Attached below are my questions and a pdf file that needs to be read in order to answer the questions. This is a qualitative written response within finance, please provide as much detail as possible in clear concise English so that I may understand the thought process and logic. Thank you. 400-450 words total.

Understanding the Fed Model, Capital Structure, and then Some JAN H. TIMMER1 ABSTRACT Twenty years after the papers by Modigliani and Miller, the introduction in 1982 of SEC rule 10b-18 fundamentally changed the rules of corporate finance, by allowing public companies open-market repurchases of their own stock and making it easier to manipulate capital structure. We present a new 'capital structure substitution' theory that is based on one simple hypothesis: company managements manipulate capital structure such that earnings-per-share are maximized. The substitution theory is used to reassess the 'Fed model', which describes the equilibrium observed between the average S&P 500 earnings yield (E/P) and the US government bond yield. We conclude that the Fed model is miss-specified: 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 proposed theory also sheds new light on a variety of other phenomena observed in corporate finance. It is used to formulate a new theory on dividend policy, explaining why some companies prefer dividends over share repurchases and why dividend policy has changed in the early 1980s. It also provides a new explanation for the stock market's reaction to monetary and fiscal policy. And it is used to explain why the positive relationship between leverage and beta, as predicted by Hamada, is not observed in market data. OUR OBJECTIVE IN THIS PAPER is to develop and test a new theoretical framework that is based on one simple hypothesis: company managements manipulate capital structure such that earningsper-share are maximized. Our interest in such new hypothesis is triggered by the positive relationship observed in the US between the average earnings yield of the S&P 500 index and government bond yields. This relationship has become popular as the 'Fed model' and states in its strongest form an equality between the one year forward looking earnings yield (E/P ratio) and the 10-year government bond yield 1 Y10 : Working paper, first internal draft March 2008, current draft August 2012 Electronic copy available at: http://ssrn.com/abstract=1322703 E y +1 Py (1) = Y10 This relationship is graphically displayed in Figure 1. The term 'Fed model' or 'Fed's stock valuation model' is first used by Yardeni (1997, 1999) who deducts the relationship from the Humphrey-Hawkins report of 22.07.1997 which states that \"...changes in this ratio [P/E of the S&P 500 index] have often been inversely related to changes in the long-term Treasury yields\". Although the Fed model was never officially endorsed by the Fed, former Fed chairman Allan Greenspan (2007) makes reference to it in his memoirs: \"The decline of real (inflation adjusted) long-term interest rates that has occurred in the last two decades has been associated with rising price-to-earnings ratios for stocks [...].\" 20% E(1)/P(0) Y10 15% 10% 5% 0% 1968 1978 1988 1998 2008 Figure 1. Basic Fed model relationship: equally weighted forward looking earnings yield of S&P 500 companies in yearly intervals and 10-year government bond yield (WRDS database) Salomons (2006) identifies three reasons why the Fed model has a \"broad consensus in the nonacademic community\". First, stocks and bonds are competing asset classes for investors. When stocks 'yield' more than bonds, stocks are perceived to be the better choice for investors and vice versa. Only when equation (1) holds, both stocks and bonds are perceived to be equally attractive by investors and prices are at equilibrium. Second, the government bond yield can be seen as a proxy for the risk free rate. In the event that the risk free rate rises, the present value of equity falls and vice versa. Third, and maybe most important, US data over the last 40 years indicate a relationship exists. Salomons finds that the correlation between the two variables since is 75% over the preceding four decades but only 19% over the period from 1881-2002. The theoretical support for the Fed model is very limited. Estrada (2006, 2007) finds that the dividend discount model only supports the Fed model if one assumes all earnings are paid out as dividends, there is no growth of dividends and investors require no equity risk premium. Both Asness (2003) and Salomons (2006) argue that the Fed model erroneously compares the real J.H.Timmer, August 2012 -2- Electronic copy available at: http://ssrn.com/abstract=1322703 stock earnings yield with the nominal bond yield. Ritter und Warr (2002) argue that investors fail to recognize the effects of inflation and make a 'capitalization rate error'2 and a 'debt capital gain error'3. They explain the long 1982-1999 bull market with these misvaluations. Salomons (2006) concludes: \"The relation between earnings yield and bond yield is not stable [over time, before 1955] and has no theoretical basis, but exists because investors suffer from money illusion\" and \"investors do set earnings yields based on bond yield, but they do so in error\". Coming from a slightly different angle Bernanke and Kuttner (2005) find that \"relatively few papers to date have attempted to provide an explanation for the [stock] market's reaction to monetary policy\" and conclude that \"the impact of monetary policy surprises on stock prices seems to come either through its effects on expected future excess returns or on expected future dividends\". Instead of government bond yield Boucher (2005) focuses on inflation and finds that \"[t]hese results testify to the strong relationship between the earning-price ratio and the inflation level, and then suggest that the decline in inflation since the early 1980s can explain (i) a large part of the run up in equity ratios observed since 1982...