F9: Cost of Capital

Relationship between capital structure and weighted average cost of capital

A discussion of capital structure could start from recognising that equity is more expensive than debt because of the relative risk of the two sources of finance. Equity is riskier than debt and so equity is more expensive than debt. This does not depend on the tax efficiency of debt, since we can assume that no taxes exist. We can also assume that as a company gears up, it replaces equity with debt. This means that the company's capital base remains constant and its weighted average cost of capital (WACC) is not affected by increasing investment. The traditional view of capital structure assumes a non-linear relationship between the cost of equity and financial risk. As a company gears up, there is initially very little increase in the cost of equity and the WACC decreases because the cost of debt is less than the cost of equity. A point is reached, however, where the cost of equity rises at a rate that exceeds the reduction effect of cheaper debt and the WACC starts to increase. In the traditional view, therefore, a minimum WACC exists and, as a result, a maximum value of the company arises. Modigliani and Miller assumed a perfect capital market and a linear relationship between the cost of equity and financial risk. They argued that, as a company geared up, the cost of equity increased at a rate that exactly cancelled out the reduction effect of cheaper debt. WACC was therefore constant at all levels of gearing and no optimal capital structure, where the value of the company was at a maximum, could be found. It was argued that the no-tax assumption made by Modigliani and Miller was unrealistic, since in the real world interest payments were an allowable expense in calculating taxable profit and so the effective cost of debt was reduced by its tax efficiency. They revised their model to include this tax effect and showed that, as a result, the WACC decreased in a linear fashion as a company geared up. The value of the company increased by the value of the 'tax shield' and an optimal capital structure would result by gearing up as much as possible. It was pointed out that market imperfections associated with high levels of gearing, such as bankruptcy risk and agency costs, would limit the extent to which a company could gear up. In practice, therefore, it appears that companies can reduce their WACC by increasing gearing, while avoiding the financial distress that can arise at high levels of gearing. It has further been suggested that companies choose the source of finance which, for one reason or another, is easiest for them to access (pecking order theory). This results in an initial preference for retained earnings, followed by a preference for debt before turning to equity. The view suggests that companies may not in practice seek to minimise their WACC (and consequently maximise company value and shareholder wealth).

Reasons why different bonds of the same company might have different costs of debt

A key factor here could be the duration of the bond issues, linked to the term structure of interest rates. Normally, the longer the time to maturity of a debt, the higher will be the interest rate and the cost of debt. Bond A has the greater time to maturity and therefore would be expected to have a higher interest rate and a higher cost of debt than Bond B, which is the case here. Liquidity preference theory suggests that investors require compensation for deferring consumption, i.e. for not having access to their cash in the current period, and so providers of debt finance require higher compensation for lending for longer periods. The premium for lending for longer periods also reflects the way that default risk increases with time. Expectations theory suggests that the shape of the yield curve depends on expectations as to future interest rates. If the expectation is that future interest rates will be higher than current interest rates, the yield curve will slope upwards. If the expectation is that future interest rates will be lower than at present, the yield curve will slope downwards. Market segmentation theory suggests that future interest rates depend on conditions in different debt markets, e.g. the short-term market, the medium-term market and the long-term market. The shape of the yield curve therefore depends on the supply of, and demand for, funds in the market segments. Since the two bonds were issued at the same time by the same company, the business risk of DD Co can be discounted as a reason for the difference between the two costs of debt. If the two bonds had been issued by different companies, a different business risk might have been a reason for the difference in the costs of debt. The size of the debt could be a contributory factor, since the Bond A issue is twice the size of the Bond B issue. The greater size of the Bond A issue could be one of the reasons it has the higher cost of debt.

