ERP and the Cost of Equity

Corporate Issuers 14 min readModule 2 of 2Save

What you'll learn

LOS 15.c
Explain historical and forward looking approaches to estimating an equity risk premium.
LOS 15.d
Compare methods used to estimate the required return on equity.
LOS 15.e
Estimate the cost of debt or required return on equity for a public company and a private company.
LOS 15.f
Evaluate a company’s capital structure and cost of capital relative to peers.

Equity risk premium (ERP) is the extra return (over the risk free rate) that an investor demands for investing in risky equity securities.

Estimates of the Equity Risk Premium

There are two types of estimates of the equity risk premium: historical estimates and forward looking estimates.

Historical Estimates

A historical estimate of the ERP consists of the difference between the historical mean return for a broad based equity market index over some time period, and a risk free rate over the same period. Its strength is its objectivity and simplicity.

Analysts making a historical estimate need to decide on four important issues:

1. Index selection: The equity market index chosen should be one that serves as a good proxy for the average returns equity investors earn over time.

2. Sample period: Analysts generally choose a longer sample period because covering multiple business cycles and a variety of market conditions, the standard error (i.e., noise) should be lower. However, older data may not reflect current market conditions. On the other hand, smaller samples using only recent data can have a higher forecast error but may be representative of expected market conditions.

3. Mean type: Analysts need to decide whether to use an arithmetic mean or a geometric mean. An arithmetic mean is a good estimate of a one period expected return, but does a poor job of estimating multiperiod return, which is needed to determine expected terminal wealth. A geometric mean gives lower weight to outliers, and estimates the expected terminal wealth more accurately.

While the geometric mean is preferred, both means are used in practice.

4. Risk free rate proxy: Analysts may use either short term or long term government bond rates as a proxy for the risk free rate. The short term (e.g., T bill) rate is a good proxy for the true risk free rate because (unlike long term rates) it does not include reinvestment (of coupon) risk.

However, because the duration of equity is long term (actually infinite), many analysts favor using long term government bond rates as proxies for the risk free rate.

A weakness of the historical approach is the assumption that the mean and variance of the returns are constant over time (i.e., the ERP time series is stationary). This does not seem to be the case. In fact, the equity risk premium actually appears to be countercyclical, it is low during good times and high during bad times.

Thus, an analyst using historical data to estimate the current equity premium should choose the sample period carefully. Another concern with a historical estimate is that it may suffer from survivorship bias: it will be upward biased if only firms that have survived during the period of measurement are included in the sample.

Forward Looking Estimates

Forward looking or ex ante estimates use current information and expectations concerning economic and financial variables. As such, they do not rely on an assumption of stationarity and are less subject to problems like survivorship bias.

There are three main categories of forward looking estimates: survey based estimates, dividend discount model estimates, and estimates from macroeconomic modeling.

Survey Estimates

Survey estimates of the ERP use a consensus of opinions, typically experts. Surveys tend to estimate higher ERPs for developing markets relative to developed markets. A weakness is that the surveys tend to be biased toward recent market returns.

Dividend Discount Models

The constant growth model (Gordon Growth Model) is a popular method for generating forward looking estimates. Rearranging the GGM to isolate the required rate of return gives:

r_{e} = (D_{1} / V_{0}) + g

The first term is the expected dividend yield on a broad based index; this measure should be relatively free from large surprises. The second term is the earnings growth rate for the index, based on consensus forecasts. Recall that the constant growth rate is also the capital gains yield on the index.

Subtracting the current risk free rate gives us the ERP estimate:

ERP = E (dividend yield) + g - r_{f}

Recall that the constant growth model assumes a constant growth rate in earnings and dividends. If this assumption is not valid, an analyst will need to include relevant expectations of expansion or contraction of the market P/E ratio. (We will discuss this in a moment in the macroeconomic model approach).

