Total Beta. An International Perspective: A Canadian Example. By Peter J. Butler, CFA, ASA

Transcription

1 Total Beta An International Perspective: A Canadian Example By Peter J. Butler, CFA, ASA Introduction: This article will highlight total beta s applicability for appraisers around the world. While I have chosen to highlight aerospace manufacturing companies operating out of Canada, I could have selected any industry in any country. Background: I have written extensively on the theory behind total beta and the total cost of equity (TCOE) 1. Therefore, this article will be from a practical perspective and show how appraisers can use the technique to more empirically (less subjectively) assign a cost of equity capital to a privately-held company in a country other than the United States. As a reminder to the reader, the following two equations are of utmost interest to the valuation of privately-held companies: Total Beta = Beta/ρ = σ s /σ m TCOE = risk-free rate + Total Beta*Equity Risk Premium Thus, the only (and very big difference) between beta and total beta is the division by the correlation coefficient, ρ. This division results in a metric dependent upon standard deviation, which captures the publicly-traded guideline s total risk. Any corporate finance textbook states that standard deviation is the most appropriate measure of risk for stand-alone assets. We also know that privately-held companies are often viewed and valued as stand-alone assets. Therefore, total beta, which captures 100% of the disclosed risks (in an efficient market) for guideline publicly-traded companies, is the most appropriate beta for appraisers to use when using the income approach to valuation. The TCOE equation should look familiar. Total beta has simply replaced beta in the famous Capital Asset Pricing Model (CAPM). Let s make one thing perfectly clear. The guideline publicly-traded companies will not be priced under such an equation because we know that some (if not all) company-specific risk (CSR) can be diversified away for well-diversified public stock investors. 1 Please see frequently asked questions (FAQs) and/or articles under the Butler Pinkerton Calculator tab at 1

2 The story is much different for the owner of a closely-held business, however. More often than not, a private business owner (or prospective business owner) is unable to shed the risk of placing such a large percentage of his or her portfolio in one basket. Hence, we have the need to improve the CAPM equation for the valuation of privatelyheld companies. Total beta is one such improvement. Therefore, the TCOE equation is a model whose underlying assumption is that total risk is priced to better match the market pricing for privately-held companies. Guidelines: To keep this article relatively short and simple, I have selected only two Canadian companies which trade on the Toronto Stock Exchange to compare with my (fictitious) subject company. The following is a quick summary available from publicly available sources. Guideline #1: Northstar Aerospace Northstar Aerospace is a leading independent manufacturer of components and assemblies to the global aerospace industry. Principal products include gears and transmissions, accessory gearbox assemblies, rotorcraft drive systems and other machined and fabricated parts for helicopters and fixed wing aircraft. In addition, Northstar provides maintenance and repair and overhaul (MRO) on these same platforms. Guideline #2: Magellan Aerospace Magellan Aerospace has comprehensive and integrated manufacturing, design and process capabilities that support four product areas - Aeroengines, Aerostructures, Defense and Space, and Specialty Products. Fictitious Subject Company Our fictitious subject company, CanAero (which stands for Canadian Aerospace ), is a privately-held company and, as the name implies, also operates in the aerospace industry and directly competes with both guidelines. Empirical Data: Since I used a weekly frequency for my look-back, I calculated five different total betas (and TCOEs) for these guidelines, around our date of value of December 31, 2009, using every day of the trading week (Monday Friday). I selected a 3.60% risk-free rate as representative of the appropriate Canadian risk-free rate as of December 31, Next, I selected an equity risk premium (ERP) of 5% for the Toronto Stock Exchange, where these two stocks trade. The following is a 2

3 summary from the Butler Pinkerton Calculator for the two guidelines: Northstar Aerospace 18 Dec 28 Dec 29 Dec 30 Dec 31 Dec Average Levered Beta Correlation Coefficient (R) Total Beta Total Cost of Equity 21.99% 19.11% 21.03% 20.80% 19.68% 20.52% Combined Size:Company Specific Risk Premium 16.51% 15.75% 16.22% 14.24% 15.32% 15.61% Additional Regression Statistics: Constant Coefficient of Determination (R2) T Stat Level of Statistical Significance 89.00% 19.00% 73.00% 99.00% 55.00% 67.00% Please note the following: Total betas can be volatile depending on the parameters of the look-back. As shown above, however, generally speaking, they are not as volatile as traditional betas. The average TCOE, which prices total risk for Northstar, was 20.52%. This will be our reference point for our subject company. Is our subject company more or less risky? That is the pertinent question. Before we look to Magellan, the obvious concern is the volatility of Northstar s beta. The build-up approach does not pick-up the sensitivity in the calculation. Moreover, if you were also only looking at the modified CAPM would you even know the severity of the sensitivity? Not if you only looked at one day of the trading week. In summary, appraisers must be aware of the sensitivity of the data whether in the build-up, modified CAPM or with total beta. Magellan Aerospace 18 Dec 28 Dec 29 Dec 30 Dec 31 Dec Average Levered Beta Correlation Coefficient (R) Total Beta Total Cost of Equity 24.69% 22.02% 24.57% 28.08% 23.62% 24.60% Combined Size:Company Specific Risk Premium 15.15% 15.44% 14.69% 17.30% 13.78% 15.27% Additional Regression Statistics: Constant Coefficient of Determination (R2) T Stat Level of Statistical Significance 99.00% 99.00% 99.00% 99.00% 99.00% 99.00% Degrees of Freedom

