### Risk Premium Toolkit Frequently Asked Questions (FAQs)

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- Risk Premium Toolkit User Guide, 2016
- CRSP Deciles Size Premia Study User Guide, 2016
- Download free webinar on using the Duff & Phelps Toolkit Data

**Q: ****What is the Duff & Phelps Risk Premium Toolkit (previously called the "Risk Premium Calculator")?**

**A:** The Toolkit is an online tool that will help the user develop cost of equity (COE) estimates tailored towards their subject company using five different COE methods which utilize empirical data from the Duff & Phelps Risk Premium Report.

**Q: What are the outputs of the Toolkit?A:** The outputs include a summary of your cost of equity estimates in a printable web presentation, a customized Executive Summary in Word, and full support documents in Excel. The Word and Excel output are fully editable.

**Q: Is the Toolkit a “black box”?A:** No, not at all. All the calculations are written out and included in the web presentation, the executive summary, and the support documents. In the Toolkit’s deliverables, all inputs are defined, documented, sourced, and you receive a full Microsoft Excel spreadsheet containing very granular support and documentation of all values, along with the equations of the models used (with your subject company inputs plugged in).

**Q: How does the Risk Premium Toolkit differ from other calculators?A:** The Risk Premium Toolkit is the most advanced and feature-rich valuation tool of its kind on the market.

The Risk Premium Toolkit provides a fully-editable executive summary of up to four different COE estimation models for your subject company, with the inputs all defined, documented, sourced, and ready to go, as well as a full Microsoft Excel spreadsheet containing very granular support and documentation of all values, along with the equations of the models used (with your subject company inputs plugged in). The Toolkit also automatically performs risk study analysis that can be used as a powerful defense of company-specific risk adjustments. Plus, it is very simple and intuitive to use.

**Q: Previously, Morningstar published a report titled Risk Premia Over Time. Is this report included in the Valuation Handbook – Guide to Cost of Capital?**

**A: **The *Risk Premia Over Time* report was a PDF report containing many data tables from the *SBBI Valuation Yearbook*. This report no longer exists. Most of the data available in that report are now published in the *Valuation Handbook – Guide to Cost of Capital*. Some notable exceptions are the full “wedge” tables for long-term, intermediate-term, and short-term historical ERPs, and the full “wedge” tables for Mid-, Low-, and Micro-cap size premia. This is not to say that this information is not available in the *Valuation Handbook – Guide to Cost of Capital* (it is), but it is only presented for the most recent ERPs and Size premia as of the book “data through” date.

**Q: It appears that the SIC code divisions are more broad than in the Valuation Handbook – Industry Cost of Capital when compared with the Morningstar/Ibbotson Cost of Capital Yearbook. There seemed to be fewer 3 and 4 digit code breakouts. Why is this? **

**A: **Yes, there were more SICs presented in the former Morningstar/Ibbotson *Cost of Capital Yearbook* than are presented in the new *Valuation Handbook – Industry Cost of Capital*. There are two primary reasons for this: **Reason 1:** The company screening process used in the *Valuation Handbook – Industry Cost of Capital* is more rigorous than the company screening process employed in the former Morningstar/Ibbotson *Cost of Capital Yearbook*. The company screening process for the analyses presented in the *Valuation Handbook – Industry Cost of Capital* mimics the screening process employed in the Risk Premium Report Study Exhibits that are now published in the *Valuation Handbook – Guide to Cost of Capital*.

This more rigorous screening process naturally results is a smaller set of “healthy” companies, but this is by design: the set of companies remaining after this screening process (i) are “seasoned” companies in that they have been traded for several years, (ii) have been selling at least a minimal quantity of product or services, and (iii) have been able to achieve a degree of positive cash flow from operations.

Moreover, “high-financial-risk” companies are identified and analyzed separately in the new *Valuation Handbook – Industry Cost of Capital*. This analysis was not provided in the former Morningstar/Ibbotson *Cost of Capital Yearbook*. **Reason 2:** Many of the SICs in the former Morningstar/Ibbotson *Cost of Capital Yearbook* were “dupes”. For example, in the 2012 Morningstar/Ibbotson *Cost of Capital Yearbook*, SIC 21, SIC 211, and SIC 2111 were comprised of the same exact set of seven companies, and every single data point presented for SICs 21, 211, and 2111 was exactly identical. This did not increase the amount of information conveyed (SICs 21, 211, and 2111 were identical in every way), it merely increased “page count”.

**Q: What is the difference in the industry betas presented in the new Valuation Handbook – Industry Cost of Capital compared with those previously presented in the former Morningstar/Ibbotson Cost of Capital Yearbook? **

The former Morningstar/Ibbotson

*Cost of Capital Yearbook presented*:

- levered “raw” OLS betas,
- levered “adjusted” betas, and
- unlevered “adjusted” betas.

