Capital Structure Modeling and LBOs 1

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1 Quantitative Research June 2013 Your Global Investment Authority Capital Structure Modeling and LBOs 1 Rama Nambimadom Executive Vice President Shisheng Qu Senior Vice President Juan Porras Vice President The Wikipedia entry for Archimedes reads Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Perhaps one should add Father of modern banking. Give me a lever long enough and I can move the world. Banksters everywhere have certainly adopted this idea (and needless to say, the Earth-moving consequences have followed in due course). High leverage is essentially a common factor across banks and brokers. However, their non-financial brethren exhibit much more variation in their earth-moving aspirations, at least through the application of leverage. Looking at the cross section of non-financial firms, one observes a wide range of leverage levels. Even in the case of an individual firm, capital structures can vary significantly over time; most notably through a leveraged buyout (LBO) or similar leveraging transaction. This wide variation of leverage levels creates an additional factor that has to be addressed in applying capital structure models to non-financial firms. Last year we presented a capital structure model for financial companies, in which we modeled a bank s debt as options on its underlying assets. We now look to applying a variation of this model to non-financial companies. Investing in corporate debt can be equated to selling a put option on the assets of the firm, with the strike of the option being determined by the leverage of the firm. Therefore, to incorporate the ability to simultaneously model firms of different levels of leverage, we need to introduce a model for volatility skew. Most option markets exhibit a skew, i.e., low strike put options trade at higher volatilities. We calibrated our capital structure model to a cross section of non-financial firms and found a similar skew. In the rest of the paper we describe the relation of this skew to the leverage levels of the firm and the volatility of the underlying business as captured by the volatility of its ROA (return on assets). We then examine the application of the model to the Heinz and Dell LBOs.

2 Model description Our capital structure model is based on Black-Cox [1976]. We assume a fixed liability structure and an asset level which equals the firm s market capitalization plus the market value of its liabilities. The value of the asset evolves over time with a constant volatility and a risk-neutral drift given by the short-rate less payments to debt and equity holders. Default occurs when the value of the firm s assets drop below a pre-defined barrier, expressed as a percentage of liabilities. We assume that upon default, the firm suffers a bankruptcy cost; the post default value of the firm is modeled as a truncated normal distribution (so that recovery cannot be negative, or above 100%). Debt can be priced from this recovery rate and the model-implied term-structure of default probabilities. The company s equity is priced as the difference between the asset level and the value of debt. See the Appendix for a more detailed description. Debt versus liabilities Fundamental credit analysis normally focuses on the debt part of the liabilities of a corporate and excludes non-debt liabilities. Analysis of the debt on the balance sheet is often augmented by considering pension liabilities and the capitalization of operating leases. However, other liabilities are generally excluded; this may lead to inaccurate conclusions. Often this exclusion is appropriate. For example, treating non-current deferred tax liabilities as liabilities can be spurious, as the company does not need to pay out anything in the future (loosely speaking, deferred tax liabilities occur because the firm claimed its tax shield early). However, sometimes such liabilities should be seen as real, such as the $30 billion legal provision of BP largely due to its Gulf oil spill (significant relative to its total debt of $50 billion), and the more common anticipated cost of product warranties. Sometimes, there are additional real liabilities that are not even reported on the balance sheet, such as Operating Lease and tax liabilities related to repatriating cash from over-sea accounts. Unfortunately, it is not always clear which part of these non-debt liabilities should be taken into account. Therefore, looking at multiple views of liabilities structure might be necessary. We should note that when we look at the same company with and without non-debt liabilities, leverage is not the only thing that changes: implicitly the asset side of the firm is different, and the recovery on debt tiers can be different as well. In Figure 1, we report composition of Total Liabilities by sector using balance sheet information of S&P 500 companies as of 31 March For the majority of the sectors less than 50% of their liabilities are debt, and most of them have large amount of miscellaneous (or Other ) liabilities. Other Liabilities in Figure 1 can include many different items that vary by sectors and individual companies. For example, energy companies usually have non-trivial accrued or expected environmental liabilities due to regulation (e.g., asset retirement cost), manufacturing companies can have significant liabilities from their product warranty programs. Under-funded pension liabilities also belong to this category. To give a few examples of the composition of Other Liabilities, ConocoPhillips has $11 billion of Environment and regulation related liabilities, compared to its total debt of $25 billion; IBM has $15 billion warranty liabilities and $9 billion unspecified other liabilities, compared to its total debt of $34 billion and pension liabilities of $17 billion; Pfizer had $3 billion current liabilities related to customer rebate, as well as other tax payable of $6 billion, significant relative to its total debt of $39 billion. 2 JUNE 2013 CAPITAL STRUCTURE MODELING AND LBOS

