Session 6 Flashcards
What are the key assumptions of a perfect capital market?
A perfect capital market is one where financial assets are traded without any frictions, allowing for efficient allocation of resources. The key assumptions include:
- No Taxes – Financial decisions are not influenced by tax considerations.
- No Bankruptcy or Financial Distress Costs – No costs related to financial distress or insolvency.
- No Information Asymmetry – All investors have access to the same information, eliminating any advantage from privileged knowledge.
- No Transaction Costs – Buying and selling securities do not incur fees or commissions, ensuring frictionless trading.
- Individuals and Corporations Borrow at the Same Rate – No preferential treatment by lenders; borrowing costs are the same.
- Other Assumptions – Rational investors, no arbitrage opportunities, and complete markets where all assets can be traded.
In reality, perfect market conditions do not exist due to taxes, transaction costs, information asymmetry, and financial distress costs.
What is financial leverage?
Financial leverage refers to the use of debt financing to increase potential returns for equity holders. Instead of relying only on equity financing, a company borrows money (debt) to fund operations or investments.
What happens to a company’s capital structure when it takes on debt to buy back equity?
The company’s capital structure shifts from being unlevered (only equity) to levered (a mix of debt and equity). This increases financial leverage and reduces the number of shares outstanding.
How does leverage impact Earnings Per Share (EPS)?
Effects on Earnings Per Share (EPS):
- At low earnings levels: EPS is lower due to fixed interest costs (disadvantage).
- Break-even point: There is an earnings level where leverage neither helps nor hurts.
- At high earnings levels: EPS grows at a faster rate than in an unlevered firm (advantage).
Benefits: Higher EPS in profitable periods, lower cost of capital.
Risks: Fixed interest payments increase financial risk, especially in downturns.
Leverage is beneficial when earnings are stable and growing but risky in uncertain environments.
What is MM Proposition I (Capital Structure Irrelevance), and what are its key assumptions?
MM Proposition I states that in a perfect market, the total value of a firm is independent of its capital structure (whether financed by equity, debt, or a mix).
Key Ideas:
- A firm’s cash flows remain the same regardless of financing.
- Follows the Law of One Price – equivalent assets should have the same value in competitive markets.
Key Assumptions:
- Investors and firms can trade securities at market prices.
- Individuals can borrow at the same rate as firms.
- No taxes, transaction costs, or financial distress costs.
- Financing decisions do not affect the firm’s cash flows.
Conclusion: Under perfect conditions, capital structure does not impact firm value.
What is MM Proposition II, and how does it explain the effect of leverage on risk and return?
MM Proposition II states that as a firm takes on more debt, the expected return on equity (cost of equity) increases due to higher financial risk borne by equity holders.
Key Insight:
- While debt is cheaper than equity, the increased risk for shareholders leads to a higher cost of equity (RE)
- In a no-tax world, the firm’s Weighted Average Cost of Capital (WACC) remains constant because the lower cost of debt is offset by the higher cost of equity.
More debt increases equity risk but does not reduce WACC under perfect market conditions.
How is the cost of capital calculated for an all-equity firm (unlevered firm)?
For an all-equity firm (no debt in capital structure), the required return is denoted as Ru (also written as Ra)
Interpretation:
- Represents the required return for a company financed entirely by equity.
- Since there is no leverage, there is no financial risk from debt, meaning all risk is business risk.
What is the formula for MM Proposition II, and what does it imply?
- Ru represents the firm’s business risk, which does not change with leverage.
- The term D/E(Ru - Rd) represents the additional risk equity holders bear due to leverage.
- Since debt is cheaper than equity, adding debt raises the cost of equity, keeping the overall cost of capital unchanged (assuming no taxes).
As a firm takes on more debt, equity holders require higher returns due to increased financial risk.
How does MM Proposition II explain the relationship between leverage and equity risk using beta formulation?
The firm’s asset beta ßA represents the overall risk of the firm and is a weighted average of debt and equity betas:
Implications: Equity beta ße increases as leverage increases.
