## Measuring Operating Leverage

One way of measuring operating leverage is to ask, If quantity sold rises by 5 percent, what will be the percentage change in operating cash flow? In other words, the degree of operating leverage (DOL) is defined such that:

Percentage change in OCF = DOL X Percentage change in Q

Based on the relationship between OCF and Q, DOL can be written as:1

'To see this, note that if Q goes up by one unit, OCF will go up by (P — v). In this case, the percentage change in Q is 1/Q, and the percentage change in OCF is (P — v)/OCF. Given this, we have: Percentage change in OCF = DOL X Percentage change in Q (P — v)/OCF = DOL X 1/Q

DOL = (P — v) X Q/OCF Also, based on our definitions of OCF:

OCF + FC = (P — v) X Q Thus, DOL can be written as: DOL = (OCF + FC)/OCF = 1 + FC/OCF

The ratio FC/OCF simply measures fixed costs as a percentage of total operating cash flow. Notice that zero fixed costs would result in a DOL of 1, implying that percentage changes in quantity sold would show up one for one in operating cash flow. In other words, no magnification, or leverage, effect would exist.

To illustrate this measure of operating leverage, we go back to the Wettway sailboat project. Fixed costs were \$500 and (P - v) was \$20, so OCF was:

Suppose Q is currently 50 boats. At this level of output, OCF is -\$500 + 1,000 = \$500.

If Q rises by 1 unit to 51, then the percentage change in Q is (51 - 50)/50 = .02, or 2%. OCF rises to \$520, a change of P - v = \$20. The percentage change in OCF is (\$520 - 500)/500 = .04, or 4%. So a 2 percent increase in the number of boats sold leads to a 4 percent increase in operating cash flow. The degree of operating leverage must be exactly 2.00. We can check this by noting that:

This verifies our previous calculations.

Our formulation of DOL depends on the current output level, Q. However, it can handle changes from the current level of any size, not just one unit. For example, suppose Q rises from 50 to 75, a 50 percent increase. With DOL equal to 2, operating cash flow should increase by 100 percent, or exactly double. Does it? The answer is yes, because, at a Q of 75, OCF is:

Notice that operating leverage declines as output (Q) rises. For example, at an output level of 75, we have:

The reason DOL declines is that fixed costs, considered as a percentage of operating cash flow, get smaller and smaller, so the leverage effect diminishes.

### Operating Leverage

The Sasha Corp. currently sells gourmet dog food for \$1.20 per can. The variable cost is 80 cents per can, and the packaging and marketing operations have fixed costs of \$360,000 per year. Depreciation is \$60,000 per year. What is the accounting break-even? Ignoring taxes, what will be the increase in operating cash flow if the quantity sold rises to 10 percent above the break-even point?

The accounting break-even is \$420,000/.40 = 1,050,000 cans. As we know, the operating cash flow is equal to the \$60,000 depreciation at this level of production, so the degree of operating leverage is:

Ross et al.: Fundamentals IV. Capital Budgeting 11. Project Analysis and of Corporate Finance, Sixth Evaluation

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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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370 PART FOUR Capital Budgeting

Given this, a 10 percent increase in the number of cans of dog food sold will increase operating cash flow by a substantial 70 percent.

To check this answer, we note that if sales rise by 10 percent, then the quantity sold will rise to 1,050,000 x 1.1 = 1,155,000. Ignoring taxes, the operating cash flow will be 1,155,000 x \$.40 - 360,000 = \$102,000. Compared to the \$60,000 cash flow we had, this is exactly 70 percent more: \$102,000/60,000 = 1.70.

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