Managerial Accounting: Break Even Point Analysis

Break Even Point:

The point where Total Revenue becomes equal to Total Cost. So at that point there is neither profit nor loss.

Methods of BEP (Break Even Point) Analysis:

(i) Graphical Method.
(ii) Equation Method.
(iii) Formula Method.

The equation and formula method are more accurate. Using equation and formula methods we can get a good graphical representation. Hand plotting graphical method won’t be that accurate.

Below are equation and formula method calculation formula. We can use any one of these methods to get same result.

Point Equation Method Formula Method
BEPQuantity \text{Total Revenue - Total Cost} \frac{\text{Fixed Cost}}{\text{Contribution Margin Ratio}}
BEPsales \text{(CM Ratio x Sales) - Fixed Cost} \frac{\text{Fixed Cost}}{\text{Contribution Margin Ratio}}
Contribution Margin (CM) \text{CM = Sales - Variable Cost} \text{CM = Sales - Variable Cost}
CM Ratio \frac{\text{CM}}{\text{Sales}} \times 100 \frac{\text{CM}}{\text{Sales}} \times 100

 

Sample:

Question:

A coffee shop owner sales per cup of coffee with a selling price of $10 and whose variable expense is $5. The owner’s monthly fixed cost is $500. Find the Break even point.

Solution :

It can be solved in many ways. We can directly plot the graph or use equation method to get the equation and then plot the graph. BEP can be found using formulas above.

To draw the graph we know that,
\text{fixed cost + variable cost = Total cost}

Also at BEP,
\text{Total Revenue - Total cost = 0}

And,
Total \ Revenue - Total \ Cost =  \begin{cases} Profit & \quad \text{if} > 0 \\ Loss & \quad \text{if} < 0 \end{cases}

Let, x be the number of coffee’s sold. Then,

Revenue for 1 cup $10.
Revenue for x cup $10x.
variable cost for 1 cup $5.
variable cost for x cup $5x.
 Total Revenue - Total Cost = 0
 => Total Revenue - (Fixed Cost + variable cost) = 0
 => 10x - (500 + 5x) = 0
 => 5x = 500
 => x = 100  units
To draw the graph we know, fixed cost is stationary so,

fixed cost,

f(x) = 500

total cost,

g(x) = fixed cost + variable cost for x cups
     = f(x) + 5x
     = 500 + 5x

total revenue,

h(x) = selling cost for x cups
     = 10x

Graphing these function, The point where total revenue and total cost touch is the Break even point.
Break even point analysis
Break even point analysis
So after selling more than 100 cups at $10 per cup the owner can expect profit.

 

Question:

ABC company distributes a single product with selling price $16 and whose variable expense is per unit $11. The company’s fixed expense is $16000 monthly.
(i) Prepare profit graph for company up to sales level of $ 4000 units.
(ii) Estimate company’s BEP in unit sales using the profit graph.

Solution:

In 4000 units,

Total revenue = 16 * 4000 
              = 64000
Total Cost = fixed cost + variable cost
           = 16000 + 11 * 4000
           = 60000
Profit = T.R - T.C
       = 64000 - 60000
       = 4000

In 4000 units BEP,

BEP = \frac{F.C}{Sales - V.C} = \frac{16000}{16 - 11} = 3200 \ units

BEP \ sales = 3200 \times 16 = 51200


Now from the information above the graph will be,
BEP analysis
BEP analysis

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