Gordon Growth Model

Delve into the world of macroeconomics with this exploration of the Gordon Growth Model. This analysis provides a clear guide to understanding this crucial economic tool, its assumptions, and how to calculate its formula. You will also gain insights into how the Gordon Growth Model relates to terminal value and comparisons with the Dividend Discount Model. Whether you're a student or seasoned economist, this is a must-read for anyone keen on expanding their comprehension of macroeconomic theories and models.

Understanding the Gordon Growth Model in Macroeconomics

Definition: What is the Gordon Growth Model?

Assumptions of the Gordon Growth Model

In order to make the model workable, there are certain assumptions that must be understood:

• The company's dividends grow at a constant rate indefinitely
• The rate of return required by the investor is greater than the growth rate of the dividends

Furthermore, Here is the Gordon Growth Model formula: \[ P = \frac{D}{(r - g)} \] where:

\( P \)	Price of the stock today
\( D \)	Dividend expected next year
\( r \)	Rate of return required by the investor
\( g \)	Growth rate in dividends

Key Assumptions in the Gordon Growth Model

As previously mentioned, the Gordon Growth Model assumes dividends will grow at a constant rate indefinitely, and that the required rate of return is greater than the growth rate. However, further assumptions include:

• The business has a stable business model that is not subject to rapid changes
• The firm's financial structure (debt and equity) and the cost of capital are constant

Potential Limitations of Gordon Growth Model Assumptions

While the Gordon Growth Model provides a straightforward and calculated approach towards stock valuation, it's important to note that the assumptions may not hold true in all circumstances. Potential limitations include:

• Not all firms pay out dividends, limiting the application of the model
• The constant growth rate of dividends may not be viable for all companies
• The model's assumption of a perfect market is rarely, if ever, observed in actual market settings

Given the potential limitations, the results derived from the Gordon Growth Model should be used as a gauge, rather than a definitive measure of a stock's intrinsic value.

Step by Step Guide to the Gordon Growth Model Formula

Having familiarised yourself with the concept and assumptions of the Gordon Growth Model, let's delve deeper into how to use the formula. Just as a reminder, the formula we're working with is: \[ P = \frac{D}{(r - g)} \] The following steps simplify the approach in using the formula effectively.

Derivation of the Gordon Growth Model Formula

To fully understand the Gordon Growth Model formula, it's crucial to know its derivation. The process starts with the present value of a perpetuity formula, which allows us to calculate the value of a series of future payments (dividends in our case) discounted back to the current time. A perpetuity is a series of infinite cash flows, and its present value can be computed by dividing the cash flow \( D \) by the discount rate \( r \). This is written as \( P = \frac{D}{r} \). However, this doesn't include the growth factor. That's where Gordon's brilliance comes in. Gordon made a crucial adaptation by assuming that dividends grow at a constant rate, resulting in the Gordon growth model, also known as the Dividend Discount Model as it emphasises the dividends' future value. Here's the equation again: \[ P = \frac{D}{(r - g)} \]

Components of the Gordon Growth Model Formula

Breaking down the components of the formula leads to a deeper understanding of the underlying principles. The four main parts include:

P	: The predicted price of the stock based on the model
D	: The dividend expected to be paid out in the upcoming year
r	: The required rate of return by the investor
g	: The growth rate of dividends, assumed to be constant indefinitely

To apply the formula, the investor must first determine their required rate of return, which should be higher than the growth rate of the dividend: \( r > g \). Then, they also need to estimate the growth rate of the future dividends. Once these inputs have been identified, you can use the formula to compute the fair value of the stock.

Working through an Example of Gordon Growth Model

Let's illustrate the model with an example. Suppose you're examining a technology firm set to pay a dividend of £1 next year, and you expect the dividends to grow by 5% each year indefinitely. If your required rate of return is 10%, then the intrinsic value of the stock can be computed as follows: Using the Gordon Growth model formula \( P = \frac{D}{(r - g)} \), you can replace \( D \) with £1, \( r \) with 10% (or 0.10), and \( g \) with 5% (or 0.05). This will yield: \[ P = \frac{1}{(0.10 - 0.05)} = £20 \] So, based on the Gordon Growth Model, if the company's stock is selling for less than £20, it could be a good investment, because this price is lower than the calculated intrinsic value. Conversely, if the price is significantly above £20, you might want to reassess your assumptions or look elsewhere. Note that this is a simplified example. Real life situations will often require more complex considerations.

