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Capital Structure and Leverage. Chapter 13. © 2003 South-Western/Thomson Learning. Background. Capital structure refers to the mix of a firm’s debt and equity Preferred stock is assumed to be part of a firm’s debt

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capital structure and leverage

Capital Structure and Leverage

Chapter 13

© 2003 South-Western/Thomson Learning

  • Capital structure refers to the mix of a firm’s debt and equity
    • Preferred stock is assumed to be part of a firm’s debt
  • Financial leverage refers to using borrowed money to enhance the effectiveness of invested equity
  • Financial leverage of 10% means the firm’s capital structure contains 10% debt and 90% equity
the central issue
The Central Issue
  • Can the use of debt increase the value of a firm’s equity
    • Specifically, the firm’s stock price
  • Under certain conditions changing leverage increases stock price
    • An optimal capital structure maximizes stock price
  • The relationship between capital structure and stock price is not precise nor fully understood
risk in the context of leverage
Risk in the Context of Leverage
  • Leverage influences stock price
    • Alters the risk/return relationship in an equity investment
  • Measures of performance
    • Operating income (AKA: EBIT or Earnings Before Interest and Taxes)
      • Unaffected by leverage because it is calculated prior to the deduction for interest
    • Return on Equity (ROE) is Earnings after Taxes  Stockholders’ Equity
    • Earnings per Share (EPS) is Earnings after Taxes  number of shares
      • Investors regard EPS as an important indicator of future profitability
risk in the context of leverage5
Risk in the Context of Leverage
  • Redefining Risk for Leverage-Related Issues
    • Leverage-related risk is variation in ROE and EPS
      • Business risk—variation in EBIT
      • Financial risk—additional variation in ROE and EPS brought about by financial leverage
leverage and risk two kinds of each
Leverage and Risk—Two Kinds of Each
  • Relates to a company’s cost structure
    • Involves relative use of fixed and variable costs
  • Operating leverage has an influence on a firm’s business risk
financial leverage
Financial Leverage
  • Under certain conditions financial leverage can improve a firm’s ROE and EPS
    • However, at other times it may worsen EPS and ROE
table 13 1
Table 13.1

As the firm’s debt ratio rises, both EPS and ROE rise dramatically. While EAT falls, the number of shares outstanding falls at a faster rate as debt replaces equity.

financial leverage10
Financial Leverage
  • Return on Capital Employed (ROCE)
    • Measures the profitability of operations before financing charges but after taxes on a basis comparable to ROE
  • When the ROCE exceeds the after-tax cost of debt, more leverage improves ROE and EPS
  • When ROCE is less than the after-tax cost of debt, more leverage makes ROE and EPS worse
table 13 2
Table 13.2

ABC is now doing rather poorly—ROE and ROCE are quite low. As the firm adds leverage, EPS and ROE decrease.

financial leverage example

Q: Selected financial information for the Albany Corporation follows:

Albany Corporation at $10M Debt

($000 except for per-share amounts)





Interest (@12%)








Tax (@40%)


Number of shares=





Stock price = $10 per share

ROE = EAT  equity = $13,500  $90,000 = 15%

EPS = EAT  number of shares = $13,500  9,000,000 = $1.50

The treasurer feels debt can be traded for equity without immediately affecting the price of the stock or the rate at which the firm can borrow. Management believes it is in the best interest of the company and its stockholders to move the firm’s EPS from its current level up to $2.00 per share. However, no opportunities are available to increase operating profit (EBIT) above the current level of $23.7 million. Will borrow more money and retiring stock raise Albany’s EPS, and if so what capital structure will achieve an EPS of $2.00?

Financial Leverage—Example
financial leverage example13

A: EPS will rise if ROCE exceeds the after-tax cost of debt. ROCE is currently:

The after-tax cost of debt is 12% x (1 – 0.4), or 7.2%. Since 7.2% < 14.2%, trading equity for debt will increase EPS.

Using trial and error, you can determine that $45 million of debt is the approximate amount of debt that makes the firm’s EPS equal $2.00.


