Cost of Capital Professional Frequently Asked Questions (FAQs)
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Q: What is the legend for general information?
The name of the subject company being valued.
This information will be used in the summary output. (Optional)
The valuation date for the assignment.
The valuation date is used for providing information for risk-free rate, equity risk premium, and size premium. (Please see “Returns Reference – End Date” and “Treasury Constant Maturity” below.)
Returns Reference – Start Year
The starting year used to calculate the historical equity risk premium and historical size premium.
The analyst may select from 1928, 1963, 1982, or enter a custom year. CRSP data go back to the 1920s. Compustat data, used by some analysts, go back to the 1960s. Banz first documented the size premium in 1981, and size premium in listed firms has diminished or disappeared since that time.
Returns Reference – End Year
The ending year to calculate the historical equity risk premium and historical size premium.
The user’s choice for “Valuation Date” determines the options presented. Please see FAQs below for more information.
Q: What is the legend for the risk-free rate information?
U.S. Treasury Bond Constant Maturity – 20-Year
The spot yield on the 20-year U.S. Treasury bond based on the specified valuation date. The information is retrieved from the Federal Reserve, the U.S. central bank.
U.S. Treasury Bond Constant Maturity – 10-Year
The spot yield on the 10-year U.S. Treasury bond based on the specified valuation date. The information is retrieved from the Federal Reserve, the U.S. central bank.
Custom Risk-Free Rate
A custom risk-free rate entered by the analyst. Any notes associated with a custom risk-free rate may also be entered.
Q: What is the legend for the equity risk premium (ERP) information?
CRSP – Historical ERP
The historical ERP computed as the average difference between the average annualized monthly return of CRSP’s S&P 500 Universe (500 stocks since March 1957 and 90 stocks prior) value-weighted and the annualized monthly return for the 10-year U.S. Treasury or the 20-year U.S. Treasury. Sourced from the Center for Research in Security Prices (CRSP).
Damodaran – Implied ERP
A forward-looking ERP based on the analyst’s “Returns Reference – End Date,” sourced from Dr. Aswath Damodaran. Please see below FAQs for more information.
Damodaran – Implied ERP With Sustainable Payout
A forward-looking ERP based on the analyst’s “Returns Reference – End Date,” sourced from Dr. Aswath Damodaran. Please see below FAQs for more information.
Damodaran – Historical ERP
The historical ERP based on the analyst’s “Returns Reference – Start Date” and “Returns Reference – End Date,” sourced from Dr. Aswath Damodaran.
A custom ERP entered by the analyst. Any notes associated with a custom ERP may also be entered.
Q: What is the legend for the CRSP sizes premium information?
Organized by 1 = Largest to 10 = Smallest, these deciles represent 10 portfolios created by the Center for Research in Security Prices (CRSP) based on market capitalization as a measure of firm size. This measure for firm size has been used widely in academic research.The CRSP methodology for decile formation uses the universe of common stocks of eligible companies listed on the NYSE, NYSE MKT, and Nasdaq National Market. The universe omits unit investment trusts, closed-end funds, REITs, Americus Trusts, foreign stocks, and American Depository Receipts. Eligible companies trading mainly on NYSE are ranked into equally populated deciles. The largest capitalizations in each decile are the breakpoints for decile assignment for all eligible companies on all exchanges. Eligible NYSE MKT and Nasdaq National Market firms are then assigned to deciles based on these breakpoints. This practice is used frequently in academic research.
Min Size/Max Size ($000)
These represent the breakpoints for the decile for the selected Returns Reference – End Year. The breakpoints shown are the minimum market capitalization and maximum capitalization of firms by the “Returns Reference – End Year.
The number of firms in the decile by the “Returns Reference– End Year.”
The average annualized monthly common stock return of firms in the decile over the historical period specified by the “Returns Reference – Start Year” and “Returns Reference – End Year.”
Annual return information has been derived from CRSP monthly return data. Arithmetic average monthly returns have been annualized using the standard procedure: ((1+ Monthly return)^12) -1.
