Estimating risk-free rates for valuations

Estimating risk-free rates for valuations

Introduction Government bond yields are frequently used as a proxy for riskfree rates and are critical to calculating the cost of capital. Starting in 2008, significant volatility in yields presented valuers with a real challenge. Volatility in the risk-free rate, if left unadjusted, leads to volatile costs of capital and volatile value that is not always appropriate. During this turbulence, a number of articles were published commenting on difficulties in valuing assets and liabilities in Portugal, Ireland, Greece and Spain (PIGS) where, initially, there was a significant increase in government bond yields. However, the issue was not confined to these countries. The mechanical application of spot yields on government bonds has an impact on the values of assets and liabilities across Europe. QE programs in the US, UK and Japan, and equivalent programs implemented, to a lesser extent, in Europe, introduced significant quantities of capital into the markets through bond purchases, resulting in depressed yields. During these times, some valuers included quantitative easing premiums to attempt to adjust for this artificial adjustment. Following the announcement by the Federal Reserve in late 2013, the US continued to taper its bond purchases, ending in October 2014. The European Central Bank (ECB) announced a two-year asset buying scheme at the start of October 2014, although the specifics remain unclear. The risk of excessive volatility in valuations will be an issue for any owners of assets and liabilities where an income-based valuation approach is applied as the primary methodology, and will be especially relevant where: The assets or liabilities are marked to market on a regular basis or have to be valued at specified dates that might be impacted by abnormal market conditions Assets or liabilities are owned across Europe, as the impact on valuation potentially differs by country The owner of the assets or liabilities is particularly sensitive to changes in value The asset is highly geared, as the risk free rate impacts the cost of debt The assets feature a low weighted average cost of capital (WACC), as the percentage impact of the risk-free rate will be higher Assets are in regulated industries with multiyear tariff agreements This paper examines: Value implications from mechanical application of the capital asset pricing model (CAPM) Alternative approaches to assessing the inputs to CAPM The potential benefits of adopting a framework around the inputs to CAPM to ensure valuations are robust Estimating risk-free rates for valuations 1

European government bond yields: what has been happening? Figure 1: Long-term bond yields 8.0 7.0 6.0 5.0 Yield % 4.0 3.0 2.0 1.0 0.0 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 UK US Japan Germany Euro upper bound General trends in bond yields include: 1. There has been a general reduction in government bond yields across Europe as lower and more stable inflation expectations have driven yields down. Ten-year government bond yields have moved from above 6% in the mid-1990s to approximately 2% to 3% in recent times. 2. Countries within the European Union (EU) experienced a dramatic reduction in the spread of government bond yields in the period leading up to monetary union in 1999. This may be attributable to a reduction in the liquidity premium and more favorable assessments of country-specific risk. 3. The above trend was largely reversed from 2008 onwards with yields generally returning to, or to slightly below, the levels prior to monetary union. For countries such as the UK and Germany, there was a reduction in yields partially driven by a flight to quality, with government bonds preferred by investors relative to other asset classes. For PIGS and Italy, yields increased. This can be partly explained by a revision in the attitude of the market toward debt levels and revised assessments of sovereign risk. 2 Estimating risk-free rates for valuations

