Fundamentals of Financial Management (Concise 6th Edition)

416 Part 5 Capital Structure and Dividend Policy

Note that beta is the only variable in the equity cost equation that is under man-

agement’s control. The other two variables, rRF and RPM, are determined by market

forces that are beyond the! rm’s control; but bL is determined by the! rm’s operat-

ing decisions, which, as we saw earlier, affect its basic business risk, and by its

capital structure decisions as re" ected in its D/A (or D/E) ratio.

We can solve Equation 13-2 to! nd the unlevered beta, bU, obtaining

Equation 13-2a:

13-2a bU! bL/[1 # (1 " T)(D/E)]

Since the current (levered) beta is known, as are the tax rate and the debt/equity

ratio, we can insert values for these known variables and! nd the unlevered beta.

The unlevered beta can then be used in Equation 13-2 with different debt levels to

! nd the levered betas that would exist at those different debt levels. The resulting

betas can be used to! nd the cost of equity at different debt levels.

We can illustrate all this with Bigbee Electronics. First, assume that the risk-

free rate of return, rRF , is 6% and that the market risk premium, RPM, is 4%. Next,

we need the unlevered beta, bU. Because Bigbee has no debt, its D/E " 0. There-

fore, its current 1.5 beta is also its unlevered beta; hence, bU " 1.5. With bU, rRF,

and RPM speci! ed, we can use Equation 13-2 to estimate Bigbee’s betas at differ-

ent degrees of! nancial leverage and its resulting cost of equity at each debt

ratio.

Bigbee’s betas at different debt/equity ratios are shown in Column 5 of

Table 13-3. The current cost of equity is 12% as shown at the top of Column 6:

rs! rRF # Risk premium

! 6% # (4%)(1.5)

! 6% # 6%! 12%

The! rst 6% is the risk-free rate; the second is the! rm’s risk premium. Because

Bigbee currently uses no debt, it has no! nancial risk. Therefore, the 6% risk pre-

mium is attributable entirely to business risk.

If Bigbee changes its capital structure by adding debt, this would increase the

risk stockholders would have to bear. That, in turn, would result in a higher risk

premium. Conceptually, a! rm’s cost of equity consists of the following

components:

rs! rRF # Premium for business risk # Premium for! nancial risk

Figure 13-7, which is based on data shown in Column 6 of Table 13-3, graphs Big-

bee’s cost of equity at different debt ratios. As the! gure shows, rs consists of the 6%

risk-free rate, a constant 6% premium for business risk, and a premium for! nancial

risk that starts at zero but rises at an increasing rate as the! rm’s debt ratio increases.

13-3c The Optimal Capital Structure

Column 9 of Table 13-3 also shows Bigbee’s WACC at different capital structures.

Currently, it has no debt; so its debt ratio is zero and its WACC is rs = 12%. As Big-

bee begins to substitute lower-cost debt for higher-cost equity, its WACC declines.

However, as the debt ratio rises, the costs of both debt and equity rise, at! rst

slowly but then at a faster and faster rate. Eventually, the increasing costs of the

two components offset the fact that more low-cost debt is being used. Indeed, at

40% debt, the WACC hits a minimum of 11.04%; after that, it rises with further

increases in the debt ratio.

Another way of looking at this is to note that even though the component cost

of equity is higher than that of debt, using only lower-cost debt would not maximize

Unlevered Beta, bU

The firm’s beta coefficient

if it has no debt.

Unlevered Beta, bU

The firm’s beta coefficient

if it has no debt.