reasonable profit (before taxed) of $80,000. What level of sales must the Magic Shop achieve to generate this? The owner can calculate this by treating the desired profit as if it were a fixed cost. In other words, he modifies the formula to include the desired net income.
Sales ($) = Total fixed expenses + Desired net income
Contribution margin expressed as a percentage of sales
= 177,375 + 80,000
0.26
Sales ($) = $989,904
To achieve a net profit of $80,000 (before taxes), the Magic Shop must generate net sales of $989,904.
Break-Even Point in Units. Some small businesses may prefer to express the break-even point in units produced or sold instead of in dollars. Manufacturers often find this approach particularly useful. The following formula computes the break-even point in units:
Break-even volume = Total fixed costs
Sales price per unit – Variable cost per unit
For example, suppose that Trilex Manufacturing Company estimates its fixed costs for producing its line of small appliances at $390,000. The variable costs (including materials, direct labor, and factor overhead) amount to $12.10 per unit, and the selling price per unit is $17.50. So Trilex computes it contribution margin this way:
Contribution margin = Price per unit – Variable cost per unit
= 17.50 – 12.10
= $5.40
So, Trilex's break-even volume is as follows:
Total fixed costs
Break-even volume (units) = Per unit contribution margin
390,000
= $5.40
= 72.222 units
To convert this number units to break-even sales dollars, Trilex simply multiplies it by the selling price per unit
Break-even sales = 72.222 units X $17.50
= $1,263,889
Trilex could compute the sales required to produce a desired profit by treating the profit as if it were a fixed cost:
Total fixed costs + Desired net income
Sales (units) = Per unit contribution margin
For example, if Trilex wanted to earn a $60,000 profit, its required sales would be
390,000 + 60,000
5.40 = 83,333 units
The following outlines the procedure for constructing a graph that visually portrays the firm's break-even
point (that point where revenues equal expenses):
1.On the horizontal axis, mark a scale measuring sales volume in dollars (of in units sold or some
other measure of volume). The break-even chart for the Magic Shop, shown in fig. 1.9 uses sales
volume in dollars because it applies to all types of businesses, departments and products.
2. On the vertical axis, mark a scale measuring income and expenses in dollars.
3. Draw a fixed expense line intersecting the vertical axis at the proper dollar level parallel to the
horizontal axis. The area between this line and the horizontal axis represents the firm's fixed expenses.
On the break-even chart for the Magic Shop shown in fig. 1.9, the fixed expense line is drawn
horizontally beginning at the fixed expenses remain constant at all levels of activity.
4. Draw a total expense line that slopes upward beginning at the point where the fixed cost line intersects
the vertical axis. The precise location of the total expense line is determined by plotting the total cost
incurred at a particular sales volume. The total cost for a given sales level is found by the following formula.
Total expenses = Fixed expenses + Variable expenses X Sales level
expressed as a percentage of sales
Arbitrarily choosing a sales level of $950,000, the Magic Shop's total costs would be as follows:
Total expenses = $177,375 + (0.74 X $950,000)
= $880,375
Thus, the Magic Shop's total cost is $880,375 at a net sales level of $950,000 (point B). The variable
cost line is drawn by connecting points A and B. The area between the total cost line and the horizontal
axis measures the total costs the Magic Shop incurs at various levels of sales. For example, if the Magic
Shop's sales are $850,000, its total costs will be $806,375.
Fig 1.9 Break-even Chart.The Magic Shop
5. Beginning at the graph's origin, draw a 45-degree revenue line showing where total sales volume
equals total income. For the Magic Shop, point C shows that sales = income = $950,000.
6. Locate the break-even point by finding the intersection of the total expense line and the revenue line.
If the Magic shop operates at a sales volume to the left of the break-even point, it will incur a loss
because the expense line is higher than the revenue line over this range. This is shown by the triangular
section labeled "Loss Area." On the other hand, if the firm operates at a sales volume to the right of
the break-even point, it will earn a profit because the revenue line lies above the expense line over
this range. This is shown by the triangular section labeled " Profit Area."
EMPLOYING BREAK-EVEN ANALYSIS. Break-even analysis is a useful planning tool for the potential small business owner, especially when approaching potential lenders and investors for funds. It provides an opportunity for integrated analysis of sales volume, expenses, income, and other relevant factors. Break-even analysis is a simple, preliminary screening device for the entrepreneur faced with the business start-up decision. It is easy to understand and use. With just a few calculations the small business owner can determine the effects of various financial strategies on the business operation. For instance, before Donald Trump opened the billion-dollar Trump Taj Mahal, an opulent casino hotel complex in Atlantic City, a Cost-revenue analysis showed that the complex needed revenues of $400 million a year --$1.1 million a day—just to break-even!
Break-even analysis does have certain limitations. It is too simple to use as a final screening device because it ignores the importance of cash flows. Also, the accuracy of the analysis depends on the accuracy of the revenue and expense estimates. Finally, the assumptions pertaining to break-even analysis may not be realistic for some businesses. Break-even calculations assume the following: fixed expenses remain constant for all levels of sales volume; variable expenses change in direct proportion to changes in sales volume; and changes in sales volume have no effect on unit sales price. Relaxing these assumptions does not render this tool useless, however. For example, the owner could employ nonlinear break-even analysis using a graphical approach.