South African Grade 11 and 12 Accounting: Manufacturing Accounts - Break-even Point

This post is suitable for Grades 11 and 12. For work that is applicable more to Grade 12s, see the final section on this post, "Advanced Break-even"

The Break-even Point

Before we can actually look at calculating break-even, we need to look at calculating some production costs first.

Total Costs and Costs per Unit

To work out the total fixed costs, we simply add up all the fixed costs. Pretty straight-forward, right?

To work out the total fixed costs per unit, we take the total fixed costs and divide it by the number of units produced. In other words:

Fixed costs per unit = Total Fixed Costs / Number of units

Total variable costs are just equal to all the variable costs added up together. Since, in school accounting, we assume that the variable costs per unit stay the same, we may be asked to calculate the total variable costs -- it's quite straight-forward though, as it is just variable costs per unit times by the number of units produced.

Total variable costs per unit = Total variable costs / Number of units.

Lastly, to work out the total production costs, we just add the total fixed and variable costs together. If we want to work out the total production costs per unit, we just take the total production cost and divide it by the number of units produced.

Changing the Number of Units Produced

It's useful to look at what happens to these costs as the number of units produced is increased or decreased:

• As we increase the number of units produced, the fixed costs stay the same, and thus the fixed costs per unit decrease.

• As we increase the number of units produced, the variable costs per unit stay the same (although obviously the total variable costs increase).

This means that as we produce more, the total costs of production per unit begin to decrease, since the fixed costs per unit are decreasing and the variable costs per unit stay the same. This makes sense, since we all are familiar with the idea that producing things in bulk is usually cheaper.

 

The Break-even Point

The Break-even Quantity

For a business that manufactures the goods that it produces, it is very important that it know just how many units of stock it must produce and sell to make a profit. Note that when I talk about "profit" here, I'm referring to Gross Profit (so Sales less Cost of Sales).

As we saw in the previous section, as we produce more, the total costs of production per unit begin to decrease. As a result, if we choose a selling price that's not too ridiculous, we might find that if we only produce and sell a few units, we might make a loss. If we produce a few more, because the fixed costs per unit will decrease, we will find that we'll make less of a loss. As we carry on producing and selling even more, eventually we'll reach a point where we stop making a loss, and instead start to make a profit. This point is called the break-even point.

More formally, the break-even quantity is the quantity of units that a business needs to produce and sell in order to make a (gross) profit of zero.

Any quantity greater than the break-even quantity that is sold will result in a profit; any quantity that is produced and sold that is less will result in a loss.

Calculating the break-even quantity

To calculate the break-even quantity, there is a fairly simple formula to use. In Grade 11 and Grade 12, you won't be given the formula in tests, and you will be expected to remember it. The formula is:

Break even quantity = (Total Fixed Costs) / (Selling price per unit - Variable cost per unit)

For example, if we have total fixed costs of R50 000, a selling price per unit of R12, and a variable cost per unit of R7.50:

Break-even quantity = (50 000) / (12 - 7.50) = 50 000 / 4.50 = 11 111.11

This means that we would have to produce (and sell) 11 112 units to start making a profit, because it's more than the break-even quantity. If we produced only 11 111, we would make a loss (although it would be a very small loss) because it's less than the break-even quantity.

Calculating the break-even price (or value)

Sometimes a business will know what their production capacity is -- i.e. the number of units that they can produce -- and instead will want to know what selling price they should use if they want to break even. When this is the case, people tend to talk about the break-even "price" or sometimes the "value". Note that this is not always asked consistently, and some tests and exams I've seen will talk about "value" and mean quantity instead. Hopefully as you do more exercises, you will get a good feel for what they are really asking.

We've already seen the formula to calculate the break-even quantity. If we want to work out the break-even selling price, we just have to rearrange the equation (since we'll have been given the quantity):

Break-even quantity = Total Fixed Costs / (Selling price per unit - Variable cost per unit)

=> Selling price per unit - variable cost per unit = Total Fixed Costs / Break-even quantity

=> Selling price per unit = (Total Fixed Costs/Break-even quantity) + Variable Cost per unit

This selling price is the price at which a given production quantity will be sold for the business to not make a loss. If they sell it for a lower price, the business will make a loss; if they sell it for a higher price, the business will make a profit.

A bit more on the Break-even formula

Instead of having "Selling price per unit - variable cost per unit" in the denominator, people have defined a term called contribution. Instead of trying to worry about what "contribution" means, instead we just need to know that:

Contribution = Selling Price per Unit - Variable Cost per Unit

Sometimes contribution will also be referred to as marginal income. For Grade 11 and 12, the only real advantage to the idea of "contribution" is that it makes the formula look a little simpler:

Break-even quantity = Total Fixed Cost / Contribution

While understanding the idea of a contribution is not important, in tests and exams the contribution is often given, instead of giving the selling price and variable costs. It is expected that you will know how to use it in the break-even formula.

Advanced Break-even

This section is applicable to Grade 12s.

So far we have only examined the break-even point from a production perspective. Of course, a real business also has non-production costs, and it must take these into account when it does break-even analysis. The non-production costs of a business are divided up into Administration Costs and Selling & Distribution Costs.

When we calculate the break even quantity, we are only really interested in the selling price per unit, the total fixed cost, and the variable cost per unit.

Administration Costs and Selling & Distribution Costs can also be divided up into variable and fixed costs. Unless we are told otherwise, we assume at school that:

• Administration Costs are fixed costs, and
• Selling & Distribution Costs are variable costs.

This means that to calculate total fixed costs:

Fixed Cost = Factory Overhead Cost + Administration Cost,

and to calculate total variable costs:

Variable Cost = Direct Material Cost + Direct Labour Cost + Selling & Distribution Cost.

The Break-even formula remains the same.

The big advantage of this method is that it takes net profit into account, rather than just the gross profit. This gives the business a much better idea of where it will actually break-even, and thus whether it will actually make a profit or a less.