###### The F-statistic

The F-test determines whether all the independent variables help explain the dependent variable.... **Read More**

After determining the ERP, we must estimate the company’s required rate of return to be used in calculating the WACC. The following methods are used to estimate the required rate of equity return:

- Risk-based models.
- DDMs.
- The bond yield plus risk premium build-up method.

In this method, we apply the constant growth DDM to estimate a company’s required rate of equity return.

$$ r_e=\frac{D_1}{P_0}+g $$

Where:

\(D_1\) = Expected future dividend.

\(P_0\) = Current share price.

\(g\) = Expected growth rate in dividends.

Let us use an example to illustrate this.

$$ \begin{array}{c|c|c} \textbf{Company ABZ} & \textbf{Definition} & \textbf{Value} \\ \hline \text{Expected future dividend} & D_1 & $ 1.2 \\ \hline {\text{Expected (perpetual) growth}} & g & 5\% \\ \text{rate in dividends} & & \\ \hline \text{Current share price} & P_0 & $ 60 \end{array} $$

The cost of equity is:

$$ r_e=\frac{$1.2}{$ 60}+0.05=0.07=7\% $$

To use DDM for the required rate of return on equity estimation, a company must pay dividends and be publicly traded.

BYPRP is another method of estimating the required rate of equity return for a company with public debt.

$$ r_e=r_d+RP $$

Where:

\(r_d\) =The cost of debt of a company.

\(RP\) = Risk premium.

It is challenging to calculate risk premiums when using the BYPRP approach. To estimate risk premium, we use the historical mean difference in returns between a corporate bond index and an equity market index.

- Estimating a company’s debt cost provides an estimate of the return that debt investors demand.

- Risk premium is difficult to estimate.
- A company must trade debt securities to use this approach.
- Where a company has several traded debt securities with different features, there is no guidance on which bond yield to select.

The required return on equity using risk-based models is the sum of the compensation for bearing risk and compensation for the time value of money. Different models are used to calculate the required rate of return on equity, each being different based on how they model compensation for risk-bearing. The models are:

The required return on equity is estimated using the following equation:

$$ r_e=r_f+\hat{\beta}(BRP) $$

Where:

\(r_f\) = Risk-free rate.

\(\hat{\beta}\) = A company’s stock return sensitivity to REP changes.

A company’s beta is estimated using the market model, which replaces the market and company’s expected returns with their historical returns. In effect, this occasions regression of the excess returns of an equity market index against a company’s excess returns over the risk-free rate. A different market model approach involves failure to subtract the risk-free rate from the market and the stock’s return. An analyst should consider the following:

- The most appropriate equity market index.
- The period used to estimate beta.
- The proxy used for the risk-free rate.

CAPM can estimate the cost of capital of Equity even when a company is not publicly traded. To estimate the beta of a subject company, we get the beta of a comparable company that is traded publicly and with the same business risk. We then adjust the financial leverage.

In this model, the size of a company, the single market factor, and the value factor can be used to explain a company’s equity returns. Using the three-factor model, the excess return on equity will be:

$$ r_e=r_f+\beta_1ERP+\beta_2SMB+\beta_3HML $$

Where:

\(SMB\) = Size premium.

\(HML\) = Value premium.

An investment factor (CMA) and a profitability factor (RMW) are added to form a five-factor Fama-French model.

$$ r_e=r_f+\beta_1ERP+\beta_2SMB+\beta_3HML+\beta_4RMW+\beta_5CMA $$

The estimated slope coefficients in the Fama-French models represent the sensitivity of a stock’s return to factors. Just as is the case in CPM, the excess equity returns are regressed on the factors to get estimates on the factor betas. The factor risk premium estimates and the beta factors are then used to estimate the required return on equity. The use of risk-based models is similar in that:

- The relationship between the factors and a company’s excess stock returns is estimated using historical returns.
- An estimate of a company’s required return on equity is calculated using the risk-free rate, factor risk premiums, and the estimated regression of the slope coefficients.

An analyst must be aware that:

- Different risk factor estimates yield different results.
- The presence of additional factors will cause the beta coefficient on the market factor to differ between multifactor and single-factor CAPM models.
- Analysts often use a short-term risk-free rate when calculating excess returns to estimate the factor betas.

It is more challenging to estimate the cost of equity for private companies because:

- Data on security returns and prices for private companies are unavailable; thus, risk factor models cannot be applied directly to private companies.
- Private companies are often smaller, with owners as directors during the early stages of their lifecycle.
- Private companies might disclose information that is irrelevant to investors. They are also less liquid.

For private companies, the required return on equity includes the following:

- An industry risk premium (IP).
- A specific-company risk premium (SCRP).
- A size premium (SP).

Illiquidity is another risk factor associated with private companies. Higher illiquidity risk does not reflect in the required return as a risk premium. However, it appears as a discount for lack of marketability. Two approaches are used to estimate the required return on equity for private companies.

