DOL, DFL, and DTL

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.

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 following equation can express the relationship:

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

Operating income is, however, equal to the difference between revenue and total operating costs (variable and fixed costs). Considering 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.

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 following equation can express the relationship:

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

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). The degree of total leverage is a measure of the sensitivity of a company’s net income to changes in the number of units produced and sold.

The equation below can express the relationship:

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

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

The correct answer is A.

DTL = DOL × DFL = 2.1 × 1.6 = 3.36

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

    Subscribe to our newsletter and keep up with the latest and greatest tips for success
    Shop Actuarial Exams Prep Shop Graduate Admission Exam Prep


    Sergio Torrico
    Sergio Torrico
    2021-07-23
    Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
    diana
    diana
    2021-07-17
    So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
    Kriti Dhawan
    Kriti Dhawan
    2021-07-16
    A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
    nikhil kumar
    nikhil kumar
    2021-06-28
    Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
    Marwan
    Marwan
    2021-06-22
    Great support throughout the course by the team, did not feel neglected
    Benjamin anonymous
    Benjamin anonymous
    2021-05-10
    I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
    Daniel Glyn
    Daniel Glyn
    2021-03-24
    I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
    michael walshe
    michael walshe
    2021-03-18
    Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.