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Capital Structure.md

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Capital Structure.md

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The value of a firm is defined as the sum of the firms debt and its equity$$V=B+S$$The firms management should choose the optimal [[Ratio analysis#Leverage ratios|Debt-Equity]] ratio that makes $V$ as large as possible.

If we plot the earnings of a firm against its earnings per share in a levered and unlevered firm, we can see how leverage affects the returns to the investor that the firm provides ![[Pasted image 20240415171152.png|400]]

Modigliani and Miller model

Assumptions
  • Perfect competition
  • Firms and investors borrow/lend at the same interest rate
  • There is equal access to all relevant information
  • No transaction costs

Proposition 1 (No Taxes)

Homemade leverage makes the capital structure of a firm irrelevant. By taking margin to buy shares, or by lending to the firm the payoff of an unlevered firm can be replicated when there are no taxes

Example

![[Pasted image 20240415171538.png]] ![[Pasted image 20240415171550.png]]

Proposition 2 (No taxes)

Leverages increases the risk and return to stockholders. This can be calculated by using the [[Weighted Average Cost of Capital (WACC)]] equation. Without taxes,$$R_0=\frac{B}{B+S}\times R_B+\frac{S}{B+S}\times R_S$$Multiplying by [[Ratio analysis#Leverage ratios|Equity Multiplier]] on both sides, $$\frac{B+S}{S}R_0=\frac BS R_B+R_S$$Therefore, $$R_S = \frac BS(R_0-R_B)+R_0$$Where $R_S$ is the cost of unlevered equity, $R_B$ is the cost of debt and $R_0$ is the WACC. Graphically, ![[Pasted image 20240415172106.png|400]] As the debt-equity ratio increases, the returns increase but so does the risk.

Proposition 1

A firms value increases with leverage. This is because debt financing is cheaper as it is a [[Corporate income tax]] write off. $$\text{Cash Flow to Investors} = (\text{EBIT} - R_BB)(1-T)+R_BB = \text{EBIT}(1-T)+R_BBT$$Taking the present value of the second term ($BT$), we find that the cash flow is given by $$V_L = V_U+TB$$

Proposition 2

Some increase in equity risk is offset by the increased tax shield by more debt investment. The unlevered cost of equity is given by $$R_S=R_0+\frac BS(1-T)(R_0-R_B)$$Plotting this relationship, ![[Pasted image 20240415173300.png|400]] we find that levered firms pay less in taxes than unlevered firms, and this have a lower cost to raising equity the higher their debt to equity ratio.