Gordon Growth Model

Equity Valuation 8 min readModule 2 of 3Save

What you'll learn

LOS 18.c
Calculate the value of a common stock using the Gordon growth model and explain the model’s underlying assumptions.
LOS 18.d
Calculate the value of non callable fixed rate perpetual preferred stock.
LOS 18.e
Describe strengths and limitations of the Gordon growth model and justify its selection to value a company’s common shares.
LOS 18.f
Calculate and interpret the implied growth rate of dividends using the Gordon growth model and current stock price.
LOS 18.g
Calculate and interpret the present value of growth opportunities (PVGO) and the component of the leading price to earnings ratio (P/E) related to PVGO.
LOS 18.h
Calculate and interpret the justified leading and trailing P/Es using the Gordon growth model.

The Gordon growth model (GGM) assumes that dividends increase at a constant rate indefinitely. The simplifying factor of the constant growth assumption is that the rate of growth can be expressed per period in the same way that the required return is expressed, allowing the expression to be condensed into a simple formula:

V_{0} = \frac{D _{0} ( 1 + g ) ^{1}}{( 1 + r ) ^{1}} + \frac{D _{0} ( 1 + g ) ^{2}}{( 1 + r ) ^{2}} + \frac{D _{0} ( 1 + g ) ^{3}}{( 1 + r ) ^{3}} + \dots + \frac{D _{0} ( 1 + g ) ^{n}}{( 1 + r ) ^{n}}

V_{0} = \frac{D _{0} ( 1 + g )}{r - g} = \frac{D _{1}}{r - g}

Symbol	Meaning
V₀	Fundamental value
D₀	Dividend just paid
D₁	Dividends expected to be received at end of Year 1
r	Required return on equity
g	Dividend growth rate

The model assumes that:

The firm expects to pay a dividend, $D_{1}$ , in one year.
Dividends grow indefinitely at a constant rate, g (which may be less than zero).
The growth rate, g, is less than the required return, r.

A firm’s growth rate projections can be compared to the growth rate of the economy to determine if it can continue indefinitely. It is unrealistic to assume that any firm can continue to grow indefinitely at a rate higher than the long term growth rate in real gross domestic product (GDP) plus the long term inflation rate. In general, a perpetual dividend growth rate forecast above 5% is suspect.

Worked example: Calculating value with the Gordon growth model

DownUnder Financial recently paid a dividend of 1.80 Australian dollars (A$). An analyst has examined the financial statements and historical dividend policy of DownUnder and expects that the firm’s dividend rate will grow at a constant rate of 3.5% indefinitely. The analyst also determines DownUnder’s beta is 1.5, the risk free rate is 4%, and the expected return on the market portfolio is 8%.

Calculate the current value of DownUnder’s shares.

Solution

First use the capital asset pricing model (CAPM) to estimate DownUnder’s required return:

r = 4% + [1.5 (8% - 4%)] = 10%

Then use the Gordon growth model to estimate share value:

V_{0} = \frac{A $1.80 \times 1.035}{0.10 - 0.035} = \frac{A $1.863}{0.10 - 0.035} = A $28.66

When companies have share repurchase programs, an analyst can focus on total payout (i.e., dividends plus repurchases) and use that in their valuation model. Alternatively, dividend discount models focusing on cash dividends can also be used, after adjusting for the number of shares outstanding (taking share repurchases into account).

A firm that has no additional opportunities to earn returns in excess of the required rate of return should distribute all of its earnings to shareholders in the form of dividends. Under this assumption the growth rate would be zero, and the current value of the firm would be equal to the current dividend divided by the required rate of return. This is exactly the same approach used to determine the value of fixed rate perpetual preferred shares.

value of perpetual preferred shares = \frac{D _{p}}{r _{p}}

Symbol	Meaning
Dₚ	Preferred dividend, which is assumed not to grow
rₚ	Cost of preferred equity

Worked example: Calculating the value of fixed rate perpetual preferred stock

United Publishing has a fixed rate perpetual preferred stock outstanding with a dividend of 6% (based on an issue at par of £100). If the investors’ required rate of return for holding these shares is 9.5%, calculate the current value of these shares.