Financial Leverage—Example
financial leverage and financial risk
Financial Leverage and Financial Risk
  • Financial leverage is a two-edged sword
    • Multiplies good results into great results
    • Multiples bad results into terrible results
  • ROE and EPS for leveraged firms experience more variation
  • Financial risk is the increased variability in financial results that comes from additional leverage
putting the ideas together the effect on stock price
Putting the Ideas Together—The Effect on Stock Price
  • Leverage enhances performance while it adds risk, pushing stock prices in opposite directions
    • Enhanced performance makes the expected return on stock higher, driving up the stock’s price
    • The increased risk drives down the stock’s price
      • Which effect dominates, and when?
real investor behavior and the optimal capital structure
Real Investor Behavior and the Optimal Capital Structure
  • When leverage is low an increase in debt has a positive effect on investors
  • At high debt levels concerns about risk dominate and adding more debt decreases the stock’s price
  • As leverage increase its effect goes from positive to negative, which results in an optimum capital structure
finding the optimum a practical problem
Finding the Optimum—A Practical Problem
  • There is no way to determine the exact optimum amount of leverage for a particular company at a particular time
    • Appropriate level tends to vary according to
      • Nature of a company’s business
        • If firm has high business risk it should use less leverage
      • Economic climate
        • If the outlook is poor investors are likely to be more sensitive to risk
  • As a practical matter the optimum capital structure cannot be precisely located
the target capital structure
The Target Capital Structure
  • A firm’s target capital structure is management’s estimate of the optimal capital structure
    • An approximation or best guess as to the amount of debt that will maximize the firm’s stock price
the effect of leverage when stocks aren t trading at book value
The Effect of Leverage When Stocks Aren’t Trading at Book Value
  • We’ve assumed that changes in leverage involve purchasing equity at book value
  • If this is not the case, things are more complex
    • Repurchasing stock at prices other than book value will have the same general impact on ROE, but not necessarily for EPS
      • However the important point is the direction of the stock price change, not the exact amount
the degree of financial leverage dfl a measurement
The Degree of Financial Leverage (DFL)—A Measurement
  • Financial leverage magnifies changes in EBIT into larger changes in ROE and EPS
    • The degree of financial leverage (DFL) relates relative changes in EBIT to relative changes in EPS



  • An easier method of calculating DFL is:
the degree of financial leverage dfl a measurement example

Q: Selected income statement and capital information for the Moberly Moped Manufacturing Company follow ($000):














Currently 700,000 shares of common stock are outstanding. The firm pays 15% interest on its debt and anticipates that it can borrow as much as it reasonably needs at that rate. The income tax rate is 40%

Moberly is interested in boosting the price of its stock. To do that management is considering restructuring capital to 50% debt in the hope that the increased EPS will have a positive effect on price. However, the economic outlook is shaky, and the company’s CFO thinks there’s a good chance that a deterioration in business conditions will reduce EBIT next year. At the moment Moberly’s stock sells for its book value of $10 per share.

Estimate the effect of the proposed restructuring on EPS. Then use the degree of financial leverage to assess the increase in risk that will come along with it.


The Degree of Financial Leverage (DFL)—A Measurement—Example
the degree of financial leverage dfl a measurement example23

A: Since the equity is trading at book value, this is a relatively simple example.













Shares outstanding









Interest (15% of debt)



If business conditions remain unchanged, a higher EPS will result with the addition of debt.




Tax (@40%)









The Degree of Financial Leverage (DFL)—A Measurement (Example)
the degree of financial leverage dfl a measurement example24

A: Next, calculate DFL:


EPS will be much more volatile under the proposed plan. EPS will change by a factor of 1.77 vs. 1.12.

The Degree of Financial Leverage (DFL)—A Measurement—Example
ebit eps analysis
EBIT-EPS Analysis
  • Managers need a way to quantify and analyze the tradeoffs between risk and results when changing leverage levels
  • Provides a graphical portrayal of the trade-off
    • Involves graphing EPS as a function of EBIT for each leverage level
  • Portrays the results of leverage and helps to decide how much to use
figure 13 3 ebit eps analysis for abc corporation from table 13 1 columns 1 and 2
Figure 13.3: EBIT – EPS Analysis for ABC Corporation (from Table 13.1, Columns 1 and 2)

It is important to determine the indifference point, which occurs when the two plans offer the same EBIT.

