1. 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

2. 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

3. 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)

4. 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)

5. 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.

6. 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

7. 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.

8. 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

9. = (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

10. = 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.

11. 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.