Introduction: The "Big Question" of Finance

Welcome! In this chapter, we are diving into one of the most famous debates in finance: Capital Structure. Imagine you are running a business. Does it matter if you fund it using your own money (Equity) or by borrowing from a bank (Debt)?

Franco Modigliani and Merton Miller (collectively known as MM) won Nobel Prizes for answering this. They wanted to know if a company's total value changes depending on how it slices the "financing pie." Don't worry if this seems tricky at first—at its heart, MM is just about whether the way we pay for a business changes how much that business is worth.

1. The Starting Point: MM Theory 1958 (No Taxes)

In their original 1958 theory, MM looked at a "perfect world" where there are no taxes and no costs for going bankrupt. They argued that the Total Value of a firm is independent of its capital structure.

The Pizza Analogy

Think of a company like a pizza. If you cut the pizza into 4 large slices (Equity) or 8 small slices (Debt + Equity), the total amount of pizza remains the same. You haven't created more food; you've just sliced it differently!

Key Principles of MM (1958):

1. Value of the Firm: The value of a levered firm (\(V_L\)) is exactly the same as an unlevered firm (\(V_U\)).
Formula: \(V_L = V_U\)

2. Cost of Equity (\(k_e\)): As a company takes on more debt, it becomes riskier for shareholders. Therefore, shareholders demand a higher return. This increase in the cost of equity perfectly offsets the benefit of "cheaper" debt.

3. WACC: Because the increase in equity cost perfectly cancels out the cheaper debt, the Weighted Average Cost of Capital (WACC) remains constant regardless of the debt level.

Quick Review: MM 1958

- Capital Structure: Irrelevant.
- Value: Unchanged by debt.
- WACC: Stays the same at all levels of debt.

2. The "Perfect World" Assumptions

To make their math work, MM had to make several assumptions. While these aren't realistic, you need to know them for the exam:

  • No Taxes: Governments don't take a cut.
  • No Transaction Costs: It costs nothing to issue shares or debt.
  • Symmetry of Information: Everyone (investors and managers) knows the same things.
  • No Bankruptcy Costs: Companies don't have to pay lawyers or liquidators if they fail.
  • Individuals can borrow: Investors can borrow at the same rate as companies.

3. The Real World Strikes Back: MM Theory 1963 (With Taxes)

MM later realized that in the real world, Taxes exist. This changed everything! In most countries (including Hong Kong), interest payments on debt are tax-deductible, while dividends paid to shareholders are not.

The Debt Tax Shield

Because interest reduces the tax bill, more money is left over for the investors. This is called the Tax Shield. It’s like a "discount" from the government for using debt.

Key Principles of MM (1963):

1. Value of the Firm: A firm with debt is now worth more than a firm without debt because of the tax savings.
Formula: \(V_L = V_U + (T_c \times D)\)
(Where \(T_c\) is the tax rate and \(D\) is the amount of debt)

2. Cost of Equity (\(k_e\)): It still goes up as debt increases (risk!), but it doesn't go up fast enough to cancel out the tax benefits.

3. WACC: As the company adds more debt, the WACC falls because of the tax shield. This means the firm becomes more valuable as it uses more debt.

Did You Know?

According to MM (1963), the "optimal" capital structure is 100% debt! However, we know companies don't do this in real life because they are afraid of going bankrupt—which MM 1963 still didn't account for.

4. Comparing the Two Theories

To help you remember, here is a simple comparison:

  • MM 1958 (No Tax): Debt is neutral. WACC is a flat horizontal line. Value is a flat horizontal line.
  • MM 1963 (With Tax): Debt is GOOD. WACC slopes downward. Value slopes upward.

Common Mistakes to Avoid:

1. Mixing up \(k_e\) and WACC: In both theories, the cost of equity (\(k_e\)) always goes up when you add debt. The difference is what happens to the total WACC.

2. Forgetting the Tax Shield: In the 1963 model, if you are asked to calculate the value of a levered firm, you must add the present value of the tax shield (\(T_c \times D\)).

5. Step-by-Step: Thinking Like an Examiner

When you see an MM question, follow these steps:

Step 1: Check if the question mentions taxes. If "No Taxes," use MM 1958 (Capital structure doesn't matter). If "Taxes exist," use MM 1963 (Debt adds value).

Step 2: Identify the "Unlevered Value" (the value of the business if it had zero debt).

Step 3: If taxes exist, calculate the Tax Shield: \(Tax \ Rate \times Amount \ of \ Debt\).

Step 4: Add the Tax Shield to the Unlevered Value to find the total value of the company.

6. Summary and Key Takeaways

MM Theory 1958:
- Assumptions: No taxes, no bankruptcy costs.
- Conclusion: Capital structure is irrelevant.
- Logic: The risk added by debt increases the cost of equity, perfectly cancelling out the benefit of cheaper debt.

MM Theory 1963:
- Assumptions: Corporate taxes exist; interest is tax-deductible.
- Conclusion: Debt increases firm value.
- Logic: The "Tax Shield" creates extra cash flow for investors, lowering the WACC and increasing the firm's total value.

Memory Trick:
Think of MM 58 as "Money Matters Not" (Irrelevant).
Think of MM 63 as "Money Makes More" (Debt makes value because of taxes).

Keep practicing these concepts! Once you master the logic of the "Tax Shield," the rest of the capital structure theories will fall into place much more easily.