Gordon Growth Model and Terminal Value

In financial mathematics, the Gordon Growth Model is frequently used to determine the 'Terminal Value' of a series of future cash flows. 'Terminal Value' represents the present value of all subsequent cash flows, beyond a certain date into the future, where those cash flows are assumed to grow at a steady rate indefinitely.

Understanding Gordon Growth Model Terminal Value

The application of the Gordon Growth Model, in the calculation of Terminal Value, is predicated on the core idea that a firm's cash flows are expected to grow at a constant rate forever, creating an infinite series of future cash flows. The Terminal Value is the present value of this infinite series of future cash flows and can be described as the point when a company’s future cash flows can be reasonably approximated to be growing at a constant rate. The Gordon Growth Model provides a technique to calculate this Terminal Value, which represents the value, today, of all future cash flows. Therefore, it plaits neatly with the logic of a perpetuity in mathematics. To effectively calculate the Terminal Value using the Gordon Growth Model, the formula commonly used is: \[ TV = \frac{CF * (1 + g)}{r - g} \] where: - \(TV\) is the Terminal Value - \(CF\) is the Cash Flow for the next period - \(g\) is the growth rate of the Cash Flows - \(r\) is the discount rate (required rate of return for the investor) Reviews of various valuation books suggest this as the best method for approximating Terminal Value when doing a five-year discounted cash flow analysis.

Application of Terminal Value in Gordon Growth Model

As earlier mentioned, Terminal Value has a vital role, especially in Discounted Cash Flow (DCF) models. In such models, the time horizon for projections often doesn't exceed five or ten years due to the increasing uncertainty with time. However, as a business typically continues operations post this period, the Terminal Value calculation is necessary to account for the value of cash flows beyond this projection horizon. The Gordon Growth Model hence serves as a practical method in these instances. In the Gordon Growth Model, Terminal Value calculation assumes that free cash flows will grow at a constant rate infinitely. Therefore, it is necessary to choose a realistic and conservative growth rate, often linked to the inflation rate or the GDP growth rate. It is to prevent over-estimating which might lead to inflated valuations.

Deriving Terminal Value with the Gordon Growth Model

This section illustrates the process of deriving Terminal Value using the Gordon Growth Model. Assuming we have a company with a Cash Flow of £1,000,000 in year 5, growing at a rate of 2%, and the discount rate is 10%, Terminal Value at the end of the five-year period can be calculated by substituting the values into the formula, as follows: \[ TV = \frac{CF * (1 + g)}{r - g} = \frac{1,000,000 * (1 + 0.02)}{0.10 - 0.02} = £13,750,000 \] This Terminal Value of £13,750,000 therefore represents the value today of all future Cash Flows from the end of year 5 onwards, assuming the cash flows grow at a rate of 2% indefinitely. However, to find the present value of this Terminal Value at the end of yr-5, this would then need to be discounted back to today using the formula: \[ PV = \frac{TV}{(1 + r)^n} \] where \(PV\) is Present Value, \(TV\) is Terminal Value, \(r\) is the discount rate, and \(n\) is the number of periods. When dealing with non-constant growth, multiple stages of the Gordon Growth Model can be used, but this requires more complex modelling and understanding of long-term growth patterns.

A Closer Look at the Two Stage Gordon Growth Model

While the Gordon Growth Model is a reliable valuation method, it assumes a constant growth rate, which might not always be a realistic scenario. That's where the Two Stage Gordon Growth Model comes into play, offering greater flexibility by allowing for different growth rates in two separate stages.

Understanding the Two Stage Gordon Growth Model

The Two Stage Gordon Growth Model is a variant of the famous Gordon Growth Model, which allows a company's dividends to grow at different rates in two separate stages. This model is particularly useful when the firm's dividends are expected to grow at a rapid rate in the short term, before steadily slowing to a more sustainable long-term growth rate. In the first stage of the model, dividends are expected to grow at an unusually high rate, which cannot be sustained indefinitely. This period includes the shorter-term growth. In the second stage, growth rates are expected to slow down and stabilise at a normal, constant rate, extending indefinitely. The application of this model is widespread in financial analysis due to its consideration of varying growth rates, mimicking more closely the real-world conditions and business cycles.

When to Use Two Stage Gordon Growth Model

The decision to use the Two Stage Gordon Growth Model significantly depends on the growth profile of the firm you're analysing. The key scenarios suitable for this model include: - Companies that are in the growth phase of their lifecycle, where they are experiencing an initial period of high growth, that is eventually expected to level off and stabilise. - Firms that plan significant changes in the short-term. If the company undergoes changes that will impact the dividend growth rate only in the short run (such as an investment in a new project or a temporary increase in market demand), the Two Stage Gordon Growth Model is beneficial. - Businesses operating under unique economic or industry conditions that demand different short-term and long-term growth estimations.