4 Again, look how volatile Magellan Aerospace s beta was over the look-back period. Magellan Aerospace also exhibited the most amount of risk with an average total beta equal to 4.2 and resulting TCOE equal to 24.6%. Again, the pertinent question is: Is our subject company more or less risky? Let s find out below in the Qualitative Assessment section. Before we do that, however, we have one item to discuss - leverage. Leverage may increase the riskiness of a firm s equity. For ease of illustration, I have assumed that each company has the same capital structure since both public companies have significant liquidity risk and have frequently violated financial covenants. Both Northstar and Magellan have had to renegotiate certain credit arrangements and will have to again in the future. If either one is not successful in refinancing certain debt, then their ability to remain as going concerns will be in jeopardy. In reality, if the capital structures are not the same, then appraisers should un-lever the respective total betas and select an appropriate unlevered total beta for the subject company. Next, appraisers will re-lever with the assumed capital structure of the subject company to assign an appropriate cost of equity capital to the subject company. I also determined that both stocks were efficiently traded based on an assessment of trading volume. Therefore, these total betas and TCOEs are viable to use as proxies (starting points) to select an appropriate discount rate (TCOE) for our subject company. Qualitative Assessment: Next, I went to the public disclosures of risk and compared them to the inherent risk of my subject company. Please see this analysis below and note that this is just one way to analyze these companies. Rather than show some matrix of risk assessment as I have in the past in other articles, I am only going to explain qualitatively why Magellan is more risky than Northstar. Remember, this analysis is just for illustration to help appraisers with the practical side of this technique. Other industries may require other factors to consider. While subjectivity remains at least now we have an empirical framework to analyze. In short, this is the qualitative part of the analysis. Calculating the guideline TCOEs is the quantitative part. As a reminder, the empirical TCOE benchmark for Northstar is 20.5% and Magellan is 24.6%. Northstar (20.5%) v. Magellan (24.6%) It goes without saying, but I will anyways; both companies are operating in difficult economic times in a cyclical and competitive industry which is subject to union labor risk. In 2008, however, Northstar generated approximately 70% of its revenues from 4

5 defense-related customers and 30% from commercial. On the other hand, Magellan was essentially the mirror-opposite. Generally speaking, while defense related revenues are dependent upon unknown future government spending, historically speaking this area of the aerospace industry has been less cyclical than the commercial portion. As mentioned above, they both have significant debt and liquidity risk. It appears that Magellan s financial distress cost is more severe, however, given the amount of debt it has incurred and its working capital deficit. Both companies also have interest rate risk and currency exchange rate risk. Northstar does have significant customer concentration risk in that in 2008, 81% of its revenues came from only five customers. Somewhat mitigating this issue was the fact that the relationships appear solid and the backlog with various customers has been growing. It also appears that Magellan has some customer concentration risks, but maybe not as much as Northstar. Magellan is somewhat more diversified geographically with significant revenue coming from the United States, Canada as well as the United Kingdom. Magellan (2008 Revenue: $686.4M; EBITDA: $77.4M) is bigger than Northstar (2008 Revenue: $171.7M; EBITDA: $11.7M). Ironically given their operating results, their market capitalizations were not materially different directly related to the greater financial distress that Magellan operated under. In summary, I believe that Magellan s TCOE, to be used only as a benchmark for CanAero s TCOE, is greater than Northstar s for two primary reasons: 1) Financial distress and 2) the make-up of its customer base being more heavily weighted towards commercial than defense. Of course, this does not answer the question as to the appropriate TCOE for CanAero, our subject company. Rather than make up certain facts about our fictitious subject company as I have done in other articles, I will merely mention now that we have a better idea why the TCOEs are what they are for our guideline benchmarks. Thus, we now can better determine an appropriate TCOE for CanAero by carefully comparing these guidelines to the subject company. If CanAero is more risky than Magellan, then the rate should be greater than 24.6%. If CanAero is less risky than Northstar, then its TCOE should be less than 20.5%. If CanAero s risk is bracketed by the two then CanAero s TCOE will fall somewhere in between 20.5% and 24.6%. 5

6 Conclusions: Subjective? Yes, to a certain degree. However, it is not nearly as subjective as completely guessing at a CSRP in a build-up approach. This technique provided an empirical framework to make a decision. Sometimes, this method will only provide a floor : 24.6%, for example, if the riskiest guideline is less risky than the subject company. Other times (much more unlikely) it may provide a ceiling if all of the guidelines are riskier than the subject. And sometimes it will provide a floor and a ceiling if the subject company falls somewhere between the various guidelines on the risk spectrum. In any event, it is a market approach twist to developing a discount rate an approach we as an industry have not had before when we were left to make an educated guess at the last component of risk the CSRP. This technique is another tool (although I believe it is an outstanding tool) to select an appropriate discount rate for a private company. Please compare and contrast its empirical advantages with other more subjective techniques. 6