\" The author suggests that a subjective inflation risk premium could be the cause of the relationship but concludes that \"...the reasons for which inflation makes investors more risk averse remains to be explained.\" The empirical support for the Fed Model is mixed at best. Both Salomons (2006) and Estrada (2006) show that in the US a high correlation of ~75% exists between earnings yield and bond yield over the 1968-2005 period. But over the 1881-2002 period Salomons reports a correlation of only 19% and Estrada, using 1871-2005 data, only finds 10% correlation. More recently, Thomas (2007) claims that the Fed model does not have descriptive validity after 2001. And during the 2007-2011 financial crises government bond rates reached new lows, while earnings yields spiked upwards. The correlation we calculated over this period is -31%. The equilibrium described by the Fed model relationship thus only seems to be present for a limited sub-period. When evaluating a possible equilibrium between two non-stationary time series, cointegration - and not correlation - is the preferred means for hypothesis testing. Several authors have tested for cointegration between earnings yield and bond yield in the limited time window that produced high correlations. Harasty and Roulet (2000) find cointegration in all 17 countries investigated over the period from 1988 to 1998. Koivu, Pennanen and Ziemba (2005) find cointegration in the US, UK and Germany in the 1980-2003 period. The results published by Estrada in two papers (2006, 2007) contradict with the results of the papers listed above. Estrada finds cointegration for only two out of twenty countries considered, Ireland and New Zealand, over a period from 1987 to 2005 and concludes that \"[t]he evidence [...] lends no support to this simplistic [Fed] model.\" Finally, Thomas and Zhang (2007) find no equilibrium of earnings yields and government bond yields at firm-level and conclude that \"the equivalence appears magically when [...] aggregated across all firms in the market.\" 2 Inflation has the effect of increasing both the nominal discount rate and the nominal growth rate of earnings. According to Ritter and War the 'capitalization rate error' is when investors use the nominal discount rate but fail to use a higher nominal growth rate which leads to under-valuations in times of high inflation. 3 Many analysts focus on equity net income or earnings per share (EPS) to derive valuation. Highly leveraged companies will face high nominal interest rates during inflation which depresses EPS. The 'debt capital gain error' occurs when investors or analysts do not realize this effect is offset by a decrease in real value of nominal liabilities. This would also lead to under-valuations when inflation is high. J.H.Timmer, August 2012 -3- The current state of affairs is not satisfying to us. As documented in Figure 1 the forward looking earnings yield and the 10-year government bond yield did move in tandem for a considerable period of time. And theoretical support for this observation is either absent, or based on 'investors' errors'. This paper offers a new explanation for the relationship between interest rate and stock market valuation levels. This explanation is based on behavior of company managements and not on investors' errors. In Section I an equilibrium model is developed, based on the hypothesis described above and four additional postulates, that leads to a company specific leverage target expressed in terms of marginal interest rate paid on corporate debt. From the hypothesis and postulates we deduct an equality between a company's earnings yields and the after-tax interest rate on its corporate bonds. In Section II the new model is empirically tested, and we come to the conclusion that the Fed model is miss-specified. On an aggregate level the S&P 500 earnings yield is in equilibrium with average after-tax interest rate on corporate bonds and not with the government bond yield. The Fed model equilibrium appeared to be present for a period of time only because the average after-tax interest rate on corporate bonds was roughly equal to the US government bond yield. With the emergence of the 2007-2012 financial turmoil the spread between the two yields significantly increased and the (missspecified) equilibrium disappeared. In Section II we also provide a simple explanation as to why the Fed equilibrium is not observed in all international markets and only emerged in the US in the early 1980s. The new 'capital structure substitution' model does not have 'invisible' or 'hidden' parameters - such as the equity risk premium, discount rate, expected growth rate or expected inflation - and as a consequence the theory can be tested in multiple unambiguous ways. In Section III we use the model to explain trends in corporate dividend policies. We deduct that the debt-equity ratio of a company is the most important factor when making decisions about dividend payments, and provide a simple explanation why some companies prefer dividends over repurchasing shares. In Section IV we zoom in on the relationship between company leverage and relative price volatility or beta and deduct a negative relationship between these two parameters. Finally in section V we deduct relationships to evaluate