# The Gordon Growth Model: The Dividend Discount Model

INTRODUCTION

The Gordon Growth Model also known as the Dividend Discount Model includes a methodology for computing the intrinsic value of stocks. It equates present value of the stock to the future value of dividends.

FORMULA & EXPLANATION

There are two basic forms of this model namely:

• Stable Model

Value of stock = D1 / (k-g)

Whereby D1 = Expected dividend per share for the next year k = Required rate of return (can be estimated using the CAPM or Dividend Growth Model) g = Expected dividend growth rate

• Multi-Stage Growth Model

In cases where dividends are not expected to grow at a constant rate, the investor must evaluate every year’s dividend separately. However, this model does assume that dividend growth

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Assuming the rate of return on the stock of Company ‘A’ is 15% and the current share price of $20 per share, the intrinsic value of the stock can be shown as:

D1 / (k-g) = 2 / (0.15 – 0.10) = 2/0.05 = $40

As per the model, the worth of the stock is $40 but is currently traded at $20 hence making it undervalued.

Multi-stage Growth Model:

ABD Communications is a fast-growing IT start-up and dividends for the next 5 years are projected to grow at 25%, 20%, 15%, 10% and 5% respectively. Subsequently from the 6th year, dividends will grow at a constant rate of 5%. If the current market price is $46 and the most recent dividend was $2 per share with a cost of equity is 10%, is it considered a suitable investment?

The dividends for the high growth phase (First 5 years) can be summarised as below:

Year Growth Rate Dividend per share Formula

0

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Dividend per share for the first 5 years has to be discounted back to t=0 (present value) as follows:

Year Growth Rate Dividend per share PV at t=0 Formula

1 25% 2.50 2.27 2.50 / (1 + 0.10)

2 20% 3.00 2.48 3.00 / (1 + 0.10)2

3 15% 3.45 2.60 3.45 / (1 + 0.10)3

4 10% 3.80 2.60 3.80 / (1 + 0.10)4

5 5% 4.00 2.49 4.00 / (1 + 0.10)$ 12.44

Using the Gordon Growth model, one can arrive at the PV of perpetual dividends from the 6th year (start of the stable phase). This is called as the Terminal Value.

In this case, Terminal Value = $4.20 (0.10 – 0.05) = $84

Since the PV is computed above is at the end of the 5th year (start of the stable growth phase), it shall be discounted back 5 years as:

PV at t = 0,

84 / (1+10%) ^ 5 = $52.17

Thus intrinsic value of the stock = PV of dividend in high-growth phase + PV of Terminal value = $12.44 + $52.17 = $64.61

Since the current stock market price is $64.61 and the current market price is $46, the investment should be retained.

USES

1. This model is useful to determine the relationship between Growth rates, Discount rates and Valuation.

2. There is a clear relation between Valuation and