The break-even-point of any two variable situations is the point of the value at which they become equal as the result of a common variable.
Let, cost is common variable in two situations (1) and (2), and then cost equations will be
c1 = f1 (x) ...a function of (x)
Where, c1 = may be total cost, annual cost, cost per item or cost per day etc., for situation (1)
c2 = same as c1 but application to situation (2)
x = a variable effecting c1 and c2
To solve for the variable of the x, Let c1 = c2
i.e, f1(x) = f2(x) ...(3)
Equation (3) can be solved for obtaining the value of (x). The value x making the cost equal in both the situation is called Break-Even-Value. Below the value of x one situation will be economical while above it another situation will be economical.
This Break even point theory can be applied to solve several problems of an industry such as minimum quantity to be manufactured to avoid losses, which machine will be profitable for a particular production etc. The break-even-point theory is used as a tool by management to help in making decision.
Although the break-even point may be calculated mathematically, but it is usually presented graphically because it enables managers to see more clearly, the break-even-point and the possibilities for profits and losses. By using these charts one can predict probable at various levels of output.
A break-even-chart given below is used to determine break-even point and amount of loss or profit under varying condition of output and costs.
Sales and expenditure in rupees is represented on vertical axis, while output (either in quantity or in percentage capacity) is represented on horizontal axis, Line A represents the fixed expenses. Line B represents total expenses, while line C represents sales revenue and indicates income at various levels of output. The point, where lines B and c intersect each other, is break-even point. The space between lines B and C to the right of the break-even-point represents potential profits, whereas to the left of the break-even-point potential loss is represented. The amount of loss or profit can be measured on vertical scale.
This method can be applied to various problems. For example, a manager wants to replace an old lathe machine being used for manufacturing screws by an
automatic screw machine. Then he must first know whether it will be profitable or not for which he must adopt break-even-point theory and construct the
chart as explained in figure below.
The figure shows that for a production less than Q, it must not be changed whereas for production more than Q new machines will be economical.
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