Cost of equity and preference shares - CAPM-based cost of eq...

Learning Outcomes

After reading this article, you will be able to calculate the cost of equity using the Capital Asset Pricing Model (CAPM) and determine the cost of preference shares. You will understand the distinction between systematic and unsystematic risk, explain how CAPM estimates required returns, and apply these concepts to practical exam scenarios for ACCA Financial Management (FM).

ACCA Financial Management (FM) Syllabus

For ACCA Financial Management (FM), you are required to understand both the theory and application of determining costs of equity and preference shares. In your exam, you should be comfortable with:

• Explaining the relationship between risk and return for different securities
• Distinguishing between systematic and unsystematic risk
• Calculating the cost of equity using the Dividend Growth Model (DGM) and the Capital Asset Pricing Model (CAPM)
• Explaining the assumptions, strengths, and weaknesses of CAPM
• Calculating and interpreting the cost of preference shares
• Applying these costs when determining an organisation’s weighted average cost of capital (WACC)

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 is the difference between systematic and unsystematic risk in portfolio theory?
2. Using the CAPM formula, which inputs are needed to calculate the required return on equity?
3. True or false? The cost of irredeemable preference shares is calculated by dividing the annual preference dividend by the market value per share.
4. What adjustment should be made if the given share price is cum-dividend but the DGM formula requires an ex-dividend price?
5. Briefly explain when the cost of equity from CAPM might differ from that estimated using the Dividend Growth Model.

Introduction

Companies raise long-term finance mainly through equity, preference shares, and debt. For effective financial management and accurate investment appraisal, you must estimate the cost of each source. The required return to ordinary shareholders is usually the highest — reflecting its risk. Two common methods used to assess the cost of equity are the Dividend Growth Model (DGM) and the Capital Asset Pricing Model (CAPM). Preference shares, although classed as equity, behave more like debt and have their own return profile.

Understanding how to apply CAPM and to determine the cost of preference shares is a frequent requirement in ACCA FM exams. This article focuses on the risk-return relationship, the CAPM, practical cost calculations, and application to real-world scenarios.

Key Term: cost of equity
The minimum return a company must offer to attract and retain equity investment, reflecting shareholders’ expectations of risk and reward.

Key Term: systematic risk
The element of risk affecting all investments in the market, which cannot be eliminated by diversification and is measured by beta in CAPM.

Key Term: unsystematic risk
The risk specific to an individual company or industry, which can be reduced or eliminated through holding a diversified portfolio.

Key Term: Capital Asset Pricing Model (CAPM)
A model that estimates the required return on a security as the risk-free rate plus a risk premium based on the security’s systematic risk compared to the market as a whole.

Key Term: cost of preference shares
The rate of return required by holders of preference shares, typically calculated as the fixed annual dividend divided by the current market price.

The Risk-Return Relationship and Equity Cost

Investors demand higher returns for taking more risk. Ordinary shares have no guaranteed return, so shareholders require a premium over “safe” investments such as government bonds. This risk premium reflects the volatility of the company's returns compared to the wider market.

PORTFOLIO THEORY: By holding shares in different companies, investors can largely eliminate unsystematic risk. What remains is systematic risk, which cannot be diversified away and must be rewarded by higher expected returns.

The Capital Asset Pricing Model (CAPM)

The CAPM provides a systematic approach to estimate the required return for an ordinary shareholder:

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

Where:

• $R_f$ = risk-free rate from a government bond

• $R_m$ = expected return from the overall market portfolio

• $\beta$ = measure of the share’s systematic risk (market average is 1)

• If $\beta > 1$, the share is more volatile than the market

• If $\beta < 1$, it is less volatile

CAPM assumes that investors are rational, markets are efficient, and all hold diversified portfolios — so only systematic risk requires compensation.

Worked Example 1.1

A company’s equity beta is 1.3. The current return on government T-bills is 4%, and the stock market portfolio is expected to return 11%. Calculate the cost of equity using CAPM.

Answer:

Use the CAPM formula: $R_e = 4\% + 1.3 \times (11\% - 4\%) = 4\% + 1.3 \times 7\% = 4\% + 9.1\% = 13.1\%$

The cost of equity is 13.1%.

Systematic vs. Unsystematic Risk

CAPM only rewards systematic risk. In a diversified portfolio, company-specific (unsystematic) risk is negligible. In contrast, systematic risk arises from broad economic or market changes — for example, a market downturn due to recession affects the majority of shares.

Worked Example 1.2

A portfolio holds shares in 25 companies. If a supplier strike disrupts production at only one of those companies, which risk(s) does the portfolio still face?

Answer:

The strike is an unsystematic risk, which is mostly diversified away by holding 25 shares. However, the portfolio still faces systematic risk from market-wide factors.

Calculating the Cost of Preference Shares

Preference shares generally offer a fixed dividend. Their cost is similar in concept to irredeemable debt, as the return is expected to continue indefinitely unless the shares are redeemed.

Formula for irredeemable preference shares:

$K\_{p} = \frac{D}{P_0}$

Where:

• $D$ = annual preference dividend
• $P_0$ = ex-dividend market price per share

Note: For redeemable preference shares, use the internal rate of return (IRR) based on the present value of all cash flows to redemption.

Worked Example 1.3

A company has 100,000 7% preference shares of $1 each. The market price is $1.20 per share (ex-dividend). Calculate the cost of preference shares.

Answer:

The annual dividend per share is $0.07. $K_p = \frac{0.07}{1.20} = 0.0583 \text{ or } 5.83\%$ The cost of preference shares is 5.83%.

Comparing the Dividend Growth Model and CAPM

Both the DGM and CAPM provide estimates for the cost of equity. DGM relies on dividend history and assumes a constant growth rate, while CAPM uses market data and beta. In practice, CAPM is more useful where dividend patterns are irregular, or for project/appraisal discount rates aligned with systematic risk.

Exam Warning

Do not include unsystematic risk in your required return calculations. ACCA exam questions assume all investors are diversified and are only exposed to systematic risk, as measured by beta.

Revision Tip

Learn the CAPM formula and its parts, and ensure you know how to source or estimate beta, the risk-free rate, and the expected market return.

Summary

CAPM is essential for calculating a risk-adjusted cost of equity, a critical value for project appraisal and WACC. It emphasizes only systematic risk, assessed with beta. Preference shares are usually treated as a fixed-income security when calculating their cost. Understanding these principles is fundamental for many ACCA FM exam questions.

Key Point Checklist

This article has covered the following key knowledge points:

• Define cost of equity and explain why it is higher than debt or preference shares
• Distinguish between systematic and unsystematic risk
• Calculate the cost of equity using the Capital Asset Pricing Model (CAPM)
• Identify and calculate the cost of preference shares
• Recognize when to use CAPM versus the Dividend Growth Model
• Appreciate the importance of beta in estimating risk

Key Terms and Concepts

• cost of equity
• systematic risk
• unsystematic risk
• Capital Asset Pricing Model (CAPM)
• cost of preference shares