## **Learning Outcomes**

After reading this article, you should be able to calculate project-specific discount rates using beta analysis, including how to de-gear (unlever) and re-gear (re-lever) beta factors. You will be able to distinguish between asset beta and equity beta, apply Capital Asset Pricing Model (CAPM) for project appraisal, and explain the rationale for adjusting for business and financial risk. You will also recognize pitfalls common in exam scenarios when applying these techniques.

## **ACCA Advanced Financial Management (AFM) Syllabus**

For ACCA Advanced Financial Management (AFM), you are required to understand how to assess the appropriate cost of capital for projects with differing business or financial risk. Specifically, you should be able to:

- Explain and apply the relationship between business risk, financial risk, asset beta, and equity beta
- Calculate and interpret asset beta and equity beta for specific projects
- Use proxy company betas to determine project discount rates
- Demonstrate the process of relevering and de-levering beta to reflect capital structure changes
- Apply risk-adjusted discount rates using the CAPM in investment appraisal decisions
- Identify situations where project-specific rates are appropriate and justify their use

## **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. What distinguishes asset beta from equity beta in risk analysis?
2. When using a proxy company's beta for a new project, what adjustment must you apply before using it in CAPM?
3. Why is it inappropriate to use a company's current WACC for a project with substantially different business risk?
4. If a company plans to finance a project mostly with debt, how does this affect the process for calculating the appropriate project discount rate?

## **Introduction**

When appraising new investment projects—especially those with different business activities or capital structures than a company's current operations—it is essential to adjust the discount rate for both business risk and financial risk. The Capital Asset Pricing Model (CAPM) can be used to estimate a project-specific cost of equity. This requires understanding the difference between asset beta and equity beta, as well as the process for adjusting betas for varying levels of debt (gearing) through de-gearing and re-gearing.

Applying these techniques ensures that the required return accurately reflects the risk of the cash flows being discounted, leading to better investment decisions and meeting the expectations of finance providers.

> **Key Term: Asset Beta**
> A measure of the systematic business risk of a firm's assets, excluding the additional risk from its capital structure (i.e., assumes the business is entirely equity-financed).
>
> **Key Term: Equity Beta**
> A measure of the total systematic risk perceived by a company's shareholders, incorporating both business risk and the additional risk arising from financial gearing.
>
> **Key Term: De-gearing (Unlevering) Beta**
> The process of removing the effects of a firm's debt from its equity beta to obtain the asset beta, typically using market values and adjusting for tax.
>
> **Key Term: Re-gearing (Relevering) Beta**
> The process of recalculating an equity beta by applying a desired capital structure to an asset beta, thus incorporating the required amount of financial gearing.

## **CAPM and the Need for Project-Specific Discount Rates**

The standard discount rate used by a company—the weighted average cost of capital (WACC)—is only appropriate if the project has similar risk characteristics and is financed in the same proportions as the firm's existing operations. If the project operates in a different industry sector (different business risk) or uses a different mix of debt and equity (different financial risk), the WACC will be unsuitable.

In such cases, it is necessary to estimate a project-specific cost of equity using a risk-adjusted beta and the CAPM formula:

$$
k_e = R_f + \beta_e (E(R_m) - R_f)
$$

Where:

- $ k_e $ = required return on equity
- $ R_f $ = risk free rate
- $ \beta_e $ = relevant equity beta for the project
- $ E(R_m) $ = expected return on the market portfolio

To derive $ \beta_e $ for a new project, we often start with a proxy company's beta, usually a listed firm in the same industry.

## **Steps for Calculating a Project-Specific Discount Rate**

1. **Select a Proxy Company's Equity Beta:** Identify a company with similar business activities to the project.
2. **De-gear the Proxy's Beta:** Remove the effect of the proxy's gearing to arrive at an asset beta reflecting pure business risk.
3. **Re-gear to Target Structure:** Adjust the asset beta to reflect the project’s intended capital structure (i.e., its own mix of debt and equity).
4. **Apply CAPM:** Use the project-specific equity beta to calculate the required return for the project's equity finance.

### **Worked Example 1.1**

A company is considering entering the logistics sector and will fund the project with 40% debt and 60% equity. A suitable quoted logistics firm (LogiCo) has an observed equity beta of 1.4 and is currently financed with 30% debt (market value) and 70% equity. The tax rate is 25%. The risk-free rate is 3% and the equity market premium is 6%.

