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IFT Notes for Level I CFA® Program

R31 Capital Structure

Part 1

1. Introduction

Capital structure refers to the combination of equity and debt a company uses to finance its assets and operations.

In this reading we will review some key factors affecting capital structure such as:

  • Company life cycle: As companies mature their business risk decreases and operating cash flows become more predictable, allowing for greater use of leverage.
  • Cost of capital: The cost of debt is low relative to the cost of equity. Also interest expense is tax deductible. Therefore, it is beneficial for companies to use debt in their capital structure. However, higher leverage can also increase the potential costs of financial distress.

A company’s management seeks to find an optimal capital structure that balances the benefits of higher leverage with its costs. At this point, the company’s weighted average cost of capital (WACC) is minimized and shareholder value is maximized.

  • Financing considerations: Financing decisions are typically tied to investment spending. A company’s management also has to consider the company’s ability to service debt given its nature of business and operating cash flows.
  • Competing stakeholder interest: While trying to maximize shareholder wealth, a company’s management may make capital structure decisions that favor shareholders at the expense of other stakeholders such as debt holders, suppliers, customers, or employees.

2. Capital Structure and Company Life Cycle

In this section we will look at the typical changes in a company’s capital structure as it evolves from a start-up, to a growth business, to a mature business.

2.1 Background

A company’s life cycle stage influences its cash flow characteristics, its ability to support debt; and is therefore a primary factor in determining capital structure. Any capital that is not sourced through borrowing must come from equity.

As companies mature and move from start-up, through growth, to maturity, their business risk typically declines, and their operating cash flows turn positive and become more predictable. This allows for greater use of leverage at more attractive terms. This is illustrated in Exhibit 1 from the curriculum.

2.2 Start-Ups

  • In this stage a company’s revenues are close to zero and a lot of investment is required to move from the prototype stage to commercial production.
  • Therefore, cash flow is usually negative.
  • The risk of business failure is high.
  • The company typically raises capital through equity rather than debt.
  • Equity is generally sourced through private markets (venture capital) rather than public markets.
  • Debt is generally not available or is very expensive. It is usually a negligible component of the capital structure.

2.3 Growth Businesses

  • In this stage a company typically experiences high revenue growth but investment is needed to achieve this growth.
  • Therefore, cash flow may be negative but it is likely to be improving and becoming more predictable.
  • The risk of business failure decreases.
  • As the business becomes more attractive to lenders, debt financing may be available at reasonable terms. The company may also have assets that it can use to secure debt.
  • However, most companies use debt conservatively to retain their operational and financial flexibility.
  • Equity is generally the main source of capital.

2.4 Mature Businesses

  • In this stage a company typically experiences a slowdown in revenue growth; and growth-related investment spending decreases.
  • Cash flow is usually positive and predictable.
  • The risk of business failure is low.
  • Debt financing is available at attractive terms often on an unsecured basis.
  • To take advantage of the cheaper debt (as compared to equity) companies typically use significant leverage.
  • Over time a company may experience de-leveraging due to continuous positive cash flow generation and share price appreciation.
  • To offset this de-leveraging companies typically buy back shares and reduce the proportion of equity in the capital structure.

2.5 Unique Situations

In the preceding sections we established a general relationship between company maturity and capital structure. However, there are three important exceptions:

  • Capital intensive businesses with marketable assets: Business such as real estate, utilities, shipping, airline etc. are highly capital intensive. Also, the underlying assets can be bought and sold fairly easily and make for a good collateral. Such businesses tend to use high levels of leverage irrespective of their maturity stage.
  • Cyclical industries: The revenues and cash flows of companies in cyclical industries (e.g., mining) fluctuate widely with the business cycle. Therefore, such companies tend to use less debt in their capital structure as compared to other companies in less cyclical industries.
  • “Capital-light” businesses: Some businesses such as software can scale easily and do not require substantial investments in fixed or working capital to support growth. They are typically cash flow positive from an early stage and never need to raise large amounts of capital. Therefore, they tend to use very little debt in their capital structure.

3. Modigliani–Miller Propositions

3.1 MM Proposition I without Taxes: Capital Structure Irrelevance

Economists Modigliani and Miller claimed the following proposition, given no taxes and a certain set of assumptions:

MM Proposition I: The market value of the company is not affected by the capital structure of the company.



VL = value of the levered firm

Vu = value of the unlevered firm

In other words, the value of a company is determined solely by its cash flows, not by the relative reliance on debt and equity capital.

