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# WACC, capital structure, taxes, and NPV

The cost of capital is an important ingredient in capital budgeting and valuation. A company creates value only if the return it earns on projects is greater than the cost of capital. Estimating the cost of capital is challenging, first, because it is not directly observable, and second, it depends on the characteristics of the project. In reality, companies estimate the cost of capital for the whole company and then notch it up and down depending on the risk inherent in each individual project.

The cost of capital is the return that suppliers of capital, bondholders, and shareholders, require as compensation for their contribution to capital. It is the opportunity cost of funds for suppliers of capital. Since there are multiple sources of capital, primarily debt and equity, the cost of a single source of capital is called the component cost of capital. Further, since the cost of capital is to be applied to new projects requiring additional funding, it is the marginal cost, i.e. the cost of each new dollar of capital raised and not the average cost.

At a company level, the cost of capital is the return that investors require on an average-risk investment of the company. The most popular measure of the cost of capital is the weighted average cost of capital (WACC) which is the weighted average of the marginal component costs of capital. It is calculated using the following equation:

$WACC\ =\ w_d\times\ r_d\times\ (1-t)\ +\ w_b\times r_p\ +w_e\times r_e$

Where wd, wp and we are the weights of debt, preferred stock and common stock in the capital structure. rd, rp and re are the corresponding marginal pre-tax component costs of capital and t is the tax rate.

## Impact of taxes on WACC

Cost of debt (rd) is multiplied with a factor of (1 – t) because, in many jurisdictions, interest expense is tax-deductible, which means that the effective cost of debt is lower. The cost of equity is not reduced due to the tax rate because distributions to shareholders are not tax-deductible.

Estimating the cost of debt is easier than the cost of equity because the debtholder receives a determinable stream of cash flows while equity shareholders have only the residual interest and no committed payments. The cost of equity is estimated using either the capital asset pricing model or dividend discount model.

## Capital structure weights

Ideally, a company should calculate WACC using the proportions in which it would use each source of capital in a project. However, if a company has a target capital structure, WACC can be calculated using target weights.

Since an analyst might not have access to target capital structure, it can (a) assume current capital structure is the target capital structure and find out weights based on market values, (b) study trends in a company’s capital structure or management’s statement about capital structure to infer the target capital structure, and (c) use capital structure of comparable companies (either based on arithmetic average for simplicity or weighted in accordance with the size of companies).

If we have the D/E ratio, we can calculate debt weight by dividing D/E by (1 + D/E)

## Application of WACC to to capital budgeting and security valuation

A company’s marginal cost of capital (the weighted average cost of capital) increases as the company raises additional capital. This is represented by an upward-sloping marginal cost of capital schedule. But the company’s return from new investments declines as it undertakes more projects. This is represented by a downward sloping investment opportunity schedule.

A company’s optimal capital budget is the point at which its marginal cost of capital schedule intersects the investment opportunity schedule.

### Adjustment of WACC for differences in project risk

While the WACC is appropriate for a company as a whole, individual projects or divisions should be valued at an opportunity cost of capital specifically calculated keeping in view their risk. In practice, however, an upward or downward adjustment is made to the company’s overall WACC to arrive at a project-related cost of capital if the systematic risk of the project differs from the company’s overall risk.

### Application in calculation of NPV

Cost of capital is an important input in calculations of net present value, which equals the present value of a project’s cash inflows and outflows both determined at an opportunity cost of capital, derived from WACC. If we use WACC to determine net present value, which is quite common, we are assuming that the risk of the project is the same as the overall risk of the company and that the company will have a constant target capital structure over the life of the project.

### Application to security analysis

The cost of capital is also used in security analysis to determine the value of a company’s stock. If we are working with free cash flow to the firm, we need to use WACC, but if we are using free cash flow to equity, we need to discount using the cost of equity.