the stock market's reaction to monetary and fiscal policy. I. A Capital Structure Substitution Model A. Model Introduction A simple public company is considered, holding a fixed amount of assets generating revenue and financed with equity and a limited amount of corporate bonds. It is assumed that all earnings are retained and that no new capital investments are planned. Cash piling up on the balance sheet as a consequence of retaining all earnings is ignored for now and addressed in Section III. The model describes the behavior of a hypothetical assistant of the Chief Financial Officer (CFO) of the company, assigned with the task to optimize corporate structure. The assistant receives quarterly updates on the realized earnings before interest and taxes (EBIT) but cannot influence these earnings. It is assumed that the assistant can change the capital structure of the company by substituting stocks for corporate bonds or vice versa without paying transactions costs. More specific, the assistant can float new corporate bonds and use the proceeds to buy back stock or J.H.Timmer, August 2012 -4- issue new stock to retire corporate bonds. But the assistant in this model does not know exactly how to 'optimize' capital structure. He or she is familiar with the work of Miller and Modigliani and understands the 'capital structure irrelevance principle' when taxes and bankruptcy costs are absent. But it is unclear to the assistant how to include taxes and bankruptcy costs in the evaluation of optimal capital structure. It is also unclear to the assistant whether investors are able to make this evaluation. Part of the compensation received by the assistant comes in the form of stock options, and he or she does have an incentive to manipulate capital structure such that the stock price is maximized. The assistant realizes that prices are determined by supply and demand and repurchasing shares will, ceteris paribus, at least temporarily lead to higher stock prices. The assistant decides to float bonds and to use the proceeds to repurchase shares. For the sake of the argument it is assumed that the stock price of the company rises as a consequence of the buybacks. Within a short time the assistant becomes very popular among his/her colleagues and shareholders, and the decision is made to expand the repurchase program. However, in order to sustain the program additional bonds must be floated and leverage increases. The steadily increasing leverage induces rating agencies to downgrade the credit rating of the company's corporate bonds. This reduces the popularity of the assistant significantly. It is assumed the corporate bonds have a fixed coupon rate and the downgrade does not affect the company's payments to existing bond holders. But the marginal financing cost of the company does increase as buyers of new bond issues will demand higher coupon rates, and this in turn influences the earnings after interest and taxes. At a certain point the marginal financing cost rises to a level where continuing the repurchase program has the effect of driving down the earnings-per-share after interest and taxes (EPS). The development of EPS over time of a company is intensely monitored by financial analysts and shareholders. The popularity of the assistant is now in freefall and under pressure of shareholders the repurchase program is stopped. But as soon as the share price or the marginal interest rate paid on corporate bonds drops enough, the repurchase program can be restarted without driving EPS down. By doing so, the hypothetical assistant in this model effectively manipulates capital structure to maximize EPS. More accurately, he or she attempts to manipulate capital structure to such extent as it might not be possible to reach the goal. B. Model Definition The model formalizes the actions of CFO's assistant described above. The assistant or management behavior is described by a single hypothesis and the model is supported by four postulates: Hypothesis: Postulate 1: 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 without paying transaction costs. These substitutions are not limited by debt covenants, thin-capitalization rules, earnings-stripping rules or alike. J.H.Timmer, August 2012 -5- Postulate 2: Shares can only be repurchased through open market buybacks. Information about share price Postulate 3: Px ,t of company x at time t, is available on a daily basis. The fixed interest rate payable on corporate bonds issued by company x at time t, is equal to R x ,t and set by the market. The interest rate free component R x ,t is equal to the risk Rf t plus a company specific spread S x ,t and cannot be below the interest rate of Aaa rated bonds. Postulate 4: All companies pay a uniform corporate tax rate Tt . We also assume that managements make no assumptions about future growth rates and are not facing classical 'investment decisions' but run companies in 'steady state'4. For a marginal analysis the phrase 'small denominations' of postulate 1 needs to be further specified. Company managements 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 , without paying transaction costs. It can also do the reverse and issue one share for the current market price P and use the proceeds to retire debt with value P . In mathematical terms these substitutions are defined as D n where = Px , t (2) x,t D is the total company debt, n the number of shares and P x , t the market share price of x at time t . The negative sign indicates that, in accordance with postulate 1, a reduction of the number of shares n leads to a larger debt D and vice versa. The cost of issuing one additional bond with face value P is the payment of a nominal annual interest rate R 5. It is straightforward to see that the current earnings-per-share change when one share with price P is repurchased and one bond with face value P is issued. company First, the earnings that were 'allocated' to the one share that was repurchased are redistributed over the remaining shares, causing an increase in earnings-per-share. The EPS of the remaining shares increase by the EPS of the share bought back divided by the number of shares still outstanding: EPS /(n 1) . Second, earnings are reduced by the interest payments on the additional bond6. 