Estimating the Cost of Equity Capital
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Estimating the Cost of Equity Capital

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Using Ibbotson Associates Cost of Capital Data


This chapter gives an overview of the various Ibbotson Associates publications useful in the estimation of cost of capital with emphasis on its benchmark publication. Stocks, Bonds, Bills and Inflation® (SBBI) Valuation Edition Yearbook. Topics to master in this chapter are: the Lypes of data available in each of Jbbotson's publications; the accepted uses of data within the models for estimating the cost of equity; the methodologies Ibbotson uses to derive it and. finally, the applicability of the data in specific valuation situations.


1. The most commonly used models for estimating ihc cost of equity capital are:


a. The build-up method and the Capital Asset Pricing Model (CAPM).


b. The Fama-French three-factor model and the discounted cash flow (DCF) model.


c. The build-up method and the DCF model.


d. CAPM and the DCF model.


2. The build-up method and CAPM are very similar, with the major exception of:


a. The risk-free rate.


b. The equity risk premium.


c. The firm size premium,


d. "Beta.


3. The ''size effect" or ''size phenomenon" refers to the fact that:


a. Different risk-free rates exist for large versus small companies.


b. Historically, small stocks have shown greater risk and greater return than large stocks.


c. Large companies usually have a higher cost of equity than small companies.


d. Historically, small stocks have shown greater risk and lower return than large stocks.


4. The method for computing the firm size premium (measuring the size effect) currently cm-ployed by ibbotson Associates is:


a. The difference between Ibbotson Small Company stock series returns and trie Standard & Poors (S&P) 500 Index total returns.


b. The difference between Ibbotson Small Company stock series returns and the New York Stock Exchange (NYSB) total returns.


c. The difference between Ibbotson Small Company stock series returns and the returns for each of the 1.0 deciles of the NYSE.


d. The actual return in excess of what CAPM predicts given the beta for a decile, otherwise known as the beta-adjusted premium.


5. The micro-cap size group is a consolidation of which of the following ranges of deciles?


a. Deciles 1 and 2.


b. Deciles 3 through 5.


c. Deciles 6 through 8.


d. Deciles 9 and 10.


6. The low-cap size group is a consolidation of which of the following ranges of deciles?


a. Deciles 1 and 2.


b. Deciles 3 through 5.


c. Deciles 6 through 8.


d. Deciles 9 and 10.



Estimating the Cost of Equity Capital

kless Rate

Estimating the Cost of Equity Capital u 15

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lief a


0.2


0.6


1.0


1.4


Source: Stocks, Bonds, Bills and Inflation2' Valuation Edition 2001 Yearbook, CO 2001 Ibbotson Associates. Inc. Used with permission. All rights reserved.


7. Exhibit 13.1 supports the existence of a firm size premium by showing thai:


a. As companies get smaller, their beta and CAPM-predicted return increase.


b. As companies get smaller, their beta and CAPM-predicted return decrease,


c. The full return of small companies is not fully explained by CAPM, and thai a size premium must be added.


d. "Both (a) and (c).


8. Ibbotson's position on the use of the firm size premium in connection with CAPM and the build-up method is that:


a. The beta-adjusted size premium is appropriate for application only in CAPM because the beta-adjusted prernia are consd in the context of CAPM.


b. The beta-adjusted size premium is appropriate for application in CAPM witiiout an industry" adjustment and in build-up models in conjunction with other prernia, including an ry adjustment.


c. The beta-adjusted size premium is appropriate to use only in the build-up model.


d. The non beta-adjusted size premium is appropriate to use in the build-up model because the build-up method does not include a beta.


9. 'i'he most common way of arriving at the expected equity risk premium is by:


a. Measuring the historical relationship of small stocks to large stocks.


b. Comparing the historical yields of long-term bonds to short-term notes and bills.


c. Measuring the difference in performance of a market aggregate over time.


d. .Measuring the historical relationship of slocks to U.S. government obligations.


