cfa level 1 corporate finance e book - part 6

8/13/2019 CFA Level 1 Corporate Finance E Book - Part 6

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Corporate Finance E-Book

Part 6 of 7


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Measures of Leverage


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Leverage, in the sense we use it here, refers to the amount of fixed costs a firm has. These fixed costs may

be fixed operating expenses, such as building or equipment leases, or fixed financing costs, such as interestpayments on debt. Greater leverage leads to greater variability of the firms after-tax operating earnings and

net income.

Business risk refers to the risk associated with a firm's operating income and is the result of uncertainty

about a firm's revenues and the expenditures necessary to produce those revenues. Business risk is the

combination of sales risk and operating risk.

Sales risk is the uncertainty about the firm's sales.

Operating risk refers to the additional uncertainty about operating earnings caused by fixedoperating costs. The greater the proportion of fixed costs to variable costs, the greater a firm's

operating risk.

Financial risk refers to the additional risk that the firm's common stockholders must bear when a firm uses

debt financing. When a company finances its operations with debt, it takes on fixed expenses in the form of

interest payments. The greater the proportion of debt in a firm's capital structure, the greater the firm's

financial risk.


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The degree of operating leverage (DOL) is defined as the percentage change in operating income (EBIT) that

results from a given percentage change in sales:DOL= (Percentage change in EBIT) / (Percentage change in sales) = (EBIT/EBIT) / (Q/Q)

To calculate a firm's DOL for a particular level of unit sales, Q, DOL is:

DOL= {Q(P-V)} / {Q(P-V)-F}

Where:

Q = quantity of units sold

P = price per unit

V = variable cost per unit

F = fixed costs

Multiplying, we have:

DOL = S-TVC / S-TVC-F

where:

S = sales

TVC = total variable costs

F = fixed costs

Note that in this form, the denominator is operating earnings (EBIT).


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Example: Degree of operating leverage

Consider the costs for the projects presented in the following table. Assuming that 100>000 units are produced

for each firm, calculate the DOL for A Company and B Company.

Operating Costs for A and B

A Company B Company

Price $4.00 . $4.00Variable costs $3.00 $2.00

Fixed costs $40,000 $120,000

Revenue $400,000 $400,000

For A Company:

DOL (A) = Q(P-V) / {Q(P-V)-F} = {100000 (4-3)} / {100,000 (4-3) 40,000}

DOL (A) = 100,000 / 60,000 = 1.67

For B Company:

DOL ( B) = Q(P-V) / {Q(P-V)-F} = 100,000 (4-2) / {100,000 (4-2) 120,000}

DOL (B) = 200,000 / 80,000 = 2.50

The results indicate that if B Company has a=1Dok increase in sales, its EBIT will increase by 2.50 X 10% =

25%, while for A Company, the increase in EBIT will be 1.67 x 10% = 16.7%.


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It is important to note that the degree of operating leverage for a company depends on the level of sales. For

example, if A Company sells 300,000 units, the DOL is decreased:

DOL (A) = Q (P-V) / {Q (P-V)-F} = 300,000 (4-3) / (300,000 (4-3) 40,000} = 300,000 / 260,000 = 1.15

DOL is highest at low levels of sales and declines at higher levels of sales.

The degree of financial leverage (DFL) is interpreted as the ratio of the percentage change in net income (or

EPS) to the percentage change in EBIT:

DFL = Percentage change in EPS / Percentage change in EBIT

For a particular level of operating earnings, DFL is calculated as:

DFL = EBIT / EBIT - Interest


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Example: Degree of financial leverage

From the previous example, A Company's operating income for selling 100,000 units is $60,000. Assume that

A Company has annual interest expense of $18,000. If As EBIT increases by 10%, by how much will its -

earnings per share increases?

Answer

DFL = EBIT / EBIT I = $60,000 / $60,000 - $18,000 = 1.43

%EPS = DFL X %EBIT = 1.43 X 10% = 14.3%.

Hence, earnings per share will increase by 14.3%.



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The degree of total leverage (DTL) combines the degree of operating leverage and financial leverage. DTL

measures the sensitivity of EPS to change in sales. DTL is computed as:

DTL = DOL X DFL

DTL = %EBIT / %sales X %EPS / %EBIT = %EPS / %sales

DTL = Q ( P V) / { Q ( P-V) F I

DT = S TVC / S TVC F I

Example: Degree of total leverage

Continuing with our previous example, how much will A's EPS increase if A . increases its sales by 10%?

Answer:

From the previous Example:

DOLA= 1.67

DFLA= 1.43DTL = DOL x DFL = 1,67 x 1.43 = 2.39

Note that we also, could have calculated the DTL the long way. From the previous example, the current value

of A's dollar sales is $4 X 100,000 = $400,000.

DTL = S TVC / S TVC F I = $400,000 - $300,000 / $400,000 - $300,000 - $40,000 - $18,000 = 2.38

% EPS = DTL X %sales = 2.38 X 10% = 23.8%

EPS will increase by 23.8%.



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The level of sales that a firm must generate to cover all of its fixed and variable costs is called the breakeven

quantity. The breakeven quantity of sales is the quantity of sales for which revenues equal total costs, so thatnet income is zero. We can calculate the breakeven quantity by simply determining how many units must be

sold to just cover total fixed costs.

For each unit sold, the contribution margin, which is the difference between price and variable cost per unit, is

available to help cover fixed costs. We can thus describe the breakeven quantity of sales, QBE, as:

QBE= Fixed operating costs + fixed financing costs / price variable cost per unit.


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Example: Operating breakeven quantity of sales

Calculate the operating breakeven quantity of sales for A and B, using the same data from the previous

example.

Answer:

For A, the operating breakeven quantity of sales is:

$10,000 / ($4.00 - $3.00) = 10,000 units

For B, the operating breakeven quantity of sales is:

$80,000 / ($4.00 - $2.00) = 40,000 units


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We can summarize the effects of leverage on net income. Through an examination of Figures I and 2. Other

things equal, a firm that chooses operating and financial structures that result in greater total fixed costs willhave a higher breakeven quantity of sales. Leverage of either type magnifies the effects of changes in sales on

net income. The further a firm's sales are from its breakeven level of sales, the greater the magnifying effects of

leverage on net income.

These same conclusions apply to operating leverage and the operating breakeven quantity of sales. One

company may choose a larger scale of operations (larger factory), resulting in a greater operating breakeven

quantity of sales and greater leverage, other things equal.


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