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 P R [1 T ] /( n 1) . The marginal change in earnings-per-share as function of the total number of outstanding shares n then becomes: E n = x,t E x,t n + P x , t R x , t [1 Tt ] 4 n (3) This does not exclude (organic) growth or downturns. Note that the nominal - not a real - interest rate is used in the analysis. The nominal rate gives the cost of extra debt at present; see also Ritter and War (2002). 6 For simplicity it is assumed that interest is paid upfront. This avoids the use of earnings estimates and does not significantly affect the outcome of the model. 5 J.H.Timmer, August 2012 -6- where E x , t is the earnings-per-share7 of company x at time t . The negative sign of the first factor indicates that an increase in the number of shares leads to a dilution of the earnings. The positive sign of the second factor indicates that an increase in the number of shares leads to a reduction of interest payments. The denominator is now equal to n as the average is taken of repurchasing ( n 1 ) and issuing ( n + 1) shares. To the CFO's assistant, the earnings (EBIT), the share price, the taxation level and to a large extent the payable interest rate on corporate bonds, are uncontrollable variables. The only thing the assistant can influence directly is the number of shares n 8. The equilibrium condition that holds when EPS is maximized is found by setting equation (3) equal to zero: E x ,t Px , t = R x , t [1 Tt ] (4) [1 T ] , the assistant can increase earnings-per-share E by buying back shares and substituting these for bonds. And if E / P is smaller than R [1 T ] , the As long as E / P is larger than R earnings-per-share E can be increased by issuing shares and retiring debt. Equation (4) has similarities to the original Fed model equilibrium as described by (1), with an equality between earnings yield and bond yield. C. Model Boundary Conditions Figure 2 shows the boundary and equilibrium conditions associated with (3) and (4). It is assumed that no company can issue corporate bonds with an interest rate lower than the average interest rate of Aaa rated bonds. Consequently no companies are found to the left hand side of the line A-A''. Companies above the line B-B'' are companies with low valuation ratios (P/E) and high earnings yields (E/P) compared to the after-tax interest rate they pay on their debt. These companies can increase EPS by increasing leverage and buying back shares. The model does not state what path companies follow or where exactly on the line B-B\" the company will end up. By increasing leverage companies might see their credit rating deteriorate and their marginal interest rate increase. During this process companies would move to the right in the plane of Figure 2. The model does assume that all companies above B-B\" keep buying back shares until some equilibrium point on B-B\" is reached. In theory a situation could emerge in which management is determined to maximize earnings-per-share whereas the fair value argument drives prices down. The company could keep buying back shares, adding leverage, keep increasing EPS and have a price-earnings-ratio and a share price moving to zero. In this model it is assumed that these companies finally go bankrupt, de-list and disappear from the sample. 7 EPS is equity net income or earnings per share after interest and tax; this is different from operating income or EBITA. 8 The purpose of describing the assistant's and not the CFO's behavior is to illustrate the fact that only number of shares n can be controlled. J.H.Timmer, August 2012 -7- Companies below B-B\" have high valuation ratios compared to the after-tax interest rate of their debt. These companies can increase EPS by reducing leverage and converting debt to equity. One straightforward method to do so could be the use of convertible bonds. By reducing leverage companies might see their credit rating improve and the marginal interest on debt decrease. These companies move towards the line A-B-B\" in the plane of Figure 2 and can either end on B-B\" where equilibrium condition (4) holds or on A-B without holding any debt. Companies with very high valuation ratios are not expected to hold any debt at all. The market values their growth opportunities and their E/P ratio lies below the after-tax Aaa equivalent rate. Every use of debt would lower EPS for these companies. These companies are located somewhere on the A-B line. In a world where all company managements assiduously maximize EPS at every moment in time, all companies lie on A-B-B\" or very close around it. Equilibrium condition (4) is fulfilled by all companies on B-B\". From the vertical axis of Figure 2, it can be deducted that all companies on B-B\" must fulfil condition: E R Aaa [1 T ] P where (5) R Aaa is the average interest rate payable on Aaa rated bonds. Only companies with an earnings yield higher than the level of after-tax interest rate on Aaa rated bonds are expected to have a company specific leverage