Modigliani-Miller Capital Structure Propositions

A firm’s capital structure is the mix of debt and equity it uses to finance its investments. A capital structure decision aims to determine the financial leverage to maximize a company’s value by minimizing the weighted average cost of capital (WACC).

Franco Modigliani and Merton Miller (1958) posit that, given certain assumptions, the choice of capital structure is irrelevant in determining the value of the firm. In this case, the firm’s value is the present value of the firm’s expected future cash flows discounted by WACC.

Assumptions of Modigliani-Miller Propositions

Franco Modigliani and Merton Miller suggested the following assumptions for Proposition I:

1. Investors have similar expectations regarding future cash flows.
2. Bonds and stocks are traded in a perfect capital market.
3. Investors can lend and borrow at a risk-free
4. rate.
5. There are no agency costs.
6. Financing and investing decisions are independent of each other.

Although these assumptions are unrealistic, Modigliani and Miller’s school of thought is that investors can create capital structures they prefer. Management’s capital structure does not matter because investors can change it at no cost.

Proposition I Without Taxes: Capital Structure Irrelevance

MM Proposition I, without taxes, posits that the market value of a company is unaffected by the capital structure of the company. As such, the value of a levered firm is equal to the value of an unlevered firm.

$$ \text{Value of levered firm }\left(V_L\right)=\text{value of an unlevered firm } \left(V_U\right)=\frac{EBIT}{r_{WACC}} $$

The above relationship implies that cash flows, not capital structure, determine the value of a company. Additionally, assuming no taxes, a company’s capital structure does not affect its WACC.

Assume management has set a company’s capital structure to consist of 50% debt and 50% equity. Further, assume that the investor prefers the company’s capital structure to be 60% debt and 40% equity. The investors will use borrowed money to finance their share purchase so that the ownership of the company’s assets reflects 60% debt financing. The importance of the Modigliani and Miller theory is that managers cannot use capital structure to change a firm’s value.

Proposition II Without Taxes: Higher Financial Leverage Raises the Cost of Equity

Here, Franco Modigliani and Merton Miller remove a few assumptions from Proposition I and state that the cost of equity is a linear function of a company’s debt/equity ratio.

According to this proposition, the cost of equity increases as a company uses debt financing to maintain a constant WACC. The risk of equity is contingent on business risk and financial risk. Business risk determines the cost of capital, while capital structure determines financial risk.

Mathematically, MM Proposition II without taxes implies that the cost of equity is a linear function of a company’s D/E ratio:

$$
r_e=r_0+(r_0-r_d)\frac{D}{E} $$

Where:

\(r_e\)= The cost of equity

\(r_0\)= The cost of capital for a company financed only by equity

\(r_d\)= The cost of debt

\(D\)= The market value of debt

\(D\)= The market value of equity

From the formula above, the following must be true:

• Higher leverage (D/E) increases the cost of equity \((r_e)\) but does not alter the firm’s value or WACC
• An increase in the cost of debt \((r_e)\) must precisely offset the higher use of lower-cost debt

Example: MM Proposition II Without Taxes

Genghis Investment has an all-equity capital structure. Its characteristics are as follows:

• The expected operating income is $6,000.
• The cost of equity, which is also the WACC, is 12%.
• EBIT is perpetual.
• Genghis plans to issue $18,000 in debt at 6% to buy back $18,000 worth of its equity.

The value of Genghis and its cost of equity assuming MM Proposition II without taxes is closest to:

Solution

$$ V=\frac{EBIT}{r_{WACC}}=\frac{\$6,000}{0.12}=\$ 50,000 $$

When Genghis issues the debt, it pays interest of 6% on the debt.

$$ \text{Interest Payment}=0.06\left(\$18,000\right)=\$1,080 $$

Using the MM proposition II, the cost of Genghis’ equity is given by:

$$ r_e=r_0+(r_0-r_d)\frac{D}{E} $$

Where:

$$ E=V-D=\$50,000-\$18,000=\$32,000 $$

So,

$$ r_e=0.12+\left(0.12-0.06\right)\frac{\$18,000}{\$32,000}=0.15375=15.38\% $$

Genghis makes $1,080 to debtholders and \(\$6,000-1,080=\$4,920\) to equity holders. The value of debt is calculated as follows.

$$ V=D+E=\frac{\$1,080}{0.06}+\frac{\$4,920}{0.1538}=\$50,000 $$

Proposition I With Taxes: The Tax Shield

A tax shield is the deliberate use of taxable expenses to offset taxable income. The interest expense on debt provides a tax shield that results in savings that enhance the value of a company. Ignoring the practical realities of bankruptcy and financial distress costs, the value of a company increases with increased debt levels. The level of tax benefit reduces the actual cost of debt.

Note that,

$$ \text{After-tax cost of debt}=\text{Before-tax cost of debt}\times(1-\text{marginal tax rate}) $$

According to MM Proposition I, with taxes, the value of the levered company is greater than that of the all-equity company by an amount equal to the corporate tax rate multiplied by the value of the debt (tD).

