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Break-Even Analysis

When we undertake a sensitivity analysis of a project or when we look at alternative scenarios, we are asking how serious it would be if we have misestimated sales or costs. Managers sometimes prefer to rephrase this question and ask how far off the estimates could be before the project begins to lose money. This exercise is known as break-evenanalysis.

For many projects, the make-or-break variable is sales volume. Therefore, managers most often focus on the break- even level of sales. However, you might also look at other variables, for example, at how high costs could be before the project goes into the red. As it turns out, БІАААмlosing moneyБІАААн can be defined in more than one way. Most often, the break-even condition is defined in terms of accounting profits. More properly, however, it should be defined in terms of net present value. We will start with accounting break-even, show that it can lead you astray, and then show how NPV break-even can be used as an alternative.

ACCOUNTING BREAK-EVEN ANALYSIS

The accounting break-even point is the level of sales at which profits are zero or, equivalently, at which total revenues equal total costs. As we have seen, some costs are fixed regardless of the level of output. Other costs vary with the level of output. When you first analyzed the superstore project, you came up with the following estimates:

Notice that variable costs are 81.25 percent of sales. So, for each additional dollar of sales, costs increase by only $.8125. We can easily determine how much business the superstore needs to attract to avoid losses. If the store sells nothing, the income statement will show fixed costs of $2 million and depreciation of $450,000. Thus there will be a loss of $2.45 million. Each dollar of sales reduces this loss by $1.00 $.8125 = $.1875. Therefore, to cover fixed costs plus depreciation, you need sales of 2.45 million/.1875 = $13.067 million. At this sales level, the firm will break even. More generally,

fixed costs Break-even level of revenues = including depreciation additional profit from each additional dollar of sales

Table 5.4 shows how the income statement looks with only $13.067 million of sales. Figure 5.1 shows how the break- even point is determined. The 45-degree line shows accounting revenues. The cost line shows how costs vary with sales. If the store doesn`t sell a cent, it still incurs fixed costs and depreciation amounting to $2.45 million. Each extra dollar of sales adds $.8125 to these costs. When sales are $13.067 million, the two lines cross, indicating that costs equal revenues. For lower sales, revenues are less than costs and the project is in the red; for higher sales, revenues exceed costs and the project moves into the black.

Is a project that breaks even in accounting terms an acceptable investment? If you are not sure about the answer, here`s a possibly easier question. Would you be happy about an investment in a stock that after 5 years gave you a total rate of return of zero? We hope not. You might break even on such a stock but a zero return does not compensate you for the time value of money or the risk that you have taken.

A project that simply breaks even on an accounting basis gives you your money back but does not cover the opportunity cost of the capital tied up in the project. A project that breaks even in accounting terms will surely have a negative NPV.

Let`s check this with the superstore project. Suppose that in each year the store has sales of $13.067 millionБІАААдjust enough to break even on an accounting basis. What would be the cash flow from operations?

Cash flow from operations = profit after tax + depreciation = 0 + $450,000 = $450,000

The initial investment is $5.4 million. In each of the next 12 years, the firm receives a cash flow of $450,000. So the firm gets its money back: Total cash flow from operations = initial investment

12 АГАз $450,000 = $5.4 million

But revenues are not sufficient to repay the opportunity cost of that $5.4 million investment. NPV is negative.

BREAK-EVEN ANALYSIS Analysis of the level of sales at which the company breaks even.