Solution

Dividends are not growing because the preferred dividend is based on a fixed rate of 6.0% on a stated par value of £100, so this is comparable to DDM with a fixed dividend in perpetuity.

D = 0.06 \times £ 100.00 = £ 6.00

value of preferred shares = \frac{£ 6.00}{0.095} = £ 63.16

The Gordon growth model (GGM) has a number of characteristics that make it useful and appropriate for many applications. The model:

Is applicable to stable, mature, dividend paying firms.
Is appropriate for valuing market indices.
Is easily communicated and explained because of its straightforward approach.
Can be used to determine price implied growth rates, required rates of return, and value of growth opportunities.
Can be used to supplement other, more complex valuation methods.

There are also some characteristics that limit the applications of the GGM:

Valuations are very sensitive to estimates of growth rates and required rates of return, both of which are difficult to estimate with precision.
The model cannot be easily applied to non dividend paying stocks.
Unpredictable growth patterns of some firms would make using the model difficult and the resulting valuations unreliable.

The Gordon growth model includes four variables, so if we know any three of them, we can solve for the fourth. In practice, we can typically observe the price and current dividend for a publicly traded stock. Consequently, we are usually interested in either backing out the implied required return, using an assumed growth rate, or the implied growth rate, using an assumed required return.

In this example, we calculate the implied growth rate using an estimated return.

Worked example: Calculating the implied growth rate using the Gordon growth model

Suppose that the current price and most recent annual dividend for Aurora Mining (AM) are $24.25 and $1.10, respectively. If the required return on Aurora is 8.5%, what is the implied growth rate?

Solution

We can set up the Gordon growth model in its standard form using the information we know:

P_{0} = \frac{D _{0} ( 1 + g )}{r - g} = \frac{1.10 ( 1 + g )}{0.085 - g} = $24.25

Rearranging the terms gives us:

1.10 + 1.10 g = 2.06125 - 24.25 g

25.35 g = 0.96125

g = 0.0379

So, assuming that our estimated required return is on target, the implied growth rate for Aurora Mining’s dividends is 3.8%.

A firm that has additional opportunities to earn returns in excess of the required rate of return would benefit from retaining earnings and investing in those growth opportunities rather than paying out dividends. The fundamental value then represents not only the present value of the future dividends (on a non growth basis) but also the present value of the growth opportunities (PVGO):

V_{0} = \frac{E _{1}}{r} + PVGO

Symbol	Meaning
E₁	Earnings at t = 1
r	Required return on equity

This means the value of a firm’s equity has two components:

The value of its assets in place ( $E_{1}$ /r), which is the present value of a perpetual cash flow of $E_{1}$ .
The present value of its future investment opportunities (PVGO).

A substantial portion of the value of growth companies is in their PVGO. In contrast, companies in slow growth industries (e.g., utilities) have low PVGO, and most of their value comes from their assets in place.

Worked example: Calculating PVGO

Reliable, Inc.’s shares trade at 60.00 Swiss francs (Sf) with expected earnings of Sf 5.00 per share and a required return of 10%. Suppose that the shares are properly priced, so price is equal to fundamental value. Calculate the PVGO and the portion of the leading P/E related to PVGO.

Solution

The price to earnings (P/E) ratio is the most commonly used relative valuation indicator. An analyst derives a justified P/E based on the firm’s fundamentals. The two most common forms are the leading P/E, which is based on the earnings forecast for the next period, and the trailing P/E, which is based on the earnings for the previous period.

Both of these can be derived from the DDM:

Worked example: Calculating justified leading and trailing P/E

Alliance, Inc., is currently selling for $16.00 on current earnings of $3.00 and a current dividend of $1.50. Dividends are expected to grow at 3.5% per year indefinitely. The risk free rate is 4%, the market equity risk premium is 6%, and Alliance’s beta is estimated to be 1.1. Calculate the justified leading and trailing P/E ratios of Alliance, Inc.

Solution

Next we discuss multistage growth models, which accommodate more realistic growth rate assumptions.

Finished this module?

Track your progress across all 171 modules.

Test yourself on Reading 18CFA-style practice questions