Step by Step Example of a Two Stage Gordon Growth Model

To illustrate the application of the Two Stage Gordon Growth Model, let's work through an example. Let's assume we have a company that's expected to pay a dividend of £3 next year. The company's dividends are expected to grow by 8% annually for the next 4-years. After that, the growth rate will slow to a stable 4% per year, indefinitely. If the required rate of return is 10%: For stage 1, the present value of the dividends for the first four years can be calculated individually as follows: - For Year 1: \( PV_1 = \frac{D1}{(1 + r)} \) where \( D1 = £3 \times 1.08^1 \). - For Year 2: \( PV_2 = \frac{D2}{(1 + r)^2} \) where \( D2 = £3 \times 1.08^2 \). - For Year 3: \( PV_3 = \frac{D3}{(1 + r)^3} \) where \( D3 = £3 \times 1.08^3 \). - For Year 4: \( PV_4 = \frac{D4}{(1 + r)^4} \) where \( D4 = £3 \times 1.08^4 \). For stage 2, the present value of all dividends from Year 5 onwards grows at a stable rate of 4% indefinitely. This can be calculated using the original Gordon Growth Model, remembering to discount back to present value: - For Year 5 onwards: \( PV_5 = \frac{D5}{r - g} \times \frac{1}{(1 + r)^4} \) where \( D5 = £3 \times 1.08^4 \times 1.04 \) (i.e. dividend from Year 4, growing at 4%). The intrinsic value of the stock is the sum of the calculated present values for both stages. Moreover, remember that the Two Stage Gordon Growth Model relies on many assumptions like any other valuation model, including constant growth rates and discount rates. In reality, these variables might fluctuate due to unforeseen changes in the company or market conditions.

Comparison between Dividend Discount Model and Gordon Growth Model

While both the Dividend Discount Model (DDM) and the Gordon Growth Model (GGM) are methods used in stock valuation, they function under different premises and are beneficial in various scenarios. Each model has its strengths and limitations within different contexts. Understanding the distinctive features and applications of each model helps in getting optimal results whilst conducting investment analyses.

Dividend Discount Model Vs Gordon Growth Model: An Overview

The Dividend Discount Model originates from the premise that the value of a stock should be the sum of all its future cash flows (in the form of dividends), discounted back to their present value. On the other hand, the Gordon Growth Model, a variant of the DDM, calculates the intrinsic value of a stock, assuming that dividends grow at a constant rate. To sum it up, the Gordon Growth Model is essentially the Dividend Discount Model applied to a company that is growing its dividends at a constant rate.

Main Differences between Dividend Discount Model and Gordon Growth Model

The primary distinction between these two models is rooted in the growth rate assumptions utilized: - Dividend Discount Model: No specific assumption on dividend growth rates, and the model employs distinct dividends for each period. As a result, the DDM is more adaptable and can incorporate varying dividend growth rates. - Gordon Growth Model: Assumes that the dividends grow at a constant or steady rate indefinitely. It simplifies the DDM when the financial analyst believes the firm's growth rate is expected to be constant in the long run. The table below highlights key considerations that differentiate the two models:

Model	Growth Assumptions	Applicability
Dividend Discount Model	Flexible growth rates	Companies with voluminous cash flows, seasoned businesses with extensive dividend history
Gordon Growth Model	Constant growth rate	Stable, mature companies with predictable dividend growth rates

While both are comparable in that they both estimate the intrinsic value of a stock based on future dividends, these distinguishing features might make one model more applicable over the other in various scenarios.

Application: Dividend Discount Model Vs Gordon Growth Model

The selection between the DDM and GGM often relies on the firm characteristics and the purpose of the valuation: - The Dividend Discount Model is more frequently used when a company's dividends are expected to change significantly year to year. This model can be valuable for newer companies with fluctuating profits or for enterprises undergoing significant strategy changes. - The Gordon Growth Model is generally applied for established, stable companies that demonstrate a relatively stable dividend growth rate. Typically, these are mature firms in steady industries. However, it's worthy of note that no model is perfect, and each is subject to its set of limitations. While both models account for the present value of future dividends in their calculations, they neither account for extraordinary corporate events (like mergers and acquisitions) nor consider other substantial factors that might affect an investor's return (like share repurchases and issue of new shares). Hence, while understanding and comparing these models can be crucial for an investor, it's advisable to cross-validate the results of these models with other valuation methods, financial indicators, and market data for an accurate and comprehensive analysis of a firm's financial position.