## COST OF CAPITAL

Usually the cost of debt is lower than the cost of equity. This is so because debt is a fixed obligation while equity is not. However, firms cannot operate on debts alone since this will subsequently increase the risk of bankruptcy (that is the firm being unable to meet its fixed obligations). This risk of bankruptcy is also associated with the stability of sales and earnings. A firm with relatively unstable earnings will be reluctant to adopt a high degree of leverage since conceivably it might be unable to meet its fixed obligations at all.

Note: Financial leverage is the change in the EPS induced by the use of fixed securities to finance a company's operation.

Cost of Debt:

The cost of debt to a firm can be given by the following formulae:

Kd = Annual interest charges

Market value of outstanding debt

Where Kd is the yield of the company's debts. The market value of outstanding debt will therefore be given by the following formulae.

Market value of debt = Annual interest charges

Kd

Kd is the before tax cost of debt. However, the effective cost of debt is the after tax cost because interest on debt is tax deductible. The effective cost of debt (Kb) therefore is

Kb = Kd (I - T)

Where Kb is the effective (after tax) cost

T is the corporate tax rate

Cost of Preferred Stock

Preferred dividend is not tax deductible and therefore the tax adjustment is required when considering the cost of preferred stock. The cost is therefore:

Kp = Dp

Pr

Where Dp is the annual preferred dividend

Pr is market price of preferred stocks (net of floatation costs)

Cost of Equity

Equity can be divided into two:

(a) Retained Earnings

(b) External Equity

Cost of Retained Earnings

The cost of retained earnings is the rate of return shareholders require on the firm's common stock. This is an opportunity cost. The firm should earn on its retained earnings at least as much as its stockholders themselves could earn on alternative investments of equivalent risk. We can use several methods to estimate the cost of retained earnings. These are:

(a) The CAPM approach

CAPM has already been discussed in Lesson 2. Under this approach we assume that common shareholders view only market risk as being relevant. The cost of retained earnings therefore can be given as:

Kr = Kf + (Km - Kf) ßi

Where Kr is the cost of retained earnings

Km is the required rate of return on the market

Kf is the risk free rate

ßi is the stock's beta coefficient

If we can be able to estimate the risk free rate, the market rate and the stock's beta, then we can easily estimate the cost of retained earnings (or the cost of external equity).

(b)    The DCF Approach (Dividend Yield Model)
The second method is the discounted cashflow (DCF) method.  The intrinsic value of a share is the present value of its expected dividend stream:
given the above equation
Where g is a constant growth rate
D1 is the expected dividend
Po is the market value of shares

Cost of Newly issued external equity
When a firm sells shares in the market it incurs floatation costs.  This causes a difference between the cost of retained earnings and external equity.
If we use the DCF method, then
Where F is the floatation costs expressed as a percentage of market price of shares.
Weighted Average Cost of Capital (WACC)

The WACC is the overall cost of using the various forms of fund.  It can be given by:

WACC    =    Net operating Earnings (NOE)
Total Market Value of the firm

It can also be expressed as

Where
Ko is the weighted average cost of capital
Kd is the cost of debt
Kp is the cost of preference shares
Ke is the cost of equity

D,    P,    E    are the proportions of debt, preferred stocks
V    V    V    and equity in capital structure

For easy analysis we shall assume that the firm uses only debt and equity.  The overall cost of capital will therefore be given by:

With this background we can look at what happens to Kd, Ke and Ko as the degree of leverage (denoted by D/E changes).  This will be done by looking at the theories of capital structure.