Why market value weighted average cost of capital is preferred to book value weighted average cost of capital when making investment decisions

Market values of different sources of finance are preferred to their book values when calculating weighted average cost of capital (WACC) because market values reflect the current conditions in the capital market. The relative proportions of the different sources of finance in the capital structure reflect more appropriately their relative importance to a company if market values are used as weights. For example, the market value of equity is usually much greater than its book value, so using book values for weights would seriously underestimate the relative importance of the cost of equity in the weighted average cost of capital. If book values are used as weights, the WACC will be lower than if market values were used, due to the understatement of the contribution of the cost of equity, which is higher than the cost of capital of other sources of finance. If book value WACC were used as the discount rate in investment appraisal, investment projects would be accepted that would be rejected if market value WACC were used. Using book value WACC as the discount rate will therefore lead to sub-optimal investment decisions. As far as the cost of debt is concerned, using book values rather than market values for weights may make little difference to the WACC, since bonds often trade on the capital market at or close to their nominal (par) value. In addition, the cost of debt is lower than the cost of equity and will therefore make a smaller contribution to the WACC. It is still possible, however, that using book values as weights may under- or over-estimate the contribution of the cost of debt to the WACC.

How the shareholders can assess the extent to which they face the following risks, and the nature of the risk being assessed: (i) Business risk; (ii) Financial risk; (iii) Systematic risk.

Nature and assessment of business risk: Business risk arises due to the nature of a company's business operations, which determines the business sector into which it is classified, and to the way in which a company conducts its business operations. Business risk is the variability in shareholder returns that arises as a result of business operations. It can therefore be related to the way in which profit before interest and tax (PBIT or operating profit) changes as revenue or turnover changes. This can be assessed from a shareholder perspective by calculating operational gearing, which essentially looks at the relative proportions of fixed operating costs to variable operating costs. One measure of operational gearing that can be used is (100 x contribution/PBIT), although other measures are also used. Nature and assessment of financial risk: Financial risk arises due to the use of debt as a source of finance, and hence is related to the capital structure of a company. Financial risk is the variability in shareholder returns that arises due to the need to pay interest on debt. Financial risk can be assessed from a shareholder perspective in two ways. Firstly, balance sheet gearing can be calculated. There are a number of gearing measures that can be used, such as the debt/equity ratio, the debt ratio and financial gearing, and the calculation can be based on either market values or book values. Secondly, the interest coverage ratio can be calculated. Nature and assessment of systematic risk: From a shareholder perspective, systematic risk is the sum of business risk and financial risk. Systematic risk is the risk that remains after a shareholder has diversified investments in a portfolio, so that the risk specific to individual companies has been diversified away and the shareholder is faced with risk relating to the market as a whole. Market risk and undiversifiable risk are therefore other names for systematic risk. From a shareholder perspective, the systematic risk of a company can be assessed by the equity beta of the company. If the company has debt in its capital structure, the systematic risk reflected by the equity beta will include both business risk and financial risk. If a company is financed entirely by equity, the systematic risk reflected by the equity beta will be business risk alone, in which case the equity beta will be the same as the asset beta.

How the capital asset pricing model can be used to calculate a project-specific cost of capital- with references to systematic risk, business risk and financial risk.

The capital asset pricing model (CAPM) assumes that investors hold diversified portfolios, so that unsystematic risk has been diversified away. Companies using the CAPM to calculate a project specific discount rate are therefore concerned only with determining the minimum return that must be generated by an investment project as compensation for its systematic risk. The CAPM is useful where the business risk of an investment project is different from the business risk of the investing company's existing business operations. In such a situation, one or more proxy companies are identified that have similar business risk to the investment project. The equity beta of the proxy company represents the systematic risk of the proxy company, and reflects both the business risk of the proxy company's business operations and the financial risk arising from the proxy company's capital structure. Since the investing company is only interested in the business risk of the proxy company, the proxy company's equity beta is 'ungeared' to remove the effect of its capital structure. 'Ungearing' converts the proxy company's equity beta into an asset beta, which represents business risk alone. The asset betas of several proxy companies can be averaged in order to remove any small differences in business operations. The asset beta can then be 'regeared', giving an equity beta whose systematic risk takes account of the financial risk of the investing company as well as the business risk of an investment project. Both ungearing and regearing use the weighted average beta formula, which equates the asset beta with the weighted average of the equity beta and the debt beta. The project-specific equity beta resulting from the regearing process can then be used to calculate a project-specific cost of equity using the CAPM. This can be used as the discount rate when evaluating the investment project with a discounted cash (DCF) flow investment appraisal method such as net present value or internal rate of return. Alternatively, the project-specific cost of equity can be used in calculating a project-specific weighted average cost of capital, which can also be used in a DCF evaluation.