When examining the ABC Corporation you can see that the 50% Debt and No Leverage lines intersect. At the point of intersection ABC is indifferent between the two plans. However, to the left of the intersection the 50% Debt plan is preferable, but to the right of the point the No Leverage plan is preferable.

operating leverage
Operating Leverage
  • Terminology and Definitions
    • Risk in Operations—Business Risk
      • Variation in EBIT
    • Fixed and Variable Costs and Cost Structure
      • Fixed costs don’t change with the level of sales, while variable costs do
        • Fixed costs include rent, depreciation, utilities, salaries
        • Variable costs include direct labor, direct materials, sales commissions
      • The mix of fixed and variable costs in a firm’s operations is its cost structure
    • Operating Leverage Defined
      • Refers to the amount of fixed costs in the cost structure
breakeven analysis
Breakeven Analysis
  • Used to determine the level of activity a firm must achieve to stay in business in the long run
  • Shows the mix of fixed and variable cost and the volume required for zero profit/loss
    • Profit/loss generally measured by EBIT
breakeven analysis29
Breakeven Analysis
  • Breakeven Diagrams
    • Breakeven occurs at the intersection of revenue and total cost
      • Represents the level of sales at which revenue equals cost
breakeven analysis31
Breakeven Analysis
  • The Contribution Margin
    • Every sale makes a contribution of the difference between price (P) and variable cost (V)
      • Ct = P – V
    • Can be expressed as a percentage of revenue
      • Known as the contribution margin (CM)
      • CM = (P – V)  P
breakeven analysis example

Q: Suppose a company can make a unit of product for $7 in variable labor and materials, and sell it for $10. What are the contribution and contribution margin?

A: The contribution per unit is $3, or $10 - $7, while the contribution margin is $3  $10, or 30%.


Breakeven Analysis—Example
breakeven analysis33
Breakeven Analysis
  • Calculating the Breakeven Sales Level
    • EBIT is revenue minus cost, or
      • EBIT = PQ – VQ – FC
    • Breakeven occurs when revenue (PQ) equals total cost (VQ + FC), or
      • QB/E = FC (P – V)
        • Breakeven tells us how many units have to be sold to contribute enough money to pay for fixed costs
        • Can also be expressed in terms of dollar sales
          • SB/E = P(FC)  (P – V) or FC  CM
breakeven analysis example34

Q: What is the breakeven sales level in units and dollars for a company that can make a unit of product for $7 in variable costs and sell it for $10, if the firm has fixed costs of $1,800 per month?

A: The breakeven point in units is $1,800  ($10 - $7) = 600 units. The breakeven point in dollars is $10 per unit times 600 units, or $6,000, which could also be calculated as $1,800  0.30. Thus, the firm must sell 600 units per month to cover fixed costs.


Breakeven Analysis—Example
the effect of operating leverage
The Effect of Operating Leverage
  • As volume moves away from breakeven, profit or loss increases faster with more operating leverage
  • The Risk Effect
    • More operating leverage leads to larger variations in EBIT, or business risk
  • The Effect on Expected EBIT
    • Thus, when a firm is operating above breakeven, more operating leverage implies higher operating profit
      • If a firm is relatively sure of its operating level, it is in the firm’s best interests to trade variable costs for fixed cost (assuming the firm is operating above breakeven)
the effect of operating leverage example

Q: Suppose Firm A has fixed costs of $1,000 per period, sells its product for $10, and has variable costs of $8 per unit. Further, suppose Firm B has fixed costs of $1,500 and also sells its product for $10 a unit. Both firms are at the same breakeven point. What variable cost must Firm B have if it is to achieve the same breakeven point as Firm A? State the trade-off at the breakeven point. Which structure is preferred if there’s a choice?

A: Both firms have a breakeven point of 500 units (Firm A: $1,000  $2). We need to solve the breakeven formula for Firm B’s variable costs per unit:

QB/EFirm B = FC  (P – VB)

500 units = $1,500  ($10 – VB)

VB = $7

The preferred structure depends on volatility—if sales are expected to be highly volatile, the lower fixed cost structure might be better in the long run.


Thus, at breakeven, a $1

differential in contribution

makes up for a $500

difference in fixed cost.

