Lesson 7.2: Discounted Dividend Valuation

Introduction

Welcome to Lesson 7.2 of the CFA Level II course on Equity Investments. In this lesson, we will explore the concept of Discounted Dividend Valuation (DDM), which is a critical method for valuing a company's stock based on its future dividend payments. Understanding how to apply the single-stage, two-stage, and multistage models will help you evaluate investments effectively and make informed decisions.

Learning Objectives

By the end of this lesson, you will be able to:

• Understand the concepts of single-stage, two-stage, and multistage dividend discount models.
• Apply the Gordon Growth Model and assess sustainable growth rates.
• Value a stock using both single and multistage dividend models.
• Estimate growth based on fundamental analysis and apply it appropriately.
• Explain the main ideas and terminology related to Discounted Dividend Valuation.

Understanding the Dividend Discount Model (DDM)

The Dividend Discount Model is a method used to determine the value of a company's shares. The underlying principle is that the value of a stock is equal to the present value of all future dividends expected to be paid to shareholders. This concept relies heavily on the time value of money, which states that a dollar today is worth more than a dollar in the future due to its potential earning capacity.

The Formula

The general formula for the Dividend Discount Model is:

$$

$P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1 + k)^t}$

$$

where:

• $P_0$ = current price of the stock
• $D_t$ = dividend expected to be paid in year $t$
• $k$ = required rate of return
• $t$ = time period (number of years into the future)

Single-Stage Dividend Discount Model

This model is the simplest form of DDM and assumes that dividends will grow at a constant rate indefinitely. It can be expressed as:

$$

$P_0 = \frac{D_1}{k - g}$

$$

where:

• $D_1$ = expected dividend in the next year
• $g$ = constant growth rate of dividends

Worked Example: Applying the Single-Stage DDM

Suppose a company is expected to pay a dividend of $D_1 = 5$ dollars next year, and the dividends are expected to grow at a constant rate of $g = 5\%$ per year. If the required rate of return is $k = 10\%$, the stock price can be calculated as follows:

1. Identify values:

• $D_1 = 5$
• $g = 0.05$
• $k = 0.10$

1. Use the formula:

$$

P_0 = $\frac{5}{0.10 - 0.05}$ = $\frac{5}{0.05}$ = 100

$$

Thus, the calculated stock price $P_0$ is $100$ dollars.

Two-Stage Dividend Discount Model

The Two-Stage DDM allows for two distinct growth rates: an initial high-growth phase followed by a stable growth phase. This model is useful when companies are expected to grow at an accelerated rate for a certain number of years before settling into a stable growth phase.

Formula

The value of the stock in the two-stage model can be expressed as:

$$

P_0 = $\sum_{t=1}$^{N} $\frac{D_t}{(1 + k)^t}$ + $\frac{P_N}{(1 + k)^N}$

$$

where $P_N$ is the sale price of the stock calculated using the Gordon Growth Model at the end of the high growth phase.

Worked Example: Applying the Two-Stage DDM

Let's assume a company will pay dividends for the next five years as follows: $D_1 = 5$, $D_2 = 6$, $D_3 = 7$, $D_4 = 8$, $D_5 = 9$. After year five, the dividends are expected to grow at a stable rate of $g = 4\%$. The required rate of return is $k = 10\%$.

1. Calculate the present value of the first five dividends:

• For $D_1 = 5$: $\frac{5}{(1.10)^1}$ = 4.5455
• For $D_2 = 6$: $\frac{6}{(1.10)^2}$ = 4.9587
• For $D_3 = 7$: $\frac{7}{(1.10)^3}$ = 5.2536
• For $D_4 = 8$: $\frac{8}{(1.10)^4}$ = 5.6647
• For $D_5 = 9$: $\frac{9}{(1.10)^5}$ = 6.2217

Summing these values:

$$\text{PV of dividends} = 4.5455 + 4.9587 + 5.2536 + 5.6647 + 6.2217 = 26.6442$$

1. Calculate $P_N$ for year 5:

• First, calculate $D_6 = D_5 \times (1 + g) = 9 \times (1 + 0.04) = 9.36$.
• Then, calculate the terminal value:

$$

P_5 = $\frac{D_6}{k - g}$ = $\frac{9.36}{0.10 - 0.04}$ = $\frac{9.36}{0.06}$ = 156.00

$$

• Discount $P_5$ back to year 0:

$$\frac{156.00}{(1.10)^5} = \frac{156.00}{1.61051} = 96.79$$

1. Total present value:

$$P_0 = 26.6442 + 96.79 = 123.43$$

Thus, the calculated stock price $P_0$ in this two-stage DDM is $123.43$ dollars.

Multistage Dividend Discount Model

The Multistage DDM can accommodate companies that are expected to experience several phases of growth. Each stage can represent different growth rates and time periods until reaching a stable growth rate.

General Structure

The general formula for the multistage model can be complex, depending on the number of growth stages, but it typically follows the structure:

$$

P_0 = $\sum_{t=1}$^{N_1} $\frac{D_t}{(1 + k)^t}$ + $\sum_{t=N_1+1}$^{N_2} $\frac{D_t}{(1 + k)^t}$ + $\ldots$ + $\frac{P_N}{(1 + k)^N}$

$$

where $N_1$ and $N_2$ are the time durations for different growth phases.

Worked Example: Application of the Multistage DDM

Consider a company that will have a growth phase for three years with dividend payments of $D_1 = 5$, $D_2 = 6$, $D_3 = 7$ (at a growth rate of $g_1 = 10\%$), followed by a stable growth period with a growth rate of $g_2 = 4\%$. The required rate of return is $k = 10\%$.

1. Calculate PV for the first three dividends:

• For $D_1$: $\frac{5}{(1.10)^1} = 4.5455$
• For $D_2$: $\frac{6}{(1.10)^2} = 4.9587$
• For $D_3$: $\frac{7}{(1.10)^3} = 5.2536$

Summing these values:

$$\text{PV of first three dividends} = 4.5455 + 4.9587 + 5.2536 = 14.7578$$

1. Calculate $D_4$: $D_4 = D_3 \times (1 + g_2) = 7 \times (1 + 0.04) = 7.28$.
2. Calculate terminal value using D_4:

• Terminal value:

$$

P_3 = $\frac{D_4}{k - g_2}$ = $\frac{7.28}{0.10 - 0.04}$ = $\frac{7.28}{0.06}$ = 121.3333

$$

• Discount $P_3$ back to year 0:

$$\frac{121.3333}{(1.10)^3} = \frac{121.3333}{1.331} \approx 91.08$$

1. Total stock price:

$$P_0 = 14.7578 + 91.08 = 105.84$$

Therefore, the calculated stock price $P_0$ in this multistage DDM example is approximately $105.84$ dollars.

Conclusion

In this lesson, we have explored the Discounted Dividend Valuation methods, including the single-stage, two-stage, and multistage dividend discount models. Understanding and applying these models are essential for valuing equity investments based on projected future dividends. By grasping these concepts, you will be better equipped to assess the value of stocks and make informed investment decisions.

Study Notes

• The Discounted Dividend Model values a stock based on the present value of future dividends.
• The formula for single-stage DDM is $P_0 = \frac{D_1}{k - g}$.
• Two-stage DDM allows for changing growth rates, combining two formulas into one valuation.
• Multistage DDM can accommodate several growth phases and rates.
• The Gordon Growth Model is a special case of the DDM applicable when dividends grow at a constant rate.
• Understanding and correctly applying these models requires attention to estimating growth rates based on fundamental analysis.