3 FIGURE 1. COMPOSITION OF TOTAL LIABILITIES (ALL S&P 500 CONSTITUENTS BY SECTORS, EXCLUDING FINANCIALS*) Automobiles Consumer services Capital goods Comm l and prof l Food bev & tobacoo Media Utilities Telecommunication Semiconductors Household Materials Pharma, biotech Consumer durables Food/staples retailing Retailing Health care Transportation Energy Software Hardware 0% 20% 40% 60% 80% 100% Debt Account payables Tax payables Source: Compustat, as of 31 March 2013 Deffered tax Other liab Volatility modeling Asset volatility is obviously one of the key inputs to the capital structure model. A common strategy to obtain model inputs such as asset volatility is to calibrate to the prices of traded securities. However, LBOs pose a particular problem. The fact that some investors are willing to make an offer for the firm at a premium to market valuation probably signifies that the valuation prior to the LBO being priced into the market was low. So implying asset valuation and asset volatilities from pre LBO equity prices and equity options could be misleading. Here we take a different approach. We use the LBO valuation to imply the asset value of the firm. To estimate asset volatility, we first obtain implied asset volatilities for a cross section of non-financial firms by calibrating to their 5Y CDS levels and equity prices. Then we look at the cross-sectional relationship between these implied asset volatilities and trailing 10Y historical return on asset (ROA) volatilities and leverage levels. Once we have this relationship, we can use the ROA volatility and leverage level for the firm of our interest and estimate a fair implied asset volatility. To estimate a model for implied asset volatility, we start by looking at the empirical relation between implied asset volatilities and historical ROA volatilities. We observe a strong positive relationship between them (see Figure 2). Note that while ROA volatility and implied asset volatility are similar in that they measure business risk, there are a few major differences. First, ROA is based on accounting numbers, whereas implied asset volatility is risk neutral. There is a rich stream of literature in finance, starting with Shiller (1981), noting that market volatility is often much higher than the volatility of economic outcomes. For in-stance, price volatility for S&P 500 in the last 20 years was about 16%, which is nearly 4 times the accounting return on equity (ROE) volatility over the same period, 4.5%. Second, both numerators and denominators of returns underlying ROA volatility and implied asset volatilities are different. For numerator, ROA uses Net Income to equity holders, whereas the asset return underlying the model re-quires a return attributing to both equity capital and debt capital, and EBITDA is a better candidate than Net Income. Because EBITDA is larger than Net Income, and is not smoothed as much by management, EBITDA over asset is more volatile than ROA. For example, during the last two decades, S&P 500 had ROA volatility of 0.83%, while EBITDA over assets had volatility of 1.18%, a factor of 1.4 between them. For denominators, ROA uses total book assets, while implied asset volatility is calibrated using Net Debt plus Equity as asset value; for S&P 500 companies, this is a factor of approximately 2. Third, market implied volatilities are generally higher than realized volatilities of market prices. Due to the variation in leverage levels, ROA volatility is not sufficient to arrive at the appropriate level of implied asset volatility. Figure 3 shows the ratio of the actual implied asset volatility to the asset volatility predicted from ROA volatility, plotted against leverage (leverage is measured as the ratio of asset value to its distance to default barrier). As we can see, implied asset volatilities clearly show a negative relation to the leverage levels. It may be counterintuitive that asset volatilities should decrease as leverage increases. However, CAPITAL STRUCTURE MODELING AND LBOS JUNE