10. The long-term government bond rate used in the compiitationof the equity risk premium is


typically most appropriate for business valuation purposes because (select the best answer):


a. The data are readily available in daily financial publications such as The Wall Street Journal.


b. The longer-term yields usually are higher than the short-term ones, leading to a more conservative equity risk premium estimate.


c. Ibbotson chose the long-term rate because its equity risk premium calculations start as far back as 1926.


d. Because most companies do not have a defined life span, they usually are valued as going concerns with indefinite lives.


11. The long-term equity risk premium is calculated by Ibbotson Associates as:


a. The geometric average total return on the S&P 500 less the geometric average income return on long-term Treasury bonds, using annual data for the last 30 years.


b. The arithmetic average total return on the S&P 500 less the arithmetic average income return on long-term Treasury bonds, using annual data from 1926 to the present.


c. The arithmetic average total return on the S&P 500 less the arithmetic average total return on long-term Treasury bonds, using annual data from 1926 to the present.


d. The arithmetic average total return on the S&P 500 less the arithmetic average income return on long-term Treasury bonds, using annual data for the last 30 years.


1.2. Exponential weighting of historical data is a method that places:


a. Higher weighting on more important events in the past.


b. Lower weighting on less important events in the past.


c. Higher weighting on the present and recent past,


d. No weighting on extreme events.


13. All of the following are conditions a company must meet to be included in the Ibbotson Associates Beta Book EXCEPT:


a. The company must have a beta lower than 1.5.


b. The company must have sales greater than $100,000 in the most recent year.


c. The company must have at least 36 months of return data,


d. The company must have a market capitalization greater than $ 10,000 for the most recent month,


14. Beta, the systematic risk for a company or a decile, is used in all of the following calculations EXCEPT:


a. The build-up method to estimate the cost of equity capital.


b. The Fama-French three-factor model to estimate the cost of equity.


c. CAPM to estimate the cost of equity,


d. The CAPM-predicted return in the calculation of the size premiuiii by decile of NYS E/AMEX/NAS D AQ.


15. In the contest of CAPM, a beta of 1.0 for a company means thai:


a. The company's estimated cost of equity is equal to the returns on the risk-free asset.


b. CAPM is unable to predict a meaningful result given the imperfect data available.


c. When the stock market goes down by a certain percentage, the company's return goes up by the same amount,


d. The expected movement in return on an equity investment in flic company is equal to that of the market.


16. Beta can be characterized as all of the following EXCEPT1:


a. Company-specific, unsystematic risk in CAPM.


b. The slope of the best fit line between the (excess) return on the individual security and the (excess) return on the market.


c. The modifier of the equity risk premium in CAPM.


d. A measure of the sensitivity' of the movement in returns on a particular stock to movement in returns on some measure of the market.


1 7. All the following methods can be used to find a proxy for a beta for a private company CBPf'i


a. Using an average beta for the industry as provided in the Ibbotson Associates Cost of Capital Yearbook.


b. Selecting specific guideline public companies and using some composites such as the median or average of their betas as provided in the Tbhotson Associates Beta Book.


c. Using a peer group beta as illustrated in the Ibbotson Associates Beta Book.


d. Regressing readily available excess returns on the private company against excess returns on the market,


18. Which of the following are about the industry riskpremia data developed by Ibbotson Associates and included in the SBBS Valuation Edition1'


I. CAPM has the ability to incorporate industry risk into the beta measure.


II. For the build-up method, it is possible to incorporate industry risk into a company-spe­cific premium,


III. The non-beta-adjusted size premium is more appropriate than the simple excess re­turns size premium to use in conjunction with an industry premium,


IV. The method Ibbotson uses for its industry risk premia relies on the full information beta estimation process.


a. 1, II, if!


b. 1,111, IV


c. 1,11, IV


d. II. Ill, IV


19. Readily available empirical data sources exist for betas of private companies.


20. In the Ibbotson Associates publications for valuation analysts, there is no distinction in meaning, compulation methodologies, or applications between the lssize premium" (beta-adjusted size premium) and the "small stock premium" (non-beta-adjusted premium).


