# Capital structure substitution theory

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In finance, the capital structure substitution theory (CSS) [1] 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. [2] [3]

Finance is a field that is concerned with the allocation (investment) of assets and liabilities over space and time, often under conditions of risk or uncertainty. Finance can also be defined as the art of money management. Participants in the market aim to price assets based on their risk level, fundamental value, and their expected rate of return. Finance can be split into three sub-categories: public finance, corporate finance and personal finance.

In finance, particularly corporate finance capital structure is the way a corporation finances its assets through some combination of equity, debt, or hybrid securities.

Earnings per share (EPS) is the monetary value of earnings per outstanding share of common stock for a company.

## The formula

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

The bond is a debt security, under which the issuer owes the holders a debt and is obliged to pay them interest or to repay the principal at a later date, termed the maturity date. Interest is usually payable at fixed intervals. Very often the bond is negotiable, that is, the ownership of the instrument can be transferred in the secondary market. This means that once the transfer agents at the bank medallion stamp the bond, it is highly liquid on the secondary market.

The stock of a corporation is all of the shares into which ownership of the corporation is divided. In American English, the shares are commonly called as stocks. A single share of the stock represents fractional ownership of the corporation in proportion to the total number of shares. This typically entitles the stockholder to that fraction of the company's earnings, proceeds from liquidation of assets, or voting power, often dividing these up in proportion to the amount of money each stockholder has invested. Not all stock is necessarily equal, as certain classes of stock may be issued for example without voting rights, with enhanced voting rights, or with a certain priority to receive profits or liquidation proceeds before or after other classes of shareholders.

${\displaystyle \left[{\frac {\partial D}{\partial n}}\right]_{\text{x,t}}=-P_{\text{x,t}}}$

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:

Share repurchase is the re-acquisition by a company of its own stock. It represents a more flexible way of returning money to shareholders.

1. 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: ${\displaystyle E/n}$
2. 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: ${\displaystyle P\cdot R\cdot [1-T]/n}$

Combining these two effects, the marginal change in EPS as function of the total number of outstanding shares becomes:

${\displaystyle \left[{\frac {\partial E}{\partial n}}\right]_{\text{x,t}}=-{\frac {E_{\text{x,t}}}{n}}+{\frac {P_{\text{x,t}}\ R_{\text{x,t}}\ [1-T]}{n}}}$

where

• E is the earnings-per-share
• R is the nominal interest rate on corporate bonds
• T is the corporate tax rate

A corporate tax, also called corporation tax or company tax, is a direct tax* imposed by a jurisdiction on the income or capital of corporations or analogous legal entities. Many countries impose such taxes at the national level, and a similar tax may be imposed at state or local levels. The taxes may also be referred to as income tax or capital tax. Partnerships are generally not taxed at the entity level. A country's corporate tax may apply to:

EPS is maximized when substituting one more share for one bond or vice versa leads to no marginal change in EPS or:

${\displaystyle {\frac {E_{\text{x,t}}}{P_{\text{x,t}}}}=R_{\text{x,t}}\ [1-T]}$

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 theory and the Trade-off theory. The two theories make some contradicting predictions and for example Fama and French conclude: [4] "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 (${\displaystyle R_{\text{x,t}}}$) 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". [5]

In corporate finance, the pecking order theory postulates that the cost of financing increases with asymmetric information.

The trade-off theory of capital structure is 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 dead-weight costs of bankruptcy and the tax saving benefits of debt. Often agency costs are also included in the balance. This theory is often set up as a competitor theory to the pecking order theory of capital structure. A review of the literature is provided by Frank and Goyal.

Eugene Francis "Gene" Fama is an American economist, best known for his empirical work on portfolio theory, asset pricing, and the efficient-market hypothesis.

## Asset pricing

The equilibrium condition can be easily rearranged to an asset pricing formula:

In financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from general equilibrium asset pricing or rational asset pricing.

${\displaystyle P_{\text{x,t}}={\frac {E_{\text{x,t}}}{R_{\text{x,t}}[1-T]}}}$

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. Some companies are offering stock screeners based on the CSS theory.