The assumptions made were:

  1. Homogeneous expectations: All investors have the same expectations with respect to the cash flows from an investment in bonds or stock.
  2. Perfect capital markets: There are no transaction costs, no taxes, no bankruptcy costs, and everyone has the same information.
  3. Risk-free rate: Investors can borrow and lend at the risk-free rate.
  4. No agency costs: Managers always act to maximize shareholder wealth.
  5. Independent decisions: Financing and investment decisions are independent of each other. Operating income is unaffected by changes in the capital structure.

We can explain MM’s capital structure irrelevance proposition in terms of a pie. Suppose the total value of a company is represented by a pie. Slices represents how much of the total capital is contributed by debt and equity. Depending on the capital structure, the pie can be split in any number of ways, but the size of the pie will remain the same. This is illustrated in the figures below.

3.2 MM Proposition II without Taxes: Higher Financial Leverage Raises the Cost of Equity

Modigliani and Miller’s second proposition focuses on the cost of capital of the company.

MM Proposition II: The cost of equity is a linear function of the company’s debt-to-equity ratio.



r0 is the cost of capital for a company financed only by equity and has zero debt

rd is the cost of debt

re is the cost of equity

D/E = debt-to-equity ratio

As D/E rises, i.e. the company increases the use of debt, the cost of equity (re) rises.  We know from MM Proposition I that the value of a company is unaffected by changes in D/E and the WACC remains constant. Proposition II then implies that the cost of equity increases in such a manner as to exactly offset the increased use of cheaper debt in order to maintain a constant WACC. Under this proposition, WACC is determined by the business risk of the company, and not by the capital structure.

MM Proposition II is illustrated in the figure below.

As leverage increases, the cost of equity increases, but WACC and the cost of debt remain constant.

Systematic Risk

The systematic risk or beta of a company’s assets is a weighted average of the systematic risks of its source of capital.

{\beta }_a=\left(\frac{D}{V}\right){\beta }_d+\left(\frac{E}{V}\right){\beta }_e


βa = asset beta

βd = debt beta

βe = equity beta

According to MM, as the use of debt rises the risk borne by equity holders rises, and therefore the equity beta rises.

{\beta }_e={\beta }_a+({\beta }_a-{\beta }_d)\ \left(\frac{D}{E}\right)

3.3 MM Propositions with Taxes: Taxes, Cost of Capital, and Value of the Company

The discussion so far has ignored taxes. In this section, we will present MM propositions I and II with taxes. As interest paid is tax deductible, the use of debt provides a tax shield that increases the value of a company. If we ignore the costs of financial distress and bankruptcy, the value of the company increases as we take on more debt.

MM Proposition I with taxes: The value of a levered company is equal to the value of an unlevered company plus the value of the debt tax shield.



VL = value of the levered firm

Vu = value of the unlevered firm

t = marginal tax rate

D = value of debt in the capital structure

The term tD is often referred to as the debt tax shield

MM Proposition II with taxes: The cost of equity is a linear function of the company’s debt-to-equity ratio with an adjustment for the tax rate.

The cost of equity increases as the company increases the amount of debt in its capital structure, but the cost of equity does not rise as fast as it does in the no tax case.


WACC for a leveraged company falls as debt increases, and therefore the overall company value increases. This is illustrated in the figure below:

The table below provides a summary of MM propositions.

  Without Taxes With Taxes
Proposition I VL = VU VL = VU + tD
Proposition II r_e=r_0+(r_0-r_d)\frac{D}{E} r_e=r_0+(r_0-r_d)(1-t)\frac{D}{E}

3.4 Costs of Financial Distress

The disadvantage of operating and financial leverage is that earnings are magnified downward during economic slowdown. Lower or negative earnings put companies under stress, and this financial distress adds costs to a company.

The costs of financial distress can be classified into direct and indirect costs. Direct costs include the actual cash expenses associated with the bankruptcy process, such as legal and administrative fees. Indirect costs include forgone investment opportunities, impaired ability to conduct business, and agency costs associated with the debt during periods in which the company is near or in bankruptcy.

The costs of financial distress are lower for companies whose assets have a ready secondary market. For example, airlines, shipping companies etc.

The probability of financial distress and bankruptcy increases as the degree of leverage increases. The probability of bankruptcy depends, in part, on the company’s business risk. Other factors that affect the likelihood of bankruptcy include the company’s corporate governance structure and the management of the company.

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