Break-even

D- Break-even analysis

Break-even analysis is used to determine the impact of price and cost strategies on firm's ability to remain solvent in the coming year without excessive risk. The analytical procedure is short run, i.e. a time framework within which a firm does not consider changing its methods of production. This very popular method consists in calculating the volume of sales for which profits are null, that is, the point where the dollar amount of contribution margin is just equal to total fixed costs.

See review questions Q-9D.1 through Q-9D.4.

1)- Graphical presentation:

To calculate the break-even point of a firm, it is first necessary to sort out costs:
1- UVC = unit variable costs are those that change with the volume of production, such as raw materials and production costs included in costs of goods sold, as well as selling, freight, and other costs that increase as volume increases;
2- FC = fixed costs are those that are unavoidable, such as rent, staff and executive salary, insurance, depreciation, general and administrative expenses.
Some costs have both, a fixed and a variable portion, such as cost of utilities or advertising. They must be separated in their constituent parts.

The break-even point is that quantity Q* for which

Q* = FC / (P - UVC)

where Q* = break-even volume: FC = fixed costs
P = unit price
UVC = unit variable cost
(P-UVC) = contribution margin

The formula is obtained by setting total revenue equal total cost (i.e. profits are zero)

Q x P = Q x UVC + FC

and solving for Q.

Table T-9.1 presents a hypothetical example of sales and profit illustrating break-even analysis. The unit price is $5 and unit variable cost is $3. The fixed cost is $300.

Table T-9.1

Break-even example

Units sold 100 110 120 130 140 150 160 170 180 190 200

Total revenue 500 550 600 650 700 750 800 850 900 950 1000

Variable costs 300 330 360 390 420 450 480 510 540 570 600

Gross profit margin 200 220 240 260 280 300 320 340 360 380 400

Fixed costs 300 300 300 300 300 300 300 300 300 300 300

Net profit -100 -80 -60 -40 -20 0 20 40 60 80 100

Table T-9.1 shows that the break-even sales volume is at 150 units. At this level of sales volume, the total revenue is $750 and total cost is $750 ($300 + 150x$3). We can also calculate the break-even volume Q with the formula above

Q = 300 / (5 - 3) = 300 / 2 = 150

The analysis is usually conducted on a graph such as Graph G-9.1 which reproduces the data given in Table T-9.1 above.

Graph G-9.1

The graph shows the total sales revenues are rising with each additional unit sold at the rate of price P (i.e. $5), the total cost starts at FC and is rising at the rate of unit variable cost UVC (i.e. $3). PROFIT is zero where TOTAL COST intersects REVENUE (i.e. that is where units sold equal 150).

See review questions Q-9D1.1 through Q-9D1.5.

2)- Interpretation of break-even analysis

The actual (or projected) sales volume is compared with the break-even volume. If the actual volume is smaller or very close to the break-even volume, it indicates that either the pricing strategy should be revised or the product should be discontinued because it is not sufficiently profitable. If the actual volume is only slightly above the break-even volume, the profitability may be adequate or not depending on the sales stability. If sales are unstable the actual sales must be significantly above the break-even volume; otherwise, there is a good chance that falling revenues will put the company in financial difficulty.

This approach brings into focus an aspect of sales touched upon earlier. That is the importance of a permanent clientele. Brand loyalty is of great importance to a firm and needs to be maintained and enhanced. Losing customers is unforgivable, even if it is the result of actions by competitors, but especially if the cause is attributable to the firm itself.

See review questions Q-9D2.1 through Q-9D2.3.

3)- Extensions of break-even analysis

There are several variations of the break-even analysis. The break-even analysis by product lines illustrates the pattern of sales with different contribution margins. Lower profit margin products are mature products with stable markets; they make up total sales revenue starting from zero and rising in lower left portion of the curve. Higher profit margins products are newer products with unstable markets; they add to total sales revenue to the right. The higher margin products may be those with the greatest potential threat from competitors. The graph then shows whether the sales on the more risky products may put the company in financial difficulty. Another interpretation of this presentation is that the lower contribution margin sales can be viewed as necessary to absorb some of the fixed costs, so that the higher contribution margin products can be produced.

Another use of break-even analysis compares choices between costs strategies with different levels of automation (i.e. operating leverage) conducted in Chapter 10 Section D-1; and break-even analysis will also be used to study financial leverage in Chapter 11 Section D-2.

See review questions Q-9D3.1 through Q-9D3.3.

See research assignment R-9D.1.

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Last modified: Jun/01/01 Next: Analysis