3. Hypothesis and Methodology
3.3. The Parameters
3.3.2. The Bankruptcy Cost
In the trade-off theory, the tax shield is the reason why company should take advantage of debt.
By increasing their debts, companies can increase their tax shield. The tax shield is equal to the corporate tax rate multiplied by the amount of debt. Because the tax shield effect is directly related to the corporate tax rate, a first hypothesis is that marginal-debt companies might have a corporate tax rate close to zero. It would explain the absence of debt as a corporate tax rate close to zero would not provide any tax shield. Obviously, we also expect marginal-debt companies to have a much lower corporate tax rate than their indebted peers. In order to estimate a company´s corporate tax rate, we use the Bloomberg data RR037 (EFF_TAX_RATE). It is defined as the income tax expenses divided by the pretax income.
3.3.2. The Bankruptcy Cost
The bankruptcy cost is the second and last element of the equation to be analyzed. It is defined as the probability of default multiplied by the loss observed in case of default. A high bankruptcy cost could be a good explanation of the existence of marginal-debt companies. The first component of this parameter, is already filtered with the Altman Z-score. All companies analyzed in the study should have, according to the Altman Z-score, a low probability of default.
However, it might still be interesting to analyze the difference in score between marginal-debt and indebted companies. A second approach is to look at the cash flow volatility. To measure it, we look at the operational cash flow volatility. A higher cash flow volatility increases the probability of default of a company because of the uncertainty of its cash generation.
While calculating and comparing the average corporate tax between our two samples was intuitive and provides a clear numerical value which could be used to estimate the tax shield
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effect, estimating the cost of bankruptcy is more difficult and less precise. Because this thesis does not aim to calculate an exact value for the cost of bankruptcy, but to determine whether marginal-debt companies have a higher bankruptcy cost than their indebted peers. Then, the study will focus on comparing key parameter affecting the cost of bankruptcy rather than estimating a value for cost of bankruptcy.
Probability of default
The probability of default is defined as the percent chance that a company goes bankrupt during a defined time horizon. Most common way to determine the probability of default of a company is to look at its credit rating. However, this data is not available for all the data sample. Hence, as mentioned earlier, we use the Altman Z-score as a substitute for credit rating. Companies have already been filtered on their Altman Z-score. They all have a score above 3 for three consecutive years between 2011 and 2013, meaning that they all have the healthy financials which should easily allow them to access debt. In order to go further and check if there is any difference in terms of likelihood of default between indebted companies and marginal-debt companies, we first compare their Altman Z-score.
As a reminder, the Altman Z-score is calculated with the following formula:
1.2 1.4 3.3 0.6
Where
X 0.6 ∗ Market Capitalization Total Liabilities
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In this formula, X4 is equal to the market capitalization divided by the total liabilities. This factor of the equation is the only one which is significantly impacted by the capital structure of the company. Then, to reduce the impact of capital structure in the analysis, we deleverage the Z-score formula by modifying the X4 component as shown in the following formula:
Deleveraged X 0.6 ∗ / ∗ Market Capitalization Total Liabilities – &
In order to find the above formula, we virtually turn Short & Long Term Financial Debt into equity. Owing to that, we removed it from the total liabilities in the denominator. Moreover, we took the assumption that transforming Short & Long Term Financial Debt into equity would also increase its market capitalization by the percentage increase of equity resulting from this operation.
In a third approach, we study the volatility of operational cash flow for each company. We select operational cash flow instead of cash flow as it only focuses of companies operations and allows us to ignore capital structure factors (e.g. debt reimbursement). A higher volatility of cash flow means that the cash generated by a company is not stable, it is more likely that during some years it has an extremely low cash flow generation. It is problematic when this low cash flow generation during some time does not allow the company to reimburse its debt or even finance its own operations. Then, a company with higher cash flow volatility will have a higher likelihood of default. We calculate the volatility of operational cash flow generated by each company during the 3 years period and then divide it by the average operational cash flow generated by the same company over the same period, as described by the formula bellow:
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% ̅
Where is the standard deviation of operational cash flow ̅ is the average operational cash flow
% is the operational cash flow volatility
Dividing the operational cash flow by the average cash flow allows us to express the volatility in terms of percentage, so that we can compare companies regardless of their size.
