Dividend Discount Model
- [b] Compute and explain the valuation of a common stock using the dividend discount model (DDM) for both single and multiple holding periods.
- 00:08 – Introduction to Present Value Models
- 00:28 – One-Year Holding Period DDM
- 01:22 – Multi-Year Holding Period DDM
- 01:36 – Example: 3-Year Holding Period Calculation
- 03:27 – The Most Fundamental Form of the DDM
Introduction to Present Value Models
Present Value Models, also known as Discounted Cash Flow (DCF) Models, are used to estimate the intrinsic value of a security. The core principle is that the value of an asset today is equal to the present value of all the future benefits it is expected to generate.
Intrinsic Value = Present Value (PV) of expected future benefits
The Dividend Discount Model (DDM)
The Dividend Discount Model (DDM) is a specific type of present value model where the “future benefits” are defined as the expected future dividends that will be distributed to shareholders.
The Holding Period Dividend Discount Model
The DDM can be applied to a specific investment horizon or holding period.
One-Year Holding Period
For an investor with a one-year holding period, the intrinsic value of the stock today (\(V_0\)) is the sum of the present value of the expected dividend at the end of the year (\(D_1\)) and the present value of the expected selling price of the stock at the end of the year (\(P_1\)). This expected selling price is also known as the Terminal Value.
The formula is:
\[ V_0 = \frac{D_1}{(1+r)^1} + \frac{P_1}{(1+r)^1} \]
Where:
- \(V_0\) = Intrinsic value of the stock today
- \(D_1\) = Expected dividend per share at the end of year 1
- \(P_1\) = Expected stock price per share at the end of year 1 (Terminal Value)
- \(r\) = Required rate of return on the stock
Example: One-Year Holding Period
Assume the following:
- Expected Dividend (\(D_1\)): $2.00
- Expected Stock Price in one year (\(P_1\)): $53.00
- Required Rate of Return (\(r\)): 8%
The intrinsic value is calculated as:
\[ V_0 = \frac{\$2.00}{(1+0.08)} + \frac{\$53.00}{(1+0.08)} = \frac{\$55.00}{1.08} = \$50.93 \]
The intrinsic value of the stock today is $50.93.
Multi-Year Holding Period
The model can be extended to any number of years (\(n\)). The intrinsic value is the sum of the present values of all dividends received during the holding period, plus the present value of the terminal value (\(P_n\)) at the end of the period.
The general formula for an n-year holding period is:
\[ V_0 = \sum_{t=1}^{n} \frac{D_t}{(1+r)^t} + \frac{P_n}{(1+r)^n} \]
This can be expanded as:
\[ V_0 = \frac{D_1}{(1+r)^1} + \frac{D_2}{(1+r)^2} + \dots + \frac{D_n}{(1+r)^n} + \frac{P_n}{(1+r)^n} \]
Example: 3-Year Holding Period Calculation
Problem: XYZ stock recently paid a dividend of $5 (\(D_0\)). For the next 3 years, the dividend is expected to grow at 4% per year. The stock price is expected to be $122 at the end of 3 years. The required rate of return is 9%. Calculate the intrinsic value of the stock today.
Step 1: Calculate the expected future dividends.
- Dividend at Year 1 (\(D_1\)): \(D_0 \times (1+g)^1 = \$5.00 \times (1.04)^1 = \$5.20\)
- Dividend at Year 2 (\(D_2\)): \(D_0 \times (1+g)^2 = \$5.00 \times (1.04)^2 = \$5.41\)
- Dividend at Year 3 (\(D_3\)): \(D_0 \times (1+g)^3 = \$5.00 \times (1.04)^3 = \$5.62\)
Step 2: Identify other variables.
- Terminal Value (\(P_3\)): $122
- Required Rate of Return (\(r\)): 9% or 0.09
Step 3: Calculate the present value of each cash flow.
The valuation formula is:
\[ V_0 = \frac{\$5.20}{(1.09)^1} + \frac{\$5.41}{(1.09)^2} + \frac{\$5.62}{(1.09)^3} + \frac{\$122}{(1.09)^3} \]
Year (t) Cash Flow Type Amount (CFt) PV Calculation Present Value 1 Dividend (D1) $5.20 \( \frac{5.20}{(1.09)^1} \) $4.77 2 Dividend (D2) $5.41 \( \frac{5.41}{(1.09)^2} \) $4.55 3 Dividend (D3) $5.62 \( \frac{5.62}{(1.09)^3} \) $4.34 3 Terminal Value (P3) $122.00 \( \frac{122.00}{(1.09)^3} \) $94.21 Total Intrinsic Value (V0) $107.87
The intrinsic value of XYZ stock today, based on a 3-year holding period, is $107.87.
The Most Fundamental Form of the DDM
Theoretically, the holding period for a stock could be infinite. The most fundamental version of the DDM states that a stock’s value is the present value of all of its future dividends into perpetuity.
The formula is:
\[ V_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1+r)^t} \]
Forecasting individual dividends into infinity is impossible. To make this model practical, we must make a simplifying assumption about how dividends grow in the long term. A common assumption is that after a certain point, dividends will grow at a constant rate (\(g\)) forever.
This assumption is the foundation of the Gordon Growth Model, a crucial variation of the DDM.
Summary
- The Dividend Discount Model (DDM) values a stock as the present value of its expected future dividends.
- For a finite holding period, the stock’s value is the sum of the present values of the dividends during the period and the present value of the expected selling price (terminal value) at the end of the period.
- The formula for a holding period model is: \( V_0 = \sum \text{PV(Dividends)} + \text{PV(Terminal Value)} \).
- The most fundamental DDM assumes an infinite stream of dividends. To make this practical, we must assume a constant long-term dividend growth rate, which leads to models like the Gordon Growth Model.