Shareholders bear more risk when firms take on more debt because:
- Debt holders get paid first, making equity holders exposed to more volatility.
- If the firm faces financial distress, equity becomes even riskier.
Conclusion: Higher leverage increases risk for equity holders, leading to a higher required return on equity, confirming MM Proposition II
What are the main insights from MM Proposition II?
Leverage Increases Equity Cost:
- Shareholders bear more risk when firms take on more debt.
- Therefore, the cost of equity Re increases with leverage.
WACC Remains Constant (No Taxes):
- Even though equity becomes more expensive, the cheaper cost of debt offsets it.
- This results in an unchanged WACC in a no-tax environment.
Debt is Initially Cheap but Riskier at High Levels:
- At low levels of debt, Rd (cost of debt) is stable.
- At very high leverage, Rd increases due to higher bankruptcy risk.
Conclusion: More debt raises equity risk, but WACC remains constant unless bankruptcy risk increases significantly.
What is MM Debt Policy Irrelevance, and when does capital structure matter?
MM Debt Policy Irrelevance (MM Proposition I) states that, in a perfect world, a firm’s capital structure (mix of debt and equity) does not affect its total value.
MM Assumptions (Perfect Market Conditions):
- No taxes
- No bankruptcy or financial distress costs
- No information asymmetries
- No transaction costs
When Does Capital Structure Matter?
- If any of the perfect market assumptions do not hold (e.g., taxes, bankruptcy costs, or information asymmetries exist), capital structure can impact firm value.
What MM Proposition does NOT Say:
- It does not mean all stakeholders (e.g., bondholders vs. shareholders) are indifferent to capital structure.
- Value can shift between bondholders and shareholders, but total firm value remains unchanged in a perfect world.
Conclusion: Essentially, MM Proposition I is a theoretical benchmark, but in reality, capital structure can be important due to market imperfections.
Why do firms use debt financing in relation to corporate taxes?
Firms use debt financing because interest payments on debt are tax-deductible, reducing the overall corporate tax burden. This creates a tax shield, where firms save money by deducting interest expenses from taxable income.
What is the formula for tax savings (tax shield) from interest payments?
The tax savings (tax shield) per period from interest payments is:
This means the firm reduces its taxable income by tc times its interest expense.
What is the present value (PV) of the tax shield, and what does it imply?
The present value (PV) of the tax shield, assuming perpetual debt, is:
Implication:
- For every unit of debt D, the firm gains additional value equal to tcD due to tax savings.
- This shows that higher debt increases firm value when taxes exist, contradicting MM Proposition I (which assumes no taxes).
How does debt affect firm value according to MM Proposition I with corporate taxes?
According to Modigliani-Miller Proposition I with corporate taxes, the value of a firm increases with debt due to the tax shield on interest payments.
Since debt financing reduces taxable income, firms increase in value by the amount of the tax shield, giving them an incentive to use debt.
How does MM Proposition II change with corporate taxes, and what is its formula?
With corporate taxes, MM Proposition II states that the expected return on equity Re increases as the firm’s leverage (D/E ratio) increases.
Key Implications:
- More debt → Higher Re (equity holders take on more risk).
- WACC decreases with leverage due to the tax shield on debt.
- Debt interest is tax-deductible, reducing the firm’s taxable income.
Conclusion: Unlike in a no-tax world, debt reduces WACC when taxes exist, making leverage more beneficial.
How does the WACC formula account for the tax benefits of debt?
The Weighted Average Cost of Capital (WACC) formula adjusts for the tax benefits of debt as follows:
- Since interest on debt is tax-deductible, the after-tax cost of debt is used: Rd (1-tc)
- WACC is lower in a world with corporate taxes compared to one without, because the government subsidizes debt financing through tax deductions.
Tax benefits make debt cheaper, reducing the firm’s overall cost of capital and incentivizing leverage.
What are the limits to the tax benefits of debt, and what is the optimal leverage level?
