Discount rates, a fundamental concept in finance and investing, is summarized by the old adage: a dollar today is worth more than a dollar tomorrow. Yet, discount rates are consequential, affecting income, wealth, and the value of all assets.
Discount Rate on Consumption
While prices of goods and services can go up or down in a short time period, they tend to rise (at an average of around 3%) over a long enough time frame. To measure this, governments created Consumer Price Index (CPI), which measures the price of a selection of goods and services that reflects what consumers purchase. CPI growth is known as inflation, which is a discount rate on income and wealth. If income and wealth is increasing at a slower rate than inflation, they are losing purchasing power in real terms.
Discount Rate on Investments
However, the return of assets are typically measured in nominal returns, excluding inflation. This is because in exchange for investing, the returns typically must be high enough to compensate for inflation. And so, assets are discounted by opportunity cost, as investors expect returns for taking on the risk of owning an asset.
At no risk, investors earn a return at the risk-free rate, which is typically estimated using mature market government bonds. Beyond the risk-free rate, investors are compensated with greater expected return for taking on greater expected risk. To note, investors are only rewarded for taking on undiversifiable or systematic risk, as diversifiable risk can be eliminated through diversification and sound portfolio management. This relationship is illustrated by the below equation, where 
Furthermore, 
Components of a Discount Rate
Risk Free Rate
Risk in finance is variance of actual returns from expected returns. Therefore, the risk free rate’s actual return must always equal expected return regardless of market conditions. And so, the risk free rate must have no default risk. In practice, the risk free rate is estimated with mature market government bond yields.
Risk Premium
Risk premium is the incremental expected return investors require for taking incremental expected risk. It can be thought as the level of risk relative to the market multiplied by the market’s expected return for the market’s level of risk.
Market Risk Premium (MRP)
MRP is the expected returns investors will accept for a level of risk. In stocks, MRP is either estimated through implied future returns, or through historical data. In bonds and real estate, MRP is estimated through default spreads and cap rates respectively.
Using historical data, an arithmetic or geometric average of actual returns incremental to risk-free rates over time can be calculated using regression. This is the most popular way to compute MRP. On the other hand, implied risk premiums can be calculated by forecasting the future FCFE. Then, the discount rate can be calculated given present price. The implied premium can then be calculated by subtracting the risk free rate from the discount rate.
Beta
While the fundamental drivers of beta are type of business, financial leverage, and operating leverage; beta is estimated by regression. The equation for beta is below, derived by dividing an asset’s covariance with the market by the variance of the market. Covariance measures the degree and direction in which an asset moves relative to the market. Variance normalizes covariance by providing scale of magnitude.
Discount Rates are Not Perfect
In theory, the discount rate for any asset is solely the function of a risk free rate, the level of market risk, and the market risk premium. In practice, discount rates are estimates. The risk free rate is typically based on mature market (specifically U.S) government bonds. MRP is based on the prices and forecasted cash flows of index of securities, and beta is based on how the prices of assets move relative to the market index.
Nothing is Truly Risk Free
While the U.S government bonds have virtually no default risk, U.S government bonds are not completely risk free. Currencies can be devalued significantly as countries go through cycles, fight wars, and endure periods of high inflation. For example, after world war 2, the value of Germany, Italy, Japan, and China’s currency was completely destroyed. The value of France and UK’s currency also was significantly devalued compared to gold, even though they won the war.
However, since U.S government bonds are highly unlikely to default in the foreseeable future. And since risk free rates are a reflection of the investment environment, U.S government bonds is a reasonable estimate for the risk free rate.
MRP Depends on Accurate Inputs
Neither the historical nor implied risk premiums are without issues. To start, historical risk premiums are subjected to survivor’s bias. In addition, just as past returns do not predict future returns, historical risk premiums do not predict future risk premiums. In fact, price have an inverse relationship with return. When stock prices trend up, historical MRP increases to reflect actual MRP, while implied future risk premiums decrease to reflect the increase in price.
Furthermore, MRP estimates rely on the selection of its inputs. So, time periods and the market index chosen affects historical risk premium. And forecasted cash flows and the market index chosen affect implied risk premiums. MRP also doesn’t reflect small caps or private firms, as there is an observed premium for both small cap and private firms on top of MRP estimated using S&P500. However, for valuing liquid, publicly traded companies, the S&P500 MRP is reasonable.
Beta is Noisy
Beta can be even more noisy. While beta measures how an asset moves relative to the market, correlation does not necessarily equal causation. Correlated assets and markets can move independently. For secular assets that move relatively independently vs the market, the beta of strong performing stocks are over estimated while the beta of poor performing stocks are underestimated in any market uptrend. The reverse is true during market down trends. These assets have betas that are closer to 0 than regression beta suggests.
So, investors should think critically about the beta of the firm they are valuing. For example, Exxon Mobil has the same beta as PayPal. While Exxon is highly dependant on the business cycle, oil prices, political stability (which is lower in the developing countries Exxon operate in), PayPal’s has a lower business cycle, political, and commodity price risk. And so, using the same beta for Exxon and PayPal would be questionable. Instead, investor should only use regression beta as a starting point and adjust it based on their own assessment. Various methods such as earnings sensitivity to GDP growth models, multi factor models, or bottoms up beta models can be applied to make beta more accurate.
