## **Learning Outcomes**

After reading this article, you will be able to explain the impact of gearing on risk, differentiate between asset and equity betas, and apply releveraging techniques for project and company valuations. You will understand how capital structure influences the systematic risk faced by shareholders and know when and how to use asset and equity betas in calculating appropriate discount rates, as required for the ACCA Financial Management exam.

## **ACCA Financial Management (FM) Syllabus**

For ACCA Financial Management (FM), you are required to understand how gearing (financial gearing) influences risk and return, and how this affects key calculations in project appraisal and valuation. In particular, you should be comfortable with:

- The measurement and interpretation of operating and financial gearing
- The distinction between asset beta and equity beta, and their use in assessing project risk
- The process of de-gearing (unlevering) and re-gearing (relevering) betas
- The application of the Capital Asset Pricing Model (CAPM) to derive project-specific discount rates
- The relationship between capital structure (gearing), business risk, and financial risk
- The main theories of capital structure (traditional view, Modigliani & Miller, pecking order theory)
- The impact of using proxies and betas in scenario-based calculations for investment appraisal

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. Which statement best defines the **asset beta** of a company?
   a) The risk of the company’s shares relative to the market
   b) The risk of the business itself, excluding the effects of gearing
   c) The cost of the company’s debt finance
   d) The volatility of the company’s profits before taxes

2. True or false? Increasing financial gearing will always increase a company’s asset beta.

3. Briefly explain the difference between de-gearing and re-gearing a beta.

4. When using CAPM to obtain a discount rate for a project in a new industry, why must you adjust for differences in capital structure?

## **Introduction**

Financial managers must understand how capital structure decisions influence the risk and required return for both existing operations and new investments. The relationship between debt and equity—known as **gearing**—affects how market risk is distributed between investors. For investment appraisal and valuation, distinguishing between the risk of the business (the asset beta) and the risk to shareholders (the equity beta) is critical.

This article explains the mechanics of operating and financial gearing, the meaning of asset and equity beta, and the step-by-step process to adjust (“relever”) betas for use across different capital structures. You will also see how these concepts underpin the application of capital structure theories and influence the selection of discount rates for new projects.

> **Key Term: gearing**
> The proportion of a company’s capital financed by debt, as opposed to equity, which affects both risk and potential return for shareholders.

## **Gearing and Risk**

### Types of Gearing

**Operating gearing** measures the proportion of fixed to variable operating costs within a business. High operating gearing means large fixed costs relative to revenues, resulting in greater sensitivity of profits to changes in sales volume.

**Financial gearing** (or debt financing) refers to the use of debt in the capital structure. More debt increases the fixed commitments of interest payments, amplifying the variability in returns to shareholders.

> **Key Term: operating gearing**
> The proportion of operating costs that are fixed, indicating how profit responds to changes in sales.
>
> **Key Term: financial gearing**
> The extent to which a firm's capital structure contains debt, influencing the volatility of profit available to shareholders.

### Gearing and Shareholder Risk

Companies with higher financial gearing expose shareholders to greater volatility in earnings, as debt interest must be paid before any returns to equity holders. While debt may be cheaper than equity, higher debt levels also increase the risk faced by equity investors and, therefore, the required return on equity.

## **Beta: Asset vs Equity Beta**

### Systematic Risk and Beta

**Beta** measures the systematic (market) risk of an investment. Beta values indicate how sensitively an asset’s returns move relative to the overall market.

- An **equity beta** ($\beta_e$) reflects the risk faced by shareholders, capturing both inherent business risk and the additional risk from financial gearing.
- An **asset beta** ($\beta_a$) indicates the risk of the company's assets (business risk only), assuming the business was entirely equity-financed with no debt.

> **Key Term: equity beta**
> A measure of the sensitivity of a company’s equity returns to movements in the overall market, influenced by both business and financial risk.
>
> **Key Term: asset beta**
> A measure of the systematic risk of a firm's assets, independent of capital structure, representing pure business risk.

### Why Separate Asset and Equity Beta?

When using the CAPM to discount project cash flows, the relevant beta should reflect the risk of the cash flows being valued. For a new investment, especially in a different industry or with a distinct risk profile, you should first find an asset beta that corresponds to the project's business risk. If the project's funding will introduce debt (gearing), the asset beta must be “relevered” to estimate the associated equity beta.

## **Releveraging (De-gearing and Re-gearing) Betas**

### De-gearing (Unlevering) an Equity Beta

De-gearing removes the effect of financial structure from a proxy equity beta to arrive at the asset beta:

$$\displaystyle \beta_a = \beta_e \times \frac{V_e}{V_e + V_d(1-T)}$$

Where:

- $\beta_a$ = asset beta
- $\beta_e$ = equity beta
- $V_e$ = market value of equity
- $V_d$ = market value of debt
- $T$ = corporate tax rate

Assume debt beta is zero for practical purposes.