**Question:** Calculate an appropriate equity beta and cost of equity for the project.

> **Answer:**
> **Step 1:** De-gear LogiCo's equity beta to find the asset beta:
>
> $$
> \beta_a = \frac{\beta_e}{1 + (1 - T)\frac{V_d}{V_e}}
> $$
>
> $$
> \beta_a = \frac{1.4}{1 + (1 - 0.25)\left(\frac{0.3}{0.7}\right)} = \frac{1.4}{1 + 0.225} = \frac{1.4}{1.225} = 1.14
> $$
>
> **Step 2:** Re-gear the asset beta to the project's target capital structure (40% debt, 60% equity):
>
> $$
> \beta_e = \beta_a \times \left[1 + (1 - T)\frac{V_d}{V_e}\right]
> $$
>
> $$
> \beta_e = 1.14 \times \left[1 + (1 - 0.25)\left(\frac{0.4}{0.6}\right)\right] = 1.14 \times (1 + 0.5) = 1.14 \times 1.5 = 1.71
> $$
>
> **Step 3:** Calculate cost of equity using CAPM:
>
> $$
> k_e = 3\% + 1.71 \times 6\% = 3\% + 10.26\% = 13.26\%
> $$
>
> The appropriate cost of equity for the project is 13.26%.

## **Rationale for De-gearing and Re-gearing Betas**

De-gearing ensures you isolate business risk, unaffected by how the proxy is financed. Re-gearing incorporates the project's own intended debt level, which alters the overall risk to equity holders. This is critical because higher gearing amplifies equity risk, thus increasing the equity beta.

> **Key Term: Business Risk**
> The level of systematic risk inherent in the operations of a business, regardless of how it is financed.
>
> **Key Term: Financial Risk**
> The additional risk to shareholders arising from the use of debt in the capital structure.

## **Interpreting and Selecting Proxy Companies**

The suitability of the chosen proxy is fundamental. The closer the proxy’s operations, revenue streams, and risk environment match the proposed project, the more reliable the derived asset beta. Adjusting for differences in gearing is essential for comparability.

### **Worked Example 1.2**

Marston plc is expanding into technology consulting. A proxy tech consulting firm has an observed equity beta of 1.85, geared at 20% debt to 80% equity (market value). Marston plans to finance its project with 60% equity and 40% debt. The corporation tax rate is 30%.

**Question:** What project equity beta should Marston use?

> **Answer:**
> **De-gearing the equity beta:**
>
> $$
> \beta_a = \frac{1.85}{1 + (1 - 0.3)\left(\frac{0.2}{0.8}\right)} = \frac{1.85}{1 + 0.175} = \frac{1.85}{1.175} = 1.574
> $$
>
> **Re-gearing for Marston's structure:**
>
> $$
> \beta_e = 1.574 \times \left[1 + (1 - 0.3)\left(\frac{0.4}{0.6}\right)\right] = 1.574 \times (1 + 0.467) = 1.574 \times 1.467 = 2.308
> $$
>
> Marston should use an equity beta of approximately 2.31 in CAPM for its project.

## **Worked Example 1.3**

BigBank is considering an acquisition in a sector where suitable proxies are geared with preference shares and significant leases. Should these forms of finance be included in the calculation of gearing for beta de-gearing/re-gearing?

> **Answer:**
> Any finance that increases fixed payment obligations increases financial risk. Lease obligations and preference shares should be included in market value calculations for gearing when adjusting betas, provided these are interest-bearing or have fixed payment features similar to debt.

### **Exam Warning**

> Always use **market values**, not book values, for both debt and equity in beta calculations. Failure to account for tax correctly or omitting non-traditional forms of debt (like leases) can result in significant errors.

### **Revision Tip**

_If a question provides both an equity beta and details of gearing, always use the formula to isolate the asset beta, then re-gear to the intended capital structure before proceeding to CAPM._

## **Summary**

For investment appraisal, project-specific discount rates may be required to reflect risk differences from the parent business. The process follows: select an appropriate proxy, de-gear to asset beta, re-gear to target debt/equity, then calculate the required return via CAPM. Accurate adjustment for debt levels and correct use of market values are exam critical.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Explain why a project-specific cost of capital may be needed when risk differs from existing operations
- Distinguish between asset beta, equity beta, business risk, and financial risk
- Calculate asset beta from proxy equity beta, adjusting for gearings and tax
- Re-gear asset beta to reflect the capital structure intended for your project
- Use CAPM to determine project-specific discount rates
- Use appropriate market values and include all relevant forms of fixed-charge finance in gearing calculations

## **Key Terms and Concepts**

- Asset Beta
- Equity Beta
- De-gearing (Unlevering) Beta
- Re-gearing (Relevering) Beta
- Business Risk
- Financial Risk

Cost of capital and project-specific rates - Asset and equity beta, relevering and de-levering