The MM Proposition I with taxes is:

$$ \begin{align*} V_L & =V_U+tD \\
\Rightarrow V_L & \gt V_U \end{align*} $$

Where:

\(V_L\)= value of the levered firm (debt in the capital structure).

\(V_U\)= value of the unlevered firm (no debt in the capital structure).

\(t\) = Marginal tax rate.

\(tD\) = present value of the debt tax shield.

In summary, under MM Proposition I with taxes:

• In the presence of corporate taxes (not personal taxes), a profitable firm can increase its value by using debt in its capital structure.
• The higher the corporate tax rate, the higher the benefits of including debt in a capital structure. According to Proposition I, value is maximized at 100% debt with taxes.

Proposition II with Taxes: The Impact on WACC and Return on Equity

By introducing taxes, the WACC is adjusted to reflect the impact of the tax benefit:

$$ r_e=r_0+(r_0-r_d)(1-t)\frac{D}{E} $$

We can see that the WACC for a company with debt is lower than the WACC for companies without debt. Therefore, debt financing is highly beneficial when considering taxes and ignoring financial distress and bankruptcy costs. The firm’s optimal capital structure is still 100% debt.

In summary, if MM Proposition II with taxes holds, then the following must be true:

• When corporate tax is present, the cost of equity \((r_e)\) increases as the company employs more debt but at a slower rate compared with the no-tax proposition \((r_e=r_0+(r_0-r_d)\frac{D}{E})\)
• As a firm employs more debt, its WACC decreases, increasing its value.
• Ignoring financial distress and bankruptcy costs, in the presence of corporate tax, the use of tax enhances the value of a company with the optimal benefit at 100% debt.

Example: MM Proposition I and II With Taxes

Let us use the example of Genghis Investments.

• The expected operating income is $6,000.
• The cost of equity, which is also the WACC, is 12%.
• EBIT is perpetual.
• Genghis plans to issue $18,000 in debt at 6% to buy back $18,000 worth of its equity.
• The corporate tax rate is 30%.

The value of Genghis is calculated as follows:

$$ V_U=\frac{EBIT(1-t)}{WACC}=\frac{\$6,000(1-0.3)}{0.12}=\$35,000 $$

The value of Genghis when it issues $18,00 in debt and buys back shares:

$$ V_L=V_U+t_D=\$35,000+0.3\left(\$18,000\right)=\$40,400 $$

The value of equity after buyback is $40,400–$18,000=$22,400$40,400–$18,000=$22,400, and levered equity is:

$$ r_e=0.12+\left(0.12-0.06\right)\left(1-0.3\right)\frac{\$18,000}{\$22,400}=0.15375=15.38\% $$

So that,

$$ \begin{align*} V_L & =D+E=\frac{r^{dD}}{r^d}+\frac{(EBIT-r^{dD})(1-t)}{r_e}\\ & =\frac{\$1,080}{0.06}+\frac{(\$6,000-\$1,080)(1-0.3)}{0.15375} \\ & =\$40,400 \end{align*} $$

The WACC of a levered Genghis is:

$$ \begin{align*} r_{WACC} &=\left(\frac{\$18,000}{\$40,400}\right)06\left(1-0.3\right)+\left(\frac{\$22,400}{\$40,400}\right)0.15375 \\ & =0.1039=10.39\% \end{align*} $$

Therefore,

$$ V_L=\frac{EBIT(1-t)}{WACC}=\frac{\$6,000(1-0.3)}{0.1039}\approx \$40,400 $$

Costs of Financial Distress

Financial distress is the increased uncertainty about a company’s capability to fulfill its commitments due to reduced profitability or current financial losses.

The disadvantage of operating and financial leverage is that the earnings are magnified downwards during an economic slowdown. Lower earnings put companies in financial distress, which adds costs.

The costs of financial distress can be classified as direct or indirect. Some direct costs include actual cash expenses (such as administrative costs) associated with bankruptcy. In contrast, indirect costs include agency costs associated with the debt, forgone investment opportunities, and impaired ability to conduct business.

Companies with assets that have a ready secondary market have lower costs associated with financial distress. On the other hand, companies with fewer tangible assets have less liquidity and higher costs associated with financial distress. The probability of bankruptcy increases as the degree of leverage increases.

Question

Which of the following is most likely true about the effect of asymmetric information on the cost of equity?

1. Companies with lower asymmetry of information have a greater likelihood of agency cost.
2. Some degree of asymmetric information exists because investors never have as much information as managers.
3. Managers choose financing methods according to a hierarchy that prefers the method with the most potential information content.

Solution

The correct answer is B.

Managers have more information about the company’s current performance and its future potential investments than investors.

A is incorrect. Companies with lower asymmetry of information have less likelihood of agency costs.

C is incorrect. Managers choose financing methods according to a hierarchy that prefers the method with negligible potential information content.