Accounting Assignment Help With Non-linear Break Even Point

1.5 Non-linear Break Even Point

So far we have considered that a sale is a linear function of selling price. This means that although output increases, there is a change in selling price. Similarly, we have assumed that variable cost is a linear function of output. But this seldom happens. Often variable cost bears a non-linear relationship.

In a linear cost function, the cost equation is presented as follows:

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TC = VC + FC

TC = Total Cost

VC = Variable Cost

FC = Fixed Cost

V = bX, where b is per unit variable cost is and X is no. of units.

So, TC or C = a + bX, given a is FC.

In case per unit variable cost is $ 5 and fixed cost is $ 100000, the linear cost function becomes

TC = 100000 + 5X

Given selling price of $ 10 per unit, total revenue (TR) is

TR = 10X

So, the BEP equation stands as


i.e., 10X = 100000 + 5X

or, 5X = 100000

X = 100000/5

X = 20000

It gives BEP 20000 units.

However , if the variable cost becomes non linear in the form of second degree polynomial, the BEP equation may appear as follows.

V = bX + c (X)(X)

Accordingly, TR – TC stands as follows

sX - ( a + bX + c(X)(X) ) = 0

i.e, - a + (s-b)X - c(X)(X) = 0

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