The expanded CAPM adds a premium for company-specific risks and a company’s small size. The expanded CAPM requires the estimation of beta from publicly traded companies’ peer groups.

$$ r_e=r_f+\beta_{\text{peer}}\left(ERP\right)+SP+IP+SCRP $$

The following steps are used in the estimation:

- An estimate of the industry beta is derived from a publicly traded company’s peer group in a similar industry as the subject company.
- With the ERP and risk-free rate, we calculate a CAPM estimate for \(r_e\).
- We determine if additional risk premiums for company-specific risk factors and company size are necessary.
- If necessary, we add relevant company-specific risk factors and company-size risk premiums to get the final estimate of \(r_e\).

A size premium inversely related to the company size is added to the required return on equity. Caution should be exercised when historical measures of size premium are used because the population may include previously large companies that are now in financial distress. A company-specific risk premium estimation will vary depending on quantitative and qualitative factors. These factors can be analyzed in contrast with other privately held companies in similar industries or a publicly traded peer group.

In this approach, we “build up” the required return on equity, starting with the risk-free rate, and then we add the relevant risk premia.

$$ r_e=r_f+ERP+SP+SCRP $$

The ERP is not adjusted for beta and is estimated with reference to equity indexes of publicly traded companies. With a beta of 1 multiplied by the ERP, the sum of the ERP and the risk-free rate is the required return on equity for an average risk large-cap public equity. A beta-adjusted size premium is added to account for the small size of private companies. A specific-company risk premium is added to arrive at the final required return on equity estimate after analyzing additional risk factors.

An analyst estimating the required return on equity should consider inflation rates, exchange rates, models, and data in emerging markets.

It is difficult to estimate risk premiums for emerging markets. Two methods have been proposed to deal with this issue:

- The country risk rating model.
- The country spread model.

To estimate ERP using the country spread model, investors expect the country risk premium (CRP) to compensate them for investing in a foreign country. This model is:

$$ ERP=\text{ERP for a developed market}+(\lambda\times CRP) $$

Where:

\(CRP\) = Country risk premium.

\(\lambda\) = The level of a company’s exposure to the local country.

The CRP can be calculated by using the sovereign yield spread. The CRP, in this instance, is estimated as the yield on bonds from emerging markets minus the yield on government bonds from developed markets. The problem with this approach is that a country’s ERP is estimated using a bond yield spread. Differences in the market environment and legal framework among countries make the use of yield spreads on sovereign bonds inappropriate for the cost of equity estimation.

Aswath Damodaran developed a refined version of CRP estimation.

$$ CRP=\text{Sovereign yield spread} \times\frac{\sigma_{\text{Equity}}}{\sigma_{\text{Bonds}}} $$

Where:

\(\sigma_{Equity}\) = The volatility of the local country’s equity market.

\(\sigma_{Bonds}\) = The volatility of the local country’s bond market.

This method requires bond and equity returns of the local market to be existent.

The following methods can be used to estimate the required return on equity for companies with international operations:

There are no major risk differences across countries; the single factor is a global market index. The problem is that there is a negative or low slope coefficient due to the low correlation between developed and emerging markets. Adding a domestic market index reduces this risk to some extent but is dependent on reliable financial data availability.

In this approach, stock returns from an emerging market are regressed against a global index’s risk premium and the wealth-weighted foreign currency index.

$$ E\left(r_e\right)=r_f+\beta_G\left(E\left(r_{gm}\right)-r_f\right)+\beta_C(E\left(r_c\right)-r_f) $$

Where:

\(r_f\) =The risk-free rate.

\(\beta_G\) = The sensitivity to the global index.

\(r_{gm}\) = The risk premium of a global index.

\(\beta_C\) =The sensitivity to the foreign currency index.

\(r_c\) = The foreign currency index.

FTSE All-World Index and MSCI All-Country World Index (MSCI ACWI) are proxies for the global index. The foreign currency index sensitivity depends on the sensitivity of a company’s cash flows to exchange rates through its investments, imports, and exports. The global index sensitivity depends on the relationship between a company and the global and local economies.

ICAPM and GCAPM estimate the cost of equity for companies with global operations in developed countries only. The sovereign yield approach can be used when a country operates in a developing country. Still, since the estimations are based on historical rates, they might not reflect the risk premium.

## Question

A downward revision of the growth rate on dividends will

most likely:

- Increase the required rate of return on equity.
- Decrease the required rate of return on equity.
- Not affect the required rate of return on equity.
## Solution

The correct answer is

B.If the growth rate is revised downward, both the growth rate and dividend yield will decrease, leading to a decrease in the required rate of return on equity.

A is incorrect. This would happen if the growth rate were revised upwards.

C is incorrect. This would happen if the growth rate remained constant.

Reading 20: Cost of Capital: Advanced Topics

*LOS 20 (d) Compare methods used to estimate the required return on equity.*