For developing economies, where the current high growth rate is transitory, we might incorporate three stages of growth (high, moderate, and mature) and model the stock market index value this way:

current index value = PV (stage 1) + PV (stage 2) + PV (stage 3)

The IRR that balances this equation is then our estimate of required rate of return. After subtracting the current risk free rate, we can obtain the ERP for that market.

Macroeconomic Models

We will use the Grinold Kroner (2001) model to illustrate a macroeconomic model. The Grinold Kroner model decomposes ‘g’ (the capital gains yield, CGY) in the dividend discount model as:

CGY = Δ P / E + expected inflation (i) + real economic growth rate (G) - Δ S

Where:

$Δ P / E$ = expected repricing or expansion/contraction in P/Es.

$Δ S$ = % change in shares outstanding, on an aggregate basis.

ΔS reflects the net buyback of stock, which is another way corporations can effectively pay cash to their shareholders. If ΔS is positive, it is a dilution effect (hence, is subtracted).

The Grinold Kroner model can be used to express the expected market equity return as a function of five factors:

ERP = [DY + Δ P / E + i + G - Δ S] - r_{f}

Where:

DY = dividend yield; the expected income component of the equity investment.

$i$ = expected inflation.

One approach to estimate expected inflation is to compare the nominal yield on a U.S. Treasury bond to the yield on an equivalent inflation protected Treasury security (TIPS).

i = \frac{1 + YTM _{Treas}}{1 + YTM _{TIPS}} - 1

Worked example: Macroeconomic model

Patrick McGill is trying to estimate the equity risk premium for the U.S. market. McGill uses the S&P 500 index as the proxy for the market and estimates that the dividend yield is 1.2%. The real GDP growth rate is forecast to be 3% and McGill believes that the market is currently fairly valued.

The current 10 year Treasury yield is 2.4%, while 10 year TIPS yield 0.25%. McGill assumes no net change in shares outstanding, and that the risk free rate is 0.50%.

Calculate the equity risk premium.

Solution

i = \frac{1 + YTM _{Treas}}{1 + YTM _{TIPS}} - 1 = (1.024/1.0025) - 1 = 2.1%

ERP = [DY + Δ P / E + i + G - Δ S] - r_{f} = [1.2% + 0 + 2.1% + 3% - 0] - 0.5% = 5.8%

There are several approaches to estimating the required rate of return on equity including the DDM, bond yield plus risk premium, build up approaches, and risk premium models.

Dividend Discount Model (DDM)

For an individual company, cost of equity is dividend yield plus capital gains yield.

r_{e} = DY + CGY

(Note that since we are calculating required return and not risk premium, we do not subtract the risk free rate.)

If the company’s earnings growth rate was not constant, then a 2 stage model could be used instead.

Worked example: Cost of equity using DDM

Cogenics, Inc., is expected to pay a dividend of $4 at the end of its first year. Dividends are expected to grow at a constant rate of 4% per year. The current Cogenics stock price is $100.

Betagenics, Inc., is expected to pay a dividend of $1.50, $2.00, $2.50, and $3.00 at the end of each of the next four years, respectively. The current Betagenics stock price is $50, and is expected to be $60 at the end of four years.

Based on this data, calculate the cost of equity for Cogenics and Betagenics.

Solution

Dividend yield for Cogenics = 4 / 100 = 4%

re(Cogenics) = DY + CGY = 4% + 4% = 8%

For Betagenics, we need to solve for re in the following equation:

$50 = \frac{1.50}{1 + r _{e}} + \frac{2.00}{( 1 + r _{e} ) ^{2}} + \frac{2.50}{( 1 + r _{e} ) ^{3}} + \frac{3.00 + 60}{( 1 + r _{e} ) ^{4}}

On our TI BA II PLUS calculator: CF0 = −50; C01 = 1.50; C02 = 2.00; C03 = 2.50; C04 = 63

CPT IRR = 8.78%

Thus, the cost of equity for Betagenics is 8.78%.

