chapter 4 measures of leverage

CHAPTER 4MEASURES OF LEVERAGEPresenter’s namePresenter’s titledd Month yyyy

Copyright © 2013 CFA Institute 2

1. INTRODUCTIONLeverage is the use of fixed costs in a company’s cost structure.

- Operating leverage relates to the company’s operating cost structure.- Financial leverage relates to the company’s capital structure.

Fixed Costs Fixed

Costs


WHY WORRY ABOUT LEVERAGE?1. A company’s use of leverage affects its risk and return.

2. Operating leverage and financial leverage provide insight into a company’s business and its future.

3. Leverage helps us understand a company’s future cash flows and the risk associated with those cash flows and, hence, its valuation.


2. LEVERAGE• Leverage increases the volatility of earnings and cash flows → hence, it

increases risk to suppliers of capital (creditors and owners).• Consider two companies, Company One and Company Two, with the following

information:Company

OneCompany

TwoNumber of units produced and sold 1,000 1,000Sales price per unit €250 €250Variable cost per unit €125 €25Fixed operating cost €50,000 €100,000Fixed financing expense €5,000 €55,000

Debt €50,000 €550,000Equity €700,000 €200,000Total assets €750,000 €750,000


WHAT DOES LEVERAGE DO EXACTLY?

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

-€ 150,000

-€ 100,000

-€ 50,000

€ 0

€ 50,000

€ 100,000

€ 150,000

€ 200,000

Company One Company Two

Number of Units Produced and Sold

Net Income

Company Two uses more operating and financial leverage than Company One.


3. BUSINESS RISK AND FINANCIAL RISK• Business risk is the risk associated with the volatility in operating earnings.

- Business risk is composed of both operating and sales risk.• Sales risk is the uncertainty associated with the number of units produced and

sold, as well as the sales price.

Business Risk

Sales Risk

Operating Risk


OPERATING RISK• Operating risk is the risk associated with the mix of variable and fixed

operating expenses.- Operating risk is the sensitivity (i.e., elasticity) of operating earnings to

changes in unit sales.• The degree of operating leverage (DOL) is the ratio of the percentage

change in operating income to the percentage change in units sold.• The per unit contribution margin is the difference between the sales price

and the variable cost per unit. This difference is available to cover fixed operating costs.- Overall, for all units sold, the contribution margin is the difference between

total revenues and variable operating costs.


DOLThe DOL is at Q units produced and sold:

(4-2)

where

Q is the number of units

P is the price per unit

V is the variable operating cost per unit and

F is the fixed operating cost


EXAMPLE: COMPANY ONE AND COMPANY TWO

COMPANY ONE

1.667%

COMPANY TWO

1.800


FINANCIAL RISK• Financial risk is the risk associated with the choice of financing the business.

- The greater the reliance on fixed-cost obligations, such as debt, the greater the financial risk.

- Similar to operating risk, financial risk elasticity is the sensitivity of income available to owners to a change in operating earnings.

• The degree of financial leverage (DFL) is the ratio of the percentage change in net income to the percentage change in operating income.


DFLAt a specific level of operating earnings (and, therefore, Q):

(4-4)

where Q, P, V, and F are as before, and C is the fixed financial cost.


EXAMPLE: COMPANY ONE AND COMPANY TWOCompany One

1.071%

Company Two

1.786%


RETURN ON EQUITY AND THE DFL• The greater the degree of financial leverage, the greater the financial risk.• We can see the leveraging effect by looking at the return on equity (ROE) for

different levels of units produced and sold.• The greater the DFL, the more sensitive the ROE is to changes in the units

produced and sold.


EXAMPLE: RETURN ON EQUITYConsider the example of Company One and Company Two:

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

-80%-60%-40%-20%

0%20%40%60%80%

100%Company One Company Two

Units Produced and Sold

Return on Equity


DEGREE OF TOTAL LEVERAGE• Total leverage is the combined effect of operating leverage and financial

leverage.• The degree of total leverage (DTL) is the product of the degree of operating

leverage and the degree of financial leverage:

(4-6)

Or, equivalently:

DTL = DOL × DTL• If DOL is 3 and DFL is 2, DTL = 2 × 3 = 6.

- So, a 1% change in the units produced and sold results in a 6% change in the earnings to owners.


EXAMPLE: COMPANY ONE AND COMPANY TWOCompany One

1.786

Company Two

3.214


BREAKEVEN QUANTITY• The breakeven point (QBE) is the level of units produced and sold at which the

costs (both variable and fixed) are just covered—that is, net income is zero.• The breakeven point is

(4-7)

• The operating breakeven point (QOBE) is the level of units produced and sold at which the operating costs are covered.


EXAMPLE: COMPANY ONE AND COMPANY TWOCompany One Operating b = 400 units

Company Two Operating b = 444 units


RISKS TO CREDITORS AND OWNERS• Business risk is affected by demand uncertainty, output price uncertainty, and

cost uncertainty.• Financial risk adds to the company’s business risk, increasing the risk to

creditors and owners.• The creditor claims are fixed, whereas the equity claims are residual.• In the event that creditor claims cannot be satisfied, there may be legal

statuses that help sort out the claims:- Reorganization is the restructuring of claims, with the expectation that the

company will be able to continue, in some form, as a going concern.- Liquidation is the situation in which assets are sold and then the proceeds

distributed to claimants.


4. SUMMARY• Leverage is the use of fixed costs in a company’s cost structure. • Business risk is the risk associated with operating earnings and reflects

- sales risk (uncertainty with respect to the price and quantity of sales) and- operating risk (the risk related to the use of fixed costs in operations).

• Financial risk is the risk associated with how a company finances its operations (i.e., the split between equity and debt financing of the business).


SUMMARY (CONTINUED)

• The degree of operating leverage (DOL) is the sensitivity of operating earnings to changes in units produced and sold.

• The degree of financial leverage (DFL) is the sensitivity of cash flows to owners to changes in operating earnings.

• The degree of total leverage (DTL) is the sensitivity of the cash flows to owners to changes in unit sales.

• The breakeven point, QBE, is the number of units produced and sold at which the company’s net income is zero.

• The operating breakeven point, QOBE, is the number of units produced and sold at which the company’s operating income is zero.

chapter 4 measures of leverage

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