# Break-even by AdminUpdated: August 21, 2020

## The break-even point is the minimum sales volume required to avoid making a loss Image credit

Whether in business or personally, it’s important to be aware of your break-even point, at least approximately, because it translates to the minimum you need to do in order to make a profit and increase your wealth. This could be the total amount of income you need each month to cover your costs/bills, but it is better broken down into the number of individual things you need to achieve.

The most critical thing to remember about the break-even point is that it represents the minimum that needs to be done, so it’s important to actually operate well above this level.

Break-even calculations can become very complicated depending on how much information needs to be included. At the most basic level there are two kinds:

1. Unitary - for evaluating the minimum value (selling price) of a unit (an individual task/sale).
2. Overall - for determining the minimum number of unitary operations (tasks) needed to cover all costs.

### Unitary

The unitary, or per-unit, break-even is when gross profit is zero:

Selling price = Cost to produce

The selling price is easy to determine. The cost to produce can be a little more complicated because of the difficulty in allocating semi-variable costs.

Things like raw materials are usually direct costs (unless they have limited life) and things like production workers are usually semi-variable, i.e. production can be increased only up to a certain point before it becomes necessary to employ another worker.

For example, if \$1 of materials is required to make one unit and a worker costs \$1,000 per week & produces 1000 units per week then the cost per unit is \$2 and the break-even selling price is \$2. If the market can only stand 500 units per week, the extra production capability of the worker is irrelevant and the labor cost per unit doubles (\$1,000 ÷ 500). Unitary break-even is now \$3.

### Overall (simple version)

Breaking even on unit costs will always result in a net loss because it doesn’t take fixed costs into account. Things like buildings and administrative staff need to be paid for regardless of sales volume.

The overall break-even is when net profit is zero:

Total sales = Total variable costs + Total fixed costs

Total sales is, of course, Total units × Unit price and Total variable costs = Total units × Unit cost so we get:

n(p - c) = F

where n is the number of units sold, p is the unit price, c is the unit cost and F is the total fixed costs.

i.e. the higher the gross profit per unit (p-c), the fewer units need to be sold to cover costs. Alternatively, the higher the number of units that can be sold, the cheaper the price they can be sold for.

In order to keep the calculation simple we usually roll the semi-variable costs into the fixed costs so that the unit cost, c, is only the cost of the raw materials.

Continuing the example from the previous section, if the unit cost is \$1 (raw materials only) and fixed costs are \$500 per week for the building plus \$1,000 per week for a worker, the per-week break-even is n(p-1)=1500. A selling price (p) of \$3 means n=750 which is within the capacity of the worker but might be a high sales target. Increasing the price to \$4 reduces n to 500.

### Overall (stepped costs)

Semi-variable or stepped costs make the calculation more complicated. A basic formula will look something like this:

F+c*n+C*ROUNDUP(n/R)

where C is the cost per step (e.g. an additional worker) and R is the maximum number of units the extra step brings.

Continuing the example, we can see the relationship between total costs and production volume: Dividing the total costs by the sales volume, we can see how the break-even unit selling price changes as sales volume increases: Note how, in this example, every time a worker is added the break-even unit selling price goes back up.

### Example

An artist buys \$100 worth of paint and ten canvases at \$20 each intending to sell complete artworks for \$40 but runs out of paint after completing only four. This reveals that the cost of paint for each painting is \$100 ÷ 4 = \$25 and the unitary break-even is therefore \$20 (canvas) + \$25 (paint) = \$45.

In order to avoid making a loss of \$5 on every sale, the artist must increase the selling price to at least \$45.

If the artist lives on \$500 per week and can command \$250 per painting. The contribution per painting is now \$250 - \$45 = \$195 and the artist’s break-even as a professional is 500 ÷ 195 ≈ 2.56 paintings per week.