Valuing a stock by discounting
How do you decide whether a share price is reasonable? Start from the most basic idea there is: a dollar today is worth more than a dollar tomorrow. Follow that idea and you arrive at the classic valuation formulas for bonds and stocks, and you also see why they are unreliable.
1. Discounting: converting future money into today's money
One dollar today is worth more than one dollar tomorrow, for two reasons: money received today can earn interest in the bank, and inflation erodes money over time. Discounting converts a future sum into its value today.
With discount rate r and n years:
2. What goes into the discount rate
- The risk-free rate: the interest available on the lowest-risk investment, such as bank deposits or government bonds.
- A risk premium: the extra return you should earn for bearing investment risk.
- Other factors: inflation, for example.
The higher the discount rate, the less future money is worth.
3. A simple case first: a perpetual bond
A perpetual bond in theory pays a fixed coupon D every year, forever, with no compounding. To value it, discount every year's D to today and add them up:
That is a geometric series, and the sum is clean:
An example. A perpetual bond with a face value of 100 and a 4.5% coupon pays D = 4.5 a year. Assume a discount rate of 3% risk-free plus a 1% risk premium plus 4% inflation, so r = 8%.
| Item | Value |
|---|---|
| Annual coupon D | 4.5 |
| Discount rate r | 3% + 1% + 4% = 8% |
| Price P = D / r | 4.5 ÷ 8% = 56.25 |
A bond with a face value of 100 is worth only 56 at that rate.
4. From bonds to stocks: the dividend discount model
Valuing a stock looks a lot like valuing a bond. A stock pays you in two ways: the dividends the company pays shareholders each year, and price appreciation when you sell.
The dividend discount model discounts every future year's dividend to today and adds them up, giving what the stock is worth now.
Constant dividends
Identical to the perpetual bond. Take a large bank stock with an expected dividend per share of D = 0.25 and a discount rate of r = 3% risk-free + 4% inflation + 1% risk = 8%:
Dividends growing at g every year
This is the Gordon growth model. The denominator shrinks from r to r − g, so a slightly higher growth rate lifts the value a lot. The same bank stock with a growth assumption of g = 4%:
Adding a 4% growth assumption doubles the value from 3.125 to 6.25.
5. What about companies that don't pay dividends: free cash flow
Companies don't necessarily pay all their profit out; some never pay a dividend and their shares rise anyway. The free-cash-flow model (FCFF) replaces the dividend D with free cash flow, the cash that could be distributed, and discounts each year's free cash flow. The company may reinvest that cash rather than pay it out, but it still belongs to shareholders.
Still the same bank stock, with average free cash flow per share of 1.6, g = 4%, r = 8%:
6. The limits: same company, 3 or 40?
Three models, one company, and the answers differ by more than ten times. The gap comes from two inputs that are hard to pin down:
- The discount rate r is hard to estimate, especially the risk premium and inflation.
- The growth rate g is hard too, whether for cash flow or dividends.
Discounting is on the complex side for a typical investor. Its value is not in producing a precise number but in showing you which few assumptions a valuation really rests on. Simpler methods come later.
Disclaimer · Educational material. The companies and numbers are worked examples to show the arithmetic, not investment advice. Investing involves risk; make your own decisions.