Capital structure substitution theory
Encyclopedia
In finance
, the capital structure substitution theory (CSS) 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
(EPS) 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.
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:
Combining these two effects, the marginal change in EPS as function of the total number of outstanding shares becomes:
where
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.
and the Trade-off theory
. The two theories make some contradicting predictions and for example Fama
and French
conclude: "In sum, we identify one scar on the tradeoff model (the negative relation between leverage and profitability), one deep wound on the pecking order (the large equity issues of small low-leverage growth firms)...". The capital structure substitution theory has the potential to close these gaps. It predicts a negative relation between leverage and valuation (=reverse of earnings yield) which in turn can be linked to profitability. But it also predicts that high valued small growth firms will avoid the use of debt as especially for these companies the cost of borrowing (
) is higher than for large companies, which in turn has a negative effect on their EPS. This is consistent with the finding that "…firms with higher current stock prices (relative to their past stock prices, book values or earnings) are more likely to issue equity rather than debt and repurchase debt rather than equity".
The CSS theory suggests that company share prices are not set by shareholders but by bondholders. As a result of active repurchasing or issuing of shares by company managements, equilibrium pricing is no longer a result of balancing shareholder demand and supply. In a way the CSS theory turns asset pricing upside-down, with bondholders setting share prices and shareholders determining company leverage. The asset pricing formula only applies to debt-holding companies.
index and government bond yields has been present over the last several decades. This relationship has become popular as the Fed model
and states in its strongest form an equality between the one year forward looking E/P ratio or earnings yield and the 10-year government bond
yield. The CSS equilibrium condition suggests that the Fed model is misspecified: the S&P 500 earnings yield is not in equilibrium with the government bond yield but with the average after-tax interest rate on corporate bonds. The CSS theory suggests that the Fed equilibrium was only observable after 1982, the year in which the United States Securities and Exchange Commission
allowed open-market repurchases of shares.
should prefer dividends as a means to distribute cash to shareholders, where
Low valued, high leveraged companies with limited investment opportunities and a high profitability use dividends as the preferred means to distribute cash to shareholders.
target is associated with a 1% increase in broad stock indexes in the US. The CSS theory suggests that the monetary policy transmission mechanism is indirect but straightforward: a change in the federal funds rate affects the corporate bond market which in turn affects asset prices through the equilibrium condition.
where
is the market average interest rate on corporate bonds. The CSS theory predicts that companies with a low valuation and high leverage will have a low beta. This is counter-intuitive as traditional finance theory links leverage to risk, and risk to high beta.
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, the capital structure substitution theory (CSS) describes the relationship between earnings, stock price and capital structure
Capital structure
In finance, capital structure refers to the way a corporation finances its assets through some combination of equity, debt, or hybrid securities. A firm's capital structure is then the composition or 'structure' of its liabilities. For example, a firm that sells $20 billion in equity and $80...
of public companies. The CSS theory hypothesizes that managements of public companies manipulate capital structure such that earnings per share
Earnings per share
Earnings per share is the amount of earnings per each outstanding share of a company's stock.In the United States, the Financial Accounting Standards Board requires companies' income statements to report EPS for each of the major categories of the income statement: continuing operations,...
(EPS) are maximized. Managements have an incentive
Incentive
In economics and sociology, an incentive is any factor that enables or motivates a particular course of action, or counts as a reason for preferring one choice to the alternatives. It is an expectation that encourages people to behave in a certain way...
to do so because shareholders and analysts value EPS growth. The theory is used to explain trends in capital structure, stock market valuation
Valuation (finance)
In finance, valuation is the process of estimating what something is worth. Items that are usually valued are a financial asset or liability. Valuations can be done on assets or on liabilities...
, dividend policy, the monetary transmission mechanism
Monetary policy
Monetary policy is the process by which the monetary authority of a country controls the supply of money, often targeting a rate of interest for the purpose of promoting economic growth and stability. The official goals usually include relatively stable prices and low unemployment...
, and stock volatility
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
, 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.
The formula
The CSS theory assumes that company managements can freely change the capital structure of the company – substituting bondsBond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
for stock
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...
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
Share repurchase
Stock repurchase is the reacquisition by a company of its own stock. In some countries, including the U.S. and the UK, a corporation can repurchase its own stock by distributing cash to existing shareholders in exchange for a fraction of the company's outstanding equity; that is, cash is exchanged...
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 taxCorporate taxMany countries impose corporate tax or company tax on the income or capital of some types of legal entities. A similar tax may be imposed at state or lower levels. The taxes may also be referred to as income tax or capital tax. Entities treated as partnerships are generally not taxed at the...
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.
Capital structure
The two main capital structure theories as taught in corporate finance textbooks are the Pecking order theoryPecking Order Theory
In the theory of firm's capital structure and financing decisions, the Pecking Order Theory or Pecking Order Model was first suggested by Donaldson in 1961 and it was modified by Stewart C. Myers and Nicolas Majluf in 1984...
and the Trade-off theory
Trade-off theory of capital structure
The Trade-Off Theory of Capital Structure refers to the idea that a company chooses how much debt finance and how much equity finance to use by balancing the costs and benefits. The classical version of the hypothesis goes back to Kraus and Litzenberger who considered a balance between the...
