## **Learning Outcomes**

After reading this article, you will be able to explain the Capital Asset Pricing Model (CAPM), differentiate systematic and unsystematic risk, calculate a required return using CAPM, and apply CAPM to determine an appropriate project discount rate in investment appraisal. You will be able to identify when CAPM is suitable, calculate asset and equity betas, and recognise practical issues in using CAPM for ACCA Financial Management (FM).

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

For ACCA Financial Management (FM), you are required to understand how CAPM links risk and return, and how to apply CAPM in project appraisal. Specifically, revision should focus on:

- The distinction between systematic and unsystematic risk
- The concept of portfolio diversification and its effect on risk
- The meaning and calculation of beta (β) as a measure of systematic risk
- The structure and use of the CAPM formula to determine required return
- Application of CAPM in setting project-specific discount rates
- The process for asset beta (de-gearing) and equity beta (re-gearing) calculations for projects with differing risk profiles
- Advantages and limitations of using CAPM in 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 of the following risks can be reduced by holding a diversified portfolio?
   a) Systematic risk  
   b) Unsystematic risk  
   c) Market risk  
   d) Interest rate risk

2. A project in a new industry has a higher systematic risk than the current business. How should the required return for this project be determined?
   a) Use the company’s existing WACC  
   b) Use the risk-free rate  
   c) Use CAPM with a suitable project beta  
   d) Use the cost of debt

3. What does a beta (β) of 1.6 indicate about a share’s risk and expected return compared to the overall market?

4. Briefly describe the steps required to adjust a proxy equity beta to set a project discount rate using CAPM.

## **Introduction**

Investment projects involve risk and require an appropriate return. The required return reflects investors’ desire to be compensated for both the time value of money and the risk they take. The CAPM provides a market-driven, systematic approach to setting this required return, especially for projects with risk levels different from the current business.

You will need to distinguish between types of risk, understand how diversification works, know how the CAPM formula quantifies the required return, and understand how betas are adjusted for project-specific risk.

> **Key Term: Capital Asset Pricing Model (CAPM)**
> The model that calculates the required return of a security or project based on the risk-free rate, the security’s systematic risk (beta), and the expected market risk premium.

## **Risk, Diversification, and Beta**

When assessing investments, risk can be split in two:

- **Systematic risk**: affects all firms—market-wide factors such as economic cycles or interest rates.
- **Unsystematic risk**: unique to the company or industry—such as a major supplier closing.

> **Key Term: Systematic risk**
> Risk that arises from economy-wide factors and cannot be diversified away by holding a portfolio.
>
> **Key Term: Unsystematic risk**
> Risk specific to an individual company or industry, which can be reduced through diversification.

Holding a well-diversified portfolio eliminates unsystematic risk, leaving only systematic risk. Investors demand compensation only for this remaining market risk.

Beta (β) quantifies a security’s systematic risk relative to the market as a whole:

- If β = 1: Risk and return match the market average.
- If β > 1: Higher risk and volatility than the market.
- If β < 1: Lower risk than the market.

> **Key Term: Beta (β)**
> A measure of a security’s or project’s sensitivity to market movements; beta indicates how much the return moves compared to the overall market.

## **The CAPM Formula and Required Return**

The CAPM quantifies the required return by relating it to risk:

$$ \text{Required return} = R_f + \beta (R_m - R_f) $$

where:

- $ R_f $ = risk-free rate (e.g., government bonds)
- $ R_m $ = expected market return
- $ \beta $ = systematic risk of the investment
- $ (R_m - R_f) $ = market risk premium

This formula models the return investors need for taking systematic risk in a rational, market-consistent way.

> **Key Term: Required return**
> The minimum rate of return expected by investors after considering the risk of an investment.

## **Applying CAPM in Investment Appraisal**

Firm-wide WACC should only be used for projects with risk similar to the current business. For projects outside the firm’s core area or with significantly different risk, a project-specific rate is needed.