### Re-gearing (Relevering) the Asset Beta

To estimate the project’s equity beta based on the company's intended capital structure, “relever” the asset beta:

$$\displaystyle \beta_{e, \text{project}} = \beta_a \times \frac{V_e'}{V_e' + V_d'(1-T)}^{-1}$$

Where $V_e'$ and $V_d'$ are the market values (or proportions) of equity and debt for the proposed project or the investing company.

### **Worked Example 1.1**

A company in the pharmaceutical industry (proxy) has an equity beta of 1.4 and a gearing ratio (market values) of 60% equity and 40% debt. The corporation tax rate is 25%. What is the asset beta?

> **Answer:**
>
> $$\beta_a = 1.4 \times \frac{0.6}{0.6 + 0.4 \times (1-0.25)}$$
>
> $$\beta_a = 1.4 \times \frac{0.6}{0.6 + 0.3} = 1.4 \times \frac{0.6}{0.9} = 0.933$$
>
> The asset beta is 0.93 (rounded to two decimals).

### **Worked Example 1.2**

You want to appraise a biotech project with the same business risk but with a capital structure of 75% equity and 25% debt (by market value), with the same tax rate (25%). What would be the relevant equity beta to use?

> **Answer:**
>
> Re-lever the asset beta:
>
> $$\beta_e = 0.93 \times \frac{0.75 + 0.25 \times (1-0.25)}{0.75}$$
>
> $$= 0.93 \times \frac{0.75 + 0.1875}{0.75} = 0.93 \times \frac{0.9375}{0.75} = 1.16$$
>
> The project's equity beta is 1.16.

## **Using CAPM and Betas in Project Appraisal**

The correct discount rate for a project must reflect both the business risk (asset beta) and the project's target financial structure (equity beta).

1. Identify a proxy company (or companies) already operating in the target business area.
2. Obtain or calculate the proxy equity beta (from stock market data).
3. Remove the effect of the proxy's gearing (de-gear) to find the asset beta.
4. Apply the investing company's (or the project's) intended gearing to the asset beta (re-gear) to estimate the project's equity beta.
5. Use the project equity beta in the CAPM formula to determine the minimum acceptable return for equity investors.

> **Key Term: releveraging (re-gearing/de-gearing)**
> The process of adjusting beta to account for different levels of gearing, to accurately reflect risk for use in valuation or project appraisal.

### **Worked Example 1.3**

You have identified a proxy beta of 1.25 for a technology company with 50% equity, 50% debt and a corporate tax rate of 20%. Your company plans to finance a similar project with 80% equity and 20% debt. What is the equity beta to use for the project?

> **Answer:**
>
> Step 1: De-gear proxy beta:
>
> $$\beta_a = 1.25 \times \frac{0.5}{0.5 + 0.5 \times (1-0.2)} = 1.25 \times \frac{0.5}{0.5 + 0.4} = 1.25 \times \frac{0.5}{0.9} = 0.694$$
>
> Step 2: Re-gear asset beta to 80:20 structure:
>
> $$\beta_e = 0.694 \times \frac{0.8 + 0.2 \times (1-0.2)}{0.8} = 0.694 \times \frac{0.8 + 0.16}{0.8} = 0.694 \times \frac{0.96}{0.8} = 0.833$$
>
> The equity beta for the project is 0.83.

## **Capital Structure Theories and Discount Rates**

### Main Theories

- **Traditional View:** WACC decreases at low gearing (due to cheap debt) but increases at high gearing (due to increased risk), suggesting an optimal capital structure exists.
- **Modigliani & Miller (no tax):** WACC is unaffected by changes in gearing; capital structure is irrelevant in perfect markets.
- **Modigliani & Miller (with tax):** WACC decreases as gearing increases due to the tax shield on debt, theoretically favouring very high debt levels.
- **Pecking Order Theory:** Firms exhaust internal funds first, then debt, and only issue equity as a last resort.

These theories inform the practical use of WACC and beta adjustments when the risk or funding of a project differs from that of the existing business.

### **Exam Warning**

> Do not use a company's observed equity beta for a new project without adjusting for differences in financial gearing. You must use the asset beta as an intermediate step.

### **Revision Tip**

> If using multiple proxy companies, calculate the average asset beta (after de-gearing each one) before re-gearing to your chosen capital structure.

## **Summary**

Understanding the relationships between gearing, risk, and beta is essential for applying the CAPM, valuing companies, and selecting discount rates for investment appraisal. Proper adjustment of betas ensures project appraisals reflect both business and financial risk, in line with ACCA exam requirements.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain operating and financial gearing and their impact on risk
- Distinguish between asset beta (business risk) and equity beta (business and financial risk)
- Apply de-gearing and re-gearing formulas to adjust betas for different capital structures
- Use beta adjustments with CAPM to determine project-specific discount rates
- Understand when and why capital structure theories affect WACC and valuation calculations

## **Key Terms and Concepts**

- gearing
- operating gearing
- financial gearing
- equity beta
- asset beta
- releveraging (re-gearing/de-gearing)


Gearing, beta, and structure theories - Asset vs equity beta and relevering