*Note: The concept of implied equity risk premium has been developed by Prof. Aswath Damodaran. In this article, we apply his methods to determine an implied equity risk premium for India.*

One of the most popular ways of valuing a company is to do a discounted cash flow valuation. According to this method, the value of a company is the present value of its cash flows discounted at the cost of equity, also known as the discount rate. The cost of equity calculation comprises of the following three components:

- A risk free rate;
- A beta, which is a measure of risk added to a diversified portfolio; and
- An equity risk premium, which is the expected return on the equity market minus the risk free rate.

As you can see, an equity risk premium is one of the key components of the discount rate. In its essence, a risk premium is the excess return that investors demand for holding a risky asset. Most analysts use a historical premium by comparing returns on an equity index versus government bonds over a specific period. Using a historical premium requires us to make choices about the following:

- using an arithmetic average versus a geometric average; and
- the time period over which returns are being compared.

These premiums, however, suffer from one serious problem – the standard deviation of these averages is high so as to make their calculation meaningless.

A second way (and probably a better way) is to calculate what Prof. Damodaran calls an implied equity risk premium. It uses the framework of discounting cash flows on a coupon bond to come up with the yield of that bond. Suppose we know the following details about a coupon bond:

- Current market price = Rs. 1,050
- Face Value = Rs. 1,000
- Annual coupon = 10%
- Maturity = 3 years

Given these inputs, we can calculate the yield on this bond by equating the present value of the cash flows to its current market price as follows:

The yield comes out to be 8.06%. That is, 8.06% is the return that is required to make the present value of the coupons and redemption value equal to the current market price of the bond.

### From bonds to equities

We can take the above concept and apply it to stocks to calculate an implied equity risk premium.

- The current market price is the current level of an index (usually an index which is representative of the general economy – for instance, S&P 500 in the US).

- The return on the index can be any of the following:
- the actual dividend and buy back yield of the index;
- the earnings yield of the index; or
- yield calculated on the basis of free cash flow to equity of the companies constituting the index.

This yield differs from the coupons on a bond in that returns on equity are not guaranteed (or capped) as they are on a coupon bond.

- Accordingly, we have to estimate a growth rate in the cash flows on the index. We can use a two-stage discount model with a high growth period (usually not more than 5 years) before assuming stable growth.
- The growth rate in the high growth period is usually the consensus analyst growth estimates for the index. The reason for using analyst estimates is because we are estimating what actual market participants are demanding from the equity markets (which is captured in analyst estimates).
- Once the high growth period is over, we assume a constant growth rate in perpetuity. According to economic theory, in the long run, a country cannot grow at more than its risk free rate forever. Therefore, we will set the constant growth rate equal to the risk free rate after the high growth period.

- Once we have the above inputs, we can calculate the return which equates the present value of cash flows to the current level of the index (we do this with the help of the goal seek function in excel).

- Lastly, we need to deduct the risk free rate from this return to come up with an implied equity risk premium.

### An equity risk premium for India

There are two ways we can calculate an implied premium for the Indian market:

- Using Indian index data and forecasts
~~and adding a country risk premium~~to come up with an implied risk premium. - Calculating the implied premium for a mature market (say the US), and adding a country risk premium to come up with the total risk premium.

Before we delve into the equity risk premium , lets first deal with country risk and why it is required to be computed.

### Country Risk Premium

All return models start with the estimation of the risk free rate. For an investment to be risk free, two conditions need to be satisfied:

- There should be no reinvestment risk; and
- There should be no default risk.

The yield on the 10-year Indian government bond as of 1 August 2016 was 7.14%. Can this be considered as the risk free rate for the Indian market? While the 10-year yield does not carry reinvestment risk (at least for 10 years), given India’s sovereign bond rating of Baa3[i], the bond cannot be considered risk free. Country risk tries to capture the risk that the Indian government may default on its debt.

Therefore, we need to reduce the bond yield by the amount of the default risk. Prof. Damodaran discusses various ways of computing default risk in his paper on risk free rates and country risk[ii]. As per his calculations, the average default risk of Baa3 rated countries across the world was 2.44% for 2016. However, given the improvement in the Indian economy and recognizing that fact that ratings agencies are slow to respond, I believe that a 1.50% default risk more adequately represents the risk inherent in bnods issued by the Indian government.

Now, as mentioned above, this 1.50% represents the risk present in the bonds issued by the Indian government and not Indian equities. One way to measure the risk in equities is to scale this default risk by the relative volatility of the Indian equity markets versus the debt market. The volatility (based on last 5 years’ of data) comes to 15.58% and 5.46% respectively[iii]. Accordingly, we can say that the country risk inherent in Indian equities is 4.28% which is computed as follows:

Now that we have the country risk premium, we can compute the implied equity risk premium for the Indian market by the two methods discussed above.

