The break-even point is the level of output or sales at which total revenue equals total costs. It represents the point at which a company neither makes a profit nor a loss. The document discusses break-even analysis, including its assumptions, limitations, and applications. It also provides an example problem calculating break-even points, contribution margins, and profits for a shoe company considering opening a new store.

1. Break-Even Point
The break-even point (BEP) is the point at which cost or
expenses and revenue are equal. Break-even point is a point at
which total costs just equal or break even with sales. This is the
activity point at which neither profit is made nor loss is
incurred. Break-even point of an enterprise/firm is a point
where total revenue/sale proceeds/sale or output equals total
cost.
Usefulness/Importance of Break-even analysis:
1. Fair knowledge about break even analysis can help
bankers/banking to examine loan proposal of a firm.
2. Break even analysis helps the bankers in assessing working
capital requirement of a unit.
3. This analysis helps in revealing clear projections of profit
planning of an enterprise at different production level vis-à-vis
the financial needs.
4. It also helps to find rate of return on investment of capital at
varying levels of production.
5. Break-even lies can be quite useful to management in
determining the need for action.
Assumptions of Break-even point:
1. Fixed costs will tend to remain constant. In other words,
there will not be any change in cost factor, such as, change in
property tax rate, insurance rate, salaries of staffs etc.
2. Price of variable cost factors, i.e., wage rates, price of
materials, supplies, services etc.
3. Product specifications and methods of manufacturing and
selling will not undergo a change;
4. Operating efficiency will not increase/decrease.
5. There will not be any change in pricing due to change in
volume, competition etc.
Limitations of Break-even analysis:
1. It may be difficult to segregate to segregate cost into fixed
and variable components;
2. It is not correct to assumption that total fixed cost into fixed
and variable components;
3. The assumption of constant unit variable cost is not valid;
4. Selling price may not remain unchanged over a period of
time;
5. Break-even analysis is a short run concept and has a limited
use in long range planning.
Application/Necessities of Break-even analysis:
1. It helps to provide a dynamic view of the relationships
between sales, costs and profits.
2. A better understanding of break even, for example, is
expressing break even sales as a percentage of actual sales can
give managers a chance to understand when to expect to break
even.
3. The break-even point is a special case of Target Income
Sales.
Contribution Margin(CM):
The unit Contribution Margin (CM) is the quantity of unit sales
price (P) minus the quantity of unit variable cost (V) is of
interest in its own right, it is the marginal profit per unit, or
alternatively the portion of each sale that contributes to Fixed
Costs. The break-even point can be more simply computed as
the point where Total Contribution=Total Fixed Cost.
Contribution Margin(CM) Ratio:
The margin contribution can also be expressed as a percentage.
The contribution margin ratio, which is sometimes called the
profit-volume ratio, indicates the percentage of each sales dollar
available to cover fixed costs and to provide operating revenue.
The contribution margin ratio is Contribution Margin (CM)
Ratio = Sales – Variable Costs/Sales.
Margin of Safety:
Margin of safety represents the strength of the business. It
enables a business to know what is the exact amount it has
gained or lost and whether they are over or below the break-even
point. Margin of safety=(Current output-BEP)
Implications of Margin of Safety:
A) In the point of application to investing:
1. Using margin of safety, one should buy a stock when it is
worth more than its price on the market.
2. The margin of safety protects the investor from both poor
decisions and downturns in the market.
3. A common interpretation of margin of safety is how far
below intrinsic value one is paying for a stock.
B) In the point of application to accounting:
In investing parlance, margin of safety is the difference
between the expected sales level and the break-even sales
level. It can be expressed in the equation from as follows:
Margin of Safety = Expected/Actual Sales Level –
Breakeven sales Level.
What is meant by sales mix? What assumptions are
casually made concerning sales mix in cost-volume
profits (CVP) analysis?
Sales mix is the components of Cost volume profit analysis.
CVP analysis expands the use of information provided by
breakeven analysis.
Assumptions:
1. The behavior of both costs and revenue is linear
throughout the relevant range of activity.
2. Costs can be classified accurately as either fixed or
variable.
