The Effect of Operating Leverage on Profit

RELATIONSHIP BETWEEN EBIT AND EPS (6)

 Indifference point = Total assets x Interest payable

 If EBIT is lower than the indifference point => Equity financing generates higher EPS than debt financing

 If EBIT exceeds the indifference point => Option

FINANCIAL LEVERAGE (1)

- Financial leverage measures the extent to which a company uses debt.

- Degree of Financial Leverage (DFL) measures the change in EPS in response to a change in EBIT.

Debt financing yields higher EPS than equity financing

DFL 

 EPS / EPS

 EBIT / EBIT

(9.6)

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FINANCIAL LEVERAGE (2)

- DFL in case the capital structure includes common stock, debt and preferred stock.

FINANCIAL LEVERAGE (3)

- DFL of preferential stock financing plan.

DFL EBIT (9.7)

EBIT I PD /(1  t )

DFL 2,700,000

 2,700,000

2,700,000  550,000 /(1  0.4)

 1.51

- DFL in case the capital structure consists of common stock and debt.

- DFL of debt financing option.

DFL EBIT (9.8)

EBIT I

DFL

2,700,000

 2,700,000

2,700,000  600,000

 1.29

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TOTAL LEVERAGE - DTL (1)

Combined leverage measures the impact of changes in sales or output on EPS.

DTL DOLxDFL

(9.9)

DTL 

Q ( P  V )

Q ( P  V ) F I   PD /(1 t ) 

EBIT F

EBIT  I   PD /(1  t ) 

(9.10)

(9.11)

Fulbright Economics Teaching Program Financial Analysis Lecture 8 Academic Year 2006-2007 Lecture

OPERATING LEVERAGE AND FINANCIAL LEVERAGE

In mechanics, we are familiar with the concept of leverage as a tool to amplify force to turn a small force into a larger force acting on the object we need to move. In business, people borrow the term “leverage” to refer to the use of fixed costs to increase the profitability of the company. In this article, we will explore the principles of using leverage in business, including operating leverage and financial leverage.

1. Operating leverage

1.1 Analysis of the impact of operating leverage

Operating leverage is the extent to which a company uses fixed operating costs. Here we only analyze the short run because in the long run all costs are variable.

Fixed costs are costs that do not change when volume changes. Fixed costs can include things like depreciation, insurance, a portion of utility costs, and a portion of administrative costs.

Variable costs are costs that change when quantity changes, such as raw materials costs, direct labor, a portion of utilities, sales commissions, and a portion of administrative costs.

In business, we invest fixed costs in the hope that sales volume will generate enough revenue to cover both fixed and variable costs. Like a lever in mechanics, the presence of fixed operating costs causes changes in sales volume to magnify changes in profit (or loss). To illustrate this, consider the example given in Table 8.1 on page 2.

The results of the analysis of the impact of operating leverage are shown in Part B. For each company, revenue and variable costs increased by 50% while fixed costs remained unchanged. All companies showed the impact of operating leverage, which was shown in that revenue increased by only 50% but profits increased at a greater rate, namely 400, 100 and 330% for companies F, V and company 2F, respectively.

Table 8.1 : Effect of operating leverage on profits

Company F	Company V	2F Company
Part A : Before changing revenue
Revenue	10,000$	11,000$	19,500$
Operating costs
Fixed costs	7,000	2,000	14,000
Variable costs	2,000	7,000	3,000
Operating profit (EBIT)	1,000	2,000	2,500
Operating leverage ratio
Fixed cost/total cost	0.78	0.22	0.82
Fixed cost/revenue	0.70	0.18	0.72
Part B : After revenue increases by 50% in the following years
Revenue	15,000$	16,500$	29,250$
Operating costs
Fixed costs	7,000	2,000	14,000

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Fulbright Economics Teaching Program Financial Analysis Lecture 8

Lesson

Variable costs

3,000	10,500	4,500
Operating profit (EBIT)	5,000	4,000	10,750
Percentage change in EBIT	400%	100%	330%
(EBIT t – EBIT t -1 )/ EBIT t -1