Bond Yield Plus Risk Premium Method

The bond yield plus risk premium (BYRPM) method is a build up approach appropriate for estimating the cost of equity for a company that has publicly traded debt. This method simply adds a risk premium to the yield to maturity (YTM) of the company’s long term debt. One approach to selecting a risk premium is to use an average of the historical difference between equity returns and cost of debt, similar to the historical estimation of the equity risk premium.

An issue with this method is that the risk premium is rather arbitrary and if the firm has several debt securities outstanding, there is no perfect option regarding which security’s yield to use.

Worked example: Applying the bond yield plus risk premium approach

Company LMN has bonds with 15 years to maturity, a coupon of 8.2%, and a price of 101.70. An analyst estimates that the additional risk assumed from holding the firm’s equity rather than bonds justifies a risk premium of 3.8%. Calculate the cost of equity using the bond yield plus risk premium approach.

Solution

Using our calculator’s TVM keys: PV = −101.70, N = 15, PMT = 8.2, FV = 100, CPT I/Y = 8.0%.

Cost of equity = 8.0% + 3.8% = 11.8%

Risk Based Models

Capital Asset Pricing Model

The capital asset pricing model (CAPM) is a single factor model that estimates the required return on equity using the following formula:

required return on stock = risk free rate + (equity risk premium \times beta of stock)

Worked example: Using the CAPM to calculate the required return on equity

The expected risk free rate is 4%, and the equity risk premium is 3.9%. Calculate the required return on equity for a stock with beta of 0.8.

Solution

required return on stock

= risk free rate + (equity risk premium \times beta of stock) = 4% + (3.9% \times 0.8) = 7.12%

CAPM beta can be estimated using the market model, where we regress the historical return on the stock against the corresponding return on a broad based equity index. Note that the returns used are generally excess returns, that is, return over the risk free rate, but raw returns can also be used. The estimated slope coefficient in this simple linear regression is the estimated beta of the stock.

To estimate the beta of a private company, the beta of a comparable publicly traded company may be used (after adjusting for leverage differences).

Multifactor Models

Multifactor models can have greater explanatory power than the CAPM (which is a single factor model).

The general form of an n -factor multifactor model is:

required return = r_{f} + (risk premium)_{1} + (risk premium)_{2} + \dots + (risk premium)_{n}

where:

(risk premium)_{i} = (factor sensitivity)_{i} \times (factor risk premium)_{i}

The factor sensitivity (also called the factor beta) is the asset’s sensitivity to a particular factor, all else equal. The factor risk premium is the expected return above the risk free rate from a unit (i.e., = 1) sensitivity to the factor (and zero sensitivity to all other factors).

Fama French Models

The Fama French model is a multifactor model that adds two additional factors to the CAPM systematic risk factor: size (measured by market cap) and value (measured by the book to market ratio).

required return of stock = r_{f} + β_{1} ERP + β_{2} SMB + β_{3} HML

where:

SMB = size premium = average difference in return of small cap portfolios over large cap portfolios

HML = value premium = average difference in return of high book to market portfolios over low book to market portfolios.

A five factor Fama French model adds to the model two additional factors: profitability (RMW), and investment factor (CMA).

required return of stock = r f + β1 ERP + β2 SMB + β3 HML + β4 RMW + β5 CMA where:

RMW = profitability premium = average difference in portfolio returns of companies with “robust profitability” over “weak profitability”

CMA = investment premium = average difference in portfolio returns of companies with “conservative” investments over companies with “aggressive” investments

Worked example: Cost of equity using the Fama French Five Factor Model

Suppose the current risk free rate of return is 2.1%. Calculate the cost of equity for Fulton Corp. given the following information.

Solution

r e = 2.1% + (1.1 × 3.2%) + (0.2 × 1.3%) + (−0.3 × 2%) + (0.18 × 4.2%) + (0.5 × 2.4%) = 7.2%

Cost of Equity for Private Companies

Private companies are often smaller and less mature than public companies. Since they have no market price data, the CAPM and Fama French models are not suitable to apply directly to private companies. Illiquidity and the lack of transparency (e.g., no security filings and disclosures) increase the investment risk of private companies.

