The trade-off theory states that the optimal capital structure is a trade-off between interest tax shields and cost of financial distress:.

47) Value of firm = Value if all-equity financed + PV(tax shield) - PV(cost of financial distress)

The trade-off theory can be summarized graphically. The starting point is the value of the all-equity financed firm illustrated by the black horizontal line in Figure 10. The present value of tax shields is then added to form the red line. Note that PV(tax shield) initially increases as the firm borrows more, until additional borrowing increases the probability of financial distress rapidly. In addition, the firm cannot be sure to benefit from the full tax shield if it borrows excessively as it takes positive earnings to save corporate taxes. Cost of financial distress is assumed to increase with the debt level.

The cost of financial distress is illustrated in the diagram as the difference between the red and blue curve. Thus, the blue curve shows firm value as a function of the debt level. Moreover, as the graph suggest an optimal debt policy exists which maximized firm value.

Figure 10, Trade-off theory of capital structure

In summary, the trade-off theory states that capital structure is based on a trade-off between tax savings and distress costs of debt. Firms with safe, tangible assets and plenty of taxable income to shield should have high target debt ratios. The theory is capable of explaining why capital structures differ between industries, whereas it cannot explain why profitable companies within the industry have lower debt ratios (trade-off theory predicts the opposite as profitable firms have a larger scope for tax shields and therefore subsequently should have higher debt levels).

The pecking order theory of capital structure

The pecking order theory has emerged as alternative theory to the trade-off theory. Rather than introducing corporate taxes and financial distress into the MM framework, the key assumption of the pecking order theory is asymmetric information. Asymmetric information captures that managers know more than investors and their actions therefore provides a signal to investors about the prospects of the firm.

The intuition behind the pecking order theory is derived from considering the following string of arguments:

- If the firm announces a stock issue it will drive down the stock price because investors believe managers are more likely to issue when shares are overpriced.

- Therefore firms prefer to issue debt as this will allow the firm to raise funds without sending adverse signals to the stock market. Moreover, even debt issues might create information problems if the probability of default is significant, since a pessimistic manager will issue debt just before bad news get out.

This leads to the following pecking order in the financing decision:

1. Internal cash flow

2. Issue debt

3. Issue equity

The pecking order theory states that internal financing is preferred over external financing, and if external finance is required, firms should issue debt first and equity as a last resort. Moreover, the pecking order seems to explain why profitable firms have low debt ratios: This happens not because they have low target debt ratios, but because they do not need to obtain external financing. Thus, unlike the trade-off theory the pecking order theory is capable of explaining differences in capital structures within industries.

A final word on Weighted Average Cost of Capital

All variables in the weighted average cost of capital (WACC) formula refer to the firm as a whole.

Where TC is the corporate tax rate.

The after-tax WACC can be used as the discount rate if

1. The project has the same business risk as the average project of the firm

2. The project is financed with the same amount of debt and equity

If condition 1 is violated the right discount factor is the required rate of return on an equivalently risky investment, whereas if condition 2 is violated the WACC should be adjusted to the right financing mix. This adjustment can be carried out in three steps:

- Step 1: Calculate the opportunity cost of capital

- Calculate the opportunity cost of capital without corporate taxation.

- Step 2: Estimate the cost of debt, rD, and cost of equity, rE, at the new debt level

- Step 3: Recalculate WACC

o "Relever the WACC" by estimating the WACC with the new financing weights

Example:

- Consider a firm with a debt and equity ratio of 40% and 60%, respectively. The required rate of return on debt and equity is 7% and 12.5%, respectively. Assuming a 30% corporate tax rate the after-tax WACC of the firm is:

- The firm is considering investing in a new project with a perpetual stream of cash flows of $11.83 million per year pre-tax. The project has the same risk as the average project of the firm.

- Given an initial investment of $125 million, which is financed with 20% debt, what is the value of the project?

- The first insight is that although the business risk is identical, the project is financed with lower financial leverage. Thus, the WACC cannot be used as the discount rate for the project. Rather, the WACC should be adjusted using the three step procedure.

- Step 1: Estimate opportunity cost of capital, i.e. estimate r using a 40% debt ratio, 60% equity ration as well as the firm's cost of debt and equity

- Step 2: Estimate the expected rate of return on equity using the project's debt-equity ratio. As the debt ratio is equal to 20%, the debt-equity ratio equals 25%.

- Step 3: Estimate the project's WACC

- The adjusted WACC of 9.86% can be used as the discount rate for the new project as it reflects the underlying business risk and mix of financing. As the project requires an initial investment of $125 million and produced a constant cash flow of $11.83 per year for ever, the projects NPV is:

- In comparison the NPV is equal to $5.03 if the company WACC is used as the discount rate. In this case we would have invested in a negative NPV project if we ignored that the project was financed with a different mix of debt and equity.

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