Break Even Analysis
Accountants use various approaches for expressing the relationship of costs, sales(volume), and
income from operations (operating profit), The mathematical approach is one method that is
used often in practice.
The mathematical approach to cost-volume-profit analysis uses equations (1) to determine the
units of sales necessary to achieve the break-even point in operations or (2) to determine the
units of sales necessary to achieve a target or desired profit.
The break-even point is the level of operations at which a business’s revenues and expired costs
are exactly equal. At break-even, a business will have neither an income nor loss from
operations. The break-even point is useful in business planning, especially when expanding or
decreasing operations.
To illustrate the computation of the break-even point, assume that the fixed costs for Barker
Corporation are estimated to be $90,000. The unit selling price, unit variable cost, and unit
contribution margin for Barker Corporation is as follows:
Unit Selling Price
UnitVariable Cost
Contribution Margin
$25
15
$10
We can get the break-even point by formula:
Unit Selling Price*Number of Units Sold = Unit Variable Cost*Number of Units Sold + Fixed Cost + 0
25 *x
=
15 * x
+ 90,000 + 0
10x = 90,000
X = 90,000/10 = 9000 units
We can also solve for the break-even point with the following equation:
Break-even sales (units) =
fixed cost
------------------------------------Contribution margin per unit
=
I write this as B/E (units) = FC/CM per unit
90,000/10 = 9000 units
Effect of Changes in Fixed Costs
There are many reasons why fixed costs may change, such as changes in property tax rates or
factory supervisor salaries. Increases in fixed costs will raise the break-even point while
decreases in fixed costs should lower the break-even point.
Consider the following: The Bishop Company is evaluating a proposal to budget an additional
$100,000 for advertising. Fixed costs before the additional advertising are estimated at
$600,000, and the unit contribution margin is $20.
Before any additional expense is incurred, the break-even point is $600,000/$20 = 30,000 units
[ that’s fixed cost/unit contribution margin]
If the additional advertising cost is incurred, the fixed cost will now become $700,000 ; all other
relationships and figures will remain the same, and the break-even point will now become
$700,000/20 = 35,000 units.
Effect of Change in Unit Variable Costs
Unit variable costs are not affected by changes in volume of activity, but they may be affected by
other factors such as changes in the price of direct materials and/or changes in the wages of
factory workers providing direct labour. Increases in unit variable costs will raise the break-even
point whereas decreases in unit variable costs will lower the break-even point.
Consider the following: Park company is evaluating a proposal to pay an additional 2%
commission on sales to salespeople as an incentive to increase sales. Fixed costs are estimated at
$840,000, and the uniyt selling price, variable cost and unit contribution margin before the
additional 2% commission are as follows.
Unit selling price
Unit variable cost
Unit Contribution margin
$250
145
$105
The break even point in units is currently FC/unit CM or $840,000/$105 = 8000 units.
The addition of a 2% commission will add 2% of $250 = $5 per unit variable cost.
With this revision, SP= $250, variable cost (VC) = $145 + $5 = $150, and the contribution
margin drops to $100 per unit.
This increase in VC will cause the break-even point in units to increase.
FC/unitCM = $840,000/$100 = 8400 units are required to break even.
Effect of Changes in the Unit Selling Price
Increases in the unit selling price will lower the break-even point, while decreases in the unit
selling price will raise the break-even point.
Consider the following: Graham Company is evaluating a proposal to increase the unit selling
price of its product from $50 to $60. The following data have been gathered.
Current
$50
$30
$20
$600,000
Unit Selling Price
Unit Variable Cost
Unit Contribution Margin
Total Fixed costs
Proposed
$60
$30
$30
$600,000
The break-even point based on the current selling price is as follows:
B/E(units) = FC/unit CM = $600,000/$20 = 30,000 units
The break-even point based on the proposed selling price is as follows:
B/E(units) = FC/unit CM = $600,000/$30 = 20,000 units
Target Profit
At the break-even point, sales and costs are exactly equal. That, however, is not the goal of
businesses. Managers are looking to maximize profits. It is possible to modify the break-even
equation to target a desired profit, and therefore estimate the required sales volume to meet that
profit target.
Target Sales = Fixed Cost + Target Profit
CM per unit
Consider the following: Fixed costs are estimated at $200,000, and the desired profit is
$100,000. The unit selling price, unit variable cost, and unti contribution margin are as follows.
Unit selling price
Unit variable cost
Unit contribution margin
$75
45
$30
The sales volume necessary to earn a profit of $100,000 is $200,000 +$100,000/$30
$300,000/$30 = 10,000 units.
FYI
In class, we not only spoke about determining the break-even point in units, but also determining
the break-even point in sales dollars.
One way to approach this problem is to solve for the break-even point in units, take that value
and multiply by the selling price per unit.
Look at the following figures:
Selling price per unit
Variable cost per unit
Unit contribution margin
$100
$ 60
$ 40
Fixed costs = $240,000
Break even point in units = FC/CM per unit = $240,000/$40 = 60,000 units.
The break-even point in dollars = 60,000 units * $100/unit = $6,000,000
The second approach to this problem is to determine the per cent ratio of contribution margin to
sales . In this scenario, we solve for break-even sales as dollars($) by the following formula:
B/E($) =
Fixed Cost
Contribution Margin (%)
Contribution margin is 40% of the selling price (40/100)
B/E($) = $240,000/.4 = $6,000,000
Contribution Margin Format Income Statement vs Traditional Income Statement Format
Traditional Format
Sales
Less: Cost of Goods
Gross Income(Profit)
Less: Operating Expenses
(selling & administrative)
Net Income
Contribution Margin Format
$500,000
300,000
200,000
100,000
Sales
Less: Variable Costs
Contribution Margin
Less: Fixed Costs
100,000 Net Income
$500,000
170,000
330,000
230,000
$100,000
.
It was determined that the Cost of goods sold is 40% Variable, 60% fixed, and the selling and
administrative costs are 50% variable and 50% fixed.
For purposes of the contribution margin format, we need to split the cost of goods and operating
expenses into their variable and fixed components.
Cost of goods: Variable = 40% *300,000 = $120,000. Fixed = 60% *$300,000 = $180,000
Operating Expenses are 50% variable or $50,000, and 50% fixed = $50,000.
Total Variable expenses = $120,000 + $50,000 = $170,000
Total Fixed Expenses = $180,000 + $50,000 = $230,000