3. Changes in activity are the only factors those affects costs.
4. All units produced are sold.
5. When a company sells more than one type of product, the
sales mix will remain constant.
Applications:
CVP simplifies the computation of breakeven in break-even
analysis and more generally allows simple computation of
target income sales. It simplifies analysis of short run trade-offs
in operation decisions.
Limitations:
CVP is a short run marginal analysis, it assumes that unit
variable costs and unit revenues are constant which is
appropriate for small deviation from current production and
sales and assumes a neat division between fixed costs and
variable costs through in the long run all costs are variable.
For longer term analysis that considers the entire life-cycle
of a product one therefore often prefers activity-based
costing.

2. Problem: The Paduka Shoe Company sells five different styles
of ladies chappals with identical costs and selling prices. The
company is trying to find out the profitability of opening
another store, which will have the following expenses and
revenues:-
Per Pair Taka
Selling price 30.00
Variable cost 19.50
Salesman’s commission 1.50
Total Variable cost 21.00
Annual fixed expenses are:
Rent 60,000
Salaries 2,00,000
Advertising 80,000
Other fixed expenses 20,000
Total 3,60,000
Required: (1) Calculate the annual Break-even point in units
and in value. Also determine the profit or loss if 35,000 pairs of
chappals are sold;
Required: (2) The sales commission are proposed to be
discounted, but instead a fixed amount of Tk.90,000 is to be
incurred in fixed salaries. A reduction in selling price of 5% is
also proposed. What will be the Break-even point in units?
Required: (3) It is proposed to pay the store manager 50 paisa
(Tk.0.50) per pair as further commission. The selling price is
also proposed to be increased by 5%. What would be the Break-even
point in units?
Required: (4) Refer to original data, if the store manager were
to be paid 30paisa (Tk 0.30) commission on each pair of
chappal sold in excess of Break-even point, What would be the
store’s net profit, if 50,000 pairs were sold?
Solution: Required 1:
BEP in units = Fixed Cost/Contribution margin per unit
= Fixed Cost/(Selling price per unit – Varibale cost per unit)
= 3,60,000/(30-21) = 40,000 units
The required BEP in units 40,000.
Contribution margin = (Contribution margin/sales)*100
= (30-21)/30*100 = 30%
So Break even Value = Fixed cost/CM ratio
= 3,60,000/0.3 = 12,00,000 Tk.
The Break Even Value is Tk.12,00,000.
Now, we know,
Sales = Fixed cost + variable cost + profit or (loss)
Profit or (loss) = Sales – (Fixed cost + variable cost)
Profit or (loss) = (30*35,000) – (3,60,000 + 21*35,000)
Profit or (loss) = 10,50,000 – (3,60,000 + 7,35,000)
Profit or (loss) = - 45,000.
So, the loss is Tk.45,000.
Solution: Required 2:
New variable cost = Tk.19.50
New fixed expanse = (3,60,000 + 90,000) = Tk.4,50,000.
New selling price = 30 – (30*0.05) = Tk.28.50
So, BEP in units
= Fixed Cost/(Selling price per unit – Variable cost per unit)
= 4,50,000/(28.50-19.50) = 50,000 units
The required BEP in units 50,000.
The required BEP in sales volume = Total unit*Sales price
= 50,000*28.50 = Tk.14,25,000.
Solution: Required 3:
New variable cost = Tk. (19.50+1.50+0.50) = Tk.21.50
New selling price = 30 + (30*0.05) = Tk.31.50
So, BEP in units
= Fixed Cost/(Selling price per unit – Variable cost per unit)
= 3,60,000/(31.50-21.50) = 36,000 units
New BEP in sale volume = 36,000*31.50 = Tk.11,34,000.
Solution: Required 4:
Particulars amount Total amount (Tk.)
Sales revenue
15,00,000
(50,000*30)
Less,
Variable commission Tk.0.30 is imposed in escess BEP
40,000 units * 21.00 Tk.8,40,000
Excess 10,000 units
Tk.2,13,000 (10,53,000)
* 21.30
Commission margin 4,47,000
Less, fixed cost (3,60,000)
Profit 87,000