How the capital asset pricing model can be used to calculate a project-specific discount rate

The capital asset pricing model (CAPM) can be used to calculate a project-specific discount rate in circumstances where the business risk of an investment project is different from the business risk of the existing operations of the investing company. In these circumstances, it is not appropriate to use the weighted average cost of capital as the discount rate in investment appraisal. The first step in using the CAPM to calculate a project-specific discount rate is to find a proxy company (or companies) that undertake operations whose business risk is similar to that of the proposed investment. The equity beta of the proxy company will represent both the business risk and the financial risk of the proxy company. The effect of the financial risk of the proxy company must be removed to give a proxy beta representing the business risk alone of the proposed investment. This beta is called an asset beta and the calculation that removes the effect of the financial risk of the proxy company is called 'ungearing'. The asset beta representing the business risk of a proposed investment must be adjusted to reflect the financial risk of the investing company, a process called 'regearing'. This process produces an equity beta that can be placed in the CAPM in order to calculate a required rate of return (a cost of equity). This can be used as the project-specific discount rate for the proposed investment if it is financed entirely by equity. If debt finance forms part of the financing for the proposed investment, a project-specific weighted average cost of capital can be calculated.

Why the cost of equity is greater than the cost of debt

The cost of equity is the return required by ordinary shareholders (equity investors), in order to compensate them for the risk associated with their equity investment, i.e. their investment in the ordinary shares of a company. If the risk of an investment increases, the return expected by the investor also increases. If the risk of a company increases, therefore, its cost of equity also increases. If a company is liquidated, the order in which the claims of creditors are settled is a factor in determining their relative risk. The claims of providers of debt finance (debt holders) must be paid off before any cash can be distributed to ordinary shareholders (the owners). The risk faced by shareholders is therefore greater than the risk faced by debt holders, and the cost of equity is therefore greater than the cost of debt. Interest on debt finance must be paid before dividends can be paid to ordinary shareholders, so the risk faced by ordinary shareholders is greater than the risk faced by debt holders, since the necessity of paying interest may mean that dividends have to be reduced.

Whether the dividend growth model or the capital asset pricing model offers the better estimate of the cost of equity of a company

The dividend growth model has several difficulties attendant on its use as a way of estimating the cost of equity. For example, the model assumes that the future dividend growth rate is constant in perpetuity, an assumption that is not supported by the way that dividends change in practice. Each dividend paid by a company is the result of a dividend decision by managers, who will consider, but not be bound by, the dividends paid in previous periods. Estimating the future dividend growth rate is also very difficult. Historical dividend trends are usually analysed and on the somewhat risky assumption that the future will repeat the past, the historic dividend growth rate is used as a substitute for the future dividend growth rate. The model also assumes that business risk, and hence business operations and the cost of equity, are constant in future periods, but reality shows us that companies, their business operations and their economic environment are subject to constant change. Perhaps the one certain thing about the future is its uncertainty. It is sometimes said that the dividend growth model does not consider risk, but risk is implicit in the share price used by the model to calculate the cost of equity. A moment's thought will indicate that share prices fall as risk increases, indicating that increasing risk will lead to an increasing cost of equity. What is certainly true is that the dividend growth model does not consider risk explicitly in the same way as the capital asset pricing model (CAPM). Here, all investors are assumed to hold diversified portfolios and as a result only seek compensation (return) for the systematic risk of an investment. The CAPM represent the required rate of return (i.e. the cost of equity) as the sum of the risk-free rate of return and a risk premium reflecting the systematic risk of an individual company relative to the systematic risk of the stock market as a whole. This risk premium is the product of the company's equity beta and the equity risk premium. The CAPM therefore tells us what the cost of equity should be, given an individual company's level of systematic risk. The individual components of the CAPM (the risk-free rate of return, the equity risk premium and the equity beta) are found by empirical research and so the CAPM gives rise to a much smaller degree of uncertainty than that attached to the future dividend growth rate in the dividend growth model. For this reason, it is usually suggested that the CAPM offers a better estimate of the cost of equity than the dividend growth model.

