Francesco Modigliani - Nobel prize in 1986

Merton Miller - Nobel prize in 1990 ¹

Miller, Merton H. & Franco Modigliani (1958) “The cost of capital, corporate finance and the theory of investment”, The American Economic Review

“…both Modigliani and Miller were professors at the Graduate School of Industrial Administration at Carnegie Mellon University. Both were required to teach corporate finance to business students but, unhappily, neither had any experience in corporate finance. After reading the course materials that they were to use, the two professors found the information inconsistent and the concepts flawed. So, they worked together to correct them. …”

How relates:

• P1: capital structure of the firm to the Firm value;
• P2: capital structure of the firm to its Weighted Average Costs of Capital.

Firm value vs. Enterprise value - both terms are using interchangeably, but there are some minor differences. We consider them to be synonymous.

Enterprise value (EV) measures a company’s total value.

\[EnV = Market\_capitalization + Debts - cash\]

Equity value (EqV) \[EqV = Enterprise\_value + Cash – Debt \]

Cash flow is the net amount of cash and cash equivalents being transferred in and out of a company. Cash received represents inflows, while money spent represents outflows.

Free cash flow the cash flow available for the company to repay creditors or pay dividends and interest to investors. It is the cash that a company generates after accounting for cash outflows to support operations and maintain its capital assets.

FCFF (free cash flow for the firm) represents the cash from the operating activities, invests in current assets (e.g., inventory), and invests in long-term assets (e.g., equipment). FCFF includes bondholders and stockholders as beneficiaries when considering the money left over for both of them.

\[FCFF=CFO+(IE×(1−TR))−CAPEX + NDI\] where where: \(CFO\) = Cash flow from operations, \(IE\) = Interest Expense, \(CAPEX\) = Capital expenditures, \(NDI\) = Net Debt Issued.

FCFE (Free cash flow to equity) is a cash flow available to the equity shareholders of a company after all expenses, reinvestment, and debt are paid. FCFE is a measure of equity capital usage. \[FCFE = CFO – CAPEX + Net\_Debt\_Issued\] \(FCFE\) is often used as a tool to find a fair stock-prices value.

FCFF can be used to ex-ante estimates of the Enterprise value

\[EnV_{t=0} = \sum_{t=1}^\infty\frac{FCFF_t}{1+WACC_t}\] where \(1/(1+WACC_t)\) is a discount factor.

FCFE (Free cash flow to equity) is a cash flow available to the equity shareholders of a company after all expenses, reinvestment, and debt are paid. FCFE is a measure of equity capital usage. \[FCFE = CFO – CAPEX + Net\_Debt\_Issued\] \(FCFE\) is often used as a tool to find a fair stock-prices value. Its ex-ante calculation is

\[EqV_{t=0} = \sum_{t=1}^\infty\frac{FCFE_t}{1+R_{e,t}}\] where \(R_{e,t}\) is Return on equity in time \(t\).

Weighted Average Costs of the Capital (WACC) - Weighted average cost of capital (WACC) represents a firm’s average after-tax cost of capital from all sources, including common stock, preferred stock, bonds, and other forms of debt. WACC is the average rate that a company expects to pay to finance its assets. (Investopedia) \[WACC = \frac{E}{E+D}\times R_e + \frac{D}{E+D}\times R_d \times (1-R_t)\] where \(E\) = equitiy, \(D\) = Debt, \(R_e\) - dividends rate paid, \(R_d\) - interest rate paid, \(R_t\) = tax rate paid.

Note: \(R_a\), \(R_e\), \(R_d\) are used often as the returns compensating the risk of running a business \(R_a\), risk on holding the risky assets (shares) \(R_e\), risks of the creditors \(R_d\).

Scenario 1 - no corporate or personal taxes - no banctruptcy costs

Scenario 2 - corporate taxes bu no personal taxes - no banctruptcy costs

Scenario 3 - corporate taxes but no personal taxes - banctruptcy costs

Scenario 1 - no corporate or personal taxes - no banctruptcy costs

Logical Inference:

1. If cash flow does not change then value of the firm does not change.
2. If there is constant cash flow, then any change of the capital structure has no impact on the Firm value.

In Case 1, M&M assume the value of the firm does not depend on the ratio of the foreign and own financial sources of the firm.

\[(WACC =) R_a = \frac{E}{E+D}\times R_e + \frac{D}{E+D}\times R_d \times (1-R_t)\] where \(R_a\) denotes return on assets (do not be confused with ROA). If \(R_t = 0\), then

\[WACC = \frac{E}{E+D}\times R_e + \frac{D}{E+D}\times R_d\] and \[R_e = R_a + (R_a-R_d) \times \frac{D}{E}\] where \(R_d \leq R_a \leq R_e\). Any increase of the Debt-to-Equity ratio should be compensated by the Return onequity (assuming \(R_D\) is external factor, \(E+D = const.\). ).

• \(R_a\) presents here mesure on the business systemic risk (we are not to avoid),

• \((R_a+R_d)\times \frac{D}{E}\) is a return on the financial risk (can be increased / decreased by the financial leverage)

Assumptions:

• interest paid is tax deducible

• if the firm increases the debts, decreases the taxes, all else equal

• reduction of taxes increases the cash flows

• reduction in taxes reduces net income

The term cash flow refers to the net amount of cash and cash equivalents being transferred in and out of a company. Cash received represents inflows, while money spent represents outflows.

Cash flow from financing activities (CFF) is a section of a company’s cash flow statement, which shows the net flows of cash that are used to fund the company. Financing activities include transactions involving debt, equity, and dividends.

\[(WACC =) R_a = \frac{E}{E+D}\times R_e + \frac{D}{E+D}\times R_d \times (1-R_t)\] which implies

\[R_e = R_a + (R_a-R_d)\times R_d \times (1-R_t)\]

Rsulting Tax Shield is 24 USD.