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.
What you will learn
- 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
The formulas
- 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
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.
Common 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.