Limitations of using the capital asset pricing model in investment appraisal

The limitations of using the CAPM in investment appraisal are both practical and theoretical in nature. From a practical point of view, there are difficulties associated with finding the information needed. This applies not only to the equity risk premium and the risk-free rate of return, but also to locating appropriate proxy companies with business operations similar to the proposed investment project. Most companies have a range of business operations they undertake and so their equity betas do not reflect only the desired level and type of business risk. From a theoretical point of view, the assumptions underlying the CAPM can be criticised as unrealistic in the real world. For example, the CAPM assumes a perfect capital market, when in reality capital markets are only semi-strong form efficient at best. The CAPM assumes that all investors have diversified portfolios, so that rewards are only required for accepting systematic risk, when in fact this may not be true. There is no practical replacement for the CAPM at the present time, however.

Whether changing the capital structure of a company can lead to a reduction in its cost of capital and hence to an increase in the value of the company

The value of a company can be expressed as the present value of its future cash flows, discounted at its weighted average cost of capital (WACC). The value of a company can therefore theoretically be maximised by minimising its WACC. If the WACC depends on the capital structure of a company, i.e. on the balance between debt and equity, then the minimum WACC will arise when the capital structure is optimal. The idea of an optimal capital structure has been debated for many years. The traditional view of capital structure suggests that the WACC decreases as debt is introduced at low levels of gearing, before reaching a minimum and then increasing as the cost of equity responds to increasing financial risk. Miller and Modigliani originally argued that the WACC is independent of a company's capital structure, depending only on its business risk rather than on its financial risk. This suggestion that it is not possible to minimise the WACC, and hence that it is not possible to maximise the value of a company by selecting a particular capital structure, depends on the assumption of a perfect capital market with no corporate taxation. However, real world capital markets are not perfect and companies pay taxes on profit. Since interest is a tax-allowable deduction in calculating taxable profit, debt is a tax-efficient source of finance and replacing equity with debt will decrease the WACC of a company. In the real world, therefore, increasing gearing will decrease the WACC of a company and hence increase its value. At high levels of gearing, the WACC of a company will increase due, for example, to increasing bankruptcy risk. Therefore, it can be argued that use of debt in a company's capital structure can reduce its WACC and increase its value, provided that gearing is kept to an acceptable level.

Circumstances under which the weighted average cost of capital (WACC) can be used as a discount rate in investment appraisal

The weighted average cost of capital (WACC) is the average return required by current providers of finance. The WACC therefore reflects the current risk of a company's business operations (business risk) and way in which the company is currently financed (financial risk). When the WACC is used as discount rate to appraise an investment project, an assumption is being made that the project's business risk and financial risk are the same as those currently faced by the investing company. If this is not the case, a marginal cost of capital or a project-specific discount rate must be used to assess the acceptability of an investment project. The business risk of an investment project will be the same as current business operations if the project is an extension of existing business operations, and if it is small in comparison with current business operations. If this is the case, existing providers of finance will not change their current required rates of return. If these conditions are not met, a project-specific discount rate should be calculated, for example by using the capital asset pricing model. The financial risk of an investment project will be the same as the financial risk currently faced by a company if debt and equity are raised in the same proportions as currently used, thus preserving the existing capital structure. If this is the case, the current WACC can be used to appraise a new investment project. It may still be appropriate to use the current WACC as a discount rate even when the incremental finance raised does not preserve the existing capital structure, providing that the existing capital structure is preserved on an average basis over time via subsequent finance-raising decisions. Where the capital structure is changed by finance raised for an investment project, it may be appropriate to use the marginal cost of capital rather than the WACC.

Alternative approaches that could be adopted when using the WACC is not appropriate

Where the project's business risk and financial risk are not the same as those currently faced by the investing company, a marginal cost of capital or a project-specific discount rate must be used to assess the acceptability of an investment project. Where the capital structure is changed by finance raised for an investment project, it may be appropriate to use the marginal cost of capital rather than the WACC.