Analysis and Impact of Leverage Chapter 15

Learning Objectives Understand the different between business risk and financial risk. Use the technique of break-even analysis in a variety of analytical settings. Calculate the firm’s break-even point in terms of units produced and sold, and in sales dollars. Distinguish among the financial concepts of operating leverage, financial leverage, and combined leverage. Calculate the firm’s degree of operating leverage, financial leverage, and combined leverage. Explain why a firm with a high business risk exposure might logically choose to employ a low degree of financial leverage in its financial structure.

Goal of a firm Managers' objective is to maximize stockholders' wealth--maximize the price of the firm's stock. We noted in an earlier chapter that the capital structure that produces the lowest WACC (risk) is also the one that maximizes share price.

Risk Variability of the expected net income (EPS)

Risk Variability of revenues from expected Two types of Risk: Business Risk & Financial Risk

Risk Variability of revenues from expected Two types of Risk: Business Risk & Financial Risk Revenue -Variable Cost Contribution margin -Fixed cost =EBIT/operating profits -Interest =NI

Risk Variability of revenues from expected Two types of Risk: Business Risk & Financial Risk Business Risk Risk Due to Operations

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

Standard Deviation of EBIT Risk Variability of revenues from expected Two types of Risk: Business Risk & Financial Risk Business Risk Risk Due to Operations Measured by variability of EBIT (earnings before interest and taxes) Coefficient of Variation of EBIT Standard Deviation of EBIT Expected EBIT =

Risk Variability of revenues from expected Two types of Risk: Business Risk & Financial Risk Financial Risk Risk due to raising money with fixed income securities

Business Risk Major determinants of business risk 1. Demand Variability 2. Sales Price Variability 3. Input Price variability. 4. Inability to adjust output prices for a change in input prices-a utility can transfer costs more easily 5. Operating Leverage--the extent to which costs are 'fixed' (the ratio of fixed cost to total cost). Business risk not only varies from industry to industry, it varies among firms in a given industry. Business risk of a firm can change over time.

Risk Financial Risk Risk due to raising money with fixed income securities Financial risk is high with high levels of debt financing

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

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 Example Firm A is an all equity firm -- it has no financial leverage

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 Example Firm A is an all equity firm -- it has no financial leverage Firm B is financed by 50% debt and 50% equity -- it uses financial leverage

Risk Notes: 1. Business risk is largely determined by technology and by industry/market conditions, although management decisions, to some extent, do matter. 2. Financial risk is largely management determined. 3. If business risk is high, financial risk (leverage) should be restrained.

Break-even Analysis The point of sales where operating profits are zero. The point where revenues barely cover all costs. Steps to Solution Determine the quantity of output which results in an EBIT = $0

Break-even Analysis Steps to Solution Determine the quantity of output which results in an EBIT = $0 Shows output necessary to cover operating (not financial) costs

Break-even Analysis Steps to Solution Determine the quantity of output which results in an EBIT = $0 Shows output necessary to cover operating (not financial) costs Calculate EBIT at various output levels

Break-even Analysis Steps to Solution Determine the quantity of output which results in an EBIT = $0 Shows output necessary to cover operating (not financial) costs Calculate EBIT at various output levels Applications Capital Expenditure Analysis

Break-even Analysis Steps to Solution Determine the quantity of output which results in an EBIT = $0 Shows output necessary to cover operating (not financial) costs Calculate EBIT at various output levels Applications Capital Expenditure Analysis Determining Prices Evaluating Fixed vs. Variable Costs

Break-even Analysis Assumptions Fixed costs remain constant as quantity changes Fixed Costs Includes: Salaries, Depreciation, Rent

Break-even Analysis Assumptions Fixed costs remain constant as quantity changes Fixed Costs Includes: Salaries, Depreciation, Rent Variable costs vary as quantity of output changes: they are constant per unit of output Variable Costs Includes: Materials, Labor, Commissions Drop Semivariable costs

Break-even Analysis Assumptions Fixed costs remain constant as quantity changes Variable costs vary as quantity of output changes: they are constant per unit of output Costs $ Variable Costs Fixed Costs Quantity Sold

Break-even Analysis Assumptions Fixed costs remain constant as quantity changes Fixed Costs Includes: Salaries, Depreciation, Rent Variable costs vary as quantity of output changes: they are constant per unit of output Variable Costs Includes: Materials, Labor, Commissions Revenues are quantity sold times price per unit

