Discount rates and the CAPM
The discount rate is the rate used to convert future cash flows into today's value, and it is arguably the single most influential input in any valuation. The Capital Asset Pricing Model, or CAPM, is the most widely used method for estimating the part of it that applies to shareholders, called the cost of equity. It is simple to state and difficult to apply well.
What a discount rate represents
A discount rate has two jobs. It compensates for the time value of money, since cash received later is worth less than cash received now. And it compensates for risk, since forecast cash flows may not materialize. A riskier cash flow deserves a higher discount rate and therefore a lower present value.
The discount rate is not "the return I would like to earn". It reflects how risky the cash flows are, and what investors could earn on other investments with similar risk. The same company should be discounted at the same rate whatever one hopes to make.
The CAPM formula
Cost of equity = risk-free rate + beta x equity risk premium
The three inputs:
- Risk-free rate. The return on an investment with no default risk, usually the yield on US Treasury securities of a maturity that matches the cash flows being valued. Ten-year Treasuries are a common choice. See bond yields and prices.
- Beta. How sensitive the stock's returns have been to the broad market's. A beta of 1 means it moves with the market on average. See beta explained.
- Equity risk premium. The additional return investors require for holding the stock market rather than risk-free securities. See the equity risk premium.
The logic: investors can diversify away company-specific risk, so they are paid only for the risk that cannot be diversified, which is exposure to the market as a whole. Beta measures that exposure.
Example (illustrative numbers)
Assume a risk-free rate of 4% and an equity risk premium of 5%.
| Beta | Calculation | Cost of equity |
|---|---|---|
| 0.8 | 4% + 0.8 x 5% | 8.0% |
| 1.0 | 4% + 1.0 x 5% | 9.0% |
| 1.2 | 4% + 1.2 x 5% | 10.0% |
| 1.5 | 4% + 1.5 x 5% | 11.5% |
A stock with a higher beta is discounted more heavily, so its cash flows are worth less today, all else equal.
From cost of equity to WACC
When valuing the whole business, a DCF usually discounts at the weighted average cost of capital, which blends the cost of equity with the after-tax cost of debt in proportion to how the firm is financed. See WACC. The rule of consistency is simple:
- Cash flows to the whole firm go with the WACC.
- Cash flows to shareholders only (such as dividends, or free cash flow after debt payments) go with the cost of equity.
Why the discount rate matters so much
Consider an illustrative perpetuity: cash flow of $100 next year growing 3% a year forever. Its value is 100 / (r - 3%).
| Discount rate | Value |
|---|---|
| 8% | 2,000 |
| 10% | 1,429 |
| 12% | 1,111 |
Moving the rate from 8% to 12% reduces the value by about 44%. This is the same sensitivity that makes terminal value so influential in a DCF.
Limits of the CAPM
- It is a model with one factor. Academic research has found that characteristics beyond market beta, such as company size, valuation level and profitability, are associated with differences in returns. Multi-factor models try to capture these.
- Beta is an estimate. It depends on the index, the time window and the return frequency, and it changes over time.
- The premium is a choice. Reasonable analysts can use equity risk premiums that differ by a percentage point or more.
- The risk-free rate is not constant. It moves with interest rates, so the cost of equity moves with it.
- Precision is an illusion. A cost of equity quoted to two decimal places implies certainty that the inputs cannot offer.
How to use it sensibly
Rules of thumb:
- Calculate a range, not a single number. Try plus or minus one percentage point and see how much the value changes.
- Keep the inputs consistent: same currency, same time horizon, same date.
- Sanity-check against the business. A stable, low-debt consumer business and a highly leveraged, cyclical one should not end up with the same rate.
- Do not tweak the discount rate to reach a desired value. That defeats the purpose of the model.
Where to see it on StocksXray
StocksXray's data includes Damodaran datasets for betas and the equity risk premium, the two market-risk inputs to a CAPM calculation. Fair value is presented as a range because typical model error is around 40%. The methodology page has the full description.
Key takeaways
- The discount rate converts future cash into present value and reflects both time and risk.
- CAPM: cost of equity equals the risk-free rate plus beta times the equity risk premium.
- Match the rate to the cash flows: WACC for the firm, cost of equity for shareholders.
- Inputs are estimates, so run a range and treat results as approximate.
Related reading
Educational only, not financial advice. Examples use illustrative numbers.