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Chapter 14 - Web Appendix 14A

Chapter 14 - Web Appendix 14A - WEB APPENDIX 14A Degree of...

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WEB APPENDIX 14A Degree of Leverage In our discussion of operating leverage in Chapter 14, we made no mention of financial leverage; and when we discussed financial leverage, operating leverage was assumed to be given. Actually, the two types of leverage are interrelated. For example, a firm reducing its operating leverage would probably lead to an increase in its optimal use of financial leverage. On the other hand, if the firm decided to increase its operating leverage, its optimal capital structure would probably call for less debt. The theory of finance has not been developed to the point where we can specify simultaneously the optimal levels of operating and financial leverage. However, we can see how operating and financial leverage interact through an analysis of the degree of leverage concept. Degree of Operating Leverage (DOL) The degree of operating leverage (DOL) is defined as the percentage change in operating income (or EBIT) that results from a given percentage change in sales: DOL ¼ Percentage change in EBIT Percentage change in sales ¼ ± EBIT EBIT ± Q Q 14A-1 In effect, the DOL is an index number that measures the effect of a change in sales on operating income, or EBIT. DOL can also be calculated using Equation 14A-2, which is derived from Equation 14A-1: DOL Q ¼ Degree of operating leverage at Point Q ¼ Q ð P ± V Þ Q ð P ± V Þ ± F Or it can be based on dollar sales rather than units: DOL S ¼ S ± VC S ± VC ± F 14A-2a Here Q is the initial units of output, P is the average sales price per unit of output, V is the variable cost per unit, F is fixed operating costs, S is initial sales in dollars, and VC is total variable costs. Equation 14A-2 is normally used to analyze a single product such as IBM s PC, whereas Equation 14A-2a is used to evaluate an entire firm with many types of products, where quantity in units and sales price are not meaningful. Equation 14A-2 is developed from Equation 14A-1 as follows. The change in units of output is defined as D Q. In equation form, EBIT ¼ Q(P ± V) ± F, where Q is units sold, P is the price per unit, V is the variable cost per unit, and F is the total fixed costs. Since both price and fixed costs are constant, the change in EBIT is D EBIT ¼ D Q(P ± V). The initial EBIT is Q(P ± V) ± F, so the percentage change in EBIT is shown as follows: EBIT ¼ ± Q ð P ± V Þ Q ð P ± V Þ ± F 14A-2 14A-1
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The percentage change in output is D Q/Q, so the ratio of the percentage change in EBIT to the percentage change in output is shown as follows: DOL ¼ ± Q ð P ± V Þ Q ð P ± V Þ ± F ± Q Q ¼ ± Q ð P ± V Þ Q ð P ± V Þ ± F ± ² Q ± Q ± ² ¼ Q ð P ± V Þ Q ð P ± V Þ ± F 14A-2 Applying Equation 14A-2a to data for an illustrative firm, Hastings Inc., at a sales level of $200,000 as shown in Table 14A-1, we find its degree of operating leverage to be 2.0: DOL $ 200 , 000 ¼ $200,000 ± $120,000 $200,000 ± $120,000 ± $40,000 ¼ $80,000 $40,000 ¼ 2 : 0 Thus, an X% increase in sales will produce a 2X% increase in EBIT. For example, a
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