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Chapter 16

Chapter 16. Operating and Financial Leverage. After Studying Chapter 16, you should be able to:. Define operating and financial leverage and identify causes of both. Calculate a firm’s operating break-even (quantity) point and break-even (sales) point .

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Chapter 16

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  1. Chapter 16 Operating and Financial Leverage

  2. After Studying Chapter 16, you should be able to: • Define operating and financial leverage and identify causes of both. • Calculate a firm’s operating break-even (quantity) point and break-even (sales) point . • Define, calculate, and interpret a firm's degree of operating, financial, and total leverage. • Understand EBIT-EPS break-even, or indifference, analysis, and construct and interpret an EBIT-EPS chart. • Define, discuss, and quantify “total firm risk” and its two components, “business risk” and “financial risk.” • Understand what is involved in determining the appropriate amount of financial leverage for a firm.

  3. Operating and Financial Leverage • Operating Leverage • Financial Leverage • Total Leverage • Cash-Flow Ability to Service Debt • Other Methods of Analysis • Combination of Methods

  4. Leverage • Capital structure refers to the mix of long term debt and equity maintained by the firm • Leverage results from the use of fixed cost assets • to magnify returns to the firm’s owners •  increased leverage raises risk/return •  decreased leverage lowers risk/return • Management can control leverage in the capital structure, and in turn affect firm value

  5. Leverage • Three types of leverage: • Operating leverage – relates sales to EBIT • Financial leverage – relates EBIT to EPS • Total leverage – relates sales to EPS • Mathematically, these three measures of leverage are related as follows: •  Operating leverage × financial leverage = total leverage •  sales/EBIT x EBIT/EPS = sales/EPS

  6. Types of leverage and income statement:

  7. Operating Leverage Operating Leverage – The use of fixed operating costs by the firm. • One potential “effect” caused by the presence of operating leverage is that a change in the volume of sales results in a “more than proportional” change in operating profit (or loss).

  8. Impact of Operating Leverage on Profits (in thousands) Firm F Firm V Firm 2F Sales $10 $11 $19.5 Operating Costs Fixed 7 2 14 Variable 2 7 3 Operating Profit$1 $ 2 $ 2.5 FC/total costs 0.78 0.22 0.82 FC/sales 0.70 0.18 0.72

  9. Impact of Operating Leverage on Profits • Now, subject each firm to a 50% increase in sales for next year. • Which firm do you think will be more “sensitive” to the change in sales (i.e., show the largest percentage changein operating profit, EBIT)? [ ] Firm F; [ ] Firm V; [ ] Firm 2F.

  10. Impact of Operating Leverage on Profits (in thousands) Firm F Firm V Firm 2F Sales $15 $16.5 $29.25 Operating Costs Fixed 7 2 14 Variable 3 10.5 4.5 Operating Profit$5 $ 4 $10.75 Percentage Change in EBIT* 400% 100% 330% * (EBITt - EBIT t-1) / EBIT t-1

  11. Impact of Operating Leverage on Profits • Firm F is the most “sensitive” firm – for it, a 50% increase in sales leads to a 400% increase in EBIT. • Our example reveals that it is a mistake to assume that the firm with the largest absolute or relative amount of fixed costs automatically shows the most dramatic effects of operating leverage. • Later, we will come up with an easy way to spot the firm that is most sensitive to the presence of operating leverage.

  12. Break-Even Analysis • When studying operating leverage, “profits” refers to operating profits before taxes (i.e., EBIT) and excludes debt interest and dividend payments. Break-Even Analysis – A technique for studying the relationship among fixed costs, variable costs, sales volume, and profits. Also called cost/volume/profit analysis (C/V/P) analysis.

  13. Break-Even Chart Total Revenues QUANTITY PRODUCED AND SOLD Profits 250 Total Costs 175 REVENUES AND COSTS ($ thousands) Fixed Costs 100 Losses Variable Costs 50 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

  14. Break-Even (Quantity) Point How to find the quantity break-even point: EBIT = P(Q) – V(Q) – FC EBIT = Q(P – V) – FC P = Price per unitV = Variable costs per unit FC = Fixed costs Q = Quantity (units) produced and sold Break-Even Point – The sales volume required so that total revenues and total costs are equal; may be in units or in sales dollars.

