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# DOL, DFL and DTL

The Degree of Operating Leverage, Degree of Financial Leverage, and Degree of Total Leverage are three important ratios that help us to quantify a company’s exposure to operational risk, financial risk, and a combination of the two, respectively.

## Degree of Operating Leverage (DOL)

The degree of operating leverage (DOL) assists a company in quantifying its operational risk, i.e., the risk arising from its mix of fixed and variable costs.

DOL measures how sensitive a company’s operating income is to changes in product demand, as measured by unit sales. It is the ratio of the percentage change in operating income to the percentage change in units sold.

The relationship can be expressed by the following equation:

$$\text{DOL}=\cfrac {\text{Percentage change in operating income}}{\text{Percentage change in units sold}}$$

Operating income is, however, equal to the difference between revenue and total operating costs (variable and fixed costs). Taking into account the fact that fixed costs do not change, operating income will, therefore, change based on the contribution margin i.e. the product of the quantity sold and the difference between the price per unit and the variable cost per unit.

This simplifies the equation to:

$$\text{DOL}=\cfrac {Q(P-V)}{Q(P-V)-F}$$

Where:

Q = the number of units;

P = the price per unit;

V = the variable operating cost per unit;

F = the fixed operating cost;

P – V = the per unit contribution margin; and

Q (P – V) = the contribution margin

### Example: DOL

If the DOL for a company is 1.6, and unit sales increase by 3%, what is the percentage change in operating income that would be expected?

Solution

The percentage change in operating income = 1.6 × 3% = 4.8%.

## Degree of Financial Leverage (DFL)

The degree of financial leverage (DFL) assists a company in quantifying its financial risk, i.e., the risk relating to how it finances its operations.

DFL refers to the sensitivity of the cash flows available to the owners of a company when operating income changes.

The relationship can be expressed by the following equation:

$$\text{DFL}=\cfrac {\text{Percentage change in net income}}{\text{Percentage change in operating income}}$$

Alternatively,

$$\text{DFL}=\cfrac {Q(P-V)-F}{Q(P-V)-F-C}$$

DFL helps us to understand how changes in a company’s operating income translate into changes in net income after interest and tax expenses have been factored in.

For example, if a company’s DFL is 2.0, then a 5% increase in operating income is expected to give rise to a 10% increase in net income.

## Degree of Total Leverage (DTL)

If we combine a company’s degree of operating leverage with its degree of financial leverage, we get the degree of total leverage (DTL), which is a measure of the sensitivity of a company’s net income to changes in the number of units produced and sold.

The relationship can be expressed by the following equation:

$$\text{DTL}=\cfrac {\text{Percentage change in net income}}{\text{Percentage change in the number of units sold}}$$

Alternatively,

$$\text{DTL}=\cfrac {Q(P-V)}{Q(P-V)-F-C}$$

and

$$\text{DTL}=\text{DOL} \ast \text{DFL}$$

## Question

If a company’s degree of operating leverage is 2.1, and its degree of financial leverage is 1.6, then its degree of total leverage is closest to:

A. 3.36.

B. 3.70.

C. 1.85.

Solution

DTL = DOL × DFL = 2.1 × 1.6 = 3.36

Calculate and interpret the degree of operating leverage, the degree of financial leverage, and the degree of total leverage

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