1.2 Break-even analysis

Break-even analysis is a technique for analyzing the relationship between fixed costs, variable costs, profits, and sales volume. To illustrate the break-even analysis technique, let's take the following example: Suppose a bicycle manufacturing company has a unit selling price of $50, annual fixed costs of $100,000, and variable costs of $25/unit. We will analyze the relationship between total operating costs and total revenue. Figure 8.1 (page 3) illustrates the relationship between total revenue, total operating costs, and profits for each level of output and sales volume. It should be noted that here we are only interested in operating costs, so profits here are defined as operating profits before taxes. Thus, interest on debt and preferred dividends are not relevant when analyzing operating leverage. However, when analyzing financial leverage (later), we will consider this issue.

Figure 8.1 : Break-even analysis

Revenue and expenses ($1000)

Revenue

Total cost

Variable cost

Fixed cost

Production and consumption quantity

1000

2000

3000

4000

5000

6000

300

250

200

150

100

In Figure 8.1, the intersection point between the two lines of total revenue and cost is the break-even point because at this point revenue equals cost and, therefore, profit is 0. In Figure 8.1, the break-even point is the point where output is 4000. Mathematically, to find the break-even point we do the following:

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Fulbright Economics Teaching Program Financial Analysis Lecture 8

Lesson

Let EBIT = earnings before interest and taxes (operating profit) P = unit selling price

V = unit variable cost (P – V) = gross profit

Q = quantity produced and consumed F = fixed cost

Q BE = break-even quantity

At the break-even point, revenue equals costs and EBIT is 0. Therefore:

PQ BE = VQ BE + F (P – V)Q BE = F

Q BE = F/ (P – V) (8.1)

In the above example, if we apply formula (8.1), we will have break-even output Q BE = 100,000/ (50 – 25)

= 4,000 units. If the sales volume exceeds the break-even point (4,000 units), there will be a profit. Conversely, if the sales volume falls below the break-even point, the company will incur a loss.

The break-even point Q BE as determined above represents the break-even output. To find the break-even revenue, we multiply the break-even output by the unit selling price. In the above example, the break-even output Q BE = 4000 and the unit selling price P = 50$, so the break-even revenue will be 50 x 4000 = 200,000$.

1.3 Degree of operating leverage (DOL)

As analyzed in the previous section, we see that under the impact of operating leverage, a change in the number of sales results in a profit (or loss) increasing at a greater rate. To measure the impact of operating leverage, we use the degree of operating leverage (DOL). The degree of operating leverage (DOL) is defined as the percentage change in operating profit compared to the percentage change in output (or revenue). Therefore:

(8.2)

Percentage change in profit

operating profit Percentage change in output (or revenue)

Degree of operating leverage (DOL) at production level =

quantity Q (revenue S)

DOL

  EBIT / EBIT

 Q / Q

It should be noted that the degree of leverage may be different at different levels of output (or revenue). Therefore, when we talk about leverage, we should specify the leverage at a certain level of output Q or revenue S.

The above formula (8.2) is essential for defining and understanding the degree of operating leverage, but it is difficult to calculate in practice due to the difficulty of collecting EBIT data. To make the calculation of DOL easier, we make some changes. Knowing that gross profit equals revenue minus expenses, we have:

EBIT = PQ – (VQ + F) = PQ – VQ – F = Q(P – V) – F

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Fulbright Economics Teaching Program Financial Analysis Lecture 8

Lesson

Because the selling price P and fixed costs F are fixed,  EBIT =  Q(P – V). Thus:

 EBIT EBIT

  Q ( P  V )

Q ( P  V )  F

Substitute into formula (8.2), we get:

 Q ( P V )

Q ( P  V )  F

⎛  Q ( P  V ) ⎞⎛ Q ⎞ Q ( P  V )

DOL Q  Q

 ⎜ ⎜ Q ( P  V )  F ⎟ ⎟ ⎜ ⎜  Q ⎟ ⎟  Q ( P  V )  F

DOL Q

⎝

 Q ( P  V )

Q ( P  V )  F

⎠⎝⎠

(8.3)