Limits to the Tax Benefit of Debt
To maximize tax benefits, a firm must have taxable earnings (EBIT); otherwise, the tax shield is lost.
- Interest should not exceed EBIT to avoid a net operating loss and wasted tax shields.
- Excessive debt offers no corporate tax benefit and may increase investors’ personal tax burdens.
Optimal Leverage Level
The ideal leverage occurs when interest equals EBIT, maximizing tax benefits without excessive debt.
However, predicting future EBIT is challenging, posing risks:
- Interest > EBIT → Reduced tax savings.
- Unused tax shields → Lower firm value.
While debt provides tax advantages, firms must balance leverage to maintain tax benefits and minimize financial risk.
What are the key concepts of Cost of Equity, Cost of Debt, WACC, and Unlevered Cost of Capital?
Cost of Equity (rE):
- Represents the return required by shareholders.
- Increases with leverage because higher financial risk raises required returns for equity holders.
Cost of Debt (rD):
- The interest rate required by lenders.
- Initially cheaper due to tax benefits (interest deductibility).
- Higher debt → Increased financial distress → Higher borrowing costs.
Weighted Average Cost of Capital (WACC):
- The firm’s overall cost of financing, considering both debt and equity.
- Moderate debt → WACC decreases (due to tax shield).
- Excessive debt → Higher default risk → WACC increases.
Unlevered Cost of Capital (rU or rA):
- The expected return if the firm was entirely financed by equity.
- Used as a benchmark to compare leveraged vs. unleveraged cost of capital.
While debt can lower WACC up to a point, excessive leverage increases risk and borrowing costs.
What is the impact of leverage on beta, and why is beta unlevered?
Impact of Leverage on Beta:
- A stock’s equity beta (ße) depends on the asset beta (ßa), which represents business risk, and the amount of debt in the firm’s capital structure.
- More debt → Higher ße (equity becomes riskier for shareholders).
- This aligns with MM Proposition II (with taxes): Higher leverage increases both risk and return on equity.
Why Unlever Beta?
- To compare a firm’s business risk with other firms without financial leverage distortion.
- ßa represents pure business risk, while ße includes additional financial risk from leverage.
Unlevering beta isolates business risk, making firms more comparable across different capital structures.
How do you unlever beta in perfect capital markets, and why is it useful?
Why Unlever Beta?
- Removes leverage effects, allowing us to estimate the true business risk of a firm’s operations.
- Makes firms comparable across different capital structures.
Conclusion: Unlevering beta isolates pure business risk, helping investors and analysts assess the company without financial leverage distortions.
How does unlevering beta change in the MM world with corporate taxes?
Impact of Corporate Taxes on Beta:
- Debt creates a tax shield, reducing the firm’s effective risk exposure.
- Since interest on debt is tax-deductible, the effective amount of debt is reduced to (1 - tc)D
Key Takeaways:
- Higher D/E → Greater impact of leverage on equity beta.
- Corporate taxes lower the risk of debt because of tax benefits, reducing its impact on firm risk.
Conclusion: In the presence of taxes, the tax shield offsets some of the risk introduced by leverage.
What is Hamada’s equation, and how does leverage affect equity beta with and without taxes?
- Leverage increases the risk of equity by amplifying ße
- However, corporate taxes reduce this effect by creating a riskless tax shield, making equity beta increase less rapidly than in a no-tax environment.
What is the Pure-Play Method, and how is it used to assess project risk?
The Pure-Play Method estimates a project’s risk using comparable industry data by following these steps:
- Identify Pure-Play Firms – Find companies in the same industry with similar risk profiles.
- Unlever Their Betas – Remove the impact of debt to obtain the asset beta (unlevered beta).
- Relever the Beta for the Project – Adjust the unlevered beta to match the project’s target capital structure.
- Compute WACC – Use the new beta to determine the cost of equity and WACC.
- Assess Project Value (NPV Method) – Discount cash flows using WACC to evaluate project viability.
Conclusion: This method ensures a project’s risk is assessed independently of the firm’s existing capital structure, making it useful for investment decisions.