### Approach 1: Using Indian index data

We use the Nifty 500 index to represent the Indian economy. We use a 3-stage dividend discount model with a total high growth period of 10 years. We use the data as on 1 August 2016 and make the following assumptions:

- Current level of the index = Rs. 7,335.05

- Proxy for dividends and buybacks = 70% of the earnings yield

The reason for using this proxy is that the actual payout ratio[iv] of Nifty 500 is low at about 34%. The dividend yield of 1.24%[v], in our opinion, is not truly reflective of the potential earnings from the index.

- Risk free rate = 5.64% (the risk free rate is computed as the current yield on 10-year Indian government bond (7.14%) minus the default risk of the Indian government (1.50%).

- Growth rate for first 3 years = 15%; Growth rate for next 7 years = 10%

- Since India is a growing economy, we assume growth rate in stable period which is 1% higher than India’s risk free rate. Accordingly, the growth rate that we use is 6.64%

We enter the inputs in an excel sheet, and using the goal seek function calculate the equity risk premium:

Our assumptions yield an equity risk premium of 5.08%. Adding the risk free rate of 5.64% gives us a total cost of equity of 10.72%.

### Approach 2: Using mature market data

In case if US, we use a two-stage dividend discount model and restrict the high growth period to 5 years since it is a mature market. The data for S&P 500 index (which represents the US economy) as of 1 August 2016 is as follows:

- Current level of the index = 2,170.84
- Dividends and buybacks yield = 5.09%
- Growth rate for the next 5 years = 5.14%
- Risk free rate = 1.52% (10-year T-Bond rate). The growth rate in the stable period is restricted to the risk free rate.

Using the second approach yields an equity risk premium of 6.05%. Adding the country risk premium of 4.58% gives us a total risk premium of 10.33% for India. To this total premium we add the Indian risk free rate of 5.64% to yield a cost of equity of 15.98%

### Why is there a difference between the two approaches?

You may be wondering why is there such a large difference of 5.25% (10.33% – 5.08%) in the total equity risk premiums. Shouldn’t we get the same value using the two approaches? In a perfect world, yes. But as Prof. Damodaran explains, the most probable reason for this is the capital restrictions placed on Indian investors to invest outside India. We can think of the risk premiums calculated in the two approaches this way – Approach 1 is the premium that Indian investors are **currently demanding** from equities whereas Approach 2 is the premium that investors **should be demanding** from Indian equities. That is, the premium in Approach 2 is a more fairer reflection of the risk inherent in the Indian markets given the returns available elsewhere in the world.

Accordingly, the lower premium in Approach 1 implies that Indian investors are charging too less a premium given the expected returns which are available elsewhere. However, since Indian investors cannot easily invest outside India, they are likely to stay invested in Indian equities thereby not letting the markets correct enough to merge towards a more fairer value of the risk premium.

Personally, we prefer the second approach use it as the equity risk premium in our valuations.

## References:

[i] Source – Moody’s

[ii] What is the riskfree rate? A Search for the Basic Building Block – December 2008 and Country Risk: Determinants, Measures and Implications – The 2016 Edition by Aswath Damodaran.

[iii] Volatility is computed as the annualized standard deviation of the returns from Nifty 500 and S&P BSE India 10 Year Sovereign Bond Index for the period 1 August 2011 to 1 August 2016.

[iv] Payout ratio = Dividends paid / Earnings after tax

[v] Buybacks do not constitute any significant portion of payouts by Indian companies.

In the first step, have you incorporated beta (CAPM= RFR+ Beta*(MRP)), while calculating total cost of equity? If so, then how?

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Dear Madhav,

Beta is a measure of risk of the asset for which the cost of equity is being computed relative to the market. In this case, the asset itself being the market, the beta would be 1. That’s why I haven’t mentioned beta separately.

Hope that clarifies.

Regards

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Thanks.

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Sir, when you are calculating with India Data in the first method then why will we add country risk premium.

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Hi Saurav,

When we calculate the risk free rate in India, we deduct the default risk from the 10-Yr Indian government bond rate. Now that default risk needs to be incorporated in the discount rate. In case we don’t do it, we would be giving a benefit of a lower rate to India for being a risky country… The only thing one needs to remember is to scale up the default risk to reflect the risk in the equity markets than the debt markets.

Hope this clarifies.

Team Capital Surge

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On second thoughts, you are right. The country risk premium would already be incorporated when calculating the equity risk premium using Indian data. This was an oversight on our part and we would be doing an update on this shortly… Thanks for drawing our attention to this.

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