Break even analysis

The break even point for a product is the point where total revenue received equals total costs (TR=TC). A break even point is typically calculated in order to determine if it would be worthwhile to sell a proposed product, or to try to figure out whether an existing product can be made profitable.

If the product can be sold in a larger quantity than occurs at the break even point, then the firm will make a profit; below this point, a loss. Break-even quantity is calculated by:

Total fixed costs / (price - average variable costs) .  
(Explanation - in the denominator, "price minus average variable
cost" is the variable profit per unit, or contribution margin of
each unit that is sold.)

(Firms may still decide not to sell low-profit products, for example those not fitting well into their sales mix. Firms may also sell products that lose money - as a loss leader, to offer a complete line of products, etc. But if a product does not break even, or a potential product look like it clearly will sell better than the break even point, then the firm will not sell, or will stop selling, that product.)

An example:

• Assume we are selling a product for $2 each.
• Assume that the variable cost associated with producing and selling the product is 60 cents.
• Assume that the fixed cost related to the product (the basic costs that are incurred in operating the business even if no product is produced) is $1000.
• In this example, the firm would have to sell (1000/(2 - 0.6) = 714) 714 units to break even.

This analysis is also useful in comparing the consequences of alternative prices. By inserting different prices into the formula, you will obtain a number of break even points, one for each possible price charged. If the firm to change the selling price for its product, from $2 to $2.30, in the example above, then it would have to sell only (1000/(2.3 - 0.6))= 589 units to break even, rather than 714.

To make the results clearer, they can be graphed. To do this, you draw the total cost curve (TC in the diagram) which shows the total cost associated with each possible level of output, the fixed cost curve (FC) which shows the costs that do not vary with output level, and finally the various total revenue lines (R1, R2, and R3) which show the total amount of revenue received at each output level, given the price you will be charging.

The break even points (A,B,C) are the points of intersection between the total cost curve (TC) and a total revenue curve (R1, R2, or R3). The break even quantity at each selling price can be read off the horizontal, axis and the break even price at each selling price can be read off the vertical axis. The total cost, total revenue, and fixed cost curves can each be constructed with simple formuli. For example, the total revenue curve is simply the product of selling price times quantity for each output quantity. The data used in these formuli come either from accounting records or from various estimation techniques such as regression analysis.

Limitations

• This is only a supply side (ie.: costs only) analysis.
• It tells you nothing about what sales are actually likely to be for the product at these various prices.
• It assumes that fixed costs (FC) are constant
• It assumes average variable costs are constant per unit of output, at least in the range of sales (both prices and likely quantities) of interest.

See also : cost-plus pricing, pricing, production, costs, and pricing