4 note that we are looking at the underlying asset volatility, not equity volatility. Other things being equal, equity volatility and credit spread would indeed be higher for firms with higher leverage. If we view credit as an implicit option on as-set value, the strike of this option is inversely related to the leverage level. So the increase in asset volatility with decrease in leverage is consistent with the typical pattern of low strike equity puts trading at higher volatilities. Aggregating these two relations, we have the following asset volatility prediction as a function of leverage and ROA volatility: We use this forecast when corporate action introduces significant change in the capital structure (i.e., leverage) without drastic change to the nature of the business. We now look at two recent LBO examples. FIGURE 2. IMPLIED ASSET VOLATILITY OBTAINED BY CALIBRATION TO CDS AND EQUITY VS ROA VOLATILITY,FOR A SAMPLE OF IG AND HY CORPORATES, AS OF 13 FEBRUARY 2013 Implied asset volatility y = x R 2 = Source: PIMCO ROA volatility (realized, 10Y) FIGURE 3. RATIO OF THE ACTUAL IMPLIED ASSET VOLATILITY TO THE ASSET VOLATILITY PREDICTED FROM ROA VOLATILITY AGAINST LEVERAGE, FOR A SAMPLE OF IG AND HY CORPORATES, AS OF 13 FEBRUARY 2013 Ratio implied asset volatility to ROA-based prediction Source: PIMCO DELL 0.5 y=1.32x 0.95 R 2 = On 14 January 2013, Michael Dell, Microsoft and Silver Lake Capital made an offer to take the company private. The offer for the company was USD 25bn, a premium of 36% over the then market price. Before the transaction, DELL has more cash than debt; if the deal goes through, it would have significantly more total and secured debt and much smaller equity cushion. The before- and (likely) after-capital structures for DELL are: Pre LBO ($million) Pro-forma ($million) Cash 12,777 1,201 SNR secured debt 3,185 11,250 JR secured debt 1,250 SNR unsecured debt 5,900 3,900 Subordinate debt 2,000 Equity 17,600 5,801 Source: CapitalIQ and PIMCO, as of 4 January JUNE 2013 CAPITAL STRUCTURE MODELING AND LBOS

5 Pre-announcement 5Y CDS spread was 223 bps. Initial market reaction was a widening of 5Y CDS by 75 bps. As of 13 February 2013, the day for which we calibrate asset volatility for the relationships above, CDS traded at 373 bps. By our measure, the new company has a leverage of 2.1 (from 1.9) and with an ROA volatility of 1.3%, the forecast for implied asset volatility is 20.1%, which leads to a 5Y CDS spread of 538 bps. Dell provides a good illustration of the issue of non-debt liabilities. Before the LBO news surfaced, DELL effectively had negative net debt (debt of about $9 billion against over $14 billion cash), yet its CDS traded at around 200 bps. One plausible explanation for this is the presence of significant non-debt liabilities, totaling about $26 billion. Of this, about $11 billion of accounts receivable could be netted out with its current assets and thus ignored. However, this still leaves standard and extended product warranty liabilities of $13 billion, and accrued expense of about $3 billion. If we include these liabilities in our analysis, we face the further question of where should they fall in the capital structure. In the Dell example, we excluded current liabilities and added the other liabilities to debt and ran our model. If we view these liabilities as pari passu with senior unsecured, the CDS should trade at 548 bps. If we model them as subordinated to senior-unsecured, the prediction for CDS spread is 268 bps. HNZ On 12 February 2013, Berkshire Capital and 3G Capital made an offer to buy Heinz for USD 23bn, a premium of 20% over the then market price. Berkshire participated with $4.12 billion in equity and $8 billion in preferred share. The beforeand (likely) after-capital structures for HNZ are: Pre LBO ($million) Pro-forma ($million) JR secured 8,500 SNR unsecured 5,020 2,500 Preferred 8,000 Equity 19,393 9,000 Source: CapitalIQ and PIMCO, as of 12 February 2013 Market reaction was a 124 bps widening of 5Y CDS (from 44 to 168 bps). Our method would indicate that, as the leverage increases from 1.17 to 1.38, and with HNZ s ROA volatility at 0.39%, the leverage-based implied asset volatility forecast is 23.6%. At the forecast asset volatility, the new company s 5Y CDS fair value spread is 183 bps. The post LBO capital structure would be unusual in one respect: the owner of the preferred shares also has almost half of the equity interest. In our model we do not consider preferred when determining the default barrier. The rationale for this is that the firm (controlling shareholders) may skip the coupon on preferred without triggering default. In this case, however, Berkshire would have an interest in preserving the value of the preferred, hence, under adverse business conditions, they might choose to default at a higher asset value where the preferred would obtain higher recovery. Hence, in this case, one could argue that the barrier should include the preferred debt. If we do that, the valuation for the 5Y CDS spread is 116 bps. Expected change in capital structure A possible interpretation of the volatility skew, i.e., implied asset volatilities are higher for more levered companies, is that the market expects a change in leverage through corporate action: companies with high leverage are less likely to experience further levering. But for those with low leverage, the market prices-in a possibility that leverage will increase in the future. This results in a higher CDS spread than that implied purely from current leverage levels. For example, consider a firm with a current market capitalization of $5 billion, senior unsecured debt of $8 billion and no secured debt. At 20% asset volatility, 5Y CDS spread should be 78 bps. If the CDS trades at 125 bps, implied expected secured debt issuance is $1.4 billion, taking leverage from 1.76 to This is equivalent to 22% implied asset volatility. This can be viewed as a 100% probability of a $1.4 billion secured debt issuance or a 30% probability of a $4.7 billion secured debt issuance. In general, this illustrates some of the challenges in applying option valuation based methods to capital structure valuation. We are in effect valuing an option whose strike could be changed in the future by our counterparty. CAPITAL STRUCTURE MODELING AND LBOS JUNE