The asset pricing formula can be used on a market aggregate level as well. For the S&P 500 composite index, data from Shiller [6] can be used for composite earnings level, and Federal Reserve Economic Data [7] can be used for the interest rate on corporate bonds (BAA) and an estimate of corporate tax rate (by looking at the ratio of corporate profits and corporate profits after tax).

The resulting graph shows at what times the S&P 500 Composite was overpriced and at what times it was under-priced relative to the Capital Structure Substitution theory equilibrium. In times when the market is under-priced, corporate buyback programs will allow companies to drive up earnings-per-share, and generate extra demand in the stock market. In times when the index was under-priced relative to the model equilibrium, repurchase programs will be stopped and demand is reduced. Not surprisingly the index was overpriced in the period around the tech bubble. What may come more as a surprise that the market is currently (June 2018) not over-priced relative to the model as earnings are high and corporate interest rates are low. In order to reach equilibrium conditions the index would have to gain ~20% or about US\$4.9 trillion in market capitalization.

## Fed model equilibrium

In the US, a positive relationship between the average earnings yield of the S&P 500 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. [8]

## Dividend policy

It can be shown that repurchasing has a disadvantage over dividends for companies with a debt-equity ratio above

${\displaystyle {\frac {D}{E_{\text{q}}}}>{\frac {1-T_{\text{C}}}{1-T_{\text{D}}}}-1}$
Under the assumptions described above, low valued, high leveraged companies with limited investment opportunities and a high profitability are expected to use dividends as the preferred means to distribute cash. From the earnings payout graph it can be seen that S&P 500 companies with a low earnings yield (=highly valued) on aggregate changed their dividend policy after 1982, when SEC rule 10b-18 was introduced which allowed public companies open-market repurchases of their own stock.

## Monetary policy

An unanticipated 25-basis-point cut in the federal funds rate target is associated with a 1% increase in broad stock indexes in the US. [9] 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.

## Corporate tax

One unexpected result of the CSS theory is possibly that a reduction in corporate tax rate would have a negative effect of share prices and/or valuation ratios. A reduction of the nominal corporate tax rate from 35% to 20% as proposed in the United States (Nov 2017) would lead to a -17% drop in share prices to reestablish equilibrium.

${\displaystyle {\frac {dP_{\text{x,t}}}{dT}}={\frac {E_{\text{x,t}}}{R_{\text{x,t}}[T-1]^{2}}}}$

## Beta

The CSS equilibrium condition can be used to deduct a relationship for the beta of a company x at time t:

${\displaystyle Beta_{\text{x,t}}={\overline {R_{\text{t}}}}\cdot \left[{\frac {P}{E}}\right]_{\text{x,t}}\cdot [1-T]}$

where ${\displaystyle {\overline {R_{\text{t}}}}}$ 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 structure 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.

## Related Research Articles

A dividend is a payment made by a corporation to its shareholders, usually as a distribution of profits. When a corporation earns a profit or surplus, the corporation is able to re-invest the profit in the business and pay a proportion of the profit as a dividend to shareholders. Distribution to shareholders may be in cash or, if the corporation has a dividend reinvestment plan, the amount can be paid by the issue of further shares or share repurchase. When dividends are paid, shareholders typically must pay income taxes, and the corporation does not receive a corporate income tax deduction for the dividend payments.

In accounting, equity is the difference between the value of the assets and the value of the liabilities of something owned. It is governed by the following equation:

The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital. Importantly, it is dictated by the external market and not by management. The WACC represents the minimum return that a company must earn on an existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere.

The Modigliani–Miller theorem is an influential element of economic theory; it forms the basis for modern thinking on capital structure. The basic theorem states that in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed. Since the value of the firm depends neither on its dividend policy nor its decision to raise capital by issuing stock or selling debt, the Modigliani–Miller theorem is often called the capital structure irrelevance principle.

In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will overall rise in value, while overvalued stocks will generally decrease in value.

In economics and accounting, the cost of capital is the cost of a company's funds, or, from an investor's point of view "the required rate of return on a portfolio company's existing securities". It is used to evaluate new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet.