21. The 10th decile used in the calculations of the size premium is the decile formed by the companies with the highest market capitalization (the top decile)-


22. A stock's market capitalization is calculated as Lhe number of shares of stock outstanding times the price per share of stock.


23. 10a and 1 Ob refer to the breakout of the 10th decile into two components.


Rxhibils 13.1 and 13.2 show the actual returns achieved by the 10 deciles and the security mar­ket line on which CAPM would predict the decile portfolios would fall.


24. The fact that most of Lhe decile portfolios fall above the security market line depicts (graphically) that the smaller the decile, the higher the returns in excess of the CAPM-predicted return.


3.2 Long-term Returns in Excess of CAPM Estimation for Decile Portfolios of the E/AM EX/NASDAQ (1926-2000)


Estimated

Size Premium

Realized Return

Return in Excess

(Return in

Arithmetic Mean

in Excess of

of Riskless

Excess of

Decile

Beta"

Return

Riskless Rate**

Rate***

CAPM)

1-Largest

0.91

12.06%

6.84%

7.03%

-0.20%

2

1.04

13.58%

8.36%

8.05%

0.31%

3

1.09

14.16%

8.93%

8.47%

0.47%

4

1.13

14.60%

9.38%.

8.75%.

0.62%

5

1.16

15.18%

9.95%

9.03%

0.93%

6

1.18

15.48%

10.26%

9.18%

1.08%

7

1.24

15.68%

10.46%

9.58%

0.88%

8

1.28

16.60%

11.38%

9.91%

1.47%

9

1.34

17.39%

12.17%

10.43%

1.74%

10-Smallesi

1.42

20.90%

15.67%

11.05%

4.63%

Mid-Cap, 3-5

1.12

14.46%

9.23%

8.65%

0.58%

Low-Cap. 6 8

1.22

15.75%

10.52%

9.45%

1.07%

Micro-Cap, 9-1C

' 1.36

18.41%

13.18%

10.56%

2.62%

15. The fact that the returns for the largest companies fall below the security market line may be a sign that the C overestimates the returns on these stocks.


26. The expected equity risk premium is defined as the additional return investors expect to receive to compensate for the additional risk associated with investing in equities as opposed to riskless assets.


27. The equity risk premium as a forward-looking measure of what investors can expect in the market is directly observable in the market.


28. For the purposes of computing the equity risk premium, the total return on the chosen Treasury security is riskless because both its income return and its net earn/loss from its sale are riskless.


19. ibbotson Associates provides equity risk premium estimates for the short-, intermediate-, and lone-term horizons.


30. Jbbotson Associates uses the last 30 years of data for the purpose of computing the long-horizon equity risk premium.


31. The equity risk premium preferred by Ibbotson Associates is a geometric average risk premium, as opposed to an arithmetic average risk premium.


32. The Beta Book provides cost of equity estimates for more Irian 5.000 companies.


33. The difference between the levered and the unlevered beta is that the unlevered beta excludes the business risk of a company and only reflects its financial risk.


34. The Ibbotson (adjusted) beta calculated in the Beta Book using the Vasicek Shrinkage Technique is based on the theory that, in time, a company's beta tends toward its industry-average beta.


35. The peer group betas as calculated by ibbotson Associates can be helpful either for comparison purposes or in place of a company laying poor regression results.


36. Individual company betas, adj usted betas, Ibbotson betas, and peer group betas are different names for one type of beta included in the Jbbotson Beta Book.


'i'rue


37. The______________ is the market benchmark most used throughout Ibbotson publica­tions because it represents a large sample of companies across a large sample of industries,


38. Ibbotson Associates uses the income return on the________ as (lie benchmark for the riskless asset in computing the long-horizon equity risk premium.


