## Cash Flow Accounting and Financial Break Even Points

We know from the preceding discussion that the relationship between operating cash flow and sales volume (ignoring taxes) is:

If we rearrange this and solve for Q, we get:

This tells us what sales volume (Q) is necessary to achieve any given OCF, so this result is more general than the accounting break-even. We use it to find the various break-even points in Figure 11.5.

Accounting Break-Even Revisited Looking at Figure 11.5, suppose that operating cash flow is equal to depreciation (D). Recall that this situation corresponds to our break-even point on an accounting basis. To find the sales volume, we substitute the \$700 depreciation amount for OCF in our general expression:

This is the same quantity we had before.

Cash Break-Even We have seen that a project that breaks even on an accounting basis has a net income of zero, but it still has a positive cash flow. At some sales level below

Ross et al.: Fundamentals I IV. Capital Budgeting I 11. Project Analysis and I I © The McGraw-Hill of Corporate Finance, Sixth Evaluation Companies, 2002

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366 PART FOUR Capital Budgeting cash break-even

The sales level that results in a zero operating cash flow.

the accounting break-even, the operating cash flow actually goes negative. This is a particularly unpleasant occurrence. If it happens, we actually have to supply additional cash to the project just to keep it afloat.

To calculate the cash break-even (the point where operating cash flow is equal to zero), we put in a zero for OCF:

Wettway must therefore sell 25 boats to cover the \$500 in fixed costs. As we show in Figure 11.5, this point occurs right where the operating cash flow line crosses the horizontal axis.

Notice that a project that just breaks even on a cash flow basis can cover its own fixed operating costs, but that is all. It never pays back anything, so the original investment is a complete loss (the IRR is -100 percent).

financial break-even

### The sales level that results in a zero NPV.

Financial Break-Even The last case we consider is that of financial break-even, the sales level that results in a zero NPV. To the financial manager, this is the most interesting case. What we do is first determine what operating cash flow has to be for the NPV to be zero. We then use this amount to determine the sales volume.

To illustrate, recall that Wettway requires a 20 percent return on its \$3,500 (in thousands) investment. How many sailboats does Wettway have to sell to break even once we account for the 20 percent per year opportunity cost?

The sailboat project has a five-year life. The project has a zero NPV when the present value of the operating cash flows equals the \$3,500 investment. Because the cash flow is the same each year, we can solve for the unknown amount by viewing it as an ordinary annuity. The five-year annuity factor at 20 percent is 2.9906, and the OCF can be determined as follows:

Wettway thus needs an operating cash flow of \$1,170 each year to break even. We can now plug this OCF into the equation for sales volume:

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