Computed as average annualized monthly decile return minus the average annualized monthly return of CRSP’s S&P 500 Universe (500 stocks since March 1957 and 90 stocks prior) value-weighted over the historical time period specified by the “Returns Reference – Start Date” and “Returns Reference – End Date.”
Annual return information has been derived from CRSP monthly return data. Arithmetic average monthly returns have been annualized using the standard procedure: ((1 + Monthly return)^12) - 1.
Q: What is the source of the data used in the Cost of Capital Professional platform?
A: The spot risk-free rate information (10-year and 20-year Treasury bonds) for the relevant valuation data is sourced from the Federal Reserve.
The information for the CRSP ERP and CRSP Size Premium is sourced from the Center for Research in Security Prices of the University of Chicago except pre-1942 T-bond return data described below.
Historical returns on risk-free assets (10-year and 20-year Treasury bonds) after 1941 are sourced from CRSP. Prior to the early 1940s, CRSP does not provide T-bond return data because T-bonds before that time had different tax characteristics than T-bonds since then. Prior to 1942, we source T-bond returns from Dr. Aswath Damodaran’s data library where he provides returns on 10-year T-bonds. Prior to 1942, for 20-year T-bond returns, we reconstruct returns from the 10-year returns adjusted for the historic return difference between 10-year and 20-year T-bonds reported by CRSP.
The implied ERP, implied ERP with sustainable payout, and the Damodaran historical ERP are sourced from Dr. Aswath Damodaran’s data library at New York University.
Dr. Aswath Damodaran’s data are used with his permission. Dr. Aswath Damodaran has no formal role or connection with BVR or the Cost of Capital Professional.
Q: Is the Cost of Capital Professional platform a “black box”?
A: Absolutely not. The user will see the CRSP decile size premium table, as well as the calculations for the historical ERPs and size premiums.
Q: The Cost of Capital Professional allows me to choose my start year for which my equity risk premium and size premium are measured. Why is this, and which start year should I choose?
A: The Cost of Capital Professional was created to empower analysts with objective data and a flexible platform. From the platform information, the analyst still needs to apply professional judgment, which includes choosing the period of historical returns to use. According to theory, risk premiums in cost of capital models are forward looking. They represent components of what investors expect to receive as asset returns. If using historical returns to estimate investor expected returns, choose the part of history that you believe best represents investor expectations of the future by first choosing a starting year of historical return data.
Q: Why is the first start year 1928 instead of 1926?
A: The Cost of Capital Professional uses 1928 because this is the earliest date for data provided by Dr. Damodaran, and we wanted his data to align with the data provided by CRSP. Whether one starts with 1926 or 1928, average returns over 90 versus 92 years change very little.
Q: How often is the information for risk-free rates, ERPs, and size premiums updated?
A: The provided risk-free rate information is updated each trading day. The CRSP ERP and Size Premium information are updated quarterly. The ERP information provided by Dr. Aswath Damodaran is updated annually.While CRSP provides data updates frequently, our ERP and size premium calculations are annual because components in some calculations use data updated only annually. The Cost of Capital Professional applies quarterly CRSP data refreshes for any changes that CRSP makes to its year-end data for any missing data or error corrections. Although CRSP error corrections to its historical data are likely rare, we want to provide the best information possible by having quarterly CRSP data refreshes.
Q: Does the Cost of Capital Professional platform include subdivisions of the 10th decile holding smaller listed firms? If not, why?
A: No. Returns of smaller listed firms likely have multiple factors affecting their returns other than firm size. In general, smaller listed firms are small for reasons such as firm characteristics of poor profitability, cash flow problems, or high leverage. See, for example, K. C. Chan and Nai-Fu Chen, “Structural and Return Characteristics of Small and Large Firms,” The Journal of Finance, 1991, no. 4: 1467. doi:10.2307/2328867. Such characteristics of smaller listed firms may differ from those of unlisted firms being valued making simple inferences from smaller listed firms to unlisted firms possibly unreliable.
Q: I am trying to reconcile the historical equity risk premiums reported in the Cost of Capital Professional with those from another source and I am finding that they are different. Can you please explain why?