4. In late 2008 and late 2011, there were relatively sharp reductions in yields across Europe and in the US. During these periods, there were actual or anticipated increases in government purchases of financial assets and reductions in central bank interest rates, commonly referred to as QE. Various studies have estimated the impact of QE on government bond yields to be between 50 and 100 basis points, with published estimates by the Bank of England suggesting around a 45 basis point impact. 1 5. As a result of announcements in the US of the tapering of their QE policy in January 2014, bond yields increased globally to a high in December 2013. The tapering program finished in October 2014 and marked the end of the QE program everywhere other than Japan. While many expected bond yields to recover to longterm averages as a result of the reduced infusion of capital into the system, instead, yields have continued to decrease throughout 2014. This raises the question going forward of what the new normal is, and whether the assumption rates will return to historic averages. 6. To add a further twist, on 2 October 2014, the ECB announced an asset buying scheme as a result of Europe-wide inflation falling far below the ECB s goal of 2%. However, the specifics and scope are unclear. Additionally, Japan has announced a ramp-up of its QE program. 7. QE remains an option for the UK depending on economic performance, with the program having been suspended since 2012. Government bond yields and valuation The valuation of assets and liabilities for commercial purposes is commonly based on the premise of the price that a market participant would be willing to pay for a similar asset or liability. In valuing assets and liabilities, the income approach is often applied as the primary approach using the discounted cash flow (DCF) methodology. The discount rate applied in the DCF is usually a blend of the cost of debt and the cost of equity for a market participant in the relevant sector, based on a market-average level of gearing. The cost of equity is commonly derived using the CAPM. This model adds a premium to the risk-free rate to reflect the excess return required on equity investments (the market equity risk premium or ERP) and the proportion of that premium (a beta factor) applicable to the asset or liability. The link between government bond yields and valuation is due to the common practice of basing risk-free rate directly on a Government bond yield, on the assumption that government bonds offer the best observable proxy for a riskless asset. The term risk-free becomes a contradiction in terms when the economic situation means there is a possibility of default. The yield on government bonds also may not be representative of the return on a risk-free asset where the underlying bond is subject to speculative trading or where the national bank is buying bonds in the market in order to suppress yields, thereby distorting the underlying fundamental yield on the bond. In this paper, we perform illustrative valuations of equities as an asset class and consider whether adjustments are required to the inputs to CAPM used to derive discount rates applied in the DCF. 1 The United Kingdom s QE policy: design, operation and impact, Quarterly Bulletin 2011 Q3, Bank of England, 2011 Estimating risk-free rates for valuations 3

It is difficult to rationalize government bond yields that fall below inflation and offer no real return. Changes in government bond yields in the year to 31 December 2014 In the year to 31 December 2014, government bond yields have with the exception of Greece, universally decreased. All else being equal, if spot government bond yields are mechanically used as a proxy for the risk-free rate, this increases the value calculated using on a DCF methodology; in some cases, considerably. Table 1 summarizes the changes in yields on 10-year government bonds in various countries in the year to 31 December 2014, together with the volatility of yields across 2014. This is expressed both in absolute movement terms between the two dates and in the standard deviation, which is an indicator of how much fluctuation there has been between the dates. Table 1: European government bond yields in the year to 31 December 2014 As QE unwinds, government bond yields are likely to increase, which will cause values to decrease if spot yields are used as a proxy for the risk-free rate. Country Spot yield on 10 year Government bond as at 31 Dec 2013 Spot yield on 10 year Government bond as at 31 Dec 2014 Change to 31 Dec 2014 Standard deviation in yield over 2014 Austria 2.3% 0.7% -1.6% 0.4% Belgium 2.5% 0.8% -1.7% 0.5% Denmark 2.0% 0.8% -1.1% 0.3% Finland 2.1% 0.6% -1.5% 0.4% France 2.6% 0.8% -1.7% 0.5% Germany 1.9% 0.5% -1.4% 0.4% Greece 8.3% 9.4% 1.1% 1.0% Ireland 3.4% 1.2% -2.2% 0.7% Italy 4.1% 1.9% -2.2% 0.6% Netherlands 2.2% 0.7% -1.6% 0.4% Norway 3.0% 0.0% -3.0% 0.4% Portugal 6.0% 2.7% -3.4% 0.8% Spain 4.1% 1.6% -2.5% 0.6% Sweden 2.5% 0.9% -1.6% 0.4% Switzerland 1.2% 0.3% -0.9% 0.3% UK 3.0% 1.8% -1.3% 0.3% Mean 3.2% 1.6% -1.7% 0.5% Median 2.6% 0.8% -1.6% 0.4% Source: Bloomberg and EY analysis 4 Estimating risk-free rates for valuations