Dividing the numerator and denominator of (8.3) by (P – V), the formula (8.3) can be rewritten as:

Q ( P V )

DOL Q

( P  V )

Q ( P  V )  F

( P  V )

Q Q BE

(8.4)

Formulas (8.3) and (8.4) are used to calculate the degree of operating leverage in terms of output Q. These two formulas are only suitable for companies whose products are unique, such as cars or computers. For companies whose products are diverse and cannot be calculated in units, we use the degree of leverage based on revenue. The formula for calculating the degree of leverage based on revenue is as follows:

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Fulbright Economics Teaching Program Financial Analysis Lecture 8

Lesson

DOL S

 S  V

S V F

 EBIT  F

EBIT

where S is revenue and V is total variable costs.

Applying formula (8.4) to the example we have considered from the beginning of the lesson until now, we have:

So the degree of operating leverage at output level Q = 5000 is 5. What does this mean? It means

DOL 5000

DOL 6000

Q

Q Q BE

Q

Q Q BE

 5000  5

5000  4000

 6000  3

6000  4000

(8.5)

that is, from a sales volume of 5,000 units, for every percentage change in sales volume, operating profit changes by 5 percent. It should also be noted that when output increases from 5,000 to 6,000 units, the degree of operating leverage decreases from 5 to 3, meaning that from an output volume of 6,000 units, for every percentage change in sales volume, operating profit changes by 3 percent. Therefore, from the break-even point, the more output increases, the less leverage there is.

1.4 Relationship between operating leverage and break-even point

To see the relationship between operating leverage and the break-even point, we tabulate profits and operating leverage at different levels of output. Table 8.2 below shows us profits and operating leverage at different levels of output.

Table 8.2 : Profit and operating leverage at different levels of output

Production and consumption quantity

Operating profit (EBIT)	Degree of operating leverage (DOL)
(Q)
0	- 100,000	0.00
1000	- 75,000	- 0.33
2000	- 50,000	- 1.00
3000	- 25,000	- 3.00
Q BE = 4000	0	Unknown
5000	25,000	5.00
6000	50,000	3.00
7000	75,000	2.33
8000	100,000	2.00

Table 8.2 shows that the further the volume moves from the break-even point, the greater the operating profit or loss, and conversely the smaller the degree of operating leverage (DOL). The relationship between volume and operating profit is linear as shown in Figure 8.1. Figure 8.2 below illustrates the relationship between volume and operating leverage.

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Fulbright Economics Teaching Program Financial Analysis Lecture 8

Lesson

Figure 8.2 : Relationship between sales volume and operating leverage

Operating leverage

0 2000 3000

- 1

- 3

4000 5000 6000

8000

Production and consumption quantity

Figure 8.2 gives us some observations as follows:

The degree of operating leverage approaches infinity as the quantity produced and sold approaches the break-even point.

As production and consumption volumes move further beyond the break-even point, the degree of leverage approaches 1.

1.5 Relationship between operating leverage and business risk

Business risk is the risk that operating profits will decline due to fluctuations in the operations of a business. It should be noted that operating leverage is only one component of business risk. Other elements of business risk are the variability or volatility of revenues and costs of production. These are the two main elements of business risk, and operating leverage amplifies the impact of these factors on the operating profits of a business. However, operating leverage itself is not the source of risk, because high leverage is meaningless if revenues and fixed cost structures are fixed. Therefore, it would be wrong to equate operating leverage with business risk, because the root is variability in revenues and costs of production, but operating leverage has the effect of amplifying the variability of profits and, therefore, business risk.

From this perspective, operating leverage can be viewed as a form of potential risk that only becomes an operating risk when there are fluctuations in revenue and production costs.

1.6 The significance of operating leverage for financial management

After studying operating leverage, let us ask the question: How is understanding a company's operating leverage useful to a CFO? As a CFO, you need to know in advance how changes in revenue will affect operating profit. Operating leverage is a tool that helps you answer this question. Sometimes knowing the operating leverage in advance can help a company decide its revenue and cost policies more easily. But in general, companies do not like to operate under conditions of high operating leverage because in such a situation, a change in operating leverage is all it takes.

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