# How capital structure affects the beta measure of risk

Beta on assets is jmt a weighted-average of the debt and equity beta:

Similarly, MM's proposition II can tie expressed in terms of beta, since increasing the debt-equity ratio will increase the financial risk, beta on equity will be increasing in the debt-equity ratio.

Again, notice MM's proposition I transits into no effect on the beta on asset of increasing the financial leverage. The higher beta on equity ie exactly being of feet by the substitution effect as we swap equity with debt and debt has tower beta than equity.

# How capital structure affects company cost of capital

The impact of the MM-theory on company cost of capital can be illustrated graphically. Figure 9 assumes that debt is essentially risk free at low levels of debt, whereas it becomes risky as the financial leverage increases. The expected return on debt is therefore horizontal until the debt is no longer risk free and then increases linearly with the debt-equity ratio. MM's proposition II predicts that when this occur the rate of increase in, rE, will slow down. Intuitively, as the firm has more debt, the less sensitive shareholders are to further borrowing.

**Figure 9. Cost of capital: Miller and Modigliani Proposition I and II**

The expected return on equity, rE, increases linearly with the debt-equity ratio until the debt no longer is risk free. As leverage increases the risk of debt, debt holders demand a higher return on debt, this causes the rate of increase in rr to slow down.

# Capital structure theory when markets are imperfect

MM-theory conjectures that in a perfect capital market debt policy is irrelevant. In a perfect capital market no market imperfections exists. However in the real world corporations are taxed, firms can go bankrupt and managers might be self-interested. The question then becomes what happens to the optimal deUi policy when the market imperfections are taken into account. Alternative capital structure theories therefore address the impact of imperfections such as taxes, cost of bankruptcy and financial distress, transaction costs, asymmetric information and agency problems.

# Introducing corporate taxes and cost of financial distress

When corporate income is taxed, debt financing has one important advantage: Interest payments are tax deductible. The value of this tax shield is equal to the interest payment times the corporate tax rate, since firms effectively will pay (1-corporate tax rate) per dollar of interest payment.

Where TC is the corporate tax rate.

After introducing taxes MM's proposition I should be revised to include the benefit of the tax shield: Value of firm = Value if all-equity financed + PV(tax shield)

In addition, consider the effect of introducing the cost of financial distress. Financial distress occurs when shareholders exercise their right to default and walk away from the debt. Bankruptcy is the legal mechanism that allows creditors to take control over the assets when a firm defaults. Thus, bankruptcy costs are the cost associated with the bankruptcy procedure.

The corporate finance literature generally distinguishes between direct and indirect bankruptcy costs:

- Direct bankruptcy costs are the legal and administrative costs of the bankruptcy procedure such as

• Legal expenses (lawyers and court fees)

• Advisory fees

- Indirect bankruptcy costs are associated with how the business changes as the firm enters the bankruptcy procedure. Examples of indirect bankruptcy costs are:

• Debt overhang as a bankruptcy procedure might force the firm to pass up valuable investment projects due to limited access to external financing.

• Scaring off costumers. A prominent example of how bankruptcy can scare off customers is the Enron scandal. Part of Enron's business was to sell gas futures (i.e. a contract that for a payment today promises to deliver gas next year). However, who wants to buy a gas future from a company that might not be around tomorrow? Consequently, all of Enron's futures business disappeared immediately when Enron went bankrupt.

• Agency costs of financial distress as managers might be tempted to take excessive risk to recover from bankruptcy. Moreover, there is a general agency problem between debt and shareholders in bankruptcy, since shareholders are the residual claimants.

Moreover, cost of financial distress varies with the type of the asset, as some assets are transferable whereas others are non-transferable. For instance, the value of a real estate company can easily be auctioned off, whereas it is significantly more involved to transfer the value of a biotech company where value is related to human capital.

The cost of financial distress will increase with financial leverage as the expected cost of financial distress is the probability of financial distress times the actual cost of financial distress. As more debt will increase the likelihood of bankrupt, it follows that the expected cost of financial distress will be increasing in the debt ratio.

In summary, introducing corporate taxes and cost of financial distress provides a benefit and a cost of financial leverage. The trade-off theory conjectures that the optimal capital structure is a trade-off between interest tax shields and cost of financial distress.