Quoted government bond yields are nominal rates; i.e., the yield incorporates expected inflation forecasts. We have calculated implied real risk-free rates for all countries to provide an indicator of the underlying real yield without the influence of inflation, forecasts of which have themselves seen significant fluctuations in recent years. Table 2 summarizes these results. Table 2: Implied real risk-free rates Country 2015 CPI 2015 real 10-year CPI 10 year real Austria 1.4% -0.7% 1.8% -1.1% Belgium -0.5% 1.3% 1.8% -1.0% Denmark 1.3% -0.5% 1.7% -0.8% Finland 0.4% 0.2% 1.6% -1.0% France 0.3% 0.6% 1.6% -0.7% Germany 0.4% 0.1% 1.6% -1.0% Greece -0.8% 10.3% 1.6% 7.7% Ireland 0.9% 0.3% 1.8% -0.6% Italy -0.1% 2.0% 1.5% 0.4% Netherlands 0.6% 0.0% 1.5% -0.8% Norway 1.9% -1.8% 2.4% -2.3% Portugal -0.5% 3.1% 1.4% 1.2% Spain -1.1% 2.8% 1.5% 0.1% Sweden -0.5% 1.4% 2.1% -1.1% Switzerland -0.6% 0.9% 1.2% -0.9% UK 0.1% 1.6% 1.8% -0.1% Mean 0.2% 1.4% 1.7% -0.1% Median 0.2% 0.7% 1.6% -0.8% In summary, this means that most European countries are seeing a negative real yield, which effectively pays the borrower to borrow money, thereby encouraging borrowing and flows of capital through the financial system. Estimating risk-free rates for valuations 5

Impact on valuation of volatility and movement in government bond yields The trends in Tables 1 and 2 present three potential challenges in relation to the valuation of assets and liabilities: 1. Between 31 December 2013 and 31 December 2014, government bond yields have fallen for all countries, except Greece. 2. Volatility in daily yield over the year to 31 December 2014, as demonstrated by the standard deviation. 3. The real yield on 10-year yields is generally negative based upon adjusting for average inflation rates over the term of the bonds. Intuitively this is difficult to rationalize, and would not seem to be sustainable in the long term. The valuer needs to consider whether current spot yields are a reliable indicator or not, given the levels of volatility and the falling rates seen since the start of 2014. Additionally, consideration should be given to whether the current negative real yields are supportable beyond the short term. Mechanically applying the spot government bond yield as the risk-free rate in the CAPM context is an issue, where it can be argued that the spot yield is not deemed to be a good proxy for the risk-free rate. For example, if the underlying yield has been suppressed by QE or government policy, or has been subject to speculative trading. Volatility in spot government bond yields is only an issue to the extent that it is not considered reflective of volatility in the underlying risk-free rate and would therefore cause an unexplained movement in the valuation. However, market values do move and sometimes quickly, so volatility in itself may not be unreasonable. In order to illustrate the potential impact of volatility and step changes in yield on a DCFbased valuation, we constructed an example DCF using the inputs set out in Table 3. Table 3: Example DCF and cost of CAPM inputs Year-one free cash flow 100 Beta 1.0 Debt % 30.0% Equity % 70.0% ERP 5.0% Debt margin 2.0% Discrete growth rate 2.5% Terminal value growth rate 3.0% Discrete cash flow period 5 years Discounting convention Mid year Source: EY analysis 6 Estimating risk-free rates for valuations

Table 4 highlights the illustrative impact on the valuation of the change in risk-free rates between 31 December 2013 and 31 December 2014 (as summarized in Table 1), holding all other inputs constant. Table 4: Illustrative value impact based on changes in risk-free rates in the year to 31 December 2014 Country Change in the year to 31 December 2014 Austria 51.7% Belgium 57.4% Denmark 35.9% Finland 49.6% France 57.8% Germany 46.5% Greece -9.3% Ireland 43.0% Italy 37.5% Netherlands 33.6% Norway 15.9% Portugal 51.0% Spain 45.0% Sweden 26.8% Switzerland 25.9% UK 12.9% Mean 36.3% Median 40.3% Source: EY analysis To highlight the potential change in value, using the value as at 31 December 2013 as a base, we calculated the minimum and maximum value movements experienced in the year to 31 December 2014. The results are set out in Figure 2. Estimating risk-free rates for valuations 7

