11.3 Capital Structure Theory: Perfect Capital Market

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Introduction In this section, we will discuss the two Modigliani-Miller (MM) propositions and the effect of changes in capital structure on a company's overall value, cost of debt, cost of equity, and weighted-average cost of capital. As you read through this section and the next two sections (Sections 11.4 and 11.5), observe that we will progress from MM (no taxes, no cost of distress) to MM (with taxes, no cost of distress). With MM (no taxes, no cost of distress), we establish a foundation to explain the fundamental relationship between capital structure and cost of equity. Then, moving to MM (with taxes, no cost of distress), we examine how taxes affect the cost of capital and the firm's value. It is important for you to understand both MMs before we proceed to trade-off theory.

Leverage and the Cost of Capital

Leverage and the Cost of Capital Based on MM Proposition I, in a perfect capital market, the value of an unlevered firm is equal to the value of a levered firm. Thus, the market value of the assets in an unlevered firm is equal to that of a levered firm. Note that: For an unlevered firm, the firm is 100% equity and no debt. The market value of the assets (A) in an unlevered firm is simply equal to the market value of unlevered equity (U): A=U For a levered firm, the firm is financed partially with debt and partially with equity. The market value of the assets in a levered firm is the sum of the market value of levered equity (E) and the market value of debt (D): A=E+D Since the market value of the assets in an unlevered firm is equal to that of a levered firm, we have: A=U=E+D

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Since a firm's capital structure is irrelevant, the value of a levered firm (i.e., a firm with debt) is equal to the value of an unlevered firm (i.e., a firm with no debt) Since MM assumes that capital markets are frictionless, investors can borrow and lend without any cost. Thus, investors can borrow or lend on their own to achieve a capital structure different from what the firm has chosen. For example, if an investor wants more leverage than the firm has chosen, he or she can borrow and add leverage to his or her portfolio. This is known as homemade leverage. As long as the investors can borrow or lend at the same interest rate as the firm, homemade leverage is a perfect substitute for the use of leverage by the firm.

Modigliani-Miller Proposition I (Without taxes) Tóm tắt

To summarize, according to MM Proposition I, the total value of a firm's securities is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure. In other words, the firm's capital structure is irrelevant. Changing a firm's capital structure merely changes how the value of its assets is divided between debt and equity, but not the firm's total value.

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We can explain MM Proposition I using a pie analogy. Think of a firm's total capital as a pie. Each slice represents the proportion of total capital provided by a particular source of financing (debt or equity). The pie may be sliced in different ways, but its total size will remain unchanged. Since the size of the pie remains the same, the present value of the company's expected future cash flows remains the same. This means the future cash flows are unaffected by changes in capital structure.

Modigliani-Miller Proposition I (Without taxes)

Modigliani-Miller Proposition I (Without taxes) According to Modigliani-Miller (MM) Proposition I, under a very restrictive set of assumptions (i.e., perfect capital markets), the value of a firm is unaffected by its capital structure. A perfect capital market satisfies the following assumptions: Capital markets are perfectly competitive. Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows. Capital markets are frictionless. There are no taxes, transaction costs, or issuance costs associated with security trading. Financing and investment decisions are independent of each other. A firm's financing decisions do not change the cash flows generated by its investments, nor do they reveal new information about them.

Modigliani-Miller Proposition II (Without taxes)

Modigliani-Miller Proposition II (Without taxes) Introduction Recall from Section 8.1.6, a firm's cost of capital is the weighted average of the firm's cost of equity and the effective after-tax cost of debt, which is known as the weighted-average cost of capital (WACC):

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Most finance textbooks assume the cost of debt is constant in the "Without taxes" case. Berk & DeMarzo (4th ed.), however, does not follow this assumption. According to Berk & DeMarzo, as the amount of debt increases, the chance that the firm will default increases, and subsequently the debt becomes riskier. As a result, the cost of debt rDrD increases (i.e., it is not constant). However, the WACC remains unchanged, although both cost of debt and cost of equity increase as the company takes on more debt, because more weight is placed on the lower-cost debt. We can illustrate this concept in the following diagram:

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Note that: If a project is financed 100% with equity (i.e., no debt), then the equity is labeled as unlevered equity. If a project is financed partially with debt and partially with equity, then the equity in a firm that also has debt outstanding is labeled as levered equity. Promised payments to debt holders must be made before any payments can be distributed to equity holders.

