Cost Management: A Strategic Emphasis 7th Edition by Edward Blocher,David Stout ,Paul Juras,Gary Cokins

Exercise 49

Further Analysis-Degree of Operating Leverage (DOL) Based on your reading of the text and your algebraic skills, respond to the following two requirements.
Required
1. In reading the text, you should have come to the conclusion that the DOL at any output level, Q , is defined as the ratio of contribution margin (CM) to operating income (OI). Further, your subsequent study of DOL indicates that DOL can be interpreted, at any output level, Q , as the percentage change in OI for each percentage change in sales volume. From the stated definition of DOL (as the ratio of CM to OI), show the mathematical derivation of the above conclusion, thereby solidifying your understanding of the concept of DOL.
2. As indicated above in requirement 1, the DOL (at any output level, Q ) is measured as the ratio of CM to OI. The text also makes reference to the point that the notion of "operating leverage" is a risk-related measure that has something to do with the extent to which fixed costs make up an organization's cost structure. You are puzzled by the juxtaposition of these two comments. Reconcile these comments by showing that DOL can be defined in terms of fixed costs ( F ). Of what interpretive or managerial value is the resulting equation