Resultados y discusión
4.4. Estudio de las relaciones genotipo-fenotipo entre pacientes
4.4.5. Identificación de regiones conocidas asociadas a enfermedades a partir de los datos de DECIPHER
Next, I report the methodology and results for the analysis regarding financial strength of portfolio companies in the sample. For the estimation I apply probit regression, a binary classification model, with Bankruptcy as the dependent variable. Probit model estimates the probability of an event occurring through maximum likelihood procedure for a set of explanatory variables (Dougherty, 2002). In a simplified form, the regression equation is as follows:
Pr(𝐵𝑎𝑛𝑘𝑟𝑢𝑝𝑡𝑐𝑦𝑖 = 1) = Φ(𝛽0+ ∑ 𝛽𝑖𝐸𝑥𝑝𝑙𝑎𝑛𝑎𝑡𝑜𝑟𝑦𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 + 𝜀𝑖) (Equation 1)
The coefficients for dependent variables from the probit estimation are subsequently converted to marginal effects at mean values. Mean values for estimation samples are reported in Appendix. Marginal effects enable interpretation of the probit model: for the mean company in the sample, each unit increase in the independent variable increases/decreases the probability of the dependent variable by the marginal effect expressed as a percent.
However, as noted in section 5.3 the lack of financial data may expose the analysis to sample selection bias. The selection bias error arises when a non-random sample of a population causes some observations in the population to be less likely included than others. This results in a biased sample where all observations are not equally balanced or objectively represented (Dougherty, 2002). As the number of buyout companies that have adequate financial information is significantly lower compared to the sample, selection bias might yield inconsistent results. In the following subsections I will first describe methods to overcome the sample selection bias. Then, I analyse the effects of capital structure and profitability on buyout bankruptcy.
6.1.1.Controlling for sample selection bias
I use probit model with sample selection to take into account the self-selection bias (Van de Ven & Van Praag, 1981). The latent model assumes that there exists an underlying relationship for the dependent variable 𝑦𝑖
𝑦𝑖∗ = 𝑥
𝑖𝛽 + 𝑢1𝑖 (Latent equation)
such that only the binary outcome is observed
𝑦𝑗𝑝𝑟𝑜𝑏𝑖𝑡 = (𝑦𝑗∗ > 0) (Probit equation)
However, if sample selection bias exists, the dependent variable is not always observed. Instead, the dependent variable for observation i is observed if
𝑦𝑖𝑠𝑒𝑙𝑒𝑐𝑡 = (𝑧 𝑗𝜆 + 𝑢2𝑖 > 0) (Selection equation) where 𝑢1~𝑁(0,1) 𝑢2~𝑁(0,1) corr(𝑢1, 𝑢2) = 𝜌
When 𝜌 ≠ 0, standard probit techniques applied to the first equation would yield biased results. The inclusion of selection equation provides consistent, asymptotically efficient estimates for all the parameters in such models. The selection model should have a minimum of one variable that does not belong to the main probit equation. (Press, 2005)
The selection correction procedure estimates the sample-selection correlation term denoted as Mills ratio 𝜆. I structure the selection equation on the basis of whether there is adequate financial data to calculate interest coverage ratios for the observations. I obtain estimates for the coefficients ω of observable variables Zi (Selection equation) by using transaction year,
portfolio company country dummies, creditor rights, transaction secondary features and company age as explanatory variables.
Depending on whether the firm has adequate financials, Mills ratio is determined as follows:
𝜆
𝑖=
𝜙(𝜔̂ ∗𝑍𝑖)
𝜆
𝑖=
−𝜙(𝜔̂ ∗𝑍𝑖)1−Φ(𝜔̂ ∗𝑍𝑖)
if Financialsi = 0
where Φ denotes the density distribution function and 𝜙 the density distribution function of the standard normal distribution. After the coefficients for
𝜆
𝑖 are determined, it is added as an independent variable to the probit regression. According to Edelen & Kadlec (2005), adding 𝜆 into a regression is similar to adding a correlated omitted variable to a misspecified regression. Adding 𝜆 causes the explanatory coefficients to be estimated with less bias, or no bias if 𝜆 completely captures the in-sample covariance between ηi and Zi.Having controlled for sample selection bias, I analyse how the firm specific capital structure, profitability and bankruptcy likelihood ratios are associated with buyout bankruptcy. The equation form is as follows (Dougherty, 2002):
𝐸(𝐵𝑎𝑛𝑘𝑟𝑢𝑝𝑡𝑐𝑦𝑖|𝐸𝑖 = 1, 𝑋𝑖) = 𝛽0+∑ 𝛽𝑖𝐸𝑥𝑝𝑙𝑎𝑛𝑎𝑡𝑜𝑟𝑦𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 +𝜎𝜎𝑢𝜀
𝜀 𝜆𝑖 (Equation 2) where σuε is the population covariance of the selection category u and ε. σε is the standard
deviation of ε and the inverse Mill’s ratio λi. The results for the second step of the model are
reported in Table 7 along with the normal probit model estimations.
6.1.2.Impact of portfolio company financial strength on bankruptcy
Table 7 reports the results for both Probit and Probit with Heckman correction model. The models estimate buyouts conducted during 1994-2009 and aim to explain hypotheses about portfolio firm characteristics presented in section 4.2. Mean values for variables in the estimation are reported in Table 12 in appendix. The target company financials refer to financial statement information one year after the buyout. The statistical significance of the Inverse Mill’s ratio in the Heckman model indicates that sample selection exists, but even with the corrected error terms the model yields significant results despite small differences in coefficients.
