The equity risk premium (ERP) is a crucial concept in corporate finance and investment analysis. It signifies the additional return that investors demand to invest in stocks versus risk-free assets like government bonds. Understanding the equity risk premium is vital for estimating the cost of equity and determining if an investment opportunity is worthwhile.

## What is Equity Risk Premium?

The equity risk premium is the excess return that investing in the stock market provides over a risk-free rate. It is the compensation to investors for taking on the relatively higher risk of equity investing compared to completely risk-free investments. For example, if the expected return on stocks is 12% and the risk-free rate is 5%, the equity risk premium is 7% (12% – 5%).

The standard formula for calculating the equity risk premium is:

ERP = Expected total return on market – Risk-free rate of return

Equity returns are volatile, so the “market return”  varies dramatically from year to year.  To calculate the equity risk premium, authoritative sources such as Messrs. Dimson Staunton and Marsh calculate the total return from capital gains and dividends reinvested in the market over extended periods of decades and compare this to the average yields on Government bonds over the same periods to derive the ERP.

## How to calculate Equity Risk Premium in Excel

Here’s how to calculate ERP in Excel:

1. Enter the annual expected return on the market in one cell, say A1.
2. In another cell, B1, enter the current risk-free rate of return. The yield on 10-year US Treasury bonds is commonly used as the risk-free rate.
3. In cell C1, use the formula =A1-B1 to calculate the equity risk premium.
4. The value in cell C1 gives you the ERP.

Notable pros and cons of using the equity risk premium are:

• Useful for estimating cost of equity capital
• Quantifies the excess return expected from equity investing
• Aids in ascertaining the viability of an investment

• Challenging to accurately estimate expected market returns
• Historical ERP may not mirror future ERP
• Difficult to pinpoint a true risk-free rate of return

## Interpreting ERP in Corporate Finance

The equity risk premium plays a crucial role in various corporate finance analyses and valuation models, such as:

• The Capital Asset Pricing Model (CAPM) utilizes ERP to determine the cost of equity. A higher ERP equates to a higher cost of equity.
• In discounted cash flow analysis, ERP is used as a component of the weighted average cost of capital  (“WACC”) used to to discount future cash flows to the present, assisting in establishing if an investment’s anticipated returns are appealing.
• When comparing potential returns across various projects and asset classes, the Equity Risk Premium provides a very useful benchmark for assessing both equity and alternative investment opportunities.

## Economic Conditions and ERP:

Understanding how economic conditions influence the ERP is important in trying to understand equity markets. During economic downturns or times of increased financial market volatility, investors might demand a higher ERP as compensation for shouldering additional risk, elevating the premium. This will lead to falling equity prices.

In stable or booming economic conditions, where market confidence is buoyant, investors might accept a lower ERP causing prices to rise faster than earnings and so for equities to trade at higher multiples of earnings.

During the 2000’s, as interest rates were kept low by Central Banks pursuing policies of quantitative easing, the equity risk premium was considered by market commentators to have reduced as investors were “forced” into purchasing more risky assets. “TINA” was a popular phrase in the markets – “There Is No Alternative” (to equities). This, together with an increase in the equity risk premium resulting from the war in Ukraine and the concomitant high inflation and risk of recession, has been used to explain the big falls in valuation of technology stocks together with the big rise in interest rates in 2022 and 2023.

## Exercises and Examples for the Equity Risk Premium

Here are some examples to elucidate the concept and calculation of equity risk premium:

### Example 1:

• Expected market return: 18%
• Risk-free rate: 6%
• ERP = Expected market return – Risk-free rate = 18% – 6% = 12%

### Example 2:

• Stock market average annual return over the last 10 years: 14%
• Current 10-year Treasury note yield: 5%
• ERP = 14% – 5% = 9%

### Example 3:

• Analyst forecast for S&P 500 return next year: 10%
• Current 3-month T-bill yield: 3%
• ERP = 10% – 3% = 7%