. The two theories make some contradicting predictions and for example Fama
Eugene Fama
Eugene Francis "Gene" Fama is an American economist, known for his work on portfolio theory and asset pricing, both theoretical and empirical. He is currently Robert R...
and French
Kenneth French
Kenneth Ronald "Ken" French is the Carl E. and Catherine M. Heidt Professor of Finance at the Tuck School of Business, Dartmouth College. He has previously been a faculty member at MIT, the Yale School of Management, and the University of Chicago Booth School of Business...
conclude: "In sum, we identify one scar on the tradeoff model (the negative relation between leverage and profitability), one deep wound on the pecking order (the large equity issues of small low-leverage growth firms)...". The capital structure substitution theory has the potential to close these gaps. It predicts a negative relation between leverage and valuation (=reverse of earnings yield) which in turn can be linked to profitability. But it also predicts that high valued small growth firms will avoid the use of debt as especially for these companies the cost of borrowing (
) is higher than for large companies, which in turn has a negative effect on their EPS. This is consistent with the finding that "…firms with higher current stock prices (relative to their past stock prices, book values or earnings) are more likely to issue equity rather than debt and repurchase debt rather than equity".Asset pricing
The equilibrium condition can be easily rearranged to an asset pricing formula:The CSS theory suggests that company share prices are not set by shareholders but by bondholders. As a result of active repurchasing or issuing of shares by company managements, equilibrium pricing is no longer a result of balancing shareholder demand and supply. In a way the CSS theory turns asset pricing upside-down, with bondholders setting share prices and shareholders determining company leverage. The asset pricing formula only applies to debt-holding companies.
Fed model equilibrium
In the US, a positive relationship between the average earnings yield of the S&P 500S&P 500
The S&P 500 is a free-float capitalization-weighted index published since 1957 of the prices of 500 large-cap common stocks actively traded in the United States. The stocks included in the S&P 500 are those of large publicly held companies that trade on either of the two largest American stock...
index and government bond yields has been present over the last several decades. This relationship has become popular as the Fed model
Fed model
The "Fed model" is a theory of equity valuation that has found broad application in the investment community. The model compares the stock market’s earnings yield to the yield on long-term government bonds...
and states in its strongest form an equality between the one year forward looking E/P ratio or earnings yield and the 10-year government bond
Government bond
A government bond is a bond issued by a national government denominated in the country's own currency. Bonds are debt investments whereby an investor loans a certain amount of money, for a certain amount of time, with a certain interest rate, to a company or country...
yield. The CSS equilibrium condition suggests that the Fed model is misspecified: the S&P 500 earnings yield is not in equilibrium with the government bond yield but with the average after-tax interest rate on corporate bonds. The CSS theory suggests that the Fed equilibrium was only observable after 1982, the year in which the United States Securities and Exchange Commission
United States Securities and Exchange Commission
The U.S. Securities and Exchange Commission is a federal agency which holds primary responsibility for enforcing the federal securities laws and regulating the securities industry, the nation's stock and options exchanges, and other electronic securities markets in the United States...
allowed open-market repurchases of shares.
Dividend policy
From the CSS equilibrium condition it can be derived that debt-free companies should prefer repurchases whereas companies with a debt-equity ratio larger thanshould prefer dividends as a means to distribute cash to shareholders, where
- D is the company’s total long term debt
-
is the company’s total equity -
is the tax rate on capital gains -
is the tax rate on dividends
Low valued, high leveraged companies with limited investment opportunities and a high profitability use dividends as the preferred means to distribute cash to shareholders.
Monetary policy
An unanticipated 25-basis-point cut in the federal funds rateFederal funds rate
In the United States, the federal funds rate is the interest rate at which depository institutions actively trade balances held at the Federal Reserve, called federal funds, with each other, usually overnight, on an uncollateralized basis. Institutions with surplus balances in their accounts lend...
target is associated with a 1% increase in broad stock indexes in the US. The CSS theory suggests that the monetary policy transmission mechanism is indirect but straightforward: a change in the federal funds rate affects the corporate bond market which in turn affects asset prices through the equilibrium condition.
Beta
The CSS equilibrium condition can be used to deduct a relationship for the beta of a company x at time t:where
is the market average interest rate on corporate bonds. The CSS theory predicts that companies with a low valuation and high leverage will have a low beta. This is counter-intuitive as traditional finance theory links leverage to risk, and risk to high beta.Assumptions
- Managements of public companies manipulate capital structure such that earnings-per-share are maximized.
- Managements can freely change the capital structureCapital structureIn finance, capital structure refers to the way a corporation finances its assets through some combination of equity, debt, or hybrid securities. A firm's capital structure is then the composition or 'structure' of its liabilities. For example, a firm that sells $20 billion in equity and $80...
of the company – substituting bonds for stock or vice versa – on a day-to-day basis and in small denominations. - Shares can only be repurchased through open market buybacks. Information about share price is available on a daily basis.
- Companies pay a uniform corporate tax rate T.
See also
- Beta (finance)
- Capital asset pricing modelCapital asset pricing modelIn finance, the capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk...
- Capital StructureCapital structureIn finance, capital structure refers to the way a corporation finances its assets through some combination of equity, debt, or hybrid securities. A firm's capital structure is then the composition or 'structure' of its liabilities. For example, a firm that sells $20 billion in equity and $80...
- DividendDividendDividends are payments made by a corporation to its shareholder members. It is the portion of corporate profits paid out to stockholders. When a corporation earns a profit or surplus, that money can be put to two uses: it can either be re-invested in the business , or it can be distributed to...
- Fed modelFed modelThe "Fed model" is a theory of equity valuation that has found broad application in the investment community. The model compares the stock market’s earnings yield to the yield on long-term government bonds...
- Modigliani–Miller theorem
- Share repurchaseShare repurchaseStock repurchase is the reacquisition by a company of its own stock. In some countries, including the U.S. and the UK, a corporation can repurchase its own stock by distributing cash to existing shareholders in exchange for a fraction of the company's outstanding equity; that is, cash is exchanged...
- P/E ratioP/E ratioThe P/E ratio of a stock is a measure of the price paid for a share relative to the annual net income or profit earned by the firm per share...