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Notice in this diagram: The cost of capital is still used on the vertical axis, but the debt-to-value ratio (rather than the debt-to-equity ratio) is used on the horizontal axis. That is how Berk & DeMarzo choose to define the horizontal axis. The weighted average cost of capital is still constant. The debt cost of capital is constant most of the time. Only at very high debt-to-value ratios does the cost of debt start to rise. The equity cost of capital is no longer linear; it increases exponentially. This is because we redefined the horizontal axis. Instead of using the debt-to-equity ratio, which is in the formula for the return on the levered equity, we are using the debt-to-value ratio. The return on levered equity does not have a linear relationship with the debt-to-value ratio. Don't get bogged down in these two approaches. The key point here is that: Regardless of whether or not the cost of debt is constant, as the firm's debt-to-equity ratio increases, the cost of capital of levered equity increases.

The "Unlevered" Cost of Capital

The "Unlevered" Cost of Capital The asset cost of capital is also called the unlevered cost of capital because the asset cost of capital equals the equity cost of capital if the company has no debt (i.e., unlevered). If a company is unlevered, all of its assets are financed only with equity, and thus the fundamental accounting equation reduces to A=E. Since the asset cost of capital does not change based on the type of financing, it follows that the unlevered cost of capital does not change either. Thus: rU=wE⋅rE+wD⋅rD We often assume the debt cost of capital is constant; however, the equity cost of capital increases as more debt is added. Intuitively, since equity holders are compensated after debt holders, their investment becomes riskier as debt increases; as result, the equity cost of capital increases. Thus, in the above equation, rE increases as wE decreases, and hence the weighted average of rU remains unchanged. Students who find the term "the unlevered cost of capital" confusing can simply use the term "the asset cost of capital" instead, as "the asset cost of capital" is a more descriptive term. Note that the term "unlevered" can be especially confusing for a company that has debt. If a company has debt, what reason is there for knowing the unlevered cost of equity? The reason we compute the unlevered cost of capital for two companies is to compare their cost of capital on an equivalent basis. In addition, we compute a company's unlevered cost of capital when we want to determine the equity cost of capital for different levels of debt.

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The following are some remarks regarding the asset cost of capital, the equity cost of capital, and the debt cost of capital; the unlevered cost of capital; and computing the unlevered cost of capital. The Costs of Capital: Assets, Equity, and Debt A company must finance its assets with capital. The two primary sources of capital are debt and equity, whose sum creates the fundamental accounting equation: A=L+E In this equation, LL stands for liabilities, which is simply another name for debt. As a result of providing all its financing, the capital providers, i.e., debt holders and equity holders, own all of a company's assets. The company, in turn, has to pay for this financing. The financing rate for debt (i.e., the required return that the debt holders demand) is called the debt cost of capital, and the financing rate for equity (i.e., the required return that the equity holders demand) is called the equity cost of capital. Regardless of a company's capital structure, however, the total risk of financing the company's assets is the same. Let's illustrate this concept with an example. Assume you purchase a restaurant. You are exposed to certain risks as a result—labor costs may increase or revenue may decrease due to competition. Now, instead assume you and a business partner purchase the restaurant together. Perhaps your business partner provides 30% of the financing in return for a fixed return, while you provide 70% for the rights to the restaurant's profits (a riskier position). Regardless of how the financing and the risk is shared, however, the total risk of owning the restaurant does not change. The total risk, after all, is based on the expenses and revenues of the restaurant, and the total risk is the same regardless of how that risk is allocated. Although the total risk of a company is not affected by a company's financing, the debt cost of capital and the equity cost of capital are not the same. Debt is less risky because it has a priority claim on the assets: if a company goes bankrupt, debt holders get compensated first. Thus, the debt cost of capital is less than the equity cost of capital. Because the asset cost of capital does not change, the weighted average of the debt cost of capital and equity cost of capital does not change either; it is constant for the same assets, regardless of any financing mix.

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You can think of a levered firm as a portfolio consisting of a firm's equity and its debt. The levered firm's WACC is really just the return on the portfolio, which is the weighted average return of its equity and debt. Since the firm's assets are made up of equity and debt, the WACC is also the return on the levered firm's assets. Also, note that: The terms equity cost of capital, cost of equity, and required return on equity are used interchangeably in this course. They mean the same thing: the rate of return that equity holders require in order for them to contribute their capital to the firm. The terms debt cost of capital, cost of debt, and required return on debt are used interchangeably in this course. They mean the same thing: the rate of return that debt holders require in order for them to contribute their capital to the firm.