Principles of Managerial Finance

514 PART 4 Long-Term Financial Decisions

5. Because the concept of leverage is linear,positive and negative changes of equal magnitude will always result in
   equal degrees of leverage when the same base sales level is used as a point of reference. This relationship holds for all
   types of leverage discussed in this chapter.


6. Technically, the formula for DOL given in Equation 12.5 should include absolute value signs because it is possible
   to get a negative DOL when the EBIT for the base sales level is negative. Because we assume that the EBIT for the
   base level of sales is positive, we do not use the absolute value signs.


7. When total sales in dollars—instead of unit sales—are available, the following equation, in which TRdollar
   level of base sales and TVCtotal variable operating costs in dollars, can be used.
   DOL at base dollar sales TR
   This formula is especially useful for finding the DOL for multiproduct firms. It should be clear that because in the
   case of a single-product firm, TRPQand TVCVCQ,substitution of these values into Equation 12.5
   results in the equation given here.

TRTVC

TRTVCFC

Whenever the percentage change in EBIT resulting from a given percentage change

in sales is greater than the percentage change in sales, operating leverage exists.

This means that as long as DOL is greater than 1, there is operating leverage.

EXAMPLE Applying Equation 12.4 to cases 1 and 2 in Table 12.4 yields the following results:^5

Case 1: 2.0

Case 2: 2.0

Because the result is greater than 1, operating leverage exists. For a given base

level of sales, the higher the value resulting from applying Equation 12.4, the

greater the degree of operating leverage.

A more direct formula for calculating the degree of operating leverage at a

base sales level, Q, is shown in Equation 12.5.^6

DOL at base sales level Q (12.5)

EXAMPLE Substituting Q1,000, P$10, VC$5, and FC$2,500 into Equation 12.5

yields the following result:

DOL at 1,000 units2.0

The use of the formula results in the same value for DOL (2.0) as that found by

using Table 12.4 and Equation 12.4.^7

Fixed Costs and Operating Leverage

Changes in fixed operating costs affect operating leverage significantly. Firms

sometimes can incur fixed operating costs rather than variable operating costs

and at other times may be able to substitute one type of cost for the other. For

example, a firm could make fixed-dollar lease payments rather than payments

equal to a specified percentage of sales. Or it could compensate sales representa-

tives with a fixed salary and bonus rather than on a pure percent-of-sales com-

$5,000



$2,500

1,000($10$5)



1,000($10$5)$2,500

Q(PVC)



Q(PVC)FC

100%



50%

100%



50%