ValuSource

Duff & Phelps Risk Premium Report Calculator

Contents

This document is divided into three sections:

Disclaimer & Limitations

Single User Site License Agreement

Frequently Asked Questions

Disclaimer & Limitations

Copyright © 2012 Duff & Phelps, LLC. All Rights Reserved. The information presented in this publication has been obtained with the greatest of care from sources believed to be reliable, but is not guaranteed to be complete, accurate or timely. ValuSource LLC and Duff & Phelps LLC expressly disclaim any liability, including incidental or consequential damages, arising from the use of this publication or any errors or omissions that may be contained in it. No part of this publication may be reproduced or used in any other form or by any other means—graphic, electronic, or mechanical, including photocopying, recording, taping, or information storage and retrieval systems—without Duff & Phelps LLC’s prior, written permission. To obtain permission, please write to: Risk Premium Report, Duff & Phelps LLC, 311 S. Wacker Dr., Suite 4200, Chicago, IL 60606.Your request should specify the data or other information you wish to use and the manner in which you wish to use it. In addition, you will need to include copies of any charts, tables, and/or figures that you have created based on that information. There is a $1500 processing fee per request. There may be additional fees depending on your proposed usage.

A source of the risk premia used in estimating the cost of equity capital (“required rate of return on equity capital”, “cost of equity, or “COE”) is the Duff & Phelps Risk Premium Report. The information and data presented in the Duff & Phelps Risk Premium Report has been obtained with the greatest of care from sources believed to be reliable, but is not guaranteed to be complete, accurate or timely. Duff & Phelps, LLC expressly disclaims any liability, including incidental or consequential damages, arising from the use of the Duff & Phelps Risk Premia Report or any errors or omissions that may be contained in it. Copyright © 2012 Duff & Phelps, LLC. All Rights Reserved.

Single User Site License Agreement

VALUSOURCE grants you access to specific information in online databases at www.vswebapp.com contingent upon your agreement to all of the following terms. Please carefully read this entire page. This is a legal agreement pertaining to content accessed on VALUSOURCE's or any of its content partner Web sites as part of a paid single or multiuser Agreement. Your consent to these terms will be binding on you, your employer, and your fellow employees. By using the online databases are consenting to be bound by this Limited Single User License Agreement and Limitation of Warranty.
You agree that you may NOT, and may NOT permit others to log in with your user name or password, use, transmit electronically, download electronically or in hard copy, post to a database or to the Internet, or otherwise reproduce in any fashion any portion of VALUSOURCE's information databases, except as expressly authorized in the next paragraphs of this Limited Single User License Agreement.
You, as the Single User, are authorized to download into electronic storage and to print hard copies of a reasonable number of pages for your personal or professional use. You agree that you will NOT attempt to download, either in electronic or in hard-copy format, any substantial portion of it.
You, as the Single User, may NOT, however, distribute, modify, transmit, reuse, re-post, resell, or use the content of the VALUSOURCE sites or content partner sites, including text, images, audio, and video, for public or commercial purposes without the written permission of VALUSOURCE.
You, as the single user, may use data from VALUSOURCE databases in conjunction with preparing a valuation report, whether written or oral, prepared by you for yourself or a client. This includes such use to support a valuation report in deposition or trial testimony.
VALUSOURCE, or its content partners, may at any time revise this Limited Single User License Agreement. You will be required to agree with these revised versions, if any, before you will be permitted access to the product again.
ValuSource, LLC, gathers its data from sources it considers reliable. Although every precaution has been taken in preparation of the products we offer, ValuSource, LLC, and the authors of the products we offer assume no responsibility for errors or omissions, regardless of the cause of such inaccuracy, non-authenticity, error, or omission. VALUSOURCE, LLC, AND THE AUTHORS OF THE PRODUCTS WE OFFER EXPRESSLY DISCLAIM ANY LIABILITY, INCLUDING INCIDENTAL OR CONSEQUENTIAL DAMAGES, ARISING FROM ERRORS OR OMISSIONS IN ITS PRODUCTS. FURTHERMORE, THE INFORMATION REPORTED MAY BE CONFIDENTIAL AND MAY NOT BE AVAILABLE FOR VERIFICATION IN SUPPORT OF LITIGATION.
This License Agreement for the Duff & Phelps Risk Premium report is in addition to ValuSource’s regular posted License agreement. If there is a discrepancy between the two agreements, Valusource’s regular License agreement will take precedence.

Last updated: May 2012

Frequently Asked Questions

General

What is the Duff & Phelps Risk Premium Calculator?
The Calculator 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
What is the main difference between using Duff & Phelps data compared with the SBBI Valuation Yearbook?
The largest difference is that SBBI only considers market capitalization as a measure of size, while the Duff & Phelps Risk Premium Report and Duff & Phelps Risk Premium Calculator consider market capitalization plus 7 other measures of size.
Will the Calculator be available on a per use basis?
Yes - when one purchases the Duff & Phelps Risk Premium Report, it comes with one complimentary use of the Calculator. Currently, there is no other single use purchase option, but you can purchase a one-year subscription.
What subscription options are available for the Calculator?
A one-year subscription to the Calculator can be purchased containing either (1) all data from 1996 through current; or (2) the two most recent years of data. A subscription to the Calculator includes a free PDF of the Duff & Phelps Risk Premium Report. You can purchase the Calculator here.
What are the outputs of the Calculator?
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.
Is the Calculator a “block box”?
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 Calculator’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).
How does the Duff & Phelps Risk Premium Calculator differ from other calculators?
The Duff & Phelps Risk Premium Calculator is the most advanced and feature-rich valuation tool of its kind on the market.

The Duff & Phelps Risk Premium Calculator 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 Calculator 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.

But maybe the most important feature is that the Duff & Phelps Risk Premium Calculator was built by the authors of the Duff & Phelps Risk Premium Report!

Inputting Data

What is the minimum number of Size Study inputs and Risk Study inputs?
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).
The Calculator asks for some inputs in millions. What about for a smaller company with revenues of $500K—would I enter that as .5?
Yes – that is correct.
I am confused as to Size Study inputs and Risk Study inputs - are these from the Duff & Phelps study or are they the subject?
They are for the subject company. The Calculator 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.
I see that the Risk Free Rate is automatically populated. Where does this information come from? Can I change it?
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 Calculator will automatically populate the last closing yield prior to your valuation date unless changed.
How is Market Value of Common Equity determined without first having ERP?

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.
In the Risk Study inputs section, can I change the date for the most recent year?
You can enter whatever year you consider to be the "most recent year" relative to the valuation date.

Methodology

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.