*Valuation Handbook – Industry Cost of Capital*presents:

- levered “raw” OLS betas,
- levered “Blume-adjusted” raw OLS betas,
- levered “Peer Group” betas,
- levered “Vasicek-adjusted” betas,
- levered “Sum” betas,
- levered “Downside” betas,
- unlevered “raw” OLS betas,
- unlevered “Blume-adjusted” raw OLS betas,
- unlevered “Peer Group” betas,
- unlevered “Vasicek-adjusted” betas,
- unlevered “Sum” betas, and
- unlevered “Downside” betas.

**Q: What is the difference in the industry cost of capital presented in the new Valuation Handbook – Industry Cost of Capital compared with those previously presented in the former Morningstar/Ibbotson Cost of Capital Yearbook? **

**A:**The former Morningstar/Ibbotson

*Cost of Capital Yearbook presented*:

- CAPM
- CAPM + Size Premium
- 3-factor Fama-French
- 1-stage discounted cash flow (DCF) model
- 3-stage discounted cash flow (DCF) model

*Valuation Handbook – Industry Cost of Capital*presents:

- CAPM
- CAPM + Size Premium (using the CRSP Deciles Size Study, which is the data previously published in the Morningstar/Ibbotson SBBI Valuation Yearbook, but now published in the Duff & Phelps Valuation Handbook – Guide to Cost of Capital)
- Build-up (using the CRSP Deciles Size Study, which is the data previously published in the Morningstar/Ibbotson SBBI Valuation Yearbook, but now published in the Duff & Phelps Valuation Handbook – Guide to Cost of Capital)
- CAPM + Size Premium (using the Risk Premium Report Study, which is the data previously published in the Duff & Phelps Risk Premium Report, but now published in the Duff & Phelps Valuation Handbook – Guide to Cost of Capital)
- Build-up (using the Risk Premium Report Study, which is the data previously published in the Duff & Phelps Risk Premium Report, but now published in the Duff & Phelps Valuation Handbook – Guide to Cost of Capital)
- 1-stage discounted cash flow (DCF) model
- 3-stage discounted cash flow (DCF) model
- 5-factor Fama-French (3-factor was presented in the 2014 book; this was changed to the 5-factor Fama-French model in the 2015 book), and
- In addition, the
*Valuation Handbook – Industry Cost of Capital*presents the Fama-French 5-factor model components calculated for each iindustry (F-F beta, SMB Premium, HML Premium, RMW Premium, and CMA Premium). This analysis was not provided in the former Morningstar/Ibbotson*Cost of Capital Yearbook*

**INTERNATIONAL**

**Q: Can the Duff & Phelps Risk Premium Report be used for non-US companies?**

**A: **The underlying data in the D&P Risk Premium Report and Toolkit are based on U.S. market data. The report and Toolkit derive a size premium of small U.S. companies relative to large U.S. companies. The data is therefore most appropriately used in valuing U.S. companies.

In the absence of any alternative data, one could arguably apply the U.S. data to non-U.S. valuations (with the thought being that, if there is nothing else available, you use what is available). However, one needs to be cognizant that (i) while the characteristics of the U.S. economy and other economies may be similar in some aspects, there can be significant differences, and (ii) by using the Report and Toolkit for non-US valuations, the implicit assumption is that a “large” or “small” company in the subject-company country are the same animals as a “large” or “small” U.S company. For example, a “small” company in the US may be a “large” company in say, Greece.

Also, the equity risk premium (ERP) is different for every country. For more information on determining an equity risk premium or developing a cost of equity capital for a non-US company it will be helpful to read Roger Grabowski and Shannon Pratt’s *Cost of Capital 5th edition* (Wiley, 2014), Chapter 39, “Global Cost of Capital Models.”

Other resources for international analysis provided by Duff & Phelps include the *International Valuation Handbook – Guide to Cost of Capital* which provides country-level equity risk premia (ERPs), relative volatility (RV) factors, and country risk premia (CRPs) which can be used to estimate country-level cost of equity capital globally, for up to 188 countries, from the perspective of investors based in any one of up to 56 countries (depending on data availability), and the *International Valuation Handbook – Industry Cost of Capital* which provides the same type of rigorous industry-level analysis published in the U.S.-centric *Valuation Handbook – Industry Cost of Capital*, on a global scale.

Another source of information can be found in Elroy Dimson, Paul Marsh, and Mike Staunton’s Credit Suisse Global Investment Returns Yearbook.

**INPUTTING DATA**

**Q: What is the minimum number of sizes study inputs and risk study inputs?**

**A: **For the size study, only 1 of the 8 inputs is required since they are independently calculated, but it is recommended that you use as many inputs as are available to you for best results.

For the risk study, no inputs are required (and the risk study will not be used). If you desire to use the risk study, a minimum of 3 years of financial data are required (5 years of data are recommended for best results).

