# Relationship between capital structure and cost of equation

### Capital structure - Wikipedia

Here is the basic formula for weighted average cost of capital: Assume newly formed Corporation ABC needs to raise $1 million in capital so it can buy office. In a capital structure model that includes bankruptcy costs and agency costs, this study calculates We examine difference between the WACC computed from . The first of Equation (2) is the case where the taxable income is positive; there. The causal relationship between capital structure and cost of capital is investigated in a simultaneous equation framework. On the one hand, we relate.

Although s x and f x in each example are specified arbitrarily, they satisfy the conditions that, and. Unless s x and f x can be proved as unrealistic, the resulting r x and w x should be deemed as possibilities in the real world.

This result does not prescribe a specific shape of w x and hence r xand does not specify whether f 1 is equal to, higher than, or lower than s 0. A non-constant r x poses a major difficulty in evaluating a new project. In this equation, xj is the debt ratio for the project. The debt ratio for the comparable firm may not be the same as the target debt ratio for the project firm; that is, x may not be equal to xj.

If they are not equal, f x is not equal to f x j and s x is not equal to s x j, although the project risk is deemed equal to that of the comparable firm. However, this method is valid only if the opportunity cost of capital is constant with respect to debt ratio or if x happens to be equal to xj.

If the opportunity cost of capital is not constant, r x is not necessarily equal to r x j unless x is equal to xj.

### Capital Structure Formula Derivation | AnalystForum

Strictly speaking, even if the two debt ratios are equal, r x is not necessarily equal to r x j unless r x and r x j are identical functions of the debt ratio.

Conclusions Theories in capital structure and costs of capital are important because they lay the foundation for making financing and investment decisions in a firm. However, inconsistent and questionable arguments exist concerning the relationships among capital structure, costs of capital, and firm value. We critically re-examine these relationships and provide several clarifications. In a perfect market with corporate taxes, given that the cost of debt is increasing and concave up and that the firm rebalances its debt, the cost of equity is increasing and concave up if and only if the third derivative of the cost of debt is non-negative; otherwise, the cost of equity is increasing but its exact shape cannot be ascertained.

## Capital structure

In all cases, however, the cost of equity must be concave up initially. Also in this world, the weighted average cost of capital is decreasing and concave down.

Even if such minimum exists, the debt ratio that results in this minimum may not be the one that maximizes the firm value. The proponents of this view would need to explain how the expected cash flow stream can be assumed constant across debt ratios in the context of the trade-off theory, if this is an assumption.

**#1 Cost of Capital [Cost of Debt, Preference Shares, Equity and Retained Earnings] ~ FM**

We prove that if the weighted average cost of capital is U-shaped, the firm opportunity cost of capital cannot be a constant across debt ratios. Since the opportunity cost of capital reflects asset risk, the proponents would also need to explain how and why the asset risk is perceived changing across debt ratios in the way implied by the shape of the opportunity cost of capital.

Strictly speaking, even if the two debt ratios are the same, the opportunity cost of capital for the comparable firm is not necessarily equal to that for the project unless the two costs of capital are identical functions of the debt ratio.

In the real world[ edit ] If capital structure is irrelevant in a perfect market, then imperfections which exist in the real world must be the cause of its relevance. Trade-off theory[ edit ] Trade-off theory of capital structure allows bankruptcy cost to exist as an offset to the benefit of using debt as tax shield.

It states that there is an advantage to financing with debt, namely, the tax benefits of debt and that there is a cost of financing with debt the bankruptcy costs and the financial distress costs of debt.

This theory also refers to the idea that a company chooses how much equity finance and how much debt finance to use by considering both costs and benefits. The marginal benefit of further increases in debt declines as debt increases, while the marginal cost increases, so that a firm optimizing its overall value will focus on this trade-off when choosing how much debt and equity to use for financing. Empirically, this theory may explain differences in debt-to-equity ratios between industries, but it doesn't explain differences within the same industry.

It states that companies prioritize their sources of financing from internal financing to equity according to the law of least effort, or of least resistance, preferring to raise equity as a financing means "of last resort".

This theory maintains that businesses adhere to a hierarchy of financing sources and prefer internal financing when available, and debt is preferred over equity if external financing is required equity would mean issuing shares which meant 'bringing external ownership' into the company.

Thus, the form of debt a firm chooses can act as a signal of its need for external finance. As a result, investors may place a lower value to the new equity issuance.

Capital structure substitution theory[ edit ] The capital structure substitution theory is based on the hypothesis that company management may manipulate capital structure such that earnings per share EPS are maximized.

The SEC rule 10b allowed public companies open-market repurchases of their own stock and made it easier to manipulate capital structure. First, it has been deducted[ by whom?

## Capital Structure

The second prediction has been that companies with a high valuation ratio, or low earnings yield, will have little or no debt, whereas companies with low valuation ratios will be more leveraged. A fourth prediction has been that there is a negative relationship in the market between companies' relative price volatilities and their leverage.

This contradicts Hamada who used the work of Modigliani and Miller to derive a positive relationship between these two variables. Agency costs[ edit ] Three types of agency costs can help explain the relevance of capital structure. As debt-to-equity ratio increases, management has an incentive to undertake risky, even negative Net present value NPV projects.

This is because if the project is successful, share holders earn the benefit, whereas if it is unsuccessful, debtors experience the downside. If debt is risky e. Thus, management have an incentive to reject positive NPV projects, even though they have the potential to increase firm value.