  15. Break-Even (Quantity) Point • EBIT = Q(P – VC) – FC, so • Q = FC/(P – VC) = Breakeven point

  16. Break-Even (Quantity) Point Breakeven occurs when EBIT = 0 Q (P – V) – FC = EBIT QBE (P – V) – FC = 0 QBE (P – V) = FC QBE = FC/ (P – V) a.k.a. Unit Contribution Margin

  17. Break-Even (Sales) Point How to find the sales break-even point: SBE =FC + (VCBE) SBE =FC + (QBE )(V) or SBE* =FC / [1 – (VC / S) ] * Refer to text for derivation of the formula

  18. Break-Even Point Example • Basket Wonders (BW) wants to determine both the quantity and sales break-even points when: • Fixed costs are $100,000 • Baskets are sold for $43.75each • Variable costs are $18.75 per basket

  19. Break-Even Point (s) Breakeven occurs when: QBE = FC/ (P – V) QBE = $100,000/ ($43.75 – $18.75) QBE = 4,000 Units SBE =(QBE )(V) + FC SBE =(4,000 )($18.75) + $100,000 SBE = $175,000

  20. Break-Even Point • Lv Xi has fixed operating costs of $2,500, the sale price per unit is $10, and variable operating cost per unit is $5. What is the BE point? • Q = 2,500/(10 – 5) = 500 units • At sales of 500 units, the firm’s EBIT equals $0. The firm will have positive EBIT for sales greater than 500 units and negative EBIT, or a loss, for sales less than 500 units. • You can confirm this by substituting values above and below 500 units, along with the other values given into the equation.

  21. Break-Even Point • LvXi wishes to evaluate the impact of several options: • (1) increasing fixed operating costs to $3000, • (2) increasing the sales price per unit to $12.50, • (3) increasing the variable operating cost per unit to $7.50, and • (4) simultaneously implementing all three of these changes. • Substituting the appropriate data into Equation 16.3 yields the following:

  22. Break-Even Point • 1. OPB = 3000/(10 – 5) = 600 units • 2. OPB = 2500/(12.50 – 5) = 333.33 units • 3. OPB = 2500/(10 – 7.50) = 1000 units • 4. OPB = 3000/(12.50 – 7.50) = 600 units • Actions 1&3 (cost increases) raise OPB • Action 2 (revenue inc.) lowers OPB • Action 4 (combined) increases OPB

  23. Break-Even Point • Break-even analysis: – sensitivity • increase in variable effect on OPB • FC increase • P decrease • VC increase • OPB = Operating break-even point

  24. Break-Even Chart Total Revenues QUANTITY PRODUCED AND SOLD Profits 250 Total Costs 175 REVENUES AND COSTS ($ thousands) Fixed Costs 100 Losses Variable Costs 50 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000

  25. Degree of Operating Leverage (DOL) DOL at Q units of output (or sales) Degree of Operating Leverage – The percentage change in a firm’s operating profit (EBIT) resulting from a 1 percent change in output (sales). Percentage change in operating profit (EBIT) = Percentage change in output (or sales)

  26. Degree of Operating Leverage (DOL)

  27. Degree of Operating Leverage (DOL) • Operating leverage: the potential use of fixed operating costs to magnify the effects of changes in sales on the firm’s EBIT •  an increase (decrease) in sales results in a more-than-proportionate increase (decrease) in EBIT • the ‘degree of operating leverage’ (DOL) equals: • DOL = (% change EBIT) / (% change sales) • An alternative formula (at base sales level, Q) is: • DOL = Q(P – VC)/[Q(P – VC) – FC]

  28. Computing the DOL DOLQ units Calculating the DOL for a single product or a single-product firm. Q (P – V) = Q (P – V) – FC Q = Q – QBE

  29. Computing the DOL DOLS dollars of sales Calculating the DOL for a multiproduct firm. S – VC = S – VC – FC EBIT + FC = EBIT

  30. Break-Even Point Example • Lisa Miller wants to determine the degree of operating leverage at sales levels of 6,000 and 8,000 units. As we did earlier, we will assume that: • Fixed costs are $100,000 • Baskets are sold for $43.75each • Variable costs are $18.75 per basket

  31. Computing BW’s DOL DOL6,000 units Computation based on the previously calculated break-even point of 4,000 units 6,000 3 = = 6,000 – 4,000 8,000 2 = • DOL8,000 units = 8,000 – 4,000

  32. Interpretation of the DOL A 1% increase in sales above the 8,000 unit level increases EBIT by 2% because of the existing operating leverage of the firm. 8,000 2 = • DOL8,000 units = 8,000 – 4,000

  33. Interpretation of the DOL 5 4 3 2 1 DEGREE OF OPERATING LEVERAGE (DOL) 0 2,000 4,000 6,000 8,000 –1 –2 –3 QBE –4 –5 QUANTITY PRODUCED AND SOLD

  34. Interpretation of the DOL • Lv Xi swaps part of its variable operating costs (eliminating sales commissions) for fixed operating costs (increasing sales salaries). Result - a reduction in the variable operating cost per unit from $5 to $4.50 and an increase in the fixed operating costs from $2,500 to $3,000. EBIT of $2,500 at the 1,000-unit sales level is unchanged. What is Lv Xi’s DOL? • DOL = Q(P – VC)/[Q(P – VC) – FC] • = 1,000(10 – 4.50)/[1,000(10 – 4.50) – 3,000] • = 2.2 • Thus, the higher the firm’s fixed operating costs relative to variable operating costs, the greater the degree of operating leverage.