A: In short, in measuring historical equity risk premiums, part of the difference is attributed to methodology, while another part may be due to differences in the data sources used.
Cost of Capital Professional measures historical ERP as:
Mean return of the CRSP’s S&P 500 Universe minus mean return of Treasury bonds (please see definition for “CRSP – Historical ERP” toward the top of the FAQ page).
CRSP measures monthly bond returns for a Treasury bond from the monthly price change plus interest, divided by last month’s price (please see CRSP 1925 Historical Indexes Guide, p. 9).
Q: I am trying to reconcile the size premiums reported in the Cost of Capital Professional with those from another source and I am finding that they are different. Can you please explain why?
A: The Cost of Capital Professional does not use a CAPM methodology (see the methodology in the “Size Premium” definition in the table above).
The Cost of Capital Professional relies on historical return data from CRSP. It compares the mean decile return to the S&P 500 mean return and takes the difference as an estimate of the decile size premium. Put differently, our size premium measure is the extra decile return over the S&P 500 return. The S&P 500 is a proxy for the market portfolio used in the equity risk premium.
A CAPM methodology to estimate size premiums uses CAPM beta. Since smaller firms have higher betas on average, size premiums for smaller firms using this methodology tend to be lower because a larger beta siphons off some of the extra decile return over the S&P 500 return.
Q: How does the Cost of Capital Professional platform measure firm size for the size premium?
A: The Cost of Capital Professional platform presents return data across firm sizes with size measured as market value of equity (market capitalization). This measure is very likely the most common measure of firm size in academic research on the cross-section of equity returns (see, for instance, Yakov Amihud and Haim Mendelson, “The Effects of Beta, Bid-Ask Spread, Residual Risk, and Size on Stock Returns,” Journal of Finance, 1989, 44:479-86; Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock Returns,” Journal of Finance, 1992, 47:427-65; Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Returns on Stocks and Bonds,” Journal of Financial Economics, 1993, 33:3-56; Mark M. Carhart, “On Persistence in Mutual Fund Performance, Journal of Finance, 1997, 52:57-82). Use of market value of equity for firm size is market-oriented and captures forward-looking expectations of market participants.
In contrast to research using market value of equity for firm size, academic studies using nonmarket measures for size (e.g., book value of assets, annual sales, number of employees) show no size premium in smaller listed firms not otherwise predicted by CAPM (see, for instance, Jonathan B. Berk, “An Empirical Re-examination of the Size Relation Between Firm Size and Returns,” working paper, University of Washington, 1996; and Jonathan B. Berk, “Does Size Really Matter?” Financial Analysts Journal, 1997, 53(5): 12-18.)
Q: What are the options for the “Returns Reference – End Year” field?
A: The provided options are dependent on the analyst’s entry in the “Valuation Date” field. Generally, the provided year will be the valuation date year - 1 year. For a valuation date in 2019, for instance, the provided end year will be 2018 unless the Q4 2018 CRSP data have not yet been published.
For valuation dates in December, the provided options are the valuation date year - 1 and, if available at the time of user access, the valuation date year. For instance, a valuation date in December 2018 will have year-end options of 2017 and, if available at the time of user access, 2018.
For valuation dates in January and February, the provided options for the valuation date year - 1, if available at the time of user access, and the valuation date year - 2, For instance, a valuation date of Jan. 15, 2019, will have year-end options of 2018, if available at the time of user access, and 2017.
Q: Will you please explain the Implied ERP and the Implied ERP With Sustainable Payout?
A: Dr. Aswath Damodaran, a professor of corporate finance and valuation at the Stern School of Business at New York University, calculates both the Implied ERP and the Implied ERP With Sustainable Payout. Implied ERP is a forward-looking measure ERP based on observed current market information rather than an average of past returns over decades. For more information, please read “Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2018 Edition.”
Q: Along with the 10 CRSP decile size premiums, does the Cost of Capital Professional platform provide any other size premiums figures?
