Stock Valuation in 27 Minutes
A share is worth the present value of the dividends it will pay you. When dividends stay flat, the stock is a perpetuity; when they grow at a steady rate, you use the Gordon growth model. Flip the same formula around and you get the return investors require.
Stock valuation (dividend discount model) explained simply
The dividend discount model values a share as the present value of its future dividends. With steady growth, use the Gordon growth model: P₀ = D₁ ÷ (r − g). In the example, 2.10 ÷ (0.10 − 0.05) gives $42.00.
What this stock valuation lesson covers
- Why a stock's price is the present value of its future dividends
- How to value a zero-growth stock as a simple perpetuity
- How to use the Gordon growth model, and why it needs D₁, not D₀
- How to back out the required return from price and growth
- Why the growth rate must be below the required return
Stock valuation formulas, explained
- D
- Constant annual dividend
- r
- Required rate of return
- D₀
- Dividend just paid
- D₁
- Next year's dividend
- g
- Constant dividend growth rate, below r
- D₁ ÷ P₀
- Dividend yield
- g
- Capital gains yield
How to value a stock step by step (worked example)
A company just paid a dividend of $2.00. Dividends grow at 5% a year forever and investors require a 10% return. What is the stock worth today?
- Next dividend: D₁ = 2.00 × 1.05 = 2.10
- Apply Gordon: P₀ = 2.10 ÷ (0.10 − 0.05)
- P₀ = 2.10 ÷ 0.05 = 42.00
- Check: dividend yield 2.10 ÷ 42 = 5%, plus 5% growth = 10% required return
Answer: The stock is worth $42.00.
Zero growth vs constant growth vs nonconstant growth
| Zero growth | Constant growth (Gordon) | Nonconstant growth | |
|---|---|---|---|
| Formula | P₀ = D ÷ r | P₀ = D₁ ÷ (r − g) | Discount early dividends one by one, then Gordon |
| Use when | Dividends stay flat | Dividends grow at a steady rate | Fast growth first, then steady |
| Typical example | Preferred shares | A mature company | A growing company that will slow down |
What are you really buying with a share? David's take
In this model a share is a machine that makes money: you pay $42 today for a stream of dividends that grows 5% a year. My line is: don't waste your time making money; use your time making machines that make money. The Gordon model is really a price tag for a money machine. The questions are the same for a stock, a business or an app: how much cash does the machine throw off, and how long will it keep running?
From David's concept: Machines That Make Money. This is David's opinion, alongside the standard textbook answer above.
Harder stock valuation questions
What happens to the price if growth is 6% instead of 5%?
D₁ becomes 2.12 and the price becomes 2.12 ÷ (0.10 − 0.06) = $53.00. One extra point of growth adds about 26% to the value, because the gap between r and g shrinks.
If the stock trades at $35, what growth is the market expecting?
Solve 35 = 2(1 + g) ÷ (0.10 − g). That gives g ≈ 4.05%. Working backwards from the price is often more useful than forecasting growth yourself.
Can you use this model for a company that pays no dividends?
Not directly. Use free cash flow (a DCF) or earnings multiples instead, or assume when dividends will start and value them from then.
Common stock valuation questions
What is the formula for stock valuation?
The basic formula says price equals the present value of all future dividends. With constant growth this simplifies to the Gordon growth model, P₀ = D₁ ÷ (r − g). For a stock with a flat dividend it becomes P₀ = D ÷ r, the perpetuity formula.
What is the difference between D₀ and D₁?
D₀ is the dividend that was just paid, so the buyer today does not get it. D₁ is the next dividend, one year away. The Gordon model needs D₁, so if a question gives you D₀, multiply it by (1 + g) first. Mixing them up is a classic exam mistake.
Why must g be less than r in the Gordon growth model?
If dividends grew as fast as or faster than the discount rate, each future dividend would be worth the same or more in today's money, and the total would never settle to a finite price. The formula only works when r is greater than g.
How do you value a stock that pays no dividends?
You can forecast when dividends will start and discount them, or switch to free cash flow or multiples such as P/E. In practice, many growth companies are valued with a discounted cash flow model of the whole firm rather than with dividends.