Seeing is believing!

Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation.

Subject 1. Business Risk and Operating Leverage PDF Download

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 17

User Comment
thud How come EBIT = [Q(P - V)] in the business risk section and in the financial risk section it's [Q(P - V) - F]???
xiong Q (P - V) is the percentage change in EBIT. It has nothing to do with F. Q (P - V) - F is EBIT itself.
jd2442424 The derivation of DFL stops short one step before the end. You also need to divide percent change in EBIT by the percent change in EPS ( delta EBIT / (EBIT - I) ) to get EBIT / (EBIT - 1).
chris76 Q(P-V) is not the percentage change in Ebit...Nonetheless both formulas as presented are correct (a little algebra will confirm this)
johntan1979 DOL: What is considered high and what is low? Is 1.67 (example in the notes) high?
johntan1979 Towards the end of the notes, it is stated that "DFL is the %change in EPS divided by the %change in EBIT."

I thought DFL = %change in NI / %change in EBIT?

NI is definitely NOT = EPS, and I don't think they are interchangeable.
johntan1979 Hmmm... just read from Kaplan's Schweser notes that the two are OK to be used interchangeably for DFL.

So confusing! :(
gill15 I just read the CFA curriculum book...just easier sometimes
robertucla You have to compare dol to comparable firms in industry
RamaG @jonathan : EPS = NI / # of share outstanding , since share float is constant , % change in EPS = % change in NI, so are interchangeable when considering % change
Shaan23 This operating profit thing is confusing. If you do Q.5 in the last section or one of those Q's. We found operating profit for a question and used

Q(P - V)

but in this section it uses FC as well
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
khalifa92 you guys wake up
Q(P-VC) or Q(P-VC) - F are mentioned in two different formulas with two different understanding
the first one is the relation between operating profit to changes in unit sold
the second one includes the first formula and moves down in the income statemet to take measure of the financial cost which leads to EBIT and relate it to net income and thus net income which in the end becomes all money the company can do whatever it wants with can become used to calculate EPS if they want to distribute it or keep it as retained earning thus they are interchangeable.
khalifa92 but iam more confused because the second part of this LOS isnt in the book so ill ignore it for now.
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.
You need to log in first to add your comment.
I used your notes and passed ... highly recommended!


My Own Flashcard

No flashcard found. Add a private flashcard for the subject.