Break even analysis

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The break even point for a product is the point where total revenue received equals total costs associated with the sale of the product (TR=TC). A break even point is typically calculated in order for businesses to determine if it would be profitable to sell a proposed product, as opposed to attempting to modify an existing product instead so it can be made lucrative. Break-Even Analysis can also be used to analyze the potential profitability of an expenditure in a sales-based business.

[edit] In unit sales

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 / (selling 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. This relationship is derived from the

profit equation: Profit = Revenues - Costs  where

Revenues = (selling price * quantity of product) and

Costs = (average variable costs * quantity) + total fixed costs. Therefore,

Profit=(selling price*quantity)-(average variable costs*quantity+total fixed costs).

Solving for Quantity of product at the breakeven point when Profit equals zero,

the quantity of product at breakeven is Total fixed costs / (selling price - average variable costs).  

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 looks like it clearly will not 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/(2.00 - 0.60) = 714) 714 units to break even. in that case the margin of safety value of nil and the value of bep is not profitable or not gaining loss.

[edit] In price changes

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 changes 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 show





s 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 formulae. For example, the total revenue curve is simply the product of selling price times quantity for each output quantity. The data used in these formulae come either from accounting records or from various estimation techniques such as regression analysis.

[edit] Limitations

• Break-even analysis is only a supply side (ie.: costs only) analysis, as 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 likely quantities of sales.
• It assumes that the quantity of goods produced is equal to the quantity of goods sold (i.e., there is no change in the quantity of goods held in inventory at the beginning of the period and the quantity of goods held in inventory at the end of the period.
• In multi-product companies, it assumes that the relative proportions of each product sold and produced are constant (i.e., the sales mix is constant).

[edit] External links

Further reading:

• Break-even Point Fixed and variable expenses, contribution margin, desired profit.

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