**Q: The Toolkit asks for some inputs in millions. What about for a smaller company with revenues of $500K—would I enter that as .5?**

**A: **Yes – that is correct.

**Q:** **I am confused as to size study inputs and risk study inputs - are these from the Duff & Phelps study or are they the subject?**

**A: **They are for the subject company. The Toolkit uses the 8 alternative measures of size (or as many as are available for your subject company) for the size study, and the subject company accounting data entered for the risk study, to calculate COE for your subject company.

**Q:** **I see that the risk free rate is automatically populated. Where does this information come from? Can I change it? **

**A: **The risk-free rate information comes from the Federal Reserve and is the yield on a 20 year treasury based on the valuation date you entered—it is automatically populated as a convenience to you, but you can change the number if you wish by typing over it. The Toolkit will automatically populate the last closing yield prior to your valuation date unless changed.

**Q: Is there a free online resource for industry betas to help me populate the beta field?A: **Yes. Aswath Damodaran publishes industry betas on the NYU Stern page here.

**Q: How is market value of common equity determined without first having ERP?**

**A: **There are up to 8 alternative size measures that can be used with any of the four methods of estimating COE provided by the Duff & Phelps Risk Premium Report's "Size Study". It is important to note that it would not be unusual for fewer than 8 of these measures to be available for any given subject company. For example, market value of equity will probably not be available for a closely-held company, nor will market value of invested capital (in which market value of equity is embedded). In cases where fewer than 8 size measures are available, it is generally acceptable to use the size measures that are available.

**Q:**

**In the risk study inputs section, can I change the date for the most recent year?**

A:You can enter whatever year you consider to be the "most recent year" relative to the valuation date.

A:

**METHODOLOGY**

**Q: What Cost of Equity (COE) calculations does the Toolkit provide?A: **The Toolkit 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.

**Q: Are the formulas for the calculations given in the executive summary and support documents?A: **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.

**Q: Should I use the guideline portfolio method or the regression method?A:** The Duff & Phelps Risk Premium Report and Duff & Phelps Risk Premium Toolkit 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.

**Q: When using the normalized risk free rate, can you use the smoothed risk premium when using it at the same time?**

**A:**Yes. It is preferred you use the smoothed premium. Doing so dampens the effect of outliers, and tends to be a more “conservative” estimate in most cases (it will tend to be slightly lower, in say, the 25th portfolio).

**Q: If you are using the normalized risk free rate, do you still use the ERP adjustment? (for example, Exhibit A, must use ERP adjustment but want to make sure there is no double dipping)**

**A:**Yes.

**Q: What is the relationship of the D&P recommended ERP (p16) to the smoothed premium? Is this recommended ERP (p16) only used to adjust for the ERP but ignored when using the ERP in excess of RFR smoothed premium?**

**A:**The ERP and the smoothed risk premia from the A exhibits are two different things.

2 simple rules:

Rule 1: if you are using a “risk premium over the risk free rate” premium from the A exhibits, you are using a premium that has the “historical” 1963-present ERP embedded in it. What you do with the ERP adjustment is, in effect, extracting the 1963-present ERP from the premium, and replacing it with your own estimate of ERP.

Example: premium from A exhibits = [1963 to present ERP + some other value]. For the sake of this demonstration, let’s just say the “1963 to present ERP” is 4.5%, and the “other value” is 7%. So this A exhibit premium is 11.5%
If I choose to use the Duff & Phelps recommended ERP as of December 31, 2012 (5.5%), I can do either of two things, each for which I end up with the same answer:

1.) extract the “1963 to presen tERP” from my A exhibit premium and put the 5.5% ERP in, so that now my A exhibit premium is now [5.5% + 7%] = 12.5%, OR

2.) I can calculate the ERP adjustment as (5.5% - 4.5%) = 1%, and then add this to the original A Exhibit premium [4.5% + 7%] + 1% = 12.5%

Rule 2: If you are using a “size premium” from the B exhibits, these premia never need to have the ERP adjustment added to them.

The problem that can come up is that if a valuation professional calculates a COE using the build up method (using Exhibit A premia, which are for buildup method) and does not do the ERP adjustment, and then in the same engagement calculates COE using CAPM (using Exhibit B size premia, which are for the CAPM method), but uses a 5.5% ERP, he/she is effectively using TWO DIFFERENT ERPs in the same engagement.

**Q: If I have a valuation date of say 2011, what year does the Toolkit use data from?A:** If you had a valuation date in 2011, the Toolkit 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 Toolkit will soon include additional functionality that will allow the user to select which year they wish to use data from.

**Q: Can I use the Toolkit to value small companies with less than $1 million in financial data? A: **The Duff & Phelps Risk Premium Report and Duff & Phelps Risk Premium Toolkit 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.

