Break even analysis

(industrial engineering) Determination of the break-even point.

Financial analysis that identifies the point at which expenses equal gross revenue for a zero net difference. For example, if a mailing costs $100 and each item generates $5 in revenue, the break-even point is at 20 items sold. A profit will be made on items sold in excess of 20. A loss will result on sales under 20. The break-even point may be analyzed in terms of units, as above, or dollars.

Branch of Cost-Volume-Profit (CVP) Analysis that determines the break-even point, which is the level of sales where total costs equal total revenue. Thus, zero profit results. Breakeven sales is computed as follows:

Break-even sales in units = Fixed costs/Unit contribution margin.

Break-even sales in dollars = Fixed costs/Contribution margin ratio.

For example, assume:

Fixed costs = $15,000.

Unit contribution margin (selling price - unit variable cost) = $15, and

Contribution margin ratio (unit CM/selling price) = .6

Then, break-even sales in units = $15,000/$15 = 1000 units and break-even sales in dollars = $15,000/.6 = $25,000.

A break-even chart is one in which sales revenue, variable costs, and fixed costs are plotted on the vertical axis while volume is plotted on the horizontal axis. The Break-Even Point is the point at which the total sales revenue line intersects the total cost line. See the sample chart below.

Break-even analysis is used in cost accounting and capital budgeting to evaluate projects or product lines in terms of their volume and profitability relationship. At its simplest, the tool is used as its name suggests: to determine the volume at which a company's costs will exactly equal its revenues, therefore resulting in net income of zero, or the "break-even" point. Perhaps more useful than this simple determination, however, is the understanding gained through such analysis of the variable and fixed nature of certain costs. Break-even analysis forces the small business owner to research, quantify, and categorize the company's costs into fixed and variable groups.

"Understanding what it takes to break even is critical to making any business profitable," Kevin D. Thompson stated in Black Enterprise. "Incorporating accurate and thorough break-even analysis as a routine part of your financial planning will keep you abreast of how your business is really faring. Determining how much business is needed to keep the door open will help improve your cash-flow management and your bottom line."

The basic formula for break-even analysis is as follows:

BEQ FC /(P-VC)

Where BEQ Break-even quantity

FC Total fixed costs

P Average price per unit, and

VC Variable costs per unit.

Fixed costs include rent, equipment leases, insurance, interest on borrowed funds, and administrative salaries—costs that do not tend to vary based on sales volume. Variable costs, on the other hand, include direct labor, raw materials, sales commissions, and delivery expenses—costs that tend to fluctuate with the level of sales. A key component of break-even analysis is the contribution margin, which can be defined as a product or service's price (P) minus variable costs (VC) per unit sold. The contribution margin concept is grounded in incremental or marginal analysis; its focus is the extra revenue and costs that will be incurred with the next additional unit.

The first step in determining the level of sales needed for a small business to break even is to compute the contribution margin, by subtracting the variable costs per unit from the selling price. For example, if P is $30 and VC are $20, the contribution margin is $10. The next step is to divide the total annual fixed costs by the contribution margin. For example, a company with FC of $50,000 and a contribution margin of $10 would need to sell 5,000 units to break even. This number can easily be converted to the dollars of revenue the company would need to break even for the year. Simply multiply the break-even point in units by the average selling price per unit. In this case, a BEQ of 5,000 units multiplied by a P of $30 per unit yields break-even revenue of $150,000.

Break-even analysis has numerous potential applications for small businesses. For example, it can help managers assess the effect of changing prices, sales volume, and costs on profits. It can also help small business owners make decisions regarding whether to expand their operations or hire new employees. Break-even analysis would also be useful in the following situation: a small business owner is skeptical of her marketing manager's projection for sales of 15,000 units of a new product, and wants to know what minimum quantity of units must be sold to avoid losing money, assuming a selling price of $25, fixed costs of $100,000, and variable costs of $15. The equation tells her that these parameters will require a break-even volume of 10,000 units; fewer than that level yields losses, more than that level yields profits. This perspective of analysis may be employed where the analyst is highly confident of the estimates for price and costs, but feels less certain about the assessment of market demand. In this case, the small business owner might be interested in how low sales could fall below the marketing manager's forecast without causing an embarrassment at year-end reporting time.

Another scenario may involve the question of how to manufacture a product, in terms of the nature of operations and how they will affect fixed costs. Here, a small business owner may have a good handle on the quantity expected, the likely selling price, and the variable costs involved, but be undecided about how to structure the new operation. If the volume is expected to be 10,000 units, at a selling price of $5 and variable costs of $3.50, the break-even equation tells him that fixed costs can be no greater than $15,000. "The bottom line is that, especially for small businesses, the margins for error are much too narrow to make business decisions on gut instinct alone," Thompson concluded. "Every idea, whether it is the introduction of a new product line, the opening of branch offices, or the hiring of additional staff, must be tested through basic business analysis."

Further Reading:

Davis, Joseph M. "Project Feasibility Using Break-Even Point Analysis." Appraisal Journal. January 1998.

Dennis, Michael C. "What Credit Managers Should Know about Break-Even Analysis." Business Credit. February 1995.

Hilton, Ronald W. Managerial Accounting. New York: McGraw-Hill, 1991.

"Numbers You Should Know to Keep in Touch with Your Business." Profit-Building Strategies for Business Owners. May 1993.

Thompson, Kevin D. "Business Management: Planning for Profit." Black Enterprise. April 1993.

Worm, Mark. "Break-Even Analysis and the Commercial Loan Decision." Journal of Lending and Credit Risk Management. November 1997.

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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). ^[1]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 point (for output) = fixed cost / contribution per unit

contribution (p.u) = selling price (p.u) - variable cost (p.u)

break even point (for sales) = fixed cost / contribution (pu) * sp (pu)

Contents 1 Margin of Safety 2 In unit sales 3 In capital budgeting 4 Internet research 5 Limitations 6 References 7 Bibliography 8 External links

Margin of Safety

Margin of safety represents the strength of the business. It enables a business to know what is the exact amount he/ she has gained or lost and whether they are over or below the break even point.^[2]

margin of safety = ( sales - break-even sales) / sales) x 100% If P/V ratio is given then profit/ PV ratio

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, the firm will make 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 break even 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.

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 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 behavior 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 defense in the project analysis.

Internet research

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

• Break-even analysis is only a supply side (i.e. 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. (i.e. linearity)
• 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).

References

1. ^ Horngren, C.,Sundem, G & Stratton, W. "Introduction to Management Accounting" (2002) Prentice Hall
2. ^ The Margin of Safety in MAAW, Chapter 11.

Bibliography

1. D Dayananda – R Irons – S Harrison - J Herbohn - P Rowland, 2002, Capital Budgeting: Financial appraisal of investment projects – Cambridge University Press. pp. 150

External links

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

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