Cost of equity and preference shares - Dividend growth model...

Learning Outcomes

After reading this article, you will be able to calculate and explain the cost of equity using the dividend valuation model (DVM), including growth. You will also learn to determine the cost of preference shares, estimate dividend growth, and discuss the main exam pitfalls related to these calculations. You will be equipped to apply these principles to ACCA Financial Management (FM) exam questions.

ACCA Financial Management (FM) Syllabus

For ACCA Financial Management (FM), you are required to understand how to determine the cost of equity and preference shares using the dividend growth model. Be sure you are comfortable with:

• Calculating a share price and cost of equity using the dividend valuation model (DVM), with and without growth
• Applying and rearranging the DVM formula for cost of equity estimation
• Estimating dividend growth rates using historical dividend data and retention models
• Calculating the cost of preference shares
• Appreciating the limitations and assumptions of the dividend growth model
• Recognising common exam pitfalls, including the distinction between cum-div and ex-div share prices

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. A company has just paid a dividend of 12p per share. Dividends are expected to grow by 6% per year. The current ex-div share price is £2.40. What is the cost of equity using the DVM?
2. True or false? Preference shares usually pay a fixed dividend, so their cost can be estimated like irredeemable debt.
3. A share price is quoted cum-div at 150p and a dividend of 8p is about to be paid. What is the ex-div price used in DVM calculations?
4. Briefly state one reason why the cost of equity calculated from the DVM may not be reliable.

Introduction

Valuing ordinary shares and calculating their cost of equity are key tasks for ACCA FM. The dividend valuation model (DVM) is a core technique used to estimate the return shareholders require from their investment, based on the dividend stream they expect to receive. Preference shares, which typically pay fixed dividends, are also common in exam questions, and their cost is calculated using a related but simpler formula.

This article will cover the application of the DVM with and without dividend growth, growth estimation methods, and the calculation of the cost of preference shares. You will see step-by-step examples and learn the main pitfalls to avoid in your exam.

Key Term: dividend valuation model (DVM)
A share valuation approach estimating share price as the present value of all expected future dividends, discounted at the required return of equity holders.

Key Term: cost of equity
The minimum return required by ordinary shareholders, often estimated as the rate used to discount future dividends to the current share price.

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

Cost of Equity: Dividend Valuation Model (DVM)

The DVM states that a share’s value is the present value of all its future dividends discounted at the required return. The formula can be rearranged to solve for the cost of equity if the current share price and dividends are known.

No Growth Case

If dividends are expected to stay constant:

$P_0 = \frac{D}{k_e}$

Where:

• $P_0$ = ex-div share price
• $D$ = annual dividend (first dividend in one year)
• $k_e$ = cost of equity (required return)

So,

$k_e = \frac{D}{P_0}$

Dividend Growth Model (Constant Growth)

If dividends are expected to grow at a constant rate $g$:

$P_0 = \frac{D_0(1+g)}{k_e - g} = \frac{D_1}{k_e - g}$

Where:

• $D_0$ = dividend just paid
• $D_1$ = next year’s expected dividend
• $g$ = steady annual dividend growth rate

Rearranged for $k_e$:

$k_e = \frac{D_1}{P_0} + g$

Ex-div and Cum-div Prices

The correct price to use in these calculations is the ex-div price. If given a cum-div price (includes the imminent dividend), subtract the dividend due to obtain the ex-div price.

Estimating Dividend Growth

There are two main ways provided in the exam:

(1) Historic Growth Rate:

If past dividends are known,

$g = \left( \frac{D*0}{D*{n}} \right)^{1/n} - 1$

Where $D_0$ is the most recent dividend, $D_n$ is the dividend n years ago.

(2) Retention (Gordon’s Growth) Model:

$g = b \times r_e$

Where:

• $b$ = retention rate (proportion of earnings retained)
• $r_e$ = accounting return on equity

Worked Example 1.1

A company has just paid a dividend of 10p per share. Dividends are expected to grow at 5% per year, and the current ex-div share price is £1.80. Calculate the cost of equity.

Answer:

1. Next dividend: $D_1 = 10p \times 1.05 = 10.5p$
2. $P_0 = £1.80$
3. $k_e = \frac{0.105}{1.80} + 0.05 = 0.1083$, or 10.8%

Worked Example 1.2

A company’s share price is 220p cum-div. A dividend of 12p is to be paid in two weeks. Use the correct price in the DVM.

Answer:
Ex-div price = 220p – 12p = 208p. Use 208p as $P_0$ in the DVM; do not use the cum-div price.

Worked Example 1.3

Historic dividends per share were: 6.50p (4 years ago) and 8.00p (most recently). Estimate the annual dividend growth rate.

Answer:
$g = (8.00 / 6.50)^{1/4} - 1 = (1.2308)^{0.25} - 1 \approx 0.053,$ or 5.3%

Cost of Preference Shares

Preference shares typically pay a fixed dividend. Their cost is calculated using a perpetuity formula, similar to irredeemable debt (for non-redeemable preference shares):

$k_p = \frac{D}{P_0}$

Where:

• $D$ = annual preference dividend
• $P_0$ = ex-div market price per preference share
• $k_p$ = cost of preference share

Preference share dividends are usually not tax-deductible, so no adjustment for tax.

Worked Example 1.4

A company has 50,000 8% $1 preference shares, trading at $1.20 ex-div. What is the cost of preference shares?

Answer:
Annual dividend = 8% × $1 = $0.08.

$k_p = 0.08 / 1.20 = 0.0667$, or 6.67%.

Discussion of Limitations and Assumptions

• The DVM assumes constant dividend growth, which may not be realistic.
• Share price movements do not always reflect only dividend policy (market factors apply).
• Inputs (growth estimates, ex-div price, dividends) may not be fully reliable.
• For preference shares, assume dividends are fixed and always paid.

Exam Warning

Do not use the cum-dividend share price in the DVM unless you first subtract the dividend due. Using a cum-div price without adjustment will overstate the cost of equity, leading to exam errors.

Revision Tip

When estimating growth from past dividends, ensure you use the appropriate number of periods (e.g., four years’ growth between five annual payments).

Summary

Calculating the cost of equity using the dividend growth model is central to business valuation in FM. Correct selection of the annual dividend, share price (ex-div), and growth estimate is essential. Preference shares are valued using a straightforward fixed-dividend approach.

Key Point Checklist

This article has covered the following key knowledge points:

• Define and apply the dividend valuation model (DVM) for share valuation and cost of equity
• Calculate the cost of equity for constant and growing dividends
• Estimate dividend growth rates from historic data or via the retention model
• Calculate the cost of preference shares using the fixed-dividend formula
• Identify common pitfalls, including ex-div and cum-div prices
• Recognise the key limitations and assumptions of the models

Key Terms and Concepts

• dividend valuation model (DVM)
• cost of equity
• cost of preference shares