Equity valuation models - Two-stage and variable growth mode...

Learning Outcomes

After reading this article, you will be able to: explain why non-constant dividend growth is important in share valuation, apply both two-stage and variable growth models to calculate present share value, use terminal value correctly, and identify common mistakes and limitations of multi-phase equity valuation models.

ACCA Financial Management (FM) Syllabus

For ACCA Financial Management (FM), you are required to understand how to value shares when dividend growth is not constant. In preparing for the exam, you should focus your revision on:

• Explaining why constant-growth models may not apply to all companies
• Applying two-stage and variable growth equity valuation models
• Calculating share prices using forecasts with different growth phases and discounting dividends accurately
• Computing and discounting terminal value for stable-growth phases
• Recognising assumptions, limitations, and typical errors in non-constant growth share valuation

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 steps are necessary to value a share where dividends grow fast for three years before settling at a lower, constant growth?
2. Define terminal value in the context of a two-stage growth valuation and describe when it is applied.
3. True or false? In a variable growth equity valuation, each forecast dividend before the stable phase must be individually discounted.
4. What is a common calculation error students make when switching from the high-growth to the stable-growth period in a two-stage model?

Introduction

Standard dividend valuation models assume dividends grow at a single, unchanging rate. However, real-world companies—especially young or growing firms—often experience rapid growth early, then settle into a steady, lower growth as they mature. Two-stage and variable growth models allow more realistic equity valuation in these situations by splitting the calculation into high-growth and stable phases.

Key Term: two-stage growth model
A share valuation method where dividends are forecast to grow at one rate over a set initial period, then switch to a different (often lower) steady rate indefinitely.

Key Term: variable growth model
An equity valuation approach where dividends grow at varying rates year-by-year for several periods, before changing to a stable growth rate for the remaining years.

Key Term: terminal value
The calculated value, at the end of the high- or variable-growth phase, representing all future dividends expected to grow forever at a fixed rate.

Why Non-Constant Growth Models Are Used

The basic dividend growth model uses:

where $P_0$ is current share price, $D_1$ is next year's dividend, $r_e$ is required return, and $g$ is the constant expected dividend growth. This works when a company is mature and dividends grow steadily. However, for firms with high but temporary growth, this formula overstates long-run prospects. Two-stage and variable growth models reflect reality more accurately by calculating values for each phase and summing the results.

Applying the Two-Stage Growth Model

The two-stage growth model splits the company's life into two periods:

1. An initial phase with higher growth for $N$ years.
2. A stable long-term phase with lower, constant growth from year $N + 1$ onward.

Calculation steps

1. Forecast dividends for the high-growth phase: Start with the most recent dividend ($D_0$), apply the first growth rate for each year until year $N$.
2. Discount each high-growth dividend: Bring each to present value using the required return ($r_e$).
3. Find the first stable-growth dividend: $D_{N+1} = D_N \times (1 + g_2)$, where $g_2$ is the perpetual lower rate.
4. Calculate terminal value at year $N$: Use the growth perpetuity formula: $$TV_N = \frac{D_{N+1}}{r_e - g_2}$$
5. Discount the terminal value to present: Use $(1 + r_e)^N$.
6. Add up all present values: The sum is the current share price ($P_0$).

Worked Example 1.1

A company has just paid a dividend of $1.50. Dividends are forecast to increase by 10% per year for 4 years, then by 4% per year indefinitely. The required return is 9%. Calculate $P_0$.

Answer:

• $D_1 = 1.50 \times 1.10 = 1.65$
• $D_2 = 1.65 \times 1.10 = 1.815$
• $D_3 = 1.815 \times 1.10 = 1.9965$
• $D_4 = 1.9965 \times 1.10 = 2.1962$
• $D_5 = 2.1962 \times 1.04 = 2.2840$ (first stable dividend)
• Terminal value at end of Year 4: $TV_4 = 2.2840 / (0.09 - 0.04) = 45.68$
• Present values:
  • $PV_1 = 1.65 / 1.09 = 1.5147$
  • $PV_2 = 1.815 / (1.09)^2 = 1.5284$
  • $PV_3 = 1.9965 / (1.09)^3 = 1.5440$
  • $PV_4 = 2.1962 / (1.09)^4 = 1.5606$
  • $PV_{TV_4} = 45.68 / (1.09)^4 = 32.4471$
• Total $P_0 = 1.5147 + 1.5284 + 1.5440 + 1.5606 + 32.4471 = 38.595$

Variable Growth Model

This method lets each year's dividend grow at a unique forecast rate, before a final switch to stable perpetual growth.

Steps:

1. Calculate each year's dividend up to the stable phase using the expected growth for that year.
2. Discount each dividend to present value at $r_e$.
3. Find the first stable-phase dividend; use it to compute terminal value as before.
4. Discount the terminal value to present value.
5. Sum all present values for the share price.

Worked Example 1.2

Y Co's last dividend was $0.80. Dividends will grow at 9% the first year, 7% the next, 5% the following, and then 3% per year in perpetuity. Required return is 8%. What is $P_0$?

Answer:

• $D_1 = 0.80 \times 1.09 = 0.872$
• $D_2 = 0.872 \times 1.07 = 0.933$
• $D_3 = 0.933 \times 1.05 = 0.979$
• $D_4 = 0.979 \times 1.03 = 1.008$
• Terminal value at Year 3: $TV_3 = 1.008 / (0.08 - 0.03) = 20.16$
• Present values:
  • $PV_1 = 0.872 / 1.08 = 0.807$
  • $PV_2 = 0.933 / (1.08)^2 = 0.800$
  • $PV_3 = 0.979 / (1.08)^3 = 0.778$
  • $PV_{TV_3} = 20.16 / (1.08)^3 = 15.986$
• Total $P_0 = 0.807 + 0.800 + 0.778 + 15.986 = 18.371$

When Multi-Stage Models are Needed

These approaches are relevant:

• When a company or industry will experience above-average growth for only a fixed period before reverting to stability
• When analyst forecasts for early years differ from long-term expectations or macroeconomic trends

The length of the high-growth period and the different growth rates must be justified using industry and company information.

Key Term: required return to equity
The expected annual rate of return shareholders demand, given the perceived risk of owning that company's shares.

Calculation Tips

• Always forecast and discount each high- or variable-growth dividend individually.
• Apply the terminal value formula only at the start of the first fully stable growth year.
• Use the corresponding year's dividend for the terminal value (e.g., $D_{N+1}$ for the first year of the stable phase).
• All discounting should be done using the shareholders' required return ($r_e$).

Exam Warning

Forgetting to compute the correct dividend for the first year of the stable phase before calculating terminal value is a frequent cause of lost marks. Double-check which dividend your perpetuity will begin with.

Revision Tip

For clarity and accuracy, set up a table with columns for: year, dividend, discount factor, present value, and terminal value. Complete each row step-by-step.

Summary

Two-stage and variable growth models are necessary to calculate the present value of shares when companies have periods of high growth before settling to lower stable growth. Their correct use involves forecasting all dividends in the high-growth phase, discounting them, then adding the discounted terminal value for the stable phase.

Key Point Checklist

This article has covered the following key knowledge points:

• Explain why multi-stage dividend valuation models are needed for companies with changing growth rates
• Calculate share prices using two-stage and variable growth methods, including correct use of terminal value
• Discount all forecasted dividends and the terminal value to present value using the shareholders’ required return
• Identify and avoid common pitfalls with terminal value calculation and phase transitions in these models

Key Terms and Concepts

• two-stage growth model
• variable growth model
• terminal value
• required return to equity