In finance, leverage is any technique involving the use of debt rather than fresh equity in the purchase of an asset, with the expectation that the after-tax profit to equity holders from the transaction will exceed the borrowing cost, frequently by several multiples⁠ ⁠— hence the provenance of the word from the effect of a lever in physics, a simple machine which amplifies the application of a comparatively small input force into a correspondingly greater output force. Normally, the lender will set a limit on how much risk it is prepared to take and will set a limit on how much leverage it will permit, and would require the acquired asset to be provided as collateral security for the loan. For example, for a residential property the finance provider may lend up to, say, 80% of the property's market value, for a commercial property it may be 70%, while on shares it may lend up to, say, 60% or none at all on certain volatile shares.

In corporate finance, the return on equity (ROE) is a measure of the profitability of a business in relation to the equity, also known as net assets or assets minus liabilities. ROE is a measure of how well a company uses investments to generate earnings growth.

In corporate finance, a leveraged recapitalization is a change of the company's capital structure, usually substitution of equity for debt

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 (E/P) to the yield on long-term government bonds. In its strongest form the Fed model states that bond and stock market are in equilibrium, and fairly valued, when the one-year forward-looking earnings yield equals the 10-year Treasury note yield :

The dividend payout ratio is the fraction of net income a firm pays to its stockholders in dividends:

The dividend discount model (DDM) is a method of valuing a company's stock price based on the theory that its stock is worth the sum of all of its future dividend payments, discounted back to their present value. In other words, it is used to value stocks based on the net present value of the future dividends. The equation most widely used is called the Gordon growth model (GGM). It is named after Myron J. Gordon of the University of Toronto, who originally published it along with Eli Shapiro in 1956 and made reference to it in 1959. Their work borrowed heavily from the theoretical and mathematical ideas found in John Burr Williams 1938 book "The Theory of Investment Value."

The T-model is a formula that states the returns earned by holders of a company's stock in terms of accounting variables obtainable from its financial statements. Specifically, it says that:

A financial ratio or accounting ratio is a relative magnitude of two selected numerical values taken from an enterprise's financial statements. Often used in accounting, there are many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by managers within a firm, by current and potential shareholders (owners) of a firm, and by a firm's creditors. Financial analysts use financial ratios to compare the strengths and weaknesses in various companies. If shares in a company are traded in a financial market, the market price of the shares is used in certain financial ratios.

Dividend policy is concerned with financial policies regarding paying cash dividend in the present or paying an increased dividend at a later stage. Whether to issue dividends, and what amount, is determined mainly on the basis of the company's unappropriated profit and influenced by the company's long-term earning power. When cash surplus exists and is not needed by the firm, then management is expected to pay out some or all of those surplus earnings in the form of cash dividends or to repurchase the company's stock through a share buyback program.

Corporate finance is an area of finance that deals with sources of funding, the capital structure of corporations, the actions that managers take to increase the value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to maximize or increase shareholder value. Although it is in principle different from managerial finance which studies the financial management of all firms, rather than corporations alone, the main concepts in the study of corporate finance are applicable to the financial problems of all kinds of firms.

The sum of perpetuities method (SPM) is a way of valuing a business assuming that investors discount the future earnings of a firm regardless of whether earnings are paid as dividends or retained. SPM is an alternative to the Gordon growth model (GGM) and can be applied to business or stock valuation if the business is assumed to have constant earnings and/or dividend growth. The variables are:

## References

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5. Hovakimian, A.; Opler, T.; Titman, S. (2001). "The Debt-Equity Choice". Journal of Financial and Quantitative Analysis. 36 (1): 1–24. doi:10.2307/2676195. JSTOR   2676195.
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7. "Economic Research". FRED Economic Data. Federal Reserve Bank of St. Louis.
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9. Bernanke, B.S.; Kuttner, K.N. (June 2005). "What Explains the Stock Market's Reaction to Federal Reserve Policy?" (PDF). Journal of Finance. LX (3): 1221–1257. doi:10.1111/j.1540-6261.2005.00760.x. Archived from the original (PDF) on 2011-07-21.