We have discussed Capital Asset Pricing Model, used in Discounted Cash Flow Method, to calculate Cost of Equity in our earlier blogs. This time we are focusing on the two very important components of Capital Asset Pricing Model in detail: Risk-free Rate and Equity Risk Premium.

**Risk-free Rate**

Risk-free rate is the rate, which you get on a guaranteed investment with almost negligible risk. In layman terms, when the expected return is EQUAL to the actual return. Basically, for an investment to be risk-free, an investment should have two characteristics:

- No Default Risk
- No Reinvestment Risk

Lot of valuation experts came across various questions and came up with the best estimation of Risk-free rate. These questions are-

**QUESTIONS**

- Most of the valuation experts take government bond rate as the risk free rate by assuming that government will not default, however, the real question is: Do you really think it applies on high-risk countries like Zambia? Where the Zambia government bond is having a B- (S&P Global) and Caa1 (Moody’s) credit rating.
- It has been observed that valuation experts take the 10- year government bond as the Risk-free Rate, however, confusion arises when we think why a 10 year and why not 3 years or 30 years government bond rates?
- Does Risk-free rate depend on Time Horizon?
- What is the TIPS rate? And when to take it?
- It has been observed that, in Europe, different government issues Euro-denominated bonds and every government has a different rate, so which government rate is to be taken as a risk-free rate?

Let me help you in answering the above questions-

**ANSWERS**

1. It depends if you really think they have adjusted the default spread in the government bond rate and if that’s justified, then take it as Risk-free rate. Otherwise, take the government bond rate and deduct the country’s default spread to it to get to the Risk-free rate of the subject country.

**Calculation of Default Spread: –**

- Obtain CDS spread for the subject’s country and subtract US CDS spread gives you Default Spread.
- Subtract the Subject country’s US denominated bond rate with US bond rate, the difference is Default spread.
- If above two options doesn’t work, use the sovereign ratings of your country and see the default spread (Provided by Damodaran).

2. This is because if you are valuing a company by taking going concern principle you need to find other inputs like default spread, Beta, Equity risk premium etc. to run the model and it is difficult to find these inputs for the time horizon of 3 or 30 years as compared to find for 10 years.

3. Yes, every time horizon has a different risk-free rate. If your cash flows are for long-term, then your risk-free rate should be long-term risk-free rate.

4. TIPS rate is inflation protected rate. Please note that, if your Cashflow is in real terms then your risk-free rate should also be in real terms. In Layman terms, we can say if your cash flows include the inflation effect then you should also include that effect in the risk-free rate-TIPS Rate (consistency principle).

5. This is because marginal investor/market perceives different risk in different government bonds and if you are valuing a company in Euros and you need a risk-free rate in Euros then, choose the lowest one and take it as a Risk-free rate. Lower the government bond rate, lower the risk is.

**Equity Risk Premium**

It is the rate which an investor wants over and above the risk-free rate. In simple terms, it is an extra risk an investor expects to switch from riskless investment to risky investment.

We all aware that risk premium is totally depend on how risk-averse you’re and how risky the market is, in which an investor is investing. For example: An investor, who is just 30 years old would take more risk than a 60 years old investor. Also, at the time of any financial crisis, every investor would demand more premium than the normal situation.

There are different ways to calculate the Corporate Equity Risk Premium. Let’s discuss those methods in detail:

- It the subject company’s stock exchange which has enough historical data then looking Backward is a great option. See the return for 10, 20 or 50 years and what the stocks have historically earned over riskless investment, and then you would come up with the Equity risk premium.
- What if there are not enough data available for the market like for Brazil exchange or any emerging market exchange. In this case, we can calculate Corporate equity Risk Premium by using the below formula:

- Suppose country equity risk premium is equal to default spread of the bond issued by the country:
- Mature market risk premium + Default spread = Equity Risk Premium.

- The country equity risk premium is based on the volatility of equity risk premium relative to the government bond rate:
- Mature market risk premium + Default spread*(Standard deviation in the equity index/standard deviation in the government bond).

For example: US Risk Premium is 5.2%, Default spread of Brazil and US bonds is 2.5%, Standard deviation in B3 (Brazil stock exchange) is 22% and Standard deviation in the US denominated Brazilian bond is 15%. Therefore, Equity risk premium of Brazil would be 5.2%+2.5% (22%/15%) = 8.87%.

**Conclusion**

When you are valuing a company, it is very important to do a deep analysis of every component that can affect the overall valuation of the company/equity. There are different methods of calculation of every factor, however, selection of an appropriate method will depend on the purpose of valuation, situation, riskiness in the country or within a company etc.

### Author: Dheeraj C. – Analyst

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