Capital Structure Analysis of DAX 30 Firms (2018)

This project analyzes the capital structure choices of firms included in the DAX 30 stock index at the end of 2018. The objective is to identify how firm characteristics, risk measures, and growth opportunities influence debt financing decisions, measured by the debt ratio.

The analysis combines univariate and multivariate regression techniques using firm-level financial and market data, with a particular focus on industry heterogeneity.

Repository Structure

├── datasets # Raw and processed data
├── R_code # R scripts for regressions and analysis
├── output # Tables and figures
├── README.md # Project documentation

Data

The dataset includes all companies listed in the DAX 30 index (2018). For each firm, the following variables are provided:

• Market capitalization
• One-year stock return
• Equity volatility
• Equity beta
• Book value of debt
• Book value of equity
• Sales
• EBITDA
• EBIT
• Net income
• Industry classification

For firms operating in multiple industries, the most representative industry was selected to ensure consistency in the analysis.

Methodology

Dependent Variable: Debt Ratio

The primary dependent variable is the debt ratio, which measures the proportion of a firm’s assets financed through debt:

$$ [ \text{Debt Ratio} = \frac{\text{Book Debt}}{\text{Book Debt} + \text{Market Capitalization}} ] $$

The debt ratio serves as an indicator of:

• Financial leverage
• Risk profile
• Financing strategy

Industry-level patterns reveal systematic differences in leverage driven by asset tangibility, cash-flow stability, and regulatory environments.

Univariate Analysis

Book Value of Assets Book value of assets is calculated as:

$$ [ \text{Book Value of Assets} = \text{Book Debt} + \text{Book Equity} ] $$

Regression results show that the logarithm of book value of assets provides greater explanatory power than levels. This reflects the non-linear relationship between firm size and leverage, consistent with diminishing marginal benefits of debt as firm size increases.

Tobin’s Q

Tobin’s Q measures market valuation relative to asset replacement cost:

$$ [ \text{Tobin's Q} = \frac{\text{Market Capitalization} + \text{Book Debt}}{\text{Book Equity} + \text{Book Debt}} ] $$

A negative relationship between Tobin’s Q and the debt ratio is observed. Firms with stronger growth opportunities (high Tobin’s Q), particularly in technology-driven industries, tend to rely more on equity financing to preserve financial flexibility.

Equity risk measures

Regression analysis reveals a negative relationship between the debt ratio and:

• Equity volatility
• Equity beta

Firm-level volatility and beta are calculated as:

$$ [ \sigma_V = \left( 1 - \frac{\text{Book Debt}}{\text{Market Cap} + \text{Book Debt}} \right) \sigma_E ] $$

$$ [ \beta_V = \left( 1 - \frac{\text{Book Debt}}{\text{Market Cap} + \text{Book Debt}} \right) \beta_E ] $$

Higher volatility firms tend to maintain lower leverage, likely due to:

• Higher borrowing costs
• Limited access to debt markets
• Greater bankruptcy risk

This result contrasts with some theoretical expectations and highlights the role of lender risk aversion.

Explanatory Power of Variables

Among the tested variables, sales exhibit the strongest explanatory power for the debt ratio, followed by:

1. Book equity
2. EBITDA
3. EBIT
4. Net income
5. One-year return

Sales capture overall operational scale and revenue-generating capacity, making them highly informative for leverage decisions.

Multivariate Analysis

The best-fitting multivariate regression model includes:

• Log(Book Value of Assets)
• Tobin’s Q
• Firm-level beta

These variables jointly capture:

• Firm size and stability
• Growth opportunities
• Market risk exposure

Together, they provide a comprehensive explanation of observed capital structure choices among DAX 30 firms.

Notable Exception: Wirecard AG represents a significant outlier, displaying an unusually low debt ratio. This deviation is likely influenced by firm-specific circumstances and the financial irregularities that later culminated in its collapse.

R Packages Used

• dplyr
• broom
• kableExtra

References

Berger, A. N., & Udell, G. F. (1998). The economics of small business finance
Damodaran, A. (2012). Investment Valuation
Rahman, Hossain & Sen (2023)
Reuters (2022). The rise and fall of Wirecard