Cost of Capital Method Components: Risk-Free Rate & Equity Risk Premium


A reasonable cost of capital calculation hinges on accurately assigning a risk-free rate and equity risk premium to the model. While both are less prone to analyst-specific subjective criteria, there is still nuance to each. Both are moving targets, and analysts must weigh variables feeding the components closely to determine the most accurate estimate.

Luckily, broadly accepted data sources feed each determination. Still, diligent assessments weigh conventional wisdom, project or company specifics, and a bit of predictive power that external factor forecasts with historical precedent.

Risk-Free Rate

Risk-Free Rate Defined

The risk-free rate is the return investors, or companies would generate if they parked cash in a riskless asset rather than the potential project or investment. Nothing in life is guaranteed, and investment returns aren’t an exception. Therefore, risk-free is a misnomer, but the typical proxies are as close to riskless as is practical for an investment.

The return used as a proxy for a risk-free rate is typically the yield of a reliable government’s bond issues. Global analysts often use US Treasury yields as the risk-free rate. Other debt instruments, like corporate bonds, carry an inherent default risk no matter the firm’s stability. Government-issued bonds, though, are all but guaranteed.

If the United States cannot fund coupon payments for bonds issued today in ten years, they could raise taxes to bridge the difference. If the country does default on outstanding bond debt, there are much more significant concerns than fixed-income payments. So, US Treasuries are the most viable proxy for a return on a riskless investment – but which are appropriate?

Time Horizons Matter

Technically, short-dated T-Bills maturing between 4 and 52 weeks are the safest return guarantors. But they’re rarely used as a proxy in cost of capital calculations. Because analysts measure investments and company projects in terms of years and decades rather than months, longer-term Treasury Bond yields act as the rate to measure the expected return of a riskless investment over the same period.

When generating a cost of capital estimate, risk-free rates are usually assumed to remain fixed throughout the investment and don’t fluctuate with market conditions. The rate assumes the buyer purchases bonds today to generate income rather than active trading in secondary debt markets. Therefore, the risk-free rate is susceptible to today’s economic conditions but not impacted by unforeseen future events.

A Better Rate of Return

As the Federal Reserve hikes or cuts interest rates, the risk-free asset’s return follows suit. Government bonds become less attractive when interest rates fall as they generate less return. Reduced income payments increase investor interest in riskier projects. The opposite also holds. If the Federal Reserve sends rates skyrocketing, investors are guaranteed a return they’re happy with and will demand a higher return from alternate investments.

Often, companies seeing the prospect of high risk-free rates forego new projects. Additional risk factors coupled with a hefty, guaranteed return make the overall cost of capital too high to hurdle. Companies may elect to invest the money allocated to that project in the risk-free asset and wait for conditions to change.

Equity Risk Premium

The equity risk premium is the return investors demand for the increased risk of investing in the broad public market rather than the risk-free rate. Since returns in the market vary, and there is potential for losing substantial funds, investors expect extra compensation for their capital. Combined with the risk-free rate, that percentage is the market risk premium.

What’s the Difference?

The equity risk premium is the difference between the expected return of the market and the risk-free asset. But there is important nuance when pinning down the expected market return to feed the ERP calculation.

There are two ways to estimate the expected market returns:

Ex-post Approach

The most straightforward (mathematically) way of finding an ERP, the ex-post approach is a function of simple or compounding returns over a selected historical period. The primary variance in the final ERP is via selectively picking the period, but analysts should otherwise come up with similar ERPs if all else is equal.

If determined to arrive at a specific ERP, an analyst can manipulate the ERP to influence a project by selectively picking the period. For example, the US market return since inception is around 6.5%. But discounting the effects of the Great Depression boosts the return closer to 9% and dictates a higher ERP.

Forecasters can argue that the Depression was a one-time black swan event whose inclusion skews the actual data and that better returns over time in the market dictate a higher return from alternate investments. Likewise, analysts can shift the ERP by moving the time window to include or exclude events like the Dot-Com Crash and 2008’s Great Recession. Investors who argue that the post-2008 paradigm is the new order moving forward will calculate market returns closer to 14%.

These perspectives vary across firms and individuals, so clients should ensure that the model discloses the ERP’s time window when reviewing the cost of capital calculations.

Supply Side vs. Historical Inputs

Often, the least complicated return calculation, and what we referenced above, is a retrospective view of market returns generated by holding shares in a company. But in addition to the selective timing window, this method also over-relies on pattern recognition that may break down in the future.

Alternatively, stock market returns can be replaced with economic returns. When executed correctly, this method is more accurate, but more difficult to quantify. When done correctly, the model negates the effect of forward-looking earnings expansion expectations inherent in stock pricing. Because it deflates the stock price, the final ERP is often lower than historical return ERPs.

Ex-ante approach

More art than science, the ex-ante approach uses analyst’s forecasting models to predict the expected future stock prices and dividend distributions based on today’s information. More complex because of more inputs, ERP will vary drastically from analyst to analyst, dependent upon their perspective and biases. Furthermore, research indicates that current economic conditions weigh heavily and disproportionately impact the analysts’ perspective. Because of this, an analyst calculating the ERP in 2008 would have a very different outlook on the future than one doing the same in 2021. This psychological shortcoming further muddies the waters in an already subjective approach.

Regardless of the selected approach, many fine details must be accounted for when calculating an ERP, and amateurs often find themselves in a “paralysis by analysis” scenario; they cannot pin down an ERP accurately.