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 Trial and Error Method Choose arbitrary output level Calculate EBIT If EBIT < 0, choose a larger output level If EBIT > 0, choose a lower output level Continue until find a level of output which results in EBIT = $0

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

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

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

Break-even Analysis F QB = P – V Calculation of Break-even Quantity Example: 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 S* = QB x P Calculation of Break-even Sales Level (S*) To Find S* for a single product use Break-even Quantity (QB): S* = QB x P

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

Break-even Analysis S* = QB x P Calculation of Break-even Sales Level (S*) To Find S* for a single product use Break-even Quantity (QB): 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

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 from Income Statement data at a particular Sales Level

Break-even Analysis F S* = 1 - VC S 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 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*) 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 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* = $3,000,000

Break-even Analysis F S* = 1 - VC S 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 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

Break-even Analysis Limitations: The sales-volume-cost-profit relationship is assumed to be linear—it may not be. In the real world It is not, except for a small range of sales. Cost-price structure of the firm is assumed to remains constant. It generally does not. Sales price per unit is assumed to be constant regardless of the output. This is not the case in the real world—you have to ? Price if you want to sell more.

Operating Leverage Degree of Operating Leverage With FIXED operating costs, there will be operating leverage DOL measures the sensitivity of EBIT to changes in sales. DOL of a company is different at different levels of sales. High DOL implies that a relatively small change in sales will result in large change in the operating income (EBIT)

Operating Leverage Degree of Operating Leverage Operating Leverage is responsiveness of a firm’s EBIT to fluctuations in Sales

Operating Leverage Degree of 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.

Operating Leverage Degree of Operating Leverage % Change in EBIT 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 Q(P – V) DOLS = Q(P – V) – F Calculation using per unit information: Q(P – V) Q(P – V) – F DOLS =

Operating Leverage Measurement of DOL Q(P – V) DOLS = Q(P – V) – F 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 Q(P – V) DOLS = Q(P – V) – F 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 =

Operating Leverage Measurement of DOL Q(P – V) DOLS = Q(P – V) – F 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 Q(P – V) DOLS = Q(P – V) – F 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 S – VC DOLS = S – VC – F Calculation using Income Statement Information S – VC S – VC – F DOLS =

Operating Leverage Measurement of DOL S – VC DOLS = S – VC – F 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 S – VC DOLS = S – VC – F 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 S – VC DOLS = S – VC – F 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 S – VC DOLS = S – VC – F 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 =

Operating Leverage Measurement of DOL S – VC DOLS = S – VC – F 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 S – VC DOLS = S – VC – F 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 is highest when the firm is closest to break-even point--DOL falls as sales rise Quantity DOL 2,500 (QB) Undefined 3,250 4.33 3,750 3 5,000 2

Operating Leverage Degree of Operating Leverage Degree of Operating Leverage is highest when the firm is closest to break-even point--DOL 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 (in %) changes as sales change

Operating Leverage Degree of Operating Leverage Degree of Operating Leverage is highest when the firm is closest to break-even point--DOL 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(in %) 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 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 (NI) as EBIT changes.

Financial Leverage Degree of Financial Leverage % Change in EPS 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 EBIT – I DFLEBIT =

Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Total Fixed Financing Costs

Financial Leverage Measurement of DFL EBIT DFLEBIT = EBIT – I Example: 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 =

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

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: For 1% change in EBIT (from an existing level of $500,000) Earnings Per Share will change 1.67%

DFL S - VC - F DFL = --------------------- S - VC - F - I

Combined Leverage Degree of Combined Leverage Measures changes in Earnings Per Share given changes in Sales

Combined Leverage Degree of Combined Leverage Measures changes in Earnings Per Share given changes in Sales Combines both Operating and Financial Leverage

Combined Leverage 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

Combined Leverage Degree of Combined Leverage % Change in EPS DCLS = 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

Combined Leverage Measurement of DCL DCLS = DOLS x DFLEBIT Example: DCL3,750 = 3.0 x 1.67 = 5.0 times

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 (NI) 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 =

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

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%

Combined Leverage Measurement of DCL--Alternative Computation- Using income statement. S - VC - F DCLS = --------------------- S - VC - F - I