Weighted Average Cost of Capital and Capital Structure Irrelevance

Firm Value and Return on Debt

The value of a firm is calculated as debt plus equity, excluding preferred stock. This total is then multiplied by the return on debt, also known as the cost of debt or the expected return on debt, which is equivalent to the yield to maturity on the firm's bonds. In formulas:

Value{Firm} = (Debt + Equity) \times Return{Debt}

Debt financing is tax-deductible, leading to what is known as the after-tax cost of debt. This is computed by multiplying the return on debt by one minus the corporate tax rate, creating a tax shield.

AfterTaxCost{Debt} = Return{Debt} \times (1 - TaxRate_{Corporate})

Where:

• TaxRate_{Corporate} represents the corporate tax rate, which will typically be provided.

Equity and its Cost

The total value of the firm also comprises the value of equity, which typically transitions from book value to market value. The overall equation representing the firm's value is:

Value{Firm} = Value{Debt} + Value_{Equity}

Equity also carries a cost, referred to as the required return on equity, the cost of equity, or the expected return on equity. This can be calculated using methods like the dividend discount model, as discussed in Chapter 8.

Capital Structure and Firm Value

Initially, the mix of debt and equity may vary widely among firms. However, the early theory suggests that the firm's capital structure—the mix of debt and equity—does not affect the firm's value.

The primary goal of a corporation is to maximize the value of the firm, thereby maximizing stockholders' wealth and the stock price. The initial stance suggests that the capital structure is irrelevant to the actual value of the firm or the stock price.

Modigliani-Miller (M&M) Theory

This theory, attributed to Franco Modigliani and Merton Miller, posits that under certain conditions, the capital structure does not impact firm value. Their first theory assumes no taxes, which is acknowledged as an unrealistic assumption.

Assumptions of M&M Theory

1. No Taxes: Assumes that there are no corporate taxes affecting the firm's financial decisions.
2. Well-Functioning Capital Markets: This implies that both the bond and stock markets operate efficiently. Key aspects include:
   • Stock prices reflect all relevant available information, meaning stocks are fairly priced.
   • Investors can borrow and lend at the same rate as corporations, simplifying financial calculations.
3. Financial Managers Cannot Increase Value by Altering the Mix of Securities: Altering the capital structure by increasing or decreasing debt or equity does not change the firm's overall value.

Example: River Cruises Inc.

Consider a company, River Cruises Inc., financed entirely by equity. It has 100,000 shares outstanding, with each share priced at $10, giving the company a market capitalization of $1,000,000.

Economic States and Operating Income

The firm plans based on three economic states:

1. Slump.
2. Expected (average economy).
3. Boom.

Operating income varies by economic state. In a normal economy, the operating income is $125,000. Since the firm is 100% equity financed, there are no interest payments.

Earnings Per Share (EPS) and Return on Shares

Earnings per share (EPS) is calculated by:

EPS = \frac{OperatingIncome}{NumberOfShares}

Under normal economic conditions:

EPS = \frac{$125,000}{100,000} = $1.25

The return on shares is:

Return = \frac{EPS}{PricePerShare} = \frac{$1.25}{$10} = 12.5\%

Recapitalization: Stock Repurchase and Bond Issuance

The company decides to repurchase $500,000 worth of stock, financing this by issuing $500,000 in bonds. This changes the capital structure to 50% equity and 50% debt, but the firm's value remains at $1,000,000.

Shares outstanding are reduced to 50,000 due to the repurchase. The stock price remains at $10 per share.

Impact on Earnings Per Share with Debt Financing

Operating income remains unaffected by the capital structure change. However, with debt financing, the company now has interest payments.

If operating income is $125,000, and interest payments are $50,000, the earnings available to equity holders are $75,000.

EPS = \frac{Earnings}{SharesOutstanding} = \frac{$75,000}{50,000} = $1.50

The earnings per share increase from $1.25 to $1.50. Despite this increase, the firm's value has not changed.

Risk and Leverage

While debt can increase earnings per share, it also increases risk. Financial risk arises from the use of financial leverage. Even though in good times the firm only pays a fixed amount to bondholders, in downturns, the firm is still obligated to pay this amount, which can strain finances.

For example, if operating income is only $50,000, it would all go to interest payments, leaving nothing for stockholders. Conversely, if the firm has a boom and earns $500,000, the bondholders still only receive their fixed interest payments.

Homemade Leverage

Instead of the firm altering its capital structure, investors can create their own leverage. This involves investors borrowing to invest in the company's stock.

Instead of using $10 of your own money to buy a share, you borrow $5 and invest $5 of your own money. However, it assumes that individual investors can borrow at the same rate as the firm, which is often not the case.

Debt-to-Equity Ratio

The debt-to-equity ratio is calculated as:

\frac{Debt}{Equity}

It measures how much debt a company has for every dollar of equity. As the debt-to-equity ratio increases, both the equity and the firm become riskier. This increased risk typically leads to a higher required return on equity. Rating agencies like S&P, Moody’s, and Fitch assess these ratios to possibly adjust a firm's credit rating; a higher risk would result in agency downgrade.

Important Formulas

• Value of Firm: Value_{Firm} = Debt + Equity
• After-Tax Cost of Debt: AfterTaxCost{Debt} = Return{Debt} \times (1 - TaxRate_{Corporate})
• Earnings Per Share (EPS): EPS = \frac{OperatingIncome}{NumberOfShares}
• Return on Shares: Return = \frac{EPS}{PricePerShare}
• Debt-to-Equity Ratio: \frac{Debt}{Equity}