Figure 2: Change in value across the year to 31 December 2014 % Change from value as at 31 December 2013-50.0% 0.0% 50.0% 100.0% 150.0% 200.0% 250.0% 300.0% Portugal Spain Ireland France Belgium Italy Netherlands Austria Finland Sweden Germany Greece Norway Switzerland Denmark UK 0.0% 0.0% 1.5% 0.4% 0.5% 0.0% 0.0% 0.0% 0.1% 0.1% 0.4% 9.7% 1.4% 0.0% 0.5% 0.1% 58.5% 57.8% 57.4% 52.5% 52.4% 51.8% 49.7% 49.3% 46.5% 33.4% 38.2% 36.7% 35.9% 30.8% 185.2% 257.8% Source: EY analysis Table 3 and Figure 2 highlight the potential impact of volatility and step changes in government bond yields on values calculated using DCF if spot government bond yields are used as a proxy for the risk-free rate. As is immediately evident, the impact is not just limited to Eurozone countries that experienced periods of distress during the financial crisis, but also to core Eurozone countries such as Germany, which saw a 47% increase in value. While there is likely a linkage effect as a result of the common currency, the resultant impact is clearly material on valuations using a spot yield. another method, such as market multiples. A potential issue arises as a result of the mechanical increases in value as a result of decreasing yields if such a change is not also reflected in the wider market. Our analysis set out in Figure 3 shows that UK FTSE 100 and UK FTSE All Share fluctuated between -8.4% and +1.9% and -8.3% and +2.1%, respectively, over the year to 2014. Meanwhile, 10-year UK government bonds have fluctuated between -41.9% and +0.6% over the same period, with correlation between the FTSE at around 7%. With income-based values increasing, what about multiplesbased cross-checks? Where the income approach is used as a primary valuation methodology, it may be appropriate to cross-check with to 8 Estimating risk-free rates for valuations

Figure 3: Changes in the FTSE relative to changes in UK spot government bond yields % Change as at 31 December 2014 5.0% 0.0% -5.0% -10.0% -15.0% -20.0% -25.0% -30.0% -35.0% -40.0% Jan-14 Feb-14 Mar-14 Apr-14 May-14 Jun-14 Jul-14 Aug-14 Sep-14 Oct-14 Nov-14 FTSE 100 Index FTSE All-Share Index 10-year bond Source: Bloomberg; EY analysis Based on the parameters set out in Table 2, a DCF-based valuation of a UK asset or liability fluctuated in either direction by almost six times the movement in the market over the period solely as a result of changes in the risk-free rate applied. As a result, there may be some issues reconciling a market-based approach to an income approach based on the mechanical application of spot rates. Selecting the risk-free rate when government bond yields are volatile During the period of stability in government bond yields between 2001 and 2008, using a spot Government bond yield as a proxy for the risk-free rate was less likely to cause movements in the value of assets and liabilities. Using a spot yield as a proxy for the risk-free rate has several advantages, including: Being directly observable and can be used without further subjective analysis on the part of the valuer Being easily checked to a number of quoted sources, therefore auditable Where it is reasonable to conclude that any movement in the value of an asset or liability should not be directly correlated to changes in spot government bond yields or volatility in yields is not deemed reflective of underlying volatility in the risk-free rate, the valuer should consider whether any adjustments are required to the methodology for assessing the risk-free rate or the ERP. Estimating risk-free rates for valuations 9

