Combined Effect Of Two Types Of Leverage

When financial leverage is combined with operating leverage, the effect of change in revenues on earnings per share is magnified. The combination of the two increases the dispersion and risk of possible earnings per share. To determine the effect of a change in units of output on earnings per share, we combine the equation for the degree of operating leverage, with that for the degree of financial leverage.

Because EBIT is simply X(P - V) - F, where as before X is the units of output, P is price per unit, V is variable cost per unit, and F is fixed cost, equation for determining the degree of financial leverage can be expressed as

EBIT X(P - V) - F --------- = ----------------- EBIT - C X(P - V) - F - C

Combining this equation with that for the degree of operating leverage, we obtain

Degree of operating and financial leverage at X units =

X(P - V) X(P - V) - F = ------------ x ---------------- X(P -V) - F X(P - V) - F - C

X(P - V) = ----------------- X(P - V) - F - C

Suppose that our hypothetical company had \$200 000 in debt at 8% interest. The selling price was \$50 a unit, variable costs \$25 a unit, and annual fixed costs were \$100 000. Assume that the tax rate is 50%, the number of shares of common stock outstanding is 10 000 shares, and the we wish to determine the combined degree of leverage at 8000 units of output. Therefore,

DO & FL at 8 000 units =

8 000(50 - 25) = --------------------------------- 8 000(50 - 25) - 100 000 - 16 000

= 2.38

Thus, a 10% increase in the number of units produced and sold would result in a 23.8% increase in earnings per share. Earning per share at the two levels of output are shown in Table 5-13.

Operating and financial leverage can be combined in a number of different ways to obtain a desirable degree of overall leverage and risk of the firm.