The Cost of Capital

Capital for a corporation can be obtained from a variety of sources. These sources can be grouped into two categories, debt and equity. The essential difference is whether the returns to the capital sources are specified by contract, as in the case of debt, or are contingent upon how much the corporation earns, as in the case of equity. In reality the debt holders may also be subject to risks associated with the performance of the corporation if the corporation does so poorly that it cannot pay the contractual obligations to them.

The cost of capital from the different sources may differ because of differences in the perceived risk associated with the different securities, but it also may differ because of the nature of the tax system. Interest paid on debt is deductible in the computation of profit taxes by the dividends paid to equity holders is not. This means that if the profit tax rate is T and the interest rate on debt is r_d then the cost of capital from debt is:

The cost of capital from equity is not affected by the profit tax rate but it is more complicated conceptually than the cost of capital from debt. suppose a corporation is growing at a rate of g and hence the dividends per share, which are now D₁. is also growing at a rate of g. If r is the discount rate, called the capitalization rate for the stock, that the market places on future dividends for this corporation Then the price P of the stock would be:

The discount rate r is, in effect, the cost of capital from equity. If we know the price, the current dividend and the growth rate then we can solve for r. It value is:

The term D₁ /P is called the yield rate for the stock. So the cost of capital from equity is the yield rate plus the growth rate.

The above analysis is for a corporation which is expected to grow at a constant rate forever. If that is not the case there is still a discount rate (capitalization rate) that equates the present value of expected future dividends and the market price, but it would be much more difficult to compute and there would not be any simple formula for it.

An alternative approach to computing the cost of capital from equity is to use the formula derived in the Capital Asset Pricing Model (CAPM). According to the CAPM the required rate of return on equity is

where r_f is the riskfree interest rate, r_m is the rate of return on the market portfolio and is the beta (or volatility coefficient) for the common stock.

The for the common stock can be represented as:

= (L+1)_assets

if the debt of the corporation is riskfree. The leverage ratio L is D/E, but it can be expressed in terms of the debt ratio d (=D/(D+E)) as L = d/(1-d). The required rate of return is the cost of capital from equity so the relationship between the cost of capital from equity and the debt ratio is:

The Weighted Average Cost of Capital (WACC)

Capital Market Segmentation