Alternatives to using a Government bond yield as a risk-free rate Where Government bond yields are not deemed to be the best proxy for the risk-free rate, a number of alternative options are available, including: Using an average Government bond yield over a period as a proxy for the risk-free rate Estimating the risk-free rate by reference to the Government bond yield from another country where there are fewer step changes or there is less volatility in yields Adjusting the ERP to compensate for movements in the spot Government bond yield Considering a specific risk premium or discount in addition to the spot Government bond yield Each of these options is discussed in more detail on the following pages. The mitigating effect of using an average yield will reduce over time. Average yield While caution needs to be applied when stepping away from current market indicators, using an average yield can smooth out any short-term volatility in risk-free rates and has the additional advantage of being consistent with the calculation of the ERP if this has also been estimated based on a historical average. The period over which the average is calculated needs to be considered. Care needs to be taken when using a longer-term average, as the general trend of declining yields across Europe needs to be factored into the analysis. Applying a longer-term average may not be appropriate if yields are not expected to revert to the longer-run average. If there are persistently high or low yields, the mitigation effect of applying an average yield will reduce over time. Adjusting the ERP has the disadvantage of potentially distorting the impact of the adjustment on the cost of equity for assets with relatively high and low betas and debt in the capital structure. Using yields from other countries or debt instruments as a reference point Where the current yield on government bonds is considered unrepresentative of the underlying risk profile for a country, the risk-free rate can be estimated based on the government bond yields for other countries with similar credit ratings, as well as geographic and economic profile. A more complex alternative is to build a regression model using country credit ratings and the yield on government bonds that solves for yield based on the underlying credit rating of a country. This option has particular relevance in the context of the revised assessments of sovereign risk since 2008. In countries such as PIGS and Italy, government bond yields increased since 2008, yet have recently fallen considerably, even when their economic outlook remains uncertain. As a result, the valuer needs to consider whether the changes in yields in these countries have had a corresponding effect on the underlying risk-free rates and, therefore, the value of assets and liabilities in those locations. Another alternative approach is to consider the yield on local corporate bonds, with a similar credit rating to the country in question, as a proxy for the risk-free rate. Care needs to be taken to select a company with significant exposure to local risk so that there is some correlation in the risk profile of the company selected and the local economy. 10 Estimating risk-free rates for valuations

Adjusting the ERP An alternative to adjusting the risk-free rate would be to adjust the ERP. However, adjusting the ERP to compensate for the volatility in government bond yields has the disadvantage of potentially distorting the impact of the adjustment on the cost of equity for assets with relatively high and low betas and assets with debt in the capital structure. For example, if 1.0% is added to the ERP of an asset with a beta of 1.0, the cost of equity increases by 1.0%. For an asset with a beta of 0.3, the cost of equity will increase by only 0.3%, and for a beta of 1.5, the cost of equity will increase by 1.5%. Similarly, there is an issue with adjusting the ERP for assets with debt in the capital structure. For example, with 50% debt in the capital structure, adding 1.0% to the ERP for an asset with a beta of 1.0 would increase the cost of equity by 1.8%. For a beta of 0.3, adding 1.0% to the ERP increases the cost of equity by 0.6%, and for a beta of 1.5, the cost of equity would increase by 2.6%. Care therefore needs to be taken in adjusting the ERP for companies with high and low betas and debt in the capital structure. This will have particular relevance for the extractive industries, where many companies have betas in excess of 1.0, and for utility companies or infrastructure assets, where asset betas are of the order of 0.3 to 0.4 and assets tend to be relatively highly geared. Aside from any adjustment specifically made to ERP to account for volatility in government bond yields, the ERP selected for the valuation must consider the approach used to calculate the risk-free rate. For example, when using an ERP calculated using a long-run average, selecting an average yield as a risk-free rate ensures consistency of approach between the two inputs. Using a specific risk premium or discount In order to remove the impact of a step change or short-term volatility in government bond yields deemed not to be reflective of the underlying risk-free rate, a premium or discount can be applied to the spot yield to estimate an appropriate risk-free rate. Making adjustments directly to the Government bond yield has the advantage of having a linear effect on the cost of equity and not being impacted by beta or gearing, which affects adjustments made to the ERP. An example of this approach would be adjusting UK government bond yields to account for the impact of QE. Various studies have quantified the impact of QE at between 50 and 100 basis points to government bond yields, with published estimates by the Bank of England suggesting around a 45 basis point impact. 2 This could be added to the spot yield to adjust for the impact of QE, although considering the length of time since the end of the program (2012), this may no longer be as appropriate. Another approach would be to adjust the current yield on government bonds based on the spreads implied by credit default swaps (CDS). These are agreements between two parties where the buyer will compensate the seller in the event of default and the spread can be used in combination with a Government bond yield or swap rate to create a proxy for the risk-free rate. Care needs to be taken with this approach, as the underlying effects of liquidity and a flight to quality within the Government bond market may not be addressed in the resulting proxy risk-free rate. 2 The United Kingdom s QE policy: design, operation and impact, Quarterly Bulletin 2011 Q3, Bank of England, 2011 Estimating risk-free rates for valuations 11