The Effect of Operating Leverage—Example
the degree of operating leverage dol a measurement
The Degree of Operating Leverage (DOL)—A Measurement
  • Operating leverage amplifies changes in sales volume into larger changes in EBIT
  • DOL relates relative changes in volume (Q) to relative changes in EBIT
the degree of operating leverage dol a measurement39

Q: The Albergetti Corp. sells its product at an average price of $10. Variable costs are $7 per unit and fixed costs are $600 per month. Evaluate the degree of operating leverage when sales are 5% and then 50% above the breakeven level.

A: First, compute the breakeven volume: $600  ($10 - $7) = 200 units. Breakeven plus 5% is 200 x 1.05 or 210 units, while breakeven plus 50% is 200 x 1.50 or 300 units. DOL at 210 units is:

DOL at 300 units is:


Note that DOL decreases

as the output level

increases above


The Degree of Operating Leverage (DOL)—A Measurement
comparing operating and financial leverage
Comparing Operating and Financial Leverage
  • Financial and operating leverage are similar in that both can enhance results while increasing variation
  • Financial leverage involves substituting debt for equity in the firm’s capital structure
  • Operating leverage involves substituting fixed costs for variable costs in the firm’s cost structure
  • Both methods involve substituting fixed cash outflows for variable cash outflows
  • Both kinds of leverage make their respective risks larger as the levels of leverage increase
    • However, financial risk is non-existent if debt is not present, while business risk would still exist even if no operating leverage existed
  • Financial leverage is more controllable than operating leverage
the compounding effect of operating and financial leverage
The Compounding Effect of Operating and Financial Leverage
  • The effects of financial and operating leverage compound one another
  • Changes in sales are amplified by operating leverage into larger relative changes in EBIT
    • Which in turn are amplified into still larger relative changes in ROE and EPS by financial leverage
      • The effect is multiplicative, not additive
    • Thus, fairly modest changes in sales can lead to dramatic changes in ROE and EPS
  • The combined effect can be measured using degree of total leverage (DTL)
    • DTL = DOL × DFL
the compounding effect of operating and financial leverage example

Q: The Allegheny Company is considering replacing a manual production process with a machine. The money to buy the machine will be borrowed. The replacement of people with a machine will alter the firm’s cost structure in favor of fixed costs, while the loan will move the capital structure in the direction of more debt. The firm’s leverage positions at expected output levels with and without the project are summarized as follows:

The economic outlook is uncertain and some managers fear a decline in sales of as much as 10% in the coming year. Evaluate the effect of the proposed project on risk in financial performance.

A: The firm’s current DTL is 2 x 1.5, or 3, meaning a 10% decline in sales could result in a 30% decline in EPS. Under the proposal, the DTL will be much higher: 8.75, or 3.5 x 2.5, meaning a 10% drop in sales could lead to a 87.5% drop in EPS.










The Compounding Effect of Operating and Financial Leverage—Example
capital structure theory
Capital Structure Theory
  • Does capital structure affect stock price and the market value of the firm?
    • If so, is there an optimal structure that maximizes either or both?
  • Results indicate that capital structure does impact stock prices but there’s no way to determine the optimal structure with any precision
background the value of the firm
Background—The Value of the Firm
  • Notation
    • Vd = market value of the firm’s debt
    • Ve = market value of the firm’s stock or equity
    • Vf = market value of the firm in total
      • Vf = Vd + Ve
  • Investors’ returns on the firm’s securities will be
    • Kd = return on an investment in debt
    • Ke = return on an investment in equity
  • Theory begins by assuming a world without taxes or transaction costs, so investors’ returns are exactly component capital costs
    • Ka = average cost of capital
background the value of the firm46
Background—The Value of the Firm
  • Value is Based on Cash Flow Which Comes from Income
    • Earnings ultimately determine value because all cash flows paid to investors come from earnings
    • Dividends and interest payments are both perpetuities
      • The firm’s market value is the sum of their present values

Returns drive value in an inverse relationship.