And like risk premium, beta depends on inputs. So, the time period length and index selected to performed the regression affect the resulting beta. Furthermore, regression is past looking, and the past doesn’t necessarily predict the future. Firms acquire and divest businesses, change their capital structure, and grow or decline in size. All of these factors affect beta.
Out of the three components in a discount rate, the risk-free rate is the most concrete, follow by MRP, then Beta. And so, in any valuation, a sensitivity analysis should be performed to understand the implication of discount rate errors.
Ultimately, discount rates are a moving estimate of expected return and expected risk for individual assets and markets. It is a reflection of the investment environment. And while discount rates are imperfect, they shouldn’t be ignored, as small changes in rates have large effect on valuations.
Discount Rates are Context Driven
Discount rates don’t exist in isolation. They exist in context of the investment environment, where all assets compete for capital. The risk free rate, estimated with mature market government bonds, reflect the central bank’s monetary policy, which is informed by a variety of economic factors. MRP for any asset class reflects investor sentiment, risk aversion, and fundamentals of the asset class. And beta reflects the relative market risk of any asset.
Discount Rates are a market driven instrument, and is relative to risk-free rate. Any time there is a change in the context, asset returns and discount rates respond, like an interdependent ecosystem.
Discount Rates are a Snapshot
In fact, discount rates and their components move quickly to reflect a new environment. The risk free rate will reflect expectations of monetary policy, as governments responds to economic factors. When economies underperform, central banks respond by lowering interest rates, and thus lowering the risk-free rate. When inflation outpaces expectations, central banks raise interest rates to curb inflation, which increase the risk-free rate.
Risk Free Rate Reflects Central Bank Monetary Policy Response to the Economy
In U.S, the risk free rates peaked around 1981, during a period with double digit inflation caused by President Richard Nixon breaking the U.S dollar link to gold. And while there were many five to ten year cycles of raising and lower interest rates, the fed has steadily lowered interest rates since 1980.
Risk Free Rates Have a Theoretical Lower Bound
The Fed has lowered treasury bill rates to effectively 0% in multiple periods in U.S history. When this happens, the treasury bond yields to drop to around 2%, reflecting time premium (of 10 year treasury bonds over short term treasury bills). This seems to suggest that unless the time premium of treasury bonds over treasury bills drop further, around 2% is the lower bound for the risk-free rate.
MRP is Volatile Short Term and Probabilistic Longer Term
MRP and can change even quicker. It does not depend on central bank policy, and instantaneously reflect investor sentiments about asset classes and individual assets.
While MRP is volatile, it has been range bound between 2 % to 6.5% from 1960 to 2019. This doesn’t mean that MRPs will never be higher than 6.5% or lower than 2%, but it does mean it is relatively unlikely.
| Statistic | MRP |
|---|---|
| Min | 2.0% |
| Max | 6.5% |
| Mean | 4.2% |
| Median | 3.9% |
| Standard Deviation | 1.1% |
All else equal, when the market expects higher returns for taking on equity risk (vs risk free rate) than average, it leans undervalued. And when markets require lower returns for taking on equity risk, it leans overvalued. When investors make investment decisions, they should consider the present risk premium, and where they expect risk premiums to be in the future.
Beta Reflects Market Perception
Like MRP, beta is also volatile. And like MRP, beta reflects market perceptions about assets and sectors. For example, during the coronavirus pandemic in 2020, markets quickly realized the cloud technology sector is more secular than previously thought, and would even benefit from the work from home implications of the pandemic. As a result, the beta of the cloud sector (denoted by SKYY ETF) decreased by around 25% (as shown by the red line) from 1.2 to 0.9. Indicating theres is a much lower relative risk than previously thought.
Discount rates change and requires periodic updates when used in valuations. The risk-free rates can be found on various government websites, the risk premiums can be calculated using cash flows projections by analysts, and beta of stocks can be found on various websites. As an alternative to calculating MRP, professor Aswath Damodaran updates his MRP forecast regularly on his website.
Discount Rates Matter
Changes in discount rates matter in valuation, as the value of any stable growth firm is equal to the discounted value of its cash flows in perpetuity. The equation below expresses that 
This equation makes it clear that as discount rates fall, valuations rise. Specifically, a change in the denominator of 
Another implication of changing discount rates is the duration effect. Consider the below equation. 
All else equal, the further away cash flows are, the more sensitive their value will be to discount rates changes. To illustrate the effects of time, consider two streams of cash flows that has the same value at 10% discount rate.
As discount rates rise or fall, the valuation of 
| Discount rate | CF1 Value | CF2 Value |
|---|---|---|
| 5% | $105 | $115 |
| 10% | $100 | $100 |
| 20% | $92 | $77 |
And so, when interest rates trend lower, assets with longer duration cash flows perform better with all else equal. And when interest rates trend higher, the reverse is true. While possibly over generalizing, this can be seen in growth vs value stocks in practice. Growth stocks, with more of its value coming from cash flows in the future, benefit more from the duration effect than value stocks in a declining interest rate environment.
While financial statement items such as revenue, cash flows, and assets are concrete, discount rates are more abstract and less visible. Yet, it is an important driver of valuation that not enough investors understand. Investor don’t invest firms without knowing the firm’s revenue, cash flows, and future prospects, and they shouldn’t invest without understanding the discount rates.