**Corporate Finance II**

**Reading 34. Measures of Leverage **

**Learning Outcome Statements**

a. define and explain leverage, business risk, sales risk, operating risk, and financial risk and classify a risk;

b. calculate and interpret the degree of operating leverage, the degree of financial leverage, and the degree of total leverage;

c. analyze the effect of financial leverage on a company's net income and return on equity;

*CFA Curriculum, 2020, Volume 4*

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### Subject 1. Business Risk and Operating Leverage

**Leverage**

Leverage is the extent to which fixed costs are used in a company's cost structure.

**Operating leverage**is the extent to which fixed operating costs (e.g., depreciation, rent) are used in a firm's operations.**Financial leverage**is the extent to which fixed-income securities (debt and preferred stock) are used in a firm's capital structure.

Leverage affects a firm's risk, as it can magnify earnings both up and down. The bigger the leverage, the more volatile the firm's future earnings and cash flows, and the greater the discount rate applied in the firm's valuation (by bondholders and stockholders).

**Business Risk and its Components**

**Business risk**is the uncertainty (variability) about projections of future operating earnings. It is the single most important determinant of capital structure. If other elements are the same, the lower a firm's business risk, the higher its optimal debt ratio.

Business risk is the combined risk of sales and operations risks.

- The
**sales risk**is the uncertainty regarding the price and quantity of the firm's goods and services. If the demand for and the price of a firm's goods and services are stable, its sales risk is considered low. - The
**operating risk**is the uncertainty caused by a firm's operating cost structure. If a high percentage of operating costs are fixed costs, operating risk is considered to be high.

In general, management has more opportunity to manage and control operating risk than sales risk.

**Operating Risk**

A company that has high operating leverage is a company with a large proportion of fixed input costs, whereas a company with largely variable input costs is said to have low operating leverage (due to its small amount of fixed costs).

A company with a high degree of operating leverage that has a small change in sales will experience a large change in profits and rate of return. This is due to the fact that because the company has a large fixed cost component, any increase in sales will cause an even greater increase in net income, since the fixed costs have already been incurred.

In many respects operating leverage is determined by technology. High (low) operating leverage is usually associated with capital (labor) intensive industries.

The

**degree of operating leverage**(

**DOL**) is defined as the percentage change in EBIT (operating income) that results from a given percentage change in sales. It measures the impact of a change in sales on EBIT.

Here Q is the number of units, P is the average sales price per unit of output, V is the variable cost per unit, F is fixed operating cost, S is sales in dollars, and VC is total variable costs.

P - V is referred to as the

**per unit contribution margin**, which is the amount that each unit contributes to covering fixed costs. S - VC is called the

**contribution margin**.

For example, assume that a firm has sales of $100,000, variable costs of $50,000, and fixed costs of $20,000. Its DOL is (100,000 - 50,000) / (100,000 - 50,000 - 20,000) = 1.67.

###
**User Contributed Comments**
6

You need to log in first to add your comment. ###### johntan1979

DOL: What is considered high and what is low? Is 1.67 (example in the notes) high?

###### robertucla

You have to compare dol to comparable firms in industry

###### jodyleesc

Can someone explain why %change in EBIT / %change in Sales = Q(P - V) / Q(P-V) - F ?

###### khalifa92

those are two different equations to find DOL

johntan higher DOL is caused bu graeter use of fixed operating cost relative to vc leads to more sensitivite in EBIT unit solds thus more risk

###### unknown

Jodyleesc: Think about it as elasticity. %change Y / %changeX.

By definition, EBIT = Q(P-V)-F and Sales = Q*P; When we do point elasticity, where dx->0,

we have %changeY / %changeX = dY/dX * X/Y; if you take derivatives of EBIT and Sales with respect to Quantity, then dY= (P-V) and dX = P; thus (P-V)/P * X/Y = (P-V)/P*(Q*P/EBIT) = (P-V)*Q/EBIT = (P-V)*Q/ ((P-V)*Q-F)

###### MathLoser

@Jodyleesc:

First: Calculate DOL using [Q(P-V)] / [Q(P-V)-F]

Example: you have DOL = 3,0.

Assume that your company has a 3% increase in sales.

%change in EBIT = DOL x %change in sales = 3 x 3% = 9%

That's the point of the formula.