Valuing stocks
A share is worth the present value of the cash it will pay its owners. Dividend discount and multiples models put this idea into practice.
The basic principle
Like any asset, a stock's value equals the present value of its expected future cash flows. For shareholders, those cash flows are dividends and the eventual sale price, which itself depends on dividends expected after the sale. So the value ultimately rests on all future dividends.
The constant growth model
If dividends grow at a constant rate g forever, the Gordon growth model gives the value: \(P_0 = \frac{D_1}{r - g}\), where \(D_1\) is next year's dividend and r is the required return. A stock expected to pay 2 dollars next year, growing 4% a year, with a required return of 9%, is worth 2 / (0.09 - 0.04) = 40 dollars.
P_0 = \frac{D_1}{r-g}Limits of the growth model
The Gordon model requires r > g and is very sensitive to inputs: if g in the example rose from 4% to 5%, the value would jump from 40 to 50 dollars. It suits mature, stable companies that pay dividends; it does not work for firms that pay no dividends or are growing very fast.
Required return and growth
Rearranging the model, the required return equals dividend yield plus growth: \(r = \frac{D_1}{P_0} + g\). A stock priced at 50 dollars with a 2-dollar expected dividend and 6% growth implies a required return of 4% + 6% = 10%. Growth can be estimated as g = retention ratio x return on equity.
Multi-stage models
Many companies grow fast for a few years before slowing. A two-stage model values dividends during the high-growth period individually, then values all later dividends with the constant growth formula at the point growth stabilises, discounting that 'terminal value' back to today.
Free cash flow valuation
For companies that pay little or no dividends, analysts value the entire firm by discounting expected free cash flows at the weighted average cost of capital, then subtract debt to find equity value. Discounted cash flow (DCF) models are widely used in investment banking and corporate finance.
Valuation multiples
Analysts often use multiples of comparable companies: price-to-earnings (P/E), price-to-book, price-to-sales, and enterprise value to EBITDA. If similar companies trade at 15 times earnings and a firm earns 3 dollars per share, a quick estimate is 45 dollars. Multiples are fast but assume the comparables are fairly valued.
Worked example
A company just paid a dividend of 1.50 dollars, which is expected to grow at 5% per year forever. Investors require 11%. Next year's dividend D1 = 1.50 x 1.05 = 1.575. Value = 1.575 / (0.11 - 0.05) = 26.25 dollars. If the market price is 22 dollars, the stock may be undervalued under these assumptions.
Key takeaways
A stock is worth the present value of expected future dividends. The Gordon growth model gives P0 = D1 / (r - g), requiring r > g, and is highly sensitive to inputs. Required return equals dividend yield plus growth. Multi-stage models handle changing growth with a terminal value. DCF models value firms by discounting free cash flow. Multiples such as P/E compare with similar companies but rely on fair comparables.
Flashcard
PV of expected future dividends
Check your understanding
A stock will pay a 3-dollar dividend next year, growing at 5% forever. Investors require 11%. What is its value?