Appropriate risk premiums for a private company include: size premium (SP), industry risk premium (IP), and specific company risk premium (SCRP). SCRP is a general risk premium covering unique risks of the private company such as key person risk, geographical location risk, etc., which are difficult to diversify away.

Factors Affecting SCRP

Qualitative factors: Industry in which the company operates, corporate governance quality, asset nature and type (e.g., tangible, liquid, fungible, etc.), customer and supplier concentration, geographical concentration, competitive position in the industry, and management quality. Lower corporate governance quality, large proportion of intangibles in total assets, poor competitive standing in the industry, management without adequate skill and experience, geographical concentration, customer concentration, or supplier concentration all indicate higher risk.

Quantitative factors: Operating and financial leverage, earnings volatility and predictability, and cash flow volatility. Higher leverage and volatility indicate higher risk.

There are two approaches to estimate the cost of equity for private companies, expanded CAPM and build up approach.

Expanded CAPM

The expanded CAPM approach starts with using the standard CAPM (with a peer beta) and then adding risk premiums as needed:

required return = rf + (βpeer × ERP) + SP + SCRP where:

βPeer = the industry beta from peer public companies

Build Up

The build up approach starts with the risk free rate, and adds the equity risk premium to arrive at the required return on an average large public company (because ERP is calculated using a market cap weighted index, large caps dominate the index, and no beta is used). Further risk premiums for size, industry, and company specific characteristics are added as needed, depending on how different the subject company from the average large public company.

required return = r_{f} + ERP + SP + IP + SCRP

International Considerations

While CAPM may work well for developed market securities, risks unique to emerging markets require additional premiums. The country spread model and the country risk rating model are alternative ways to estimate these risk premiums.

The country spread model estimates a country risk premium (CRP) (also called a country spread premium) for a specific emerging market. The estimated equity risk premium then becomes:

ERP_{emerging market} = ERP_{developed} + (λ \times CRP)

Where:

$λ$ = exposure of the company to the local (emerging market) economy.

We can use the sovereign yield spread (the difference in yields of emerging market government securities relative to developed market benchmark security) as an estimate of CRP. However, differences in legal and market environment complicate the use of just yield spreads for CRP.

Damodaran recommended adjusting the sovereign yield spread by the ratio of standard deviation of the country’s equity and bond markets:

CRP = sovereign yield spread \times \frac{σ _{equity}}{σ _{bond}}

Extended CAPM

For countries operating globally, several approaches are used to estimate r e including global CAPM, international CAPM, and country spread and risk rating models.

Global CAPM (GCAPM) uses a global market index to estimate the ERP, rather than using only a local market index. Because of low correlation between developed markets and emerging markets, the beta coefficient using a global market proxy is usually quite low (or even negative). To overcome this, a second factor representing the local market is sometimes included; but the availability of reliable market index data is a concern in many emerging markets.

International CAPM (ICAPM) is a 2 factor model, based on (1) a global market index (e.g., MSCI All Country World Index) factor, and (2) a foreign currency denominated, wealth weighted market index.

The first factor captures the company’s relationship with the local economy relative to the global economy: lower values of βG indicate lower integration of the company with the global economy. The second factor captures the sensitivity of the company’s cash flows to changes in its local currency exchange rate.

In summary, for companies with global operations that are limited to developed markets, GCAPM or ICAPM are appropriate approaches to estimating the required return on equity. For companies with exposure to developing markets, the appropriate approach is less well defined. For these firms, a country risk premium (CRP) can be used, if we can assume that the historical estimate is representative of the risk premium going forward.

This LOS uses a case study approach to pull together the concepts learned in the prior LOS. Exam questions need to be solvable in approximately three minutes each, so a full fledged case study on exam day is impractical. However, individual questions can be fair game, as illustrated in the module quiz.

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