By using CAPM, the required return accounts for:

- The project’s business risk (via the asset beta for the industry or activity)
- The level of financial risk (by re-gearing the asset beta to reflect planned financing)

### Steps for Project-Specific Discount Rate with CAPM

1. Find a suitable **proxy equity beta (βe)** from a quoted company in the same business as the project.
2. **De-gear** (asset beta): remove the effect of that company’s gearing using the asset beta formula:

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

   where $ V_e $ = equity value, $ V_d $ = debt value, $ T $ = tax rate.

3. **Re-gear**: apply your own planned gearing for the project to get the appropriate equity beta for the financing structure:

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

4. Plug the re-geared beta into the CAPM formula to determine the risk-adjusted project return.

### **Worked Example 1.1**

A company wants to appraise a project in a new industry. The proxy quoted company has an equity beta of 1.5 and a debt-to-equity ratio of 1:2 (debt is risk-free; tax rate 30%). The company plans to finance the project with a debt-to-equity ratio of 1:4. The risk-free rate is 4%, expected market return is 10%.

**Calculate a suitable required return for the project.**

> **Answer:**
>
> Step 1: De-gear the proxy beta to get asset beta:
>
> $$ \beta_a = 1.5 \times \frac{2}{2 + 1 \times (1 - 0.3)} = 1.5 \times \frac{2}{2.7} = 1.11 $$
>
> Step 2: Re-gear asset beta to the company’s proposed gearing:
>
> $$ \beta_e = 1.11 \times \frac{4 + 1 \times (1-0.3)}{4} = 1.11 \times \frac{4.7}{4} = 1.305 $$
>
> Step 3: Insert beta into CAPM:
>
> $$ \text{Required return} = 4\% + 1.305 \times (10\% - 4\%) = 4\% + 7.83\% = 11.83\% $$
>
> The project-specific discount rate is 11.8%, rounded.

### **Advantages of CAPM in Project Appraisal**

- Calculates a return that is directly linked to market and project risk.
- Improves accuracy for projects where risk differs from the firm’s core activities.
- Recognised and widely understood by investors.

### **Limitations and Practical Considerations**

- CAPM needs reliable estimates of beta and the market risk premium.
- Assumes investors are well-diversified (ignores unsystematic risk).
- Inputs (beta, returns) may not be readily available for all projects or industries.
- Fundamental assumptions (perfect markets, one-period view) rarely hold precisely.

### **Worked Example 1.2**

A company is appraising a project with the same risk profile as its current core business. Should it use its current WACC or CAPM to set the discount rate?

> **Answer:**
>
> If the project’s risk matches the firm’s core business and financing, WACC is appropriate. If the risk or financing structure is different, a project-specific rate using CAPM should be used.

### **Exam Warning**

> Do not apply a company’s existing WACC if the project has higher or lower systematic risk than the current business. Instead, use CAPM to find a suitable project-specific return.

### **Revision Tip**

> Always double-check which type of beta you are using—asset or equity—and use the correct values for both proxy and your own project’s gearing.

## **Summary**

The CAPM calculates the required return by objectively linking systematic risk to expected return. In investment appraisal, it should be used to determine the discount rate for projects where risk differs from the existing business. De-gear to find the business risk (asset beta), then re-gear if the project’s financial risk (gearing) changes.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Distinguish between systematic and unsystematic risk, and explain their relevance for diversification
- State the CAPM formula and describe each term and its purpose
- Explain what beta measures and how it is interpreted
- Calculate a suitable required return for a specific project using CAPM
- Adjust (de-gear and re-gear) betas for different business and financial risks
- List the strengths and limitations of applying CAPM in investment appraisal

## **Key Terms and Concepts**

- Capital Asset Pricing Model (CAPM)
- Systematic risk
- Unsystematic risk
- Beta (β)
- Required return

CAPM and required return - Using CAPM in investment appraisal