Accounting Break-even point. The basic model.

Accounting Break-even point. The basic model.

a) Definition. The balance or equilibrium (Latin aequilibrĭum, is composed of "aequus", which means "equal", and "libra", "balance") is the state where two opposing forces compensate and cancel each other out. Balance is the state of a body when the sum of all the forces and moments that act in it are counteracted. Balance is synonymous with counterweight, compensation or stability.

By extension, Balance is the harmony between diverse things or between the parts of a whole. Attitudes such as equanimity, moderation, sanity, good sense and composure, for example, are considered as a sign of balance, as well as we relate the balance with the mental health of a person.

In finance, the Balance or break-even Point is a concept that refers to the level of sales where fixed and variable costs are covered. This means that the company, at its point of equilibrium, has a benefit that is equal to zero (it does not earn or lose money) and covers all its costs. By increasing your sales, you will be able to place yourself above the break-even point and get a positive benefit. On the other hand, a drop in sales from the break-even point will generate losses. The equilibrium or break-even point indicates the point of activity (sales volume) where the total revenues are equal to the total costs, that is, where there is no profit or loss.

In economics, the equilibrium point shows the equality between the demand and supply of a good or service; where the buyers or consumers find in the market the quantity they need and that is what the producers bring to the market, with a price common to both.

b) Calculation of the equilibrium point. For this we build a simple, static model, with the help of algebra. The steps to follow are:

- Determine the fixed and variable costs. Accounting and engineering records (production area) allow you to determine costs, without any difficulty or ambiguity.

- Variable costs are directly related to the volume of production (higher production, greater amount of variable costs)

- Fixed costs are independent on the level of production; they are constant within the relevant range of production.

The equilibrium point model is obtained from equality:

Total income = Total costs.

In the relevant section of production, short term, the price is constant for any quantity sold in said section, therefore:

Total income = IT = Price x Quantity = P x Q      (1)

In the costs, previously defined the Unitary variable cost and the fixed costs, the Total Cost is expressed as:

Total cost = Total variable cost + Fixed costs = CVT + CFT

In the relevant section, it is assumed that the unit variable cost is constant, therefore the total variable cost is logical:

CVT = Unit variable cost x Quantity = CVu x Q

Then: CT = Cvu x Q + CFT    (2)

In equilibrium we have:

IT = CT, that is: f (P, Q) = g (Cvu, Q, CFT)

Total income = Total costs è Utility or benefit = 0

P x Q = Cvu x Q + CFT

Clearing Q, we get the equilibrium amount

Q * = CFT / (P - Cvu) = CFT / Contribution margin (3)

c) Example: Calculate the equilibrium point given the following data: Cvu = 12 um, P = 24 um, CFT = 3,600 um. Show the graph

Q * = 3,600 / (24-12) = 3,600 / 12 = 300 units

That is all? Making a decision based on the break-even point does not seem complicated. It is necessary to look beyond the formula.

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