# Capital Gearing and the Cost of Capital

## Introduction

If an all-equity company undertakes a capital project using the marginal cost of equity as its discount rate, the total market value of ordinary shares should increase by the project's NPV. However, most firms use a mix of ownership capital and borrowed funds from financial institutions for new investments. The relationship between the two is termed capital gearing or leverage. A company is highly geared (levered) when it has a significant proportion of borrowing relative to shares in its capital structure. It is lowly geared when the ratio of debt to equity is small.

In Chapter Six we observed that corporate borrowing is attractive to management because interest rates on debt are typically lower than equity and often qualify for tax relief As a consequence, a judicious amount of debt introduced into a firm's capital structure should lower the overall or weighted average cost of capital (WACC) employed as a cut-off rate for the appraisal of new projects, thereby increasing their expected NPV and corporate value.

You will also recall from Chapter Six that a company's component capital costs are derived by identifying the opportunity cost of each fund source using valuation models that determine debt and equity yields under various guises. Thus, our current analysis answers a logical series of questions, given the normative assumption of financial management, namely maximum profit at minimum cost.

How do individual capital costs combine to define WACC for use in investment appraisal? How valid are the theoretical assumptions that underpin WACC computations? What are the real-world problems associated with WACC estimations?

## The Weighted Average Cost of Capital (WACC)

Let us begin our analysis by first defining an overall cost of capital in taxless world where management has access to only two sources of finance: equity and debt.

A general formula for WACC is given by the formula for a simple weighted average:

where: K = WACC,

Ke = cost of equity K = cost of debt

VE = market value of equity VD = market value of debt

If we now introduce corporate taxation (at a rate t) the after tax cost of debt Kdt should be substituted into the preceding equation using the appropriate debt formulae from Chapter Six as follows.

This is equivalent to:

Equations (2) and (3) may be rewritten using simpler notation. For example, with tax:

where: WE = the weighting applied to equity (VE / VE + VD) WD = the weighting applied to debt (VD / VE + VD)

Thus, a firm financed equally by equity and debt yielding 10 percent and 5 percent, respectively, would calculate its WACC using Equation (4)as follows:

K = 10% (0.5) + 5% (0.5) = 7.5%

Activity 1

Given the following company data:

K = 12%, Kd = 8%, VE = £6 million, VD = 4 million

Calculate WACC and jot down your thoughts on any assumptions that might validate its use as a discount rate for project appraisal before reading the next section

The individual costs of equity and debt capital are weighted by their proportion of the company's total market value. Using Equation (1) and simplifying:

K = [(0.12 x 0.6) + (0.08 x 0.4)] / 1.0 = 0.104

So, the WACC used as the company discount rate for new project appraisal is 10.4 percent. 7.2 WACC Assumptions

WACC use as a corporate discount rate for investment appraisal depends upon three assumptions.

- New projects have the same risk-return profile as the company's existing activities.

- Each project is marginal to the scale of existing operations.

- The company will retain its existing capital structure, leaving financial risk unchanged.

The reason for the first assumption is obvious. A company's component capital costs reflect the variability of future expected dividend and interest flows. Thus, it follows, that WACC also reflects the overall risk of these combined flows. So, if we use this figure as a discount rate in project appraisal, the new investment's risk-return characteristics must satisfy the company's existing expected dividend and interest payments.

The second assumption is also common sense. When firms consider new investment, the relevant costs refer to the returns that the company must earn on relatively small incremental additions to its total capital base. From an economic viewpoint, they are marginal costs of capital and are only applicable to the appraisal of marginal investments: projects that are small relative to the size of the company.

Finally, the third assumption is necessary because WACC can only provide an appropriate discount rate if new projects are financed in the same proportion as existing assets. This arises for two reasons.

If a company alters its capital structure, the weights applied to the component costs in the WACC calculation would also change, leading to a new discount rate.

A change in the capital mix (gearing) might also affect the investors' perception of the financial risk associated with their investment in the firm. They may then react by buying or selling (as opposed to holding) their securities, thereby affecting the respective yields which determine the WACC.

For example, a new debt issue could increase the uncertainly experienced by the shareholders when they recognize that debt-holders will receive their claim to earnings (interest) before any dividend payment. With increased risk, they sell their holding equity prices may fall because the market requires a higher return as compensation. For the firm, what seems a simple change in the debt-equity ratio is, therefore, a complex decision. Quite apart from revised weightings at new market prices, it must also consider the explicit marginal cost of issuing debt and the implicit cost to the shareholders of their increased financial risk. All three may combine to produce a drastic change in WACC.

Activity 2

Changes in the financial mix (gearing) of a company and the impact of risk on its overall cost of capital and value do not necessarily invalidate the use of WACC as an investment criterion.

Can you think of any reasons for this?

Whilst corporate investment decisions should determine a firm's overall cost of capital, management should avoid the mistake of always associating the explicit marginal costs of new capital issues with a specific project. Often it will be difficult, if not impossible to assign a particular project to a particular source of finance. A company's funds should therefore be viewed collectively. In as much as finance is withdrawn from a pool of funds to invest in new projects, the pool is replenished as fresh capital is raised from outside, or profits are retained. Thus, the cost of capital used for any particular project is not the cost of a specific source of funds, but the overall cost of the company's pool: namely WACC.

In the short run, it is frequently the case that certain funds might also be secured at advantageous rates depending upon prevailing market conditions. This will encourage firms to depart briefly from their long-run capital structure. Under such circumstances, however, WACC still represents an appropriate discount rate for long-term investment, providing the projects exhibit a similar risk-return profile.

Even if funds are raised explicitly from one source to finance an incremental investment, there are sound reasons for using the WACC as a discount rate, particularly if the change in the capital structure represents a short-run deviation from the desired capital mix. First, a rational choice of funds is a financial decision taken not in relation to the investment decision but in relation to the firm's long-term capital structure. Second, there are substantial economies of scale to be gained in terms of reduced issue costs by raising large amounts of capital from one source and then another.