# Capital Gearing and the Beta Factor

The CAPM defines an individual investment's risk relative to a well-diversified portfolio as * systematic risk. *Measured by the beta coefficient, it is the only risk a company or an investor will pay a premium to avoid. You will recall from Chapter Four (Figure 4.3) that it can be sub-divided into:

- * Business risk *that arises from the variability of a firm's earnings caused by market forces,

- * Financial risk *associated with dividend policies and capital gearing, both of which may amplify business risk

Without getting enmeshed in dividend policies, we shall accept the 1961 MM hypothesis that they are * irrelevant. *Based on their "law of one price" (covered in the

*texts and for which there is considerable empirical support)*

**SFM***risk should not matter in an all-equity company. Applied to the CAPM, the*

**financial***risk of investors (who are all shareholders) can be defined by the*

**systematic***risk of the firm's underlying asset investments.*

**business**The * equity *beta of an unlevered (all-equity) firm equals an

*beta, which measures the business risk of all its investments relative to the market for ordinary shares (common stock). Using earlier notation:*

**asset**The CAPM return on project (r.) is then defined by:

If there is no debt in the firm's capital structure, the company's asset (equity) beta equals the * weighted average *of its individual project betas (bi) based on the market value of equity.

But what about companies who decide to fund future investments by gearing up, or the vast majority who already employ debt finance?

To make rational decisions, it would appear that management now require an asset beta to measure a firm's business risk that an unguarded equity beta can no longer provide. For example, an all-equity company may be considering a take-over that will be financed entirely by debt. To assess the acquisition's viability, management will now need to calculate their overall CAPM return on investment using an asset beta that reflects a * leveraged *financial mix of fixed interest on debt and dividends on shares.

Later in this chapter we shall resolve the dilemma using the predictions of MM's capital structure hypothesis (1958). Based on their law of one price, whereby similar firms with the same risk characteristics (except capital gearing) cannot sell at different prices, it confirms their dividend hypothesis, namely that financial policy is irrelevant. First, however, let us develop the CAPM, to illustrate the relationship between an asset beta and the equity and debt coefficients for a geared company.

When a firm is financed by a debt-equity mix, its earnings stream and associated risk is divided between the firm's shareholders and providers of corporate debt. The proportion of risk reflects the market values of debt and equity respectively, defined by the * debt-equity ratio. *So, the equity beta will be a

*equity beta. It not only incorporates business risk. It also determines shareholders' exposure to financial risk defined by the proportion of contractual, fixed interest securities in the capital structure. For this reason the equity beta of an unlevered company is always lower than the beta of a levered company.*

**geared**Given a geared equity beta (bE) and debt beta (bD), the asset beta (bA) for a company's investment in risky capital projects can be expressed as a weighted average of the two:

Where:

VE and VD are the * market *values of equity and debt, respectively, VE

*VD define the firm's total market value (V).*

**plus****Activity 2**

A firm with respective market values of €60m and €30m for equity and debt has an equity beta of 1.5. The debt beta is zero.

(1) Use Equation (50) to calculate the asset beta (bA).

(2) Explain a simplified mathematical structure of the calculation.

(1) The asset beta (bA) calculation

(2) The mathematical structure of bA.

When a company is financed by debt and equity, management need to derive an asset beta using the * weighted average *of its geared equity and debt components. The market values of debt and equity provide the weightings for the calculation. Note, however, that because the market risk of debt (bD) was set to zero, the right hand side of Equation (50) disappears.

This is not unusual. As explained in * SFM, *debt has priority over equity's share of profits and the sale of assets in the event of liquidation. Thus, debt is more secure and if it is risk-free, there is no variance. So if bD equals zero, our previous equation for an asset beta reduces to:

For example, if a company has an equity beta of 1.20, a debt-equity ratio of 40 per cent and we assume that debt is risk-free, the asset beta is given by:

Perhaps you also recall from * SFM *that debt is also a

*expense in many economies. If we incorporate this fiscal adjustment into the previous equations (where t is the tax rate) we can redefine the mathematical relationship between the asset beta and its geared equity and debt counterparts as follows.*

**tax deductible**Despite the tax effect, our methodology for deriving a company's asset beta still reveals a * universal *feature of the CAPM that financial management can usefully adopt to assess individual projects.

Whenever risky investments are combined, the asset beta of the resultant portfolio is a * weighted average *of the debt and equity betas.

**Activity 3**

Consider a company with a current asset beta of 0.90. It accepts a project with a beta of 0.5 that is equivalent to 10 per cent of its corporate value after acceptance.

Confirm that:

1. The new (ex-post)beta coefficient of the company equals 0.86.

2. The * new project *reduces the original

*risk of the firm's*

**(ex-ante)**

**existing portfolio.**