6 Conclusion Capital structure modeling questions are complex and cannot be reduced to a pure mathematical modeling exercise. So this kind of model is not going to let us yell Eureka (or adopt the aforementioned ancient genius s wardrobe preferences when announcing successful modeling efforts!) and reveal a precise true spread for an LBO. However, this model can be quite useful in providing a framework to evaluate the effect of various driving factors on capital structure valuation. In addition to model driven calculations, it is important to realize that conventional approaches to measuring debt can underestimate the leverage of the firm. Appendix: Capital structure model dynamics The model assumes the following dynamics for the asset (affine diffusion) with r the short-rate, c the spread over Libor paid to debt holders, N the notional debt amount, and d the dividend paid to equity holders. Default occurs at the first crossing of barrier H, upon which the value of the assets drops from level H to where has the following density (truncated normal with volatility centered around with and n, N the normal density and cumulative distribution functions. An important distinction in this framework is the one between firm value and asset value. The latter refers to the intrinsic value of the assets: it can be thought of as the value of the firm s assets if they are owned by a firm for which default probability is nil. The firm value is lower than the asset value by the expected bankruptcy costs, which are the product of the probability of default and the expected bankruptcy costs upon default. The recovery of a debt tier with attachment/detachment points a, b (as % of total liability) is given by: with We calibrate the asset volatility and initial asset level to observed equity prices and 5Y CDS spreads on a daily basis (other calibrations are possible). Other parameters are held constant with period revisions. We have estimated bankruptcy cost parameters for which the average recoveries for senior unsecured and subordinated debt are, respectively, 40% and 5%: Mean Pro-forma ($million) JR secured 80% 44% In the case of financials, SUB CDS is traded, so we calibrate directly to the SEN/SUB ratios, using Markit CDS levels for financial institutions for which both Senior Unsecured and SUB CDS are available: Mean Pro-forma ($million) U.S. financials 86% 19% Europe financials 95% 30% where we have used a representative sample of the sectors components over the period These calibration results are specific to the PIMCO model described above. References Black, F. and J. C. Cox, 1976, Valuing Corporate Securities: Some Effects of Bond Indenture Provisions, Journal of Finance, Vol. 31(2), Shiller, R., 1981, Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends? American Economic Review, Vol. 71(3), JUNE 2013 CAPITAL STRUCTURE MODELING AND LBOS

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8 1 The authors would like to thank Ravi Mattu for his valuable comments and feedback on the model and this paper. We are also indebted to Horne, Mohit Mittal, Terrence Ing, Armen Karakashian, Sen Lin and Jun Wang for their comments on model development and its application to the HNZ and Dell LBOs. Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. Hypothetical and simulated examples have many inherent limitations and are generally prepared with the benefit of hindsight. There are frequently sharp differences between simulated results and the actual results. There are numerous factors related to the markets in general or the implementation of any specific investment strategy, which cannot be fully accounted for in the preparation of simulated results and all of which can adversely affect actual results. No guarantee is being made that the stated results will be achieved. 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