  35. Interpretation of the DOL Key Conclusions to be Drawn from the previous slide and our Discussion of DOL • DOL is a quantitative measure of the “sensitivity”of a firm’s operating profit to a change in the firm’s sales. • The closer that a firm operates to its break-even point, the higher is the absolute value of its DOL. • When comparing firms, the firm with the highest DOL is the firm that will be most “sensitive” to a change in sales.

  36. DOL and Business Risk Business Risk – The inherent uncertainty in the physical operations of the firm. Its impact is shown in the variability of the firm’s operating income (EBIT). • DOL is only one component of business risk and becomes “active” only in the presence of sales and production cost variability. • DOL magnifies the variability of operating profits and, hence, business risk.

  37. Application of DOL for Our Three Firm Example Use the data in Slide 16–8 and the following formula for Firm F : DOL = [(EBIT + FC)/EBIT] 1,000 +7,000 8.0 = • DOL$10,000 sales = 1,000

  38. Application of DOL for Our Three Firm Example Use the data in Slide 16–8 and the following formula for Firm V : DOL = [(EBIT + FC)/EBIT] 2,000 +2,000 2.0 = • DOL$11,000 sales = 2,000

  39. Application of DOL for Our Three-Firm Example Use the data in Slide 16–8 and the following formula for Firm 2F : DOL = [(EBIT + FC)/EBIT] 2,500 +14,000 = • DOL$19,500 sales 6.6 = 2,500

  40. Application of DOL for Our Three-Firm Example The ranked results indicate that the firm most sensitive to the presence of operating leverage is Firm F. Firm FDOL = 8.0 Firm VDOL = 6.6 Firm 2FDOL = 2.0 Firm F will expect a 400% increase in profit from a 50% increase in sales (see Slide 16–10 results).

  41. Financial Leverage • Financial leverage is acquired by choice. • Used as a means of increasing the return to common shareholders. Financial Leverage – The use of fixed financing costs by the firm. The British expression is gearing.

  42. EBIT-EPS Break-Even, or Indifference, Analysis EBIT-EPS Break-Even Analysis – Analysis of the effect of financing alternatives on earnings per share. The break-even point is the EBIT level where EPS is the same for two (or more) alternatives. Calculate EPS for a given level of EBIT at a given financing structure. (EBIT – I) (1 – t) – Pref. Div. EPS = # of Common Shares

  43. Current common equity shares = 50,000 $1 million in new financing of either: All C.S. sold at $20/share (50,000 shares) All debt with a coupon rate of 10% All Pref.Shares with a dividend rate of 9% Expected EBIT = $500,000 Income tax rate is 30% Basket Wonders has $2 million in LT financing (100% common stock equity). EBIT-EPS Chart

  44. EBIT $500,000 $150,000* Interest 0 0 EBT $500,000 $150,000 Taxes (30% x EBT) 150,000 45,000 EAT $350,000 $105,000 Preferred Dividends 0 0 EACS $350,000 $105,000 # of Shares 100,000 100,000 EPS $3.50 $1.05 Common Stock Equity Alternative EBIT-EPS Calculation with New Equity Financing * A second analysis using $150,000 EBIT rather than the expected EBIT.

  45. EBIT-EPS Chart 6 5 Common 4 3 Earnings per Share ($) 2 1 0 0 100 200 300 400 500 600 700 EBIT ($ thousands)

  46. EBIT $500,000 $150,000* Interest 100,000 100,000 EBT $400,000 $ 50,000 Taxes (30% x EBT) 120,000 15,000 EAT $280,000 $ 35,000 Preferred Dividends 0 0 EACS $280,000 $ 35,000 # of Shares 50,000 50,000 EPS $5.60 $0.70 Long-term Debt Alternative EBIT-EPS Calculation with New Debt Financing * A second analysis using $150,000 EBIT rather than the expected EBIT.

  47. EBIT-EPS Chart Debt 6 5 Indifference point between debtand common stock financing Common 4 3 Earnings per Share ($) 2 1 0 0 100 200 300 400 500 600 700 EBIT ($ thousands)

  48. EBIT $500,000 $150,000* Interest 0 0 EBT $500,000 $150,000 Taxes (30% x EBT) 150,000 45,000 EAT $350,000 $105,000 Preferred Dividends 90,000 90,000 EACS $260,000 $ 15,000 # of Shares 50,000 50,000 EPS $5.20 $0.30 Preferred Stock Alternative EBIT-EPS Calculation with New Preferred Financing * A second analysis using $150,000 EBIT rather than the expected EBIT.

  49. EBIT-EPS Chart Debt 6 Preferred 5 Common 4 3 Earnings per Share ($) Indifference point between preferred stock andcommon stockfinancing 2 1 0 0 100 200 300 400 500 600 700 EBIT ($ thousands)

  50. What About Risk? Debt 6 Lower risk. Only a small probability that EPS will be less if the debt alternative is chosen. 5 4 Common Probability of Occurrence (for the probability distribution) 3 Earnings per Share ($) 2 1 0 0 100 200 300 400 500 600 700 EBIT ($ thousands)

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