A: Yes. It provides historical size premiums for the following combined portfolio groups: micro-cap (deciles 9-10), small-cap (deciles 6-8), mid-cap (deciles 3-5), and large-cap (deciles 1-2).
Q: Are there any free online resources for industry CAPM betas that I could use to populate the CAPM beta field or derive an industry risk premium?
Q: Am I able to select my own values for the risk-free rate and equity risk premium?
A: Yes. You can enter your own values for the risk-free rate and equity risk premium if you wish. You are also provided with an accompanying field to enter any notes that may be associated with your selection.
Q: Am I able to save any of my cost of equity calculations to revisit at a later date?
A: Yes. You can save your calculation by selecting the “Save” option in the upper-right corner of the tool. When saving your work, you have the ability to provide a unique name for your saved work, as well as a space to include any notes that may be associated with your saved calculation. You can revisit all of your saved calculations at any time by selecting the “Recent” option in the upper-right corner of the tool.
Q: What are the outputs of the Cost of Capital Professional platform?
A: The output is a summary of your cost of equity estimates that can easily be copied and pasted into your work product.
Q: My subject company is smaller than the companies in the 10th decile (the smallest listed companies). Which size premium should I select?
A: The data for the 10th decile provide premium information for the smallest listed firms (based on market capitalization). An adjustment to the 10th decile size premium may be appropriate for smaller unlisted firms based on the analyst’s professional judgment.
Q: Am I able to use the size premiums in the Cost of Capital Professional in estimating the cost of equity when using the CAPM if the size premiums shown are not size premiums “in excess of CAPM”?
A: The size premium information shown in Cost of Capital Professional is based on the difference between average decile returns and average return of the S&P 500 Universe. This methodology is logically consistent with the build-up model for estimating cost of equity capital of Ri = Rf + ERP + RPni. Our platform does not use the capital asset pricing model (CAPM) to develop size premium information.
A CAPM approach to develop size premium information uses CAPM beta (β) in a model such as:
Ri = Rf + (ERP × βi) + SPi
The use of the CAPM approach to develop size premium information (i.e., the so-called size premium in excess of CAPM) assumes that CAPM beta does not adequately explain returns of smaller listed firms. Recent studies have created doubt about the assumption that beta is an incomplete or inadequate risk measure (see, for instance, Eugene F. Fama and Kenneth R. French, "Size, Value, and Momentum in International Stock Returns," Journal of Financial Economics, 105 (3):457-472, 2012; and Ron Alquist, Ronen Israel, and Tobias Moskowitz. "Fact, Fiction, and the Size Effect," The Journal of Portfolio Management, 45 (1):34-61, 2018.)
Smaller listed firms tend to have higher CAPM betas. Logically, the CAPM approach to develop size premium information results in lower size premiums than the Cost of Capital Professional methodology because higher betas in smaller listed firms siphon off some of small-firm returns above S&P 500 returns that may appear.
Since the CAPM approach to develop size premium information uses constructed beta and a mathematical model, there is no natural way to convert size premiums derived by comparing S&P 500 Universe and decile returns to size premiums using CAPM betas. It depends, in part, on the methodology one uses to construct decile betas.
A plausible approach to transform size premiums derived by comparing decile and S&P 500 Universe (assuming beta of S&P 500 = 1.0) returns presented on the Cost of Capital Professional into size premiums using the CAPM (i.e., size premium in excess of CAPM) is taking a size premium derived by comparing S&P 500 Universe and decile returns and dividing by the relevant decile beta. Assuming a decile beta greater than 1.0, this approach results in a size premium smaller than a size premium derived by comparing S&P 500 Universe (assuming a beta = 1.0) and decile returns.
Q: Can the Cost of Capital Professional platform be used for non-U.S.-based companies?
A: Generally, one would want to use risk premia developed using U.S. data for valuations of U.S.-based firms. The data for the Cost of Capital Professional platform are on firms listed on U.S. stock exchanges. Equity risk premium and size premium measures are the results of these U.S. data. For valuations of firms in other countries, the analyst should carefully assess whether U.S. data are useful for his or her valuation or could be adapted to his or her location.