Breakeven and Leverage Byers

Risk Two types of Risk: Business Risk & Financial Risk Business Risk Risk Due to Operations Measured by variability of EBIT (earnings before interest and taxes)

Risk Two types of Risk: Business Risk & Financial Risk Financial Risk Risk due to raising money with fixed income securities Financial risk is high with high levels of debt financing Financial leverage - the use of fixed income securities to finance a portion of assets

EBIT = Sales – Variable Costs - Fixed Costs Break-even Analysis Calculation of Break-even Quantity EBIT = Sales – Variable Costs - Fixed Costs Find Quantity which results in EBIT = $0

Break-even Analysis Calculation of Break-even Quantity F QB = P – V Where: QB = Break-even Quantity P = Price per Unit F = Total Fixed Costs V = Variable Costs per Unit

Break-even Analysis Calculation of Break-even Quantity F QB = P – V Example: Calculation of Break-even Quantity F P – V QB = Fixed Costs = $1,000,000 per year Price = $800/unit Variable Costs = $400/unit

Break-even Analysis Calculation of Break-even Quantity F QB = P – V Example: Calculation of Break-even Quantity F P – V QB = Fixed Costs = $1,000,000 per year Price = $800/unit Variable Costs = $400/unit $1,000,000 $800 – $400 QB = = 2,500 Units

Break-even Analysis Calculation of Break-even Sales Level (S*) To Find S* for a single product use Break-even Quantity (QB): Calculation of Break-even Sales Level (S*) S* = QB x P S* = 2,500 units x $800 = $2,000,000

Break-even Analysis Calculation of Break-even Sales Level (S*) May want to Calculate the Break-even Sales Level (S*) for the entire firm with many products Calculate for Income Statement at one Sales Level

Break-even Analysis F S* = 1 - VC S Calculation of Break-even Sales Level (S*) F 1 - VC S* = S S = Dollar Level of Sales VC = Total Dollar Variable Costs

Break-even Analysis F S* = 1 - VC S Calculation of Break-even Sales Level (S*) F 1 - VC S* = S Example: S = Dollar Level of Sales = $3,000,000 VC = Total Dollar Variable Costs = $1,500,000

Break-even Analysis F S* = 1 - VC S Calculation of Break-even Sales Level (S*) F 1 - VC S* = S Example: S = Dollar Level of Sales = $3,000,000 VC = Total Dollar Variable Costs = $1,500,000 $1,000,000 1 – $1,500,000 S* = = $2,000,000 $3,000,000

Break-even Analysis Graphical Analysis of Break-even Point Sales & Costs $ Fixed Costs $1,000,000 Quantity of Units

Break-even Analysis Graphical Analysis of Break-even Point Sales & Costs $ Variable Costs Fixed Costs $1,000,000 Quantity of Units

Break-even Analysis Graphical Analysis of Break-even Point Sales & Costs $ Total Costs Variable Costs Fixed Costs $1,000,000 Quantity of Units

Break-even Analysis Graphical Analysis of Break-even Point Sales & Costs $ Sales Total Costs Variable Costs Fixed Costs $1,000,000 Quantity of Units

Break-even Analysis Graphical Analysis of Break-even Point Sales & Costs $ Sales Total Costs Variable Costs $2,000,000 Fixed Costs $1,000,000 QB = 2,500 Quantity of Units

Operating Leverage With FIXED operating costs, there will be operating leverage Operating Leverage is responsiveness of a firm’s EBIT to fluctuations in Sales Degree of Operating Leverage (DOL) Measurement of Operating Leverage For a unique level of sales, DOL changes as sales change. % Change in EBIT % Change in Sales DOLS = Unique Level of Sales

Operating Leverage Measurement of DOL Calculation using per unit information: Q(P – V) Q(P – V) – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year.

Operating Leverage Measurement of DOL Calculation using per unit information: Q(P – V) Q(P – V) – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year. 3,750(800 – 400) 3,750(800 – 400) – 1,000,000 DOL3,750 units = = 3 times

Operating Leverage Measurement of DOL Calculation using per unit information: Q(P – V) Q(P – V) – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year. 3,750(800 – 400) 3,750(800 – 400) – 1,000,000 DOL3,750 units = Interpretation: If sales change 1%, then EBIT will change 3% in the same direction. = 3 times

Operating Leverage Measurement of DOL Calculation using Income Statement Information S – VC S – VC – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year.

Operating Leverage Measurement of DOL Calculation using Income Statement Information S – VC S – VC – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year. Sales $3,000,000 x

Operating Leverage Measurement of DOL Calculation using Income Statement Information S – VC S – VC – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year. Variable Costs $1,500,000 x

Operating Leverage Measurement of DOL Calculation using Income Statement Information S – VC S – VC – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year. 3,000,000 – 1,500,00 3,000,000 – 1,500,000 – 1,000,000 DOL3,750 units = = 3 times

Operating Leverage Measurement of DOL Calculation using Income Statement Information S – VC S – VC – F DOLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year. 3,000,000 – 1,500,00 3,000,000 – 1,500,000 – 1,000,000 DOL3,750 units = = 3 times Same Answer as before

Operating Leverage Degree of Operating Leverage Degree of Operating Leverage falls as sales rise Quantity DOL 2,500 (QB) Undefined 3,250 4.33 3,750 3 5,000 2 The higher the sales level above break-even, the less EBIT changes as sales change If Fixed Costs = $0, Degree of Operating Leverage = 1

Financial Leverage Degree of Financial Leverage Finance a portion of the firm’s assets with securities that have fixed financial costs Debt Preferred Stock Financial Leverage measures changes in earnings per share as EBIT changes. Degree of Financial Leverage (DFL) at one level of EBIT: % Change in EPS % Change in EBIT DFLEBIT = Unique Level of EBIT

Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Example: Total Fixed Financing Costs Example: EBIT = $500,000 Interest Charges = $200,000

Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Example: Interest Charges = $200,000 500,000 500,000 – 200,000 DFLEBIT=500,000 = = 1.67 times Interpretation: When EBIT changes 1% (from an existing level of $500,000) Earnings Per Share will change 1.67%

Combined Leverage % Change in EPS DCLS = % Change in Sales Degree of Combined Leverage Measures changes in Earnings Per Share given changes in Sales Combines both Operating and Financial Leverage Computed for a specific level of sales % Change in EPS % Change in Sales DCLS = Unique Level of Sales

Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT

Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example:

Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example: DCL3,750 = 3.0 x 1.67 = 5.0 times Interpretation: When sales change 1%, Earnings Per Share will change 5.0%

Combined Leverage Measurement of DCL--Alternative Computation Q(P – V) Q(P – V) – F – I DCLS =

Combined Leverage Measurement of DCL--Alternative Computation Q(P – V) Q(P – V) – F – I DCLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year Interest = $200,000 per year

Combined Leverage Measurement of DCL--Alternative Computation Q(P – V) Q(P – V) – F – I DCLS = Example: Q = 3,750 units Price = $800 per unit Variable costs = $400 per unit Fixed Costs = $1,000,000 per year Interest = $200,000 per year 3,750(800 – 400) 3,750(800 – 400) – 1,000,000 – 200,000 DCLS = = 5 times Interpretation: When sales change 1%, Earnings Per Share will change 5.0%