Break - even analysis is also referred to as 'Cost - volume - Profit Relationship'. Cost-Volume-Profit relationship is the relationship of the cost of production and the volume of production with the profit. Profit is the excess of sales revenue over the total costs.
Symbolically :
| S = C + P | P = Profit |
| or P = S - C | S = Sales revenue |
| C = Costs (total) |
If there is a loss (L),
L = C-S, implying that the sales revenue is not adequate to cover the costs.
The first step in the break - even analysis is the segregation of costs into 'fixed' and 'variable' costs.
By fixed costs, we mean that item of cost which remains fixed, irrespective of the change in the level of operation or the number of units produced. On the other hand, variable costs vary in direct proportion to the actual achievement or capacity utilisation or units produced.
In other words,a cost which changes with the activity level is a variable cost and a cost which remains fixed in amount and does not change with the activity level is a fixed cost. There is yet another classification of cost, known as semi-variable (or semi-fixed) costs. These are costs which remain fixed upto a certain level and variable thereafter (e.g. indirect labour and water charges). For the purpose of the determination of break - even point, these costs again should be bifurcated into variable and fixed components and added up under the two respective classifications, namely fixed and variable.
Certain items of Fixed and variable costs are listed below :
Fixed
1. Depreciation
2. Interest on Term Loans
3. Rent to the Premises
4. Salaries of supervising Staff
Variable
1. Raw materials
2. Wages to labour
3. Power and fuel
4. Commission to selling agents
Example
In a taxi business, the wages of the driver and vehicle tax will be fixed costs - irrespective of whether the taxi is running or not, running to the maximum, the driver has to be paid his contracted monthly wage. However, the diesel charges will be in direct proporttion to the kilometre run and it is a variable cost.
Cost behaviour
The behaviour of variable cost is that it will remain constant per unit and the total variable cost will change depending on the number of units produced. On the other hand, Fixed cost will remain constant in volume. Therefore, the cost per unit will change depending on the number of units, i.e. the more number of units produced, lesser will be the cost per unit.
The following example illustrates the behaviour of variable and fixed costs A taxi has run 3000 Kms in a month, yielding revenue at Rs. 3/- per Km. The costs incurred during the month are:
Rs. 2500/- p.m. for the owner of the vehicle as monthly hire.
Rs. 1500/- p.m. for the salary of driver
Diesel cost is to be computed at a litre (Cost Rs. 7/-) for every 10Km. run. Repairs and general maintenance can be taken at Re. 0.30 per Km.
By listing down the variable and fixed expenses, we can understand the behaviour of costs i.e. per unit cost of of diesel remaining the same, the total cost of diesel will vary depending on the number of kilometres run. On the contrary, fixed cost being a constant figure (monthly hire charges as well as salary of driver in this case), per unit cost will keep changing, depending on the kilometres covered.
Computation of contribution
After all the items of costs are quantified / ascertained and the classification according to variability is made, the second step is to determine the 'contribution' which is nothing but the difference between the sales revenue and variable cost. This difference is called contribution because it contributes towards fixed cost and profit. The point at which the contribution just covers the fixed cost, is the break-even point. Symbolically,i.e.,
C = s-v ,C = Contribution
C = F+P ,S = Sales Value
S = V + F + P V = Variable cost
F = Fixed cost
P = Profit
If there is a loss (L),
C + L = F L = F - C
Determination of Break-even point
Once the contribution is determined, we proceed to determine the break - even point. The break - even point can be arrived at as,so many units in terms of the sales turnover a percentage of capacity
Break-even point in units
The formula for arriving at break - even point in units is given below
Fixed Expenses / Contribution per unit
i.e. F/C = F/(S-V)
This will give us the number of units to be produced, so as to yield a total contribution, just to cover up the fixed costs. In other words, we try to find out when a single unit produces so much of contribution, how many units are to be produced to yield contribution equivalent to the fixed cost.
Example
Now let us work out the break - even point in units in the Taxi example' given under para (3.4.1) above.
Revenue per Km. = Rs. 3.00 Less Variable cost per unit (Km) Diesel 7/10
| Revenue per Km. Less Variable cost per unit (Km) Diesel 7/10 | Rs. 3.00 | |
| Repairs & general maintenance | Rs. 0.70 | |
| Rs. 0.30 | |
| Contribution per Km | Rs. 2.00 | |
| Break - even point | Fixed Expenses | |
| Contribution per unit | |
| Where, Fixed Expenses | Monthly Hire | Rs 2,500 |
| Driver Salary | Rs 1,500 |
| | Rs 4,000 |
Thus BEP = 4000/2 = 2000 Km run per month
The vehicle should run minimum of 2,000 Km, so as to break - even. When it runs over and above 2000 km, it will start yielding a profit.
Check : Revenue at 2000 Km. @ Rs. 3/- per Km Rs. 6000
| Less: | Variable Cost: | Rs. 1400 |
|---|
| Diesel | Rs.2,000 |
| Repairs & Maintenance | Rs. 600 |
| Contribution | Rs.4,000 |
| Fixed Cost (2500 + 1500) | Rs. 4,000 |
| Profit /Loss | Nil |
Break - even point in terms of sales turnover
The formula for arriving at Break-even point in terms of sales turnover is a under:
| Fixed Expenses(Rs.) |
| --------------------xTotal Sales Value |
| Total contribution |
Break - even point as a percentage of capacity
The formula for arriving at Break - even point as a percentage of capacity is as under:
| Fixed Expenses(Rs.) |
| --------------------xProjected capacity utilisation at optimum level |
| Total contribution |
Profit-volume Ratio
Break - even point can also be determined with the use of Profit - Volume Ratio (PA/ Ratio). It is the ratio of contribution to sales and is expressed as a percentage. The larger the ratio, the greater is the profitability.
Once the break - even sale value is ascertained , the profit at any sales level can be computed by multiplying the difference between the given sales level and break - even sales by the P/V Ratio.
In the Taxi example cited above, let us try this
| Total Revenue @ 3,000 Km. | = | Rs. 9000 |
| Total Revenue @ BEP (2,000 Km) | = | Rs. 6000 |
| Difference | = | Rs. 3000 |
| PA/Ratio: (Contribution/Sales)x100 | = | 2/3x100 = 66.67% |
| Profit at 3000 Kms. run | = | Rs. 3,000/100 x 66.67 = Rs.2,000 |
The PA7 Ratio will help us to determine the BEP, when only total figures are available (and no unit • wise data is given)
Let us take the following example :
| Total sales | = | Rs.100 Lacs |
| Variable cost | = | Rs. 50 Lacs |
| Fixed cost | = | Rs. 20 lacs |
| Profit | = | Rs. 30 iacs |
In this case, Break - even point can be ascertained as given below:
| Fixed cost | 20 | | |
| P/V ratio | 50 x 100 | = | Rs. 40 lacs |
| Break -even sales | | = | Rs. 40 lacs |
| Check: Sales (BEP) Less: | | = | Rs. 40 lacs |
| Variable cost | | = | Rs. 20 lacs |
| Contribution | | = | Rs. 20 lacs |
| Fixed Cost | | = | Rs. 20 lacs |
| Profit / Loss | | = | Nil |
Margin of safety:
The difference between actual sales and the break - even sales is called margin of safety. The greater the margin, greater is the profitability. Margin of safety Ratio is calculated as follows:
| Actual Sales - Break-even sales |
| --------------------x100 |
| Actual sales |
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