Welcome to Discounted Dividend Valuation!

Welcome to one of the most fundamental chapters in the Equity Investments section of your CFA Level II journey. While there are many complex ways to value a company, Discounted Dividend Valuation (DDM) gets back to basics: A stock is worth the present value of all the cash it will ever give back to you as an investor. If you can master the art of valuing these cash flows, you’ve mastered the core of equity analysis. Don't worry if the formulas look intimidating at first—we will break them down into simple, logical steps!

1. The Basics: What is Intrinsic Value?

At its heart, the Intrinsic Value of a stock is the "fair" price based on its future dividends. We use the Dividend Discount Model (DDM) to calculate this.

The general formula is:
\( V_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1+r)^t} \)

Where:
- \( V_0 \) = Current value of the stock.
- \( D_t \) = Dividend expected at time \( t \).
- \( r \) = Required rate of return (the "hurdle rate").

Why Dividends?

Some argue that dividends are the only "real" return an investor gets because capital gains only happen when you sell the stock. Dividends are the cash you put in your pocket while you hold it.

Quick Review: Use DDM when the company has a clear dividend history, a policy linked to profitability, and you are taking a minority shareholder's perspective (since you can't force the company to pay you more cash).

2. The Gordon Growth Model (GGM)

The Gordon Growth Model is the simplest version of the DDM. It assumes the company is in a "steady state," meaning it will grow its dividends at a constant rate (g) forever.

The Formula:
\( V_0 = \frac{D_1}{r - g} \)

Note: \( D_1 \) is the dividend for next year. If you are given the current dividend (\( D_0 \)), you must calculate \( D_1 \) by doing \( D_0 \times (1+g) \).

Key Assumptions for GGM:
  • The required return (\( r \)) must be greater than the growth rate (\( g \)). If \( g \) is higher than \( r \), the math breaks (and the stock would be worth "infinity")!
  • The growth rate (\( g \)) is expected to be constant forever. This is usually only realistic for mature, stable companies like utilities.

Common Mistake to Avoid: Don't mix up \( D_0 \) and \( D_1 \). In the exam, read carefully. If they say "the dividend just paid," that is \( D_0 \). If they say "the dividend expected next year," that is \( D_1 \).

Key Takeaway: The GGM is a "quick and dirty" way to value a stable company. It is very sensitive to the inputs—small changes in \( r \) or \( g \) lead to huge changes in value!

3. Multistage Dividend Discount Models

Most companies don't grow at a constant rate forever. They might grow very fast for a few years and then slow down as they become mature. This is where Multistage Models come in.

A. The Two-Stage Model

This model assumes a period of high growth (Stage 1) followed by a sudden shift to a stable, long-term growth rate (Stage 2).

Step-by-Step Process:
1. Calculate the dividends for each year of the high-growth period.
2. Calculate the Terminal Value at the end of the high-growth period using the GGM.
3. Discount all those dividends and the Terminal Value back to today (\( t=0 \)) using the required rate of return (\( r \)).

B. The H-Model

In real life, growth doesn't usually "drop off a cliff" from 20% to 5%. It slows down gradually. The H-Model captures this "linear" decline.

The Formula:
\( V_0 = \frac{D_0(1+g_L)}{(r-g_L)} + \frac{D_0H(g_S-g_L)}{(r-g_L)} \)

Where:
- \( g_S \) = Short-term high growth rate.
- \( g_L \) = Long-term stable growth rate.
- \( H \) = The half-life of the high-growth period (e.g., if growth declines over 10 years, \( H = 5 \)).

Analogy: Think of the H-Model like a runner. Part of the value comes from their steady jogging pace (long-term growth), and the other part is the "bonus" value from their initial sprint (short-term growth) as they gradually slow down to a jog.

Key Takeaway: Use the Two-Stage model for sudden shifts and the H-Model for companies whose growth is slowing down smoothly over time.

4. Estimating the Growth Rate (g)

Where does that "g" come from? We don't just guess it! We use the Sustainable Growth Rate formula.

The Formula:
\( g = b \times ROE \)

Where:
- \( b \) = Retention Ratio (the % of earnings the company keeps rather than paying out).
- ROE = Return on Equity.

Did you know?

The retention ratio (\( b \)) is simply \( 1 - \text{Dividend Payout Ratio} \). If a company pays out 40% of its earnings as dividends, it retains 60% (\( b = 0.60 \)).

The PRAT Model

To go deeper, we can break down ROE using the DuPont method. Growth is driven by four factors (PRAT):
1. Profit Margin (Profitability)
2. Retention Rate (Earnings reinvested)
3. Asset Turnover (Efficiency)
4. Teverage/Financial Leverage (Debt usage)

Quick Review: If a company wants to grow faster, it must either become more profitable, keep more of its earnings, use its assets more efficiently, or take on more debt.

5. Terminal Value

In multistage models, we can't forecast dividends forever. We forecast for a "horizon" (say 5 years) and then assume the company is sold or enters a steady state. This value at the end of the forecast is the Terminal Value.

You can estimate Terminal Value using two methods:
1. Gordon Growth Method: Assume dividends grow at a constant rate \( g \) from that point on.
2. Multiples Approach: Multiply the future earnings or book value by a P/E or P/B ratio.

Common Mistake: When calculating the Terminal Value (\( TV_n \)) using GGM, make sure you use the dividend for the following year (\( D_{n+1} \)). For example, if your high-growth period is 3 years, the Terminal Value at year 3 is \( TV_3 = \frac{D_4}{r-g} \).

6. Summary of Key Concepts

Don't worry if this seems tricky at first! Equity valuation is as much an art as it is a science. Here is the "cheat sheet" of what you need to remember:

  • DDM values a stock based on the present value of future dividends.
  • GGM is for stable growth: \( V_0 = \frac{D_1}{r-g} \).
  • Multistage Models handle changing growth rates (sprints vs. jogs).
  • H-Model specifically accounts for a linear decline in growth over time.
  • Sustainable Growth (g) depends on how much the company keeps (\( b \)) and how well they invest it (\( ROE \)).
  • Always be careful with timing (don't discount \( D_1 \) as if it's happening today!).

Final Pro Tip: When working through long multistage problems, draw a timeline. It helps you visualize when each dividend occurs and ensures you discount every cash flow back to the correct year. Good luck!