39. In Ibbotson's view,...................... averages are better forward-looking point estimates, and........................ averages are better for historical analysis of a defined date range.


40. The______________ method for estimating the equity risk premium consists of inter­viewing academics, money managers, or other professionals about the expected direction of the market.


41. The______________ model estimates the equity risk premium by looking at what the economy can supply in Ihe future as opposed to its historical performance.


42. The hiaher the standard error of the beta company estimate, the weight assigned to the company beta in the Vasicek Shrinkage Technique to calculate the Ibbotson (adjusted) beta.


43. The Ibbotson (adjusted) beta is calculated using (lie Vasicek shrinkage technique, which takes the statistically weighted average of the ...................... beta and the ______________ beta.


44. The______________________________ , ____________________________ , and are components shared by both the build-up method and CAPM to calculate the cost of equity capital.


45. All of the risk premium statistics presented in any Ibbotson Associates publication are derived from returns after taxes but before taxes.


46. The Cost of Capital Yearbook from ibbotson Associates presents statistics such as cost of equity, cost of capital, capital structure ratios, growth rates, industry multiples, and other fi­nancial data for over 300.


47. Chapter 13 explains how7 Ibbotson Associates calculates its peer group beta in the Beta Boot Using the same procedure, calculate the peer group beta for Company A that has sales in four different SIC codes as follows:


SIC Code % Sales in Industry Industry OLS Beta


15 25.00 0.60


30 14.75 1.10


31 60.00 0.70 67 0.25 0.40


48. Using the following inputs, calculate the Ibbotson (adjusted) beta for Company Peer group beta: 1.25


XYZ Company beta: 1.75


The statistical significance of the XYZ beta is quite low, resulting in a 0.20 weight.


49. Given the following known variables, calculate the expected industry risk premium (IRP) for industry XYZ:


hull information beta for industry XYZ: 0.90


Expected equity risk premium: 7,8%


What can be said about industry X YZ's riskiness compared with the market?


50. Given trie following known variables, calculate the pretax capitalization rate for Company XYZ:


After-tax capitalization rate for Company XYZ: 1.5%


Tax rate for Company XYZ: 35%?


The sample page (Rxhibil 13.3) from the IbboLson Associates Cost of Capital Yearbook presents each statistic in the following forms: Median, SIC Composite, Large Composite, and Small Composite. You are valuing a private Company, XYZ, in SIC code 275 with the following sales and total capital figures:


Last Year Million


Sales SH)


Total capital $8


Which of the forms for the statistics (Medium, STC Composite, Large Composite, Small Composite) reported on this page are you likely to use Company XYZ for and why?


You are trying to estimate a cost of equity capital for Company XYZ in question 51 by looking at what comparable companies in (he industry have done. What numbers in Exhibit 13.3 are vou more likelv to look at and why?


You are trying to compute the VVACC for Company XYZ. After analysis you have con­cluded that XYZ has a cost of equity of 20% and a cost of debt after tax of 10%. Use data reported in Exhibit 13,3 to estimate the WACC for Company XYZ.


Using the price/sales multiples shown in Exhibit 13.3, estimate the market capitalization for Company XYZ. (Remember that Company XYZ had sales of S10 million.)


Calculate the cost of equity for Company XYZ given the following known variables and reported in Exhibit 13.3:


;-tree rate = 5.6%


General equity risk premium for the market as a whole = 7.8%


Assuming that you know the debt/equity ratio of Company XYZ to be 1.25 and the tax rate to be 40%, use the appropriate unlevered beta for the industry in Exhibit 13,3 and relever it to reflect XYZ/s capital structure.


57. Using the raw beta and the Ibbotson beta, calculate the cost of equi ty under the C APM for OCTEL Corp. (us&R,= 5.6%; RP^ = 7.8%).


Using the information presented for OCTEL Corp., calculate the weight assigned to the raw in order to calculate the adjusted Ibbotson beta.



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