Cost of capital

Firms finance their operations by three mechanisms: issuing stock (equity), issuing debt (borrowing from a bank is equivalent for this purpose), and reinvesting prior earnings. The cost of capital for a firm is a weighted sum of the cost of equity and the cost of debt. Re-invested money is also charged at the cost of equity, since if the money is not reinvested is will normally be returned to CAPM. It states that the return will be a function of the expected risk premium, the riskiness of the stock and the risk free rate. This value of the risk premium parameter varies over time and place, but over many countries during the twentieth century it has averaged around 4%. The β parameter is a property of the firm and it depends on both the business and the capital structure of the firm. These value cannot be measured ex ante, but can be estimated from ex post returns and experience with similar firms. This risk free rate is taken from a non-defaulting bond, such as U.S. Treasury Bills.

The cost of debt is computed by taking the rate on a non-defaulting bond whose duration matches the term structure of the corporate debt, then adding a default premium. This default premium will rise as the amount of debt increases (since the risk rises as the amount of debt rises). Since in most cases debt is a deductable expense, the cost of debt is computed as an after tax cost to make it comparable with the cost of equity (earnings are after-tax as well). Thus, for profitable firms, debt is discounted by the tax rate.

The total capital for a firm is the value of its equity (for a firm without outstanding warrants and options, this will be the market capitalization) plus the cost of its debt (again, this should be taken at market value, since the value of its debt may change due to changes in the interest rate structure aftet the debt is issued). The cost of capital is then given as:

K_c= (1-δ)K_e+δK_d;

where:

K_c

The weighted cost of capital for the firm;

δ

The debt to capital ratio, D /(D+E);

K_e

The cost of equity;

K_d

The after tax cost of debt;

D

The market value of the firm's debt, including bank loans and leases;

E

The market value of all equity (including warrants, options, and the equity portion of convertible securities).

If there were no tax advantages for issuing debt and equity could be freely issued, Miller and Modigliani showed that the cost of debt and the cost of equity should be the same. (Their paper is foundational in modern corporate finance.) Because of the tax advantages to issuing debt, profitable firms will have the lowest theoretical cost of capital using some debt.

There is an optimal structure for each firm, because adding debt increases the default risk and thus the rate that the company must pay in order to borrow money. At some point, the cost of issuing new debt will be greater than the cost of issuing equity. This point is affected as well by the profitability of the firm, since the tax breaks are realizable only when the firm is profitable.