The results indicate that higher leverage significantly increases the probability of bankruptcy, as expected. One unit increase in leverage increases the likelihood of bankruptcy by 0.7%. For the mean company in the sample, this means an increase in leverage from 5.05x to 5.09x. The benefits of leverage derive from magnifying returns and avoiding taxes, but yet many LBOs use much higher leverage than needed (Opler & Titman, 1993). High levels of leverage leave
little leeway for buyout companies in case the projected cash flows do not realise, which makes LBOs very vulnerable to unexpected changes. The finding is also in line with Axelson et al. (2012) who find that transaction-level leverage is negatively related to fund-level returns. The authors suggest that that private equity firms apply highly leveraged structures more in their own (carried) interest than their investors’.
Companies that have higher cash conversion are less likely to go bankrupt, as expected. One unit increase in cash conversion % from its mean decreases the probability of bankruptcy by 3.6%. For the mean company in the sample, this means an increase from 62.2% to 79.6%. This indicates that firms with lower investment needs, and hence higher share of free cash flow to service debt, are significantly less likely to go bankrupt.
Higher interest coverage (calculated as EBIT/Interest expenses) appears to decrease the probability of bankruptcy, as expected. Interest coverage measures the ability of a company to pay interest on its debt outstanding and lenders often require minimum levels for this in their covenants. One unit increase in interest coverage decreases the likelihood of bankruptcy by 2%. For the mean company in the sample, this means an increase from 2.2x to 2.3x.
The strength of the portfolio company country’s creditor rights appears has a very significant effect on the bankruptcy probability. The results suggest that in countries with high creditor rights, buyouts are significantly less likely to bankrupt. This in line with the findings of Acharya et al. (2011) who report that less buyout leverage is used in countries where the potential liquidation value is lower (i.e. higher creditor rights).
Finally, larger buyouts are less likely to bankrupt while more profitable companies measured by Return on Assets are less likely to bankrupt, as expected. Also, the tangibility of company’s assets does not appear to significantly affect the probability of bankruptcy.
Table 7 – Impact of portfolio company financial strength on bankruptcy
Dependent variable
Model Probit (1) Probit (2) Heckprobit (1) Heckprobit (2) Dif. (1) Dif. (2)
Leverage1 (+) 0.119*** 0.070** 0.049 (0.026) (0.033) [0.005] [0.007] Profitability1 (+) -0.004 -0.002 -0.002 (0.007) (0.008) [-0.000] [-0.000] Cash conversion (-) -0.316** -0.387** 0.071 (0.158) (0.174) [-0.014] [-0.036] Leverage2 (+) 0.010*** 0.010*** 0.000 (0.003) (0.003) [0.001] [0.003] Profitability2 (-) -0.041*** -0.041*** 0.000 (0.014) (0.015) [-0.006] [-0.013] Tangibility (-) 0.289 0.232 0.057 (0.357) (0.390) [0.040] [0.071] Interest Coverage (-) 0.012 0.001 -0.182** -0.024 0.194 0.025 (0.410) (0.030) (0.091) (0.035) [0.001] [0.000] [-0.017] [-0.007] Firm size (+/-) -0.293** -0.247** -0.387** -0.285** 0.094 0.038 (0.142) (0.125) (0.154) (0.131) [-0.013] [-0.034] [-0.036] [-0.087] Creditor rights (-) -0.557*** -0.328*** -0.320*** -0.188 -0.237 -0.140 (0.089) (0.113) (0.036) (0.071) [-0.024] [-0.045] [-0.051] [-0.058]
Inverse Mill's ratio -0.262* -0.323*
(0.205) (0.189) Constant -5.219*** -1.789*** -4.281*** -0.932 (0.444) (0.481) (0.799) (0.667) Observations 693 794 558 629 Adjusted R2 0.2320 0.2020 - - Wald chi2 931.31 89.85 456.22 77.39
Year fixed effects Yes Yes Yes Yes
Industry fixed effects Yes Yes Yes Yes
Bankruptcy rate 13.6 % 12.8 % Exp.
Sign
Bankruptcy
This table reports the results for Probit and Heckman correction regressions estimating the cross- sectional portfolio firm characteristics’ effect on the probability of buyout bankruptcy during 1994- 2009. Financials refer to financial statement information one year after the buyout. The dependent variable, Bankruptcy, a binary variable has the value of one if the buyout bankrupts. Leverage1 is the portfolio company’s cash-based leverage, calculated as Net debt to EBITDA. Interest Coverage is the ability to pay interest on debt outstanding, calculated as EBIT to Interest expenses. Firm size is the logarithm of Total Assets. Profitability1 is cash flow-based profitability calculated as EBITDA to Revenue. Tangibility is Fixed assets to Total assets. Leverage2 is Total debt to Total Assets.
Profitability2 is Net income to Total assets. Cash conversion is the share of operational cash flow converted into free cash flow, calculated as (EBITDA-Capital expenditures)/EBITDA. Inverse Mill’s ratio adjusts the error term for missing observations. All the ratios are winsorised with p(0.1).
White’s heteroskedasticity robust standard errors are reported in parentheses. Marginal effects at variable means are reported in square brackets. ***, **, and * denote the statistical significance of regression coefficients at the level of 1%, 5%, and 10% respectively.