Duff & Phelps Risk Premium Report Calculator > Frequently Asked Questions

What Cost of Equity (COE) calculations does the Calculator provide?

The Calculator gives the user the following COE calculations:

Size Study

Buildup 1 Model: COE = (Risk Free Rate) + (Risk Premium Over Risk Free Rate) + (Equity Risk Premium Adjustment)

Buildup 2 Model: COE = (Risk Free Rate) + (Equity Risk Premium) + (Size Premium) + (Adjusted Industry Risk Premium)

CAPM Model: COE = (Risk Free Rate) + (Beta x Equity Risk Premium) + (Size Premium)

Unlevered Model: COE = (Risk Free Rate) + (Unlevered Risk Premium Over Risk Free Rate) + (Equity Risk Premium Adjustment)

Risk Study

Buildup 3 Model: COE = (Risk Free Rate) + (Risk Premium Over Risk Free Rate; includes company-specific risk) + (Equity Risk Premium Adjustment)

Company Specific Risk: In addition, the Risk Study gives users an indication of direction for company specific risk. This is done through providing comparative risk characteristics of companies similar in size to your subject company for each of the 8 alternative measures of size.

Are the formulas for the calculations given in the Executive Summary and Support Documents?

Yes – the Executive Summary and Support Documents include the formulas for the cost of equity calculations, as well as the inputs selected by the user.

Should I use the Guideline Portfolio Method or the Regression Method?

The Duff & Phelps Risk Premium Report and Duff & Phelps Risk Premium Calculator provide two ways for users to match their subject company’s size (or risk) characteristics with the appropriate smoothed premia: the “guideline portfolio” method, and the “regression equation” method. When the subject company’s size (or risk) does not exactly match the average company size (or risk) of the guideline portfolio, the regression equation method is a straightforward and easy way to interpolate between the guideline portfolios.

In general, the regression equation method is preferred because this method allows for interpolation between the individual guideline portfolios, although the guideline portfolio method can still be used if the desired.

If I have a valuation date of say 2011, what year does the Calculator use data from?

If you had a valuation date in 2011, the Calculator would use the 2011 Duff & Phelps Risk Premium Report which contains data from 2010. If your valuation date was in 2010, the 2010 Report containing 2009 data would be used. The convention is that the year of the valuation date should match the year of the report, which contains data for the prior year. The Calculator will soon include additional functionality that will allow the user to select which year they wish to use data from.

Can I use the Calculator to value small companies with less than $1 million in financial data?

The Duff & Phelps Risk Premium Report and Duff & Phelps Risk Premium Calculator can be used for smaller companies.

Sometimes the required rate of return for a company that is significantly smaller than the average size of even the smallest of the Report’s 25 portfolios is being estimated. In such cases, it may be appropriate to extrapolate the risk premium to smaller sizes using the regression equation method.

As a general rule, extrapolating a statistical relationship far beyond the range of the data used in the statistical analysis is not recommended. However, extrapolations for companies with size characteristics that are within the range of companies comprising the 25th portfolio are within reason.

In some cases, the size of the subject company may be equal to or greater than the smallest size of the companies included in the 25th portfolio for one size measure (e.g., sales), but less than the smallest size of the companies included in the 25th portfolio for another size measure (e.g., 5-year average income). In this case, analysts may consider including the size measure for sales, but excluding the size measure for 5-year average net income. One should never use those size measures for which the subject company’s size is equal to zero or negative.

The Duff & Phelps Risk Premium Report includes a description of the size characteristics of the 25th portfolio, by percentile.

Can you please explain your regression equation?

The following information and statistics are published for each equation used in the "regression equation method" for each of the exhibits in the Duff & Phelps Risk Premium Report:

Dependent Variable (Average Premium), Independent Variable (Log of Average Market Value of Equity), Constant, Standard Error, R Squared, Number of Observations, Degrees of Freedom, X Coefficient, t-Statistic

Can you explain how you move from the cost of equity presented into a cost of capital building in leverage considering you are using an unlevered beta?

Both levered betas and unlevered betas are developed for each of the portfolios in the Report and Calculator.

I believe CoVars with smaller percents are less variable or risky – is this correct?

