Break-Even Analysis

Quick Summary of Break-Even Analysis

The break even point for a product is the point where total revenue received equals the 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.

Break-even analysis is a managerial tool used in business to estimate a fair, competitive and profitable price for products and services. Break-even analysis categorizes costs as a variable (changing with the volume of production) and fixed (unrelated to volume). In break-even analysis, first, break-even point – where total revenue equals total cost – is calculated. Break-even analysis finds this by dividing total fixed costs by per unit contribution to fixed costs (unit price – unit variable cost). Dollar value is calculated by multiplying break-even point by price per unit. Any per unit contribution to fixed costs beyond break-even point goes to profit. Thus break-even analysis measures the volume of activity required by businesses to remain profitable after covering all fixed expenses. Mangers use break-even analysis to assess multiple price levels and variable-fixed price combinations. Break-even analysis also helps in determining optimal costs, prices and product mix. In macroeconomics, break-even analysis yields the point where income exceeds consumption resulting in savings.

The break-even point for a product, brand, or company is the point where total revenue received equals total costs (TR=TC). At a price or quantity greater than this point, the firm is making a profit; below this point, a loss. Break-even quantity is calculated by:

Total fixed costs / (price – average variable costs)

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 of operations (the basic cost of 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 particularly useful in comparing the profit 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 was able to increase the selling price for its product, from $2 to $2.30, then it would have to sell only (1000/(2.3 – 0.6) = 589) 589 units to break even.

Break-Even Analysis with Multiple Prices
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 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.

Margin Of Safety

In break-even analysis, the margin of safety is how much output or sales level can fall before a business reaches its break-even point (BEP).

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) = 715) 715 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.

Break Even = FC / (SP − VC)

where FC is Fixed Cost, SP is selling Price and VC is Variable Cost

In Capital Budgeting

Break-even analysis is a special application of sensitivity analysis. It aims at finding the value of individual variables at which the project’s NPV is zero. In common with sensitivity analysis, variables selected for the break-even analysis can be tested only one at a time.

The break-even analysis results can be used to decide abandon of the project if forecasts show that below break-even values are likely to occur.

In using Break-even analysis, it is important to remember the problem associated with Sensitivity analysis as well as some extension specific to the method:

• Variables are often interdependent, which makes examining them each individually unrealistic.
• Often the assumptions upon which the analysis is based are made by using past experience/data which may not hold in the future.
• Variables have been adjusted one by one; however, it is unlikely that in the life of the project only one variable will change until reaching the break-even point. Management decisions made by observing the behaviour of only one variable are most likely to be invalid.
• Break-even analysis is a pessimistic approach by essence. The figures shall be used only as a line of defence in the project analysis.

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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 715.

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 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.

Limitations

• This is only a supply-side (ie.: costs only) analysis.
• It tells you nothing about whether you can actually sell the product at these prices.
• It assumes that fixed costs (FC) are constant
• It assumes variable costs are constant per unit of output

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