Leverage

1
Leverage
2
The Impact of Leverage

• Business Risk
• The variability in the earnings before interest
  and taxes
• Financial Risk
• The additional variability in the net income due
  to leverage

3
Break-Even Analysis

• Break-even Point
• It is that quantity at which earnings before
  interest and taxes, EBIT, is zero
• The earning before interest and taxes is EBIT
  TR - (VC FC)
• Letting p, q, avc, and FC represent price,
  quantity, average variable cost and fixed cost,
  respectively, the EBIT can also be represented
  as EBIT p q - avc q - FC (p - avc) q - FC

4
Break-Even Analysis

• The break-even quantity
• Setting EBIT equal to zero and letting b denote
  the break-even quantity, yields
• The break-even sales
• Let revenue be proportional to variable cost,
  i.e., tr a vc. Setting EBIT equal to zero and
  letting B denote the break-even revenue, yields

5
Break-Even Analysis

• The break-even point is random if the firms
  sales are random. Increasing the product price
  decreases the break-even point as the movie
  shows.
• This slide shows how the cost and EBIT functions
  are affected by changes in the average variable
  cost movie.
• The break-even point can also be affected by
  changing the operating leverage, i.e., fixed cost.

6
Business Risk

• Leverage
• The use of credit or borrowed funds to improve
  one's speculative capacity
• Operating Leverage
• This notion refers to the fixed cost in EBIT,
  independent of how it is financed.
• Operating leverage is a business risk concept,
  i.e., as opposed to a financial risk concept.
• In this case, the speculative capacity is that
  capacity that allows the firm to engage in risky
  business transactions on the chance of quick or
  considerable profit.

7
Operating Leverage

• The degree of operating leverage is denoted by
  DOL and defined asor as

8
Operating Leverage

• Observations
• The DOL is undefined at the break-even point.
• Operating leverage exists when DOL gt 1.
• At sales levels above the break-even point, the
  DOL is a decreasing function of sales.
• The following figure provides a characterization
  of that decrease.
• Note that the slope of the EBIT function is p -
  avc while the slope of a chord from the origin to
  a point on the EBIT function is EBIT/q. Since
  the slope of the chord increases, the DOL
  decreases.

dollars
R
V F
EBIT
quantity
c
d
b
9
Financial Risk

• Financial Leverage
• This notion refers to the fixed costs due to debt
  issues
• Financial leverage is a financial risk concept.
• Degree of Financial Leverage (DFL)
• The DFL is a measure of the responsiveness of
  shareholder returns to the EBIT.
• The measure of shareholder returns used to
  determine eps is net income, NI. The NI is
  defined as NI EBIT - I - T, where I represents
  interest on debt and T represents taxes.
• NI EBIT - I - t (EBIT - I) (1 - t) (EBIT - I)
• The DFL is defined as

10
Financial Leverage

• Alternate Representation
• Observations
• The DFL 1 for the unlevered firm
• The DFL is undefined for EBIT I
• The condition EBIT lt I defines a financial
  distress event.
• The DFL is greater than one and increasing in
  leverage for EBIT gt I.
• A larger DFL implies a larger fluctuation in NI
  and EPS.

11
Leverage

• For the levered firm, a one percentage change in
  sales implies a larger percentage change in EBIT
  which in turn implies an even larger percentage
  change in NI and EPS.
• The degree of combined leverage, DCL, is a
  measure designed to capture these percentage
  changes. It is defined as

12
Leverage

• Alternate Representation

13
Leverage

• Alternate Representationsince NI (1
  - t) (EBIT - I) (1 - t) ((p - avc) q - F - I)
  and

14
Leverage Observations

• The DCL is undefined at the financial distress
  point f.
• Leverage exists when DCL gt 1.
• At sales levels above the financial distress
  point, the DCL is a decreasing function of sales.
• The following figure provides a characterization
  of that decrease.
• Note that the slope of the NI function is (1 - t)
  (p - avc) while the slope of a chord from the
  origin to a point on the NI function is NI/q.
  Since the slope of the chord increases, the DCL
  decreases.

dollars
R
V F
EBIT
NI
quantity
f