**Q: Can you please explain your regression equation?A:
**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

**Q: 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?**

**A: **Both levered betas and unlevered betas are developed for each of the portfolios in the Report and Toolkit.

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

**A:**The Duff & Phelps Risk Premium Report and the Duff & Phelps Risk Premium Toolkit 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 use 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.

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

**A: **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 this rudimentary adjustment, while not perfect, attempts to account for those differences.

**Q:**

**Currently, the authors of the Toolkit recommend entering an ERP of 5.0% (as of December 31, 2015). Why is this?**

**A:**The equity risk premium (or “ERP”; often interchangeably referred to as the “market risk premium”) is defined as the extra return over the expected yield on risk-free securities that investors expect to receive from an investment in a diversified portfolio of common stocks. Duff & Phelps regularly reviews fluctuations in global economic and financial conditions that warrant periodic reassessments of ERP.

- As of December 31, 2015, the Duff & Phelps Recommended U.S. ERP is 5.0%, used in conjunction with a 4.0% normalized risk free rate. This implies a base cost of capital of 9.0% (5.0% + 4.0%) in the U.S. for valuations as of December 31, 2015.
- However, for valuation dates as of January 31, 2016 (and thereafter, until further notice) we are increasing our concluded conditional ERP to 5.5%, matched with a normalized yield on 20-year U.S. government bonds equal to 4.0%, implying a 9.5% base cost of equity capital in the United States.

To ensure that you are using the most recent Duff & Phelps ERP recommendation (and for a free download of a historical table of Duff & Phelps Recommended U.S. ERP and accompanying risk free rates, and other important information on cost of capital issues), please visit www.DuffandPhelps.com/CostofCapital and click on "View Historical Equity Risk Premium Recommendations".

NOTE: If an ERP is not entered, all calculations will default to the historical ERP as calculated from 1963–year of the Report year chosen minus 1. For example, if an ERP is not entered, and the source of risk premia data is the 2016 Report, the ERP defaults to the historical ERP (4.9%) as calculated over the time period 1963 to 2015 (2016 minus 1).

**Q: What is the ERP Adjustment?**

**A: **The ERP Adjustment is calculated as the simple difference between the ERP the user has selected for use in his or her cost of equity capital estimates minus the historical 1963–present ERP. In the *2016 Valuation Handbook*, the historical ERP used as a convention in the calculations of the Risk Premium Report exhibits was 4.93% (4.9% rounded). The ERP adjustment for Risk Premium Report data published in the *2016 Valuation Handbook* is therefore calculated as follows:*ERP Adjustment = ERP that User has selected – Historical* ERP (1963–2015)*ERP Adjustment = ERP that User has selected* – 4.9%

For more information on the equity risk premium (also known as the market risk premium), see *Cost of Capital: Applications and Examples 5th ed*., by Shannon P. Pratt and Roger J. Grabowski (John Wiley & Sons, Inc., 2014), Chapter 8, “Equity Risk Premium”.

**Q: I see that the Toolkit 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?A:** For z-scores less than one, you might consider using "high financial risk premia" provided by the Toolkit.

**Q: Does the Toolkit work for non-US-based companies?**

**A: **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 Toolkit.

**Q: Do the final cost of equity (COE) results in the Toolkit include company-specific risk?**

**A: **All of the COE estimates are before unsystematic risk (sometimes referred to as company-specific risk) is added. This is something the practitioner comes up with (and must independently justify and support).

Duff & Phelps includes the “RPu” in all the equations to remind users that it is technically supposed to be there as a “possible” additional adjustment.

**Q: What is the company screening process Duff & Phelps employs and why are there sometimes fewer companies per SIC code listed within the Industry Cost of Capital when compared with the Guide to Cost of Capital?**

**A:** The company screening process employed by Duff & Phelps looks for (i) “seasoned” companies in that they have been publicly traded for several years, (ii) have been selling at least a minimal quantity of product or service, and (iii) have been able to achieve a degree of positive cash flow from operations.

Once the company screening process is complete, an industry must have at least (5) companies in order to be included in the analyses.

The *Industry Cost of Capital* takes the company screening process one step further by identifying those companies that have at least 75% of their revenue derived from a single business segment. This is why the *Industry Cost of Capital* may list fewer companies for an SIC when compared with the industry risk premium (IRP) section of the *Guide to Cost of Capital*: Any publicly traded company that meets the above screening process and with operations in that SIC code will be utilized to compute the IRP in the Guide to Cost of Capital, but the company must derive at least 75% of their revenue from that industry to be included in that SIC code in the Industry Cost of Capital.

For more information about the company screening process and how it differs between the two publications, please refer to the “Methodology” sections of the Valuation Handbook – Industry Cost of Capital and Valuation Handbook – Guide to Cost of Capital.