the early theory by modigliani and miller mm
The Early Theory by Modigliani and Miller (MM)
  • Restrictive Assumptions in the Original Model
    • In 1958 MM published their first paper on capital structure
      • Included numerous restrictions such as
        • No income taxes
        • Securities trade in perfectly efficient capital markets with no transaction costs
          • No costs to bankruptcy
        • Investors and companies can borrow as much as they want at the same rate
the early theory by modigliani and miller mm49
The Early Theory by Modigliani and Miller (MM)
  • The Assumptions and Reality
    • Realistically income taxes exist
    • Realistically the costs of bankruptcy are quite large
    • Realistically individuals cannot borrow at the same rate as companies and interest rates usually rise as more money is borrowed
the early theory by modigliani and miller mm50
The Early Theory by Modigliani and Miller (MM)
  • The Result
    • Under MM’s initial set of restrictions, value is independent of capital structure
    • As cheaper debt is added the cost of equity increases because of increased risk
      • However the weight of the more expensive equity is decreasing while the weight of the cheaper debt is increasing, leading to a constant weighted average cost of capital
the early theory by modigliani and miller mm52
The Early Theory by Modigliani and Miller (MM)
  • The Arbitrage Concept
    • Arbitrage means making a profit by buying and selling the same thing at the same time in two different markets
    • MM proposed that arbitrage by equity investors would hold the value of the firm constant as debt levels changed
      • Equity investors could sell shares in a leveraged firm and buy shares in an unleveraged firm by borrowing money on their own
  • Interpreting the Result
    • The MM result implies that leverage affects value because of market imperfections
      • Such as taxes and transaction costs (including bankruptcy)
relaxing the assumptions more insights
Relaxing the Assumptions—More Insights
  • Financing and the U.S. Tax System
    • Tax system favors debt financing over equity financing
      • Interest expense on debt is tax deductible while dividends on stock are not
table 13 4

The All Equity firm pays more taxes because it receives no interest expense deduction.

Total payments to investors are higher for the leveraged company.

Table 13.4
relaxing the assumptions more insights55
Relaxing the Assumptions—More Insights
  • Including Corporate Taxes in the MM Theory
    • When taxes exist operating income (OI) must be split between investors and the government
      • This lowers the firm’s value compared to what it would be if no taxes existed
        • Amount of reduction depends on the firm’s use of leverage
          • Use of debt reduces taxable income which reduces taxes
including corporate taxes in the mm theory
Including Corporate Taxes in the MM Theory
  • In the MM model with taxes interest provides a tax shield that reduces government’s share of the firm’s earnings
    • When a firm uses debt financing the government’s take is reduced by (corporate tax rate × interest expense) every year
      • Present value of tax shield = (corporate tax rate × interest expense)  kd
      • Since interest is the amount of debt (B) times the interest rate on the debt, the above equation can be written as
including corporate taxes in the mm theory57
Including Corporate Taxes in the MM Theory
  • Having debt in the capital structure increases a firm’s value by the magnitude of that debt times the tax rate
  • The benefit of debt accrues entirely to stockholders because bond returns are fixed
figure 13 12 mm theory with taxes

In the MM model with taxes value increases steadily as leverage is added. Thus, the firm’s value is maximized with 100% debt. Note that kd remains constant across all levels of debt.

Figure 13.12: MM Theory with Taxes
including bankruptcy costs in the mm theory
Including Bankruptcy Costs in the MM Theory
  • As leverage increases past a certain point, investors begin raising their required rates of return
    • The probability of bankruptcy failure increases
  • Eventually the weighted average cost of capital will be minimized and the firm value will be maximized
    • The MM model with taxes and bankruptcy costs concludes that an optimal capital structure exists
an insight into mergers and acquisitions
An Insight into Mergers and Acquisitions
  • In many mergers one company buys the stock of another company called the target
  • The buying company needs to buy shares of the target company at a premium over the current market price
    • Paying twice the current market value for a target firm is not unheard of
    • Why do companies do this?
an insight into mergers and acquisitions62
An Insight into Mergers and Acquisitions
  • One argument is that target firms may be underutilizing their debt capacity
    • Thus, a restructuring of capital may raise the value of the target firm
  • Acquiring firms often raise the cash needed to buy the target firm’s shares with debt
    • The resulting merged business ends up with more debt than the individual firms had before the merger
      • May theoretically be justified if adding debt adds value