From a valuers perspective, it is difficult to defend doing nothing. Conclusion There have been significant changes in the environment for European government bond yields in the past 10 years. This is relevant to the valuation of assets and liabilities, given that government bond yields are used as a proxy for the risk-free rate within income-based valuation approaches such as DCF. In the year to 31 December 2014, government bond yields have universally reduced, with a median reduction of over 1% in the collective yields. Depending on gearing and beta selection, this could result in a purely mechanical increase in value based upon adoption of the spot rate. Real yields based on average inflation over the bond term are generally negative, which seems counterintuitive and unsustainable beyond the short term. In order to avoid inappropriate movement and step changes in value, a combination of the following approaches might be considered in order to build a more robust framework to estimate the risk-free rate: Using an average yield as a proxy for the risk-free rate Assessing the risk-free rate by reference to government bond yields in another country where there has been less volatility in yields Adjusting the ERP to compensate for movements in spot government bond yields Considering a specific risk premium or discount in addition to the spot Government bond yield This is still an area for academic debate, but it is clear to us that, from a valuers perspective, it is difficult to defend doing nothing. Of the more commonly applied techniques, normalizing the risk-free rate will lead to more stable valuation results over time; increasing the ERP and maintaining the use of spot government bond yields is also defendable, so long as the ERP is revised on a regular basis (for example, quarterly). The framework designed by the valuer for estimating the inputs to CAPM will ultimately depend on the specific circumstances of the subject asset or liability, the correlation of its value with government bond yields and the current economic environment of the country where the asset or liability is located. The framework needs to be designed so that it is consistently applied and is not unduly impacted by changes in the underlying inputs, but not at the expense of good judgement on the part of the valuer. A framework that is consistently applied will also rightly appeal to both auditors and investors. However, the resulting valuations should still be dynamic and correlated to the underlying value drivers for the subject asset or liability and the market s perception of value. The EY Valuation and Business Modelling team is an integrated mix of valuers and economists. We would be happy to discuss how an appropriate framework might be created around the inputs to CAPM in order to meet your specific needs. We can also provide insight into the economic fundamentals of bond yields and current practices adopted by market participants, valuation practitioners and regulators for assessing the risk-free rate. 12 Estimating risk-free rates for valuations

Contact details Jim Eales Partner, Valuation & Business Modelling Global Leader Valuation & Business Modelling Office: + 44 20 7951 4566 Mobile: + 44 7785 727 809 Email: jeales@uk.ey.com Steve Taylor Partner, Valuation & Business Modelling EMEIA Leader Valuation & Business Modelling Office: + 44 20 7951 4302 Mobile: + 44 7799 350 262 Email: staylor11@uk.ey.com Adrian Nicholls Partner, Valuation & Business Modelling UK&I Leader Valuation & Business Modelling Office: + 44 20 7951 3853 Mobile: + 44 7710 438 573 Email: anicholls@uk.ey.com Mark Gregory Partner, Valuation & Business Modelling Chief Economist UK&I Office: + 44 20 7951 5890 Mobile: + 44 7802 882 671 Email: mgregory@uk.ey.com Alay Patel Partner, Valuation & Business Modelling Telecommunications, Media and Technology Office: + 44 20 7951 5649 Mobile: + 44 7725 005 050 Email: apatel2@uk.ey.com Maria Bengtsson Assistant Director, Valuation & Business Modelling Energy Office: + 44 20 7951 4846 Mobile: Email: mbengtsson@uk.ey.com Duncan Mills Executive Director, Valuation & Business Modelling Mining, Oil & Gas, Utilities and Infrastructure Office: + 44 20 7951 4522 Mobile: + 44 7966 398 354 Email: dmills@uk.ey.com Mike Evans Director, Valuation & Business Modelling Mining, Oil & Gas, Utilities and Infrastructure Office: + 44 20 7951 1346 Mobile: + 44 7962 646 025 Email: mevans5@uk.ey.com Estimating risk-free rates for valuations 13

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