Break Even Point Analysis-Definition, Explanation Formula and Calculation:
Learning Objectives:
- Define and explain break even point.
- How is it calculated?
- What are its advantages, assumptions, and limitations?
Definition of Break Even point:
Break even pointis the level of sales at which profit is zero. According to this definition, atbreak even pointsales are equal tofixed costplusvariable cost. This concept is further explained by the the followingequation:
[Break even sales =fixed cost+ variable cost]
The break even point can be calculated using either theequationmethodorcontribution marginmethod. These two methods are equivalent.
Equation Method:
Theequationmethodcenters on thecontributionapproach to theincome statement. The format of this statement can be expressed inequationform as follows:
Profit = (Sales − Variable expenses) − Fixed expenses
Rearranging thisequationslightly yields the followingequation, which is widely used in cost volume profit (CVP) analysis:
Sales = Variable expenses + Fixed expenses + Profit
According to the definition of break even point, break even point is the level of sales where profits are zero. Therefore the break even point can be computed by finding that point where sales just equal the total of the variable expenses plus fixed expenses and profit is zero.
Example:
Forexamplewe can use the following data tocalculatebreak even point.
|
Calculation:
Sales = Variable expenses + Fixed expenses + Profit
$250Q*= $150Q*+ $35,000 + $0**
$100Q = $35000
Q = $35,000 /$100
Q = 350 Units
Q* = Number (Quantity) of units sold.
**The break even point can be computed by finding that point where profit is zero |
The break even point in sales dollars can be computed by multiplying the break even level of unit sales by the selling price per unit.
350 Units × $250 Per unit = $87,500
Contribution Margin Method:
Thecontribution marginmethod is actually just a short cut conversion of theequationmethod already described. The approach centers on the idea discussed earlier that each unit sold provides a certain amount ofcontribution marginthat goes toward coveringfixed cost. To find out how many units must be sold to break even, divide the totalfixed costby the unitcontribution margin.
Break even point in units = Fixed expenses / Unitcontributionmargin
$35,000 / $100* per unit
350 Units
*S250 (Sales) − $150 (Variable exp.)
|
A variation of this method uses theContribution Margin ratio(CM ratio) instead of theunitcontributionmargin. The result is the break even in total sales dollars rather than in total units sold.
Break even point in total sales dollars = Fixed expenses / CM ratio
$35,000 / 0.40
= $87,500
|
This approach is particularly suitable in situations where a company has multiple products lines and wishes to compute a single break even point for the company as a whole.
The following formula is also used tocalculatebreak even point
Break Even Sales in Dollars = [Fixed Cost/ 1 – (Variable Cost / Sales)]
This formula can produce the same answer:
Break Even Point = [$35,000 / 1 – (150 / 250)]
= $35,000 / 1 – 0.6
= $35,000 / 0.4
= $87,500
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Benefits / Advantages of Break Even Analysis:
The mainadvantages of break even point analysisis that it explains the relationship between cost, production, volume and returns. It can be extended to show how changes infixed cost, variable cost,commodity prices, revenues will effect profit levels and break even points. Break even analysis is most useful when used with partial budgeting, capital budgeting techniques. The majorbenefitsto use break even analysis is that it indicates the lowest amount of business activity necessary to prevent losses.
Assumption of Break Even Point:
The Break-even Analysisdependson three key assumptions:
- Average per-unit sales price (per-unit revenue):This is the price that you receive per unit of sales. Take into account sales discounts and special offers. Get this number from your Sales Forecast. For non-unit based businesses, make the per-unit revenue $1 and enter your costs as a percent of a dollar. The most common questions about this input relate to averaging many different products into a single estimate. The analysis requires a single number, and if you build your Sales Forecast first, then you will have this number. You are not alone in this, the vast majority of businesses sell more than one item, and have to average for their Break-even Analysis.