Loss given default
The loss given default represents the money the lender would lose in case of default of the borrowing company. A company with a high amount of tangible assets will have more collateral to sell in case of default, meaning that it reduces its loss given default. Then, we could expect marginal-debt companies to have a lower amount of tangible assets.
When a financial institution lends money to a company it often requires the company to use its assets as collateral to secure the loan. In this case, if the company goes into bankruptcy, the bank can recover a part of the money it let by selling the assets. The amount a company´s worth in case of bankruptcy, called the liquidation value, is mainly represented by the amount of physical assets it owns. Physical assets are real estate, fixtures, equipments and inventories.
Bloomberg provides the information for physical assets, called tangible assets. A higher tangible assets values implies a lower bankruptcy cost. We then study the asset tangibility of marginal-debt companies and compare it with their indebted peers. We expect marginal-debt companies to have a lower asset tangibility ratio, meaning that they have a higher proportion of intangible assets, which are much less valuable as collateral. The asset tangibility ratio is
‧
calculated by dividing tangible assets into total assets.
The cash flow represents the amount of cash a company is generating. When applying for debt, it is a key parameter as it indicates the company’s ability to reimburse its debt. Insufficient cash flow compared to the amount of debt a company has. In practice, most banks allow their customers to have debt equals to three times of the free cash flow.
The loss given default is defined as the expected loss a borrower will face in case the company he lend money to, goes bankrupt. Tangibility of asset is the first key variable for estimating the loss given default as tangible assets have a clear value given by the market, while intangible assets are more difficult to value and sell. For instance, the value of the real estate a company owns is given by the real estate prices. In case of bankruptcy, we know that these assets can easily be sold at a price close to market prices. On the other hand, patents or brand value do not have clearly defined market value and are much more difficult to sell, especially in a stress scenario.
In a second approach, we try to quantify the average net amount of tangible assets each sample has. This number is calculated by subtracting short and long term financial debt to the amount of tangible assets the company has. This variable tells how much tangible assets companies have left when selling part of them to reimburse the amount of financial debt they have. The resulting number provides a good indicator of the quantity of collateral which could be used for new debt issuance. Because both our sample have significant size difference, we use total equity as a denominator. It will help us having a sound comparison between the two samples.
Moreover, it will help us interpreting the ratio by telling us, as a percentage of equity, how much asset can potentially be used as collateral for new debt issuance. The formula applied here is as
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following:
Tangible Assets Short &
Short &
Beside assets which can be used as collateral to secure the loan in case of bankruptcy, cash flow generated by a company´s operations are the main source of cash used to reimburse debt. The higher the cash flow is relative to the amount of debt the company has, the lower the loss given default is. To properly compare the two samples´ cash flow, we divide the operating cash flow of a company by its total equity and total financial debt as describe in the following formula:
Operational Cash Flow
Short &
3.4. Statistical Method
For each financial parameter, we extract the data for fiscal year 2011, 2012, and 2013 (FY2011, FY2012, and FY2013). We then calculate the average for the period. When having both samples mean and standard deviation, we test their mean having the following hypothesis:
: " "
: " "
In order to test this hypothesis, we compute a two sided Welch t test. The Welch t test is an adaptation of the classical Student t test when samples are expected to have different standard deviations. The t statistic from the Welch t test is calculated with the following formula:
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̅ ̅
⁄ ⁄
Where ̅ , and ̅ are the sample means , and are the sample variances , and are the sample sizes
We need the degree of freedom to compute the test. The degree of freedom is calculated with the formula bellow:
. . ⁄
1 ⁄
1
Where ̅ , and ̅ are the sample means , and are the sample variances , and are the sample sizes
For all tests conducted in the study, we have an extremely large value for the degree of freedom.
Hence, we will consider it to be close to infinite. We test all sample means at 90%, 95% and 99% significance level. Then, H0 will be rejected at all respective significance level in case we find the t statistic superior to 1.645, 1.960, and 2.576.
This statistical method has been used in previous literature such as Agrawal and Nagarajan (1990), Strebulav and Yang (2013), and Devos et. Al. (2012).