page_title: Capital structure substitution theory
section_title: The formula
hierarchical_section_title: Capital structure substitution theory / The formula
caption_attribution_description: English: CSS Equilibrium as function of time for the S&amp;P500 index Aug 2020
context_page_description: In finance, the capital structure substitution theory describes the relationship between earnings, stock price and capital structure of public companies. The CSS theory hypothesizes that managements of public companies manipulate capital structure such that earnings per share are maximized. Managements have an incentive to do so because shareholders and analysts value EPS growth. The theory is used to explain trends in capital structure, stock market valuation, dividend policy, the monetary transmission mechanism, and stock volatility, and provides an alternative to the Modigliani–Miller theorem that has limited descriptive validity in real markets. The CSS theory is only applicable in markets where share repurchases are allowed. Investors can use the CSS theory to identify undervalued stocks.
context_section_description: The CSS theory assumes that company managements can freely change the capital structure of the company – substituting bonds for stock or vice versa – on a day-to-day basis and in small denominations without paying transaction costs. Companies can decide to buy back one single share for the current market price P and finance this by issuing one extra corporate bond with face value P or do the reverse. In mathematical terms these substitutions are defined as 
  where D is the corporate debt and n the number of shares of company x at time t. The negative sign indicates that a reduction of the number of shares n leads to a larger debt D and vice versa. The earnings-per-share change when one share with price P is repurchased and one bond with face value P is issued: 
  The earnings that were ‘allocated’ to the one share that was repurchased are redistributed over the remaining outstanding shares, causing an increase in earnings per share of: 
  The earnings are reduced by the additional interest payments on the extra bond. As interest payments are tax-deductible the real reduction in earnings is obtained by multiplying with the tax shield. The additional interest payments thus reduce the EPS by: 
  Combining these two effects, the marginal change in EPS as function of the total number of outstanding shares becomes:
  where
  E is the earnings-per-share
  R is the nominal interest rate on corporate bonds
  T is the corporate tax rate
  EPS is maximized when substituting one more share for one bond or vice versa leads to no marginal change in EPS or: 
  This equilibrium condition is the central result of the CCS theory, linking stock prices to interest rates on corporate bonds.
caption: CSS Equilibrium as function of time for the S&P500 index - August 2020. Extreme economic events like the global financial crisis in 2007 push the index out of equilibrium, but subsequent modification to corporate capital structures push the index back towards the equilibrium line.
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