- Average per-unit cost:This is the incremental cost, or variable cost, of each unit of sales. If you buy goods for resale, this is what you paid, on average, for the goods you sell. If you sell a service, this is what it costs you, per dollar of revenue or unit of service delivered, to deliver that service. If you are using a Units-Based Sales Forecast table (for manufacturing and mixed business types), you can project unit costs from the Sales Forecast table. If you are using the basic Sales Forecast table for retail, service and distribution businesses, use a percentage estimate, e.g., a retail store running a 50% margin would have a per-unit cost of .5, and a per-unit revenue of 1.
- Monthly fixed costs:Technically, a break-even analysis defines fixed costs as costs that would continue even if you went broke. Instead, we recommend that you use your regular running fixed costs, including payroll and normal expenses (total monthly Operating Expenses). This will give you a better insight on financial realities. If averaging and estimating is difficult, use your Profit and Loss table tocalculatea workingfixed costestimate—it will be a rough estimate, but it will provide a useful input for a conservative Break-even Analysis.
Limitations of Break Even Analysis:
It is best suited to the analysis of one product at a time. It may be difficult to classify a cost as all variable or all fixed; and there may be a tendency to continue to use a break even analysis after the cost and income functions have changed.
Review Problem:
Voltar Company manufactures and sells a telephone answering machine. The company'scontributionformat income statement for the most recent year is given below:
| Total | Per unit | Percent of sales | |
| Sales | $1,200,000 | $60 | 100% |
| Less variable expenses | 900,000 | 45 | ?% |
| -------- | -------- | -------- | |
| Contributionmargin | 300,000 | 15 | ?% |
| Less fixed expenses | 240,000 | ====== | ====== |
| -------- | |||
| Net operating income | $60,000 | ||
| ====== |
Calculatebreak even point both in units and sales dollars. Use theequationmethod.
Solution:
Sales = Variable expenses + Fixed expenses +Profit
$60Q = $45Q + $240,000 + $0
$15Q = $240,000
Q = $240,000 / 15 per unit
Q = 16,000 units; or at $60 per unit, $960,000
Alternative solution:
X = 0.75X + 240,000 + $0
0.25X = $240,000
X = $240,000 / 0.25
X = $960,000; or at $60 per unit, 16,000 units
Formula for cost volume relationship (CVP)
1 Marginal
Cost = Prime cost + variable cost
2
Contribution
Margin = Sales – Variable cost
Contribution Margin = Unit Sales x Unit contribution
Contribution Margin = Fixed Cost + Profit
or – Loss
Contribution per unit= Selling Price Per
Unit – Variable Cost Per Unit
Contribution Margin Ratio= Profit volume
Ratio (P/v ratio):
Contribution Margin Ratio = Contribution
Margin x 100
Sales
Contribution Margin Ratio = Sales-Variable
Cost x 100
Sales
P/V Ratio = Contribution per unit
x 100
Selling Price per unit
3 Margin
of Safety = Total Sales – Break even Sales
4 Margin
of Safety = Profit
C/M
Ratio
5 Sales =
Contribution Variable Cost
=
Variable Cost + Fixed Cost + Profit
6 Variable
cost = Total cost- fixed cost
= Sales – contribution Margin
= Sales – (Fixed Cost + Profit)
7 Fixed
Cost = Total Cost – Variable Cost
= Sales – Variable Cost – Profit
= Contribution –profit or + loss
8 Profit = Sales
– Variable cost- fixed Cost
= Contribution – Fixed Cost
= (Sales x P/V Ratio) – Fixed Cost
9 Profit
Ratio = Profit
x 100
Sales
Break
Even Points in Unit:
1. Fixed Cost .
Contribution Margin Per Unit
2. BEP (SELLS) .
Unit
Selling Price
1 1.
BEP
RATIO: BEP x
1oo
Sales
1 2.
Required
sales for a target or desired net profit before tax:
i.
Required
sales in units = Fixed Cost + desired
profit
Contribution Per unit
ii.
Required
sales in Tk. = Fixed Cost +
desired profit
1 – Variable Cost
Sales
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