The Duff & Phelps Risk Premium Report and the Duff & Phelps Risk Premium Calculator include both a Size Study and a Risk Study.

The Risk Study is based on an extension of the Size Study. Instead of ranking companies into portfolios by size, the Risk Study ranked companies into 25 portfolios based on 3 alternate measures of financial risk. These measures included the 5-year operating income margin, the coefficient of variation in operating income margin, and the coefficient of variation in return on book equity, where coefficient of variation is defined as the standard deviation divided by the mean. All 3 measures used average financial data for the 5 years preceding the formation of annual portfolios. The first statistic measures profitability and the other two statistics measure the volatility of earnings. The result of the study was a clear relationship between risk and return, whereby higher returns were associated with low profitability and high volatility of earnings.

I have heard that mixing Ibbotson & Duff & Phelps was not recommended because of the differences in methodology. Does the Calculator automatically make adjustments for these differences?

The Duff & Phelps Risk Premium Report's "Size Study" provides two methods of estimating COE for a subject company, Buildup 1 and CAPM (Capital Asset Pricing Model), plus one method for estimating unlevered COE (the cost of equity capital assuming a firm is financed 100% with equity and 0% debt).

Some users have inquired whether the Size Study can be used in conjunction with the industry risk premia (IRPs) published in the SBBI Valuation Edition Yearbook, so we also include an alternative method in which a rudimentary adjustment is made to an IRP and then utilized in a modified buildup model, Buildup 2, that includes a separate variable for the industry risk premium. There are differences in methodologies, but and this rudimentary adjustment, while not perfect, attempts to account for those differences.

Currently, the authors of the Calculator recommend entering an ERP of 5.5% (as of January 15, 2012). Why is this?

The ERP that is used by convention to calculate the risk premia in the Duff & Phelps Risk Premium Report and in the Duff & Phelps Risk Premium Calculator is the historical ERP calculated as the average annual return of stocks minus the average return of 20-year bond income returns over the period 1963-present. For example, to perform the analysis necessary for the 2012 Duff & Phelps Risk Premium Report, the historical ERP from 1963-2011 was 4.3%.

However, users oftentimes wish to use a forward-looking ERP estimate as of their valuation dates that differs from the historical 1963–present ERP (for instance, many users use the Duff & Phelps Recommended ERP, which was 5.5% as of January 15, 2012). The ERP adjustment is simply the difference between the user’s own forward-looking ERP and the historical 1963–present ERP. For example, for a 2012 valuation using the Duff & Phelps 2012 Risk Premium Report, and assuming the user has decided to use 5.5% as his forward-looking ERP, the calculation would be 5.5% - 4.3% = 1.2%. So, 1.2% would be added to the Buildup 1 Model, the Buildup 1-Unlevered Model, and the Buildup 3 (Risk Study) Model. This adjustment would NOT be made to the CAPM model or the Buildup 2 model.

The nice thing is that the Duff & Phelps Risk Premium Calculator does all of these adjustment automatically, and then documents them in the output for you.

The rule of thumb is that an ERP adjustment is necessary when the risk premia has an embedded measure of "market" risk. For example, Buildup 1 utilizes the risk premia from the "A" exhibits that have an embedded measure of market risk (the subscripted "m" in Rpm+s), and so an ERP adjustment is needed, but the CAPM model utilizes the risk premia from the "B" exhibits that do not have an embedded measure of market risk (Rps), and so an ERP adjustment is not necessary.

For more information on the equity risk premium (also known as the market risk premium), see Cost of Capital: Applications and Examples 4th ed., by Shannon P. Pratt and Roger J. Grabowski (John Wiley & Sons, Inc., 2010), Chapter 9, “Equity Risk Premium”, pages 115–158.

I see that the Calculator calculates a z-score for my subject company. Can I still use the regression equations if my company’s z-score is less than one?

For z-scores less than one, you might consider using "high financial risk premia" provided by the Report and Calculator.

Does the Calculator work for non-US-based companies?

Generally, one would want to use risk premia developed using US data for valuations of US firms, risk premia developed using European data for valuations of European firms, etc. We are looking at developing non-US versions of the Calculator.

Methodology