Ch.6 Break-even and Leverage Analysis

Goals:

1. Fixed and variable costs

2. Operating and cash break-even points

3. Business risks and financial risk

4. DOL, DFL and DCL

1. Variable and fixed costs

Variable costs: costs which are expected to change at the same rate as the firm ‘s level of sales

Fixed costs: costs that are constant regardless of production or sales

2. Operating Break-even points

Level of sales (either units or dollars) which cause profits (EBIT) to be equal to zero.

Ex) In terms of units

Q(P-V) - F = EBIT

If EBIT = 0, then

Q = F/ (P-V)

Ex) In terms of dollars

BE = P * Q

= P * F/(P-V) = F/[(P-V)/P]

Here (P-V) is called “ contribution margin”

It is useful in dealing with Target EBIT.

Q(P-V) - F = EBIT

If EBIT not 0, then

Q = (F + EBIT)/ (P-V)

3. Cash Break-even point

Q = (F- Depreciation)/(P-V)

4. Leverage Analysis

Leverage: a multiplication of changes in sales resulting in even larger changes in profitability measure. This is due to fixed costs.

4-1) Business risk:

• Defined as the variability of EBIT due to fixed costs.

• The more variable a firm’s revenues, the more variable its EBIT

4-2) Financial risk:

• Defined as the variability of NI due to financial obligation

• Defined as the incapability of meeting its fixed financial obligation

• The more debts, the higher probability that the firm won’t be able to pay interest and dividends.

• Now, our new question is how to measure these risks.

• 4-3) Degree of Operating Leverage:

• If a firm’s costs are variable, changes in sales will lead to the same percentage change in EBIT. However, if the firm has fixed costs, EBIT will change by more than sales.

• This is directly related to the business risk.

• Degree of Operating Leverage (DOL):

= % change in EBIT / % change in Sales

= (Sales - Variable Costs) / EBIT

4-4) Degree Of Financial Leverage

• Here concerns are fixed financial costs composed of interest expenses and preferred dividends.

• This is measured by degree of financial leverage

= % change in EPS / % change in EBIT

• = EBIT/(EBT - PD/(1-t))

• Here PD means preferred dividends

• and t means tax rate

4-5) Degree of Combined Leverage

• = % change in EPS / % change in Sales

• = DOL*DFL

• It is about combined effect.

• Ex) comparing 2001 to 2002

• DCL declines. Due to the constant fixed costs, relative to increasing sales.

• As sales increase above the break-even point, leverage will decline regardless of the measure which is used.