target (4), expressed in terms of marginal interest rate paid on corporate debt. We will refer to (5) as the 'dynamic' testing condition as it implicitly assumes that C Figure 2. Boundary and equilibrium conditions of the capital structure substitution model. The line A-A'' represents Aaa equivalent interest rate after-tax below which companies cannot issue debt. The dashed line parallel to A-A'' indicates average after-tax interest rate for Baa rated corporate bonds (example for 2006). In equilibrium all companies are found on the line A-B-B''. All companies fulfilling (4) are found on B-B''. All companies with E/P 0 D + Eq where (6) E q is the total company equity and D is total debt. We will refer to (6) as the 'static' condition, as it is expected to be less sensitive to short term fluctuations in the earnings yield. The hypothesis and postulates of the model are compatible with real market phenomena such as bankruptcy costs. Assume that the market has (under)valued a company with a high E/P ratio and the company has been buying back stocks and building up significant leverage. Bankruptcy costs would reach our hypothetical CFO assistant through two channels. First, customers could jump off as they lose confidence in the solvability of the company. These bankruptcy costs would reach the assistant in the form of lower EBIT numbers. Second, rating agencies might downgrade the bonds of the company. The assistant would find that emitting new bonds is more costly as the interest rate spread has increased. D. SEC Rule 10b-18 At this point we need to revisit Postulate 1, which states that managements can freely substitute bonds for stocks or vice versa. But in some countries open-market repurchases are prohibited and considered price manipulation. In the US share repurchases have never been explicitly prohibited but there is ample evidence that corporations were reluctant to repurchase shares before the year 1982 because of the potential risk of violating the anti-manipulative provisions of the Security Exchange Act (SEA) of 1934. Then in 1982 rule 10b-18 was adopted to provide a safe harbor for repurchasing firms against the anti-manipulative provisions of the SEA, provided only one broker is used on a single day, trading on an uptick is avoided, and the purchases are limited to a daily volume to a previously specified amount. Grullon and Michaely (2002) present strong empirical evidence that rule 10b-18 facilitated share repurchasing enormously and conclude: \"Overall, the evidence [...] suggests that the adoption of Rule 10b-18 had a positive and significant impact on share repurchase activity. It seems that corporations were deterred from repurchasing share before the adoption of Rule 10b-18. The work of Grullon and Michaely strongly indicates that legal obstacles made postulate 1 unrealistic before 1982, and we expect that equilibrium condition (4) will not be reached before this time. E. Upside-Down Asset Pricing Equation (4) is easily rearranged to be an asset pricing formula: Px , t = E x ,t R x , t [1 Tt ] (4a) For companies fulfilling inequality (5) this formula can be used to calculate share prices. Interestingly enough for these companies share prices are not set by shareholders but by bondholders. As a result of active repurchasing or issuing of shares by company managements, J.H.Timmer, August 2012 -9- equilibrium pricing is no longer a result of balancing shareholder demand and supply. Suppose investor demand for a certain stock fulfilling (5) drops sharply. A small deviation from equilibrium condition (4) will trigger additional share buybacks. As long as bondholders do not require a higher coupon rate R x , t the share price will not significantly change. Reduced shareholder demand will in this case only lead to increased leverage. In a way (4a) turns asset pricing upside-down, with bondholders setting share prices and shareholders determining company leverage. This implies that bondholders can have a significant effect on the equity risk premium of stock. II. Basic Model Tests At this point we acknowledge that the most important contribution of this paper is new model development. But to illustrate the model potential, this and next sections include straightforward empirical model tests. The capital structure substitution model deviates from the Fed model in two important aspects. First, the model does not assume that all companies fulfill the equilibrium condition but only those satisfying inequalities (5) or (6). Second, for those companies satisfying (5) or (6) it should be tested whether earnings yield is in equilibrium with the after-tax interest rate paid on corporate bonds, and not with the 10-year Treasury note yield. The 'dynamic' inequality (5) and the 'static' inequality (6) are tested separately. A. Corporate Tax Rate A precondition for testing (4) is knowing the historical time series of the corporate tax rate Tt . Yin (2003) published estimates for the 1995-2000 time period with values between 30.6% and 26.8%. But for this analysis an estimate over the 1968-2010 time period is needed. In absence of a published set of values we follow an approach similar to Martin A. Sullivan's9. An effective corporate tax rate is defined as \"the ratio of some measure of corporate taxes over some measure of corporate profits\". As a measure of corporate taxes the 'Corporation Income Taxes' as published by the U.S. Government Printing Office10 are used. As a measure of corporate profits the "profits before tax" are used from Table 1.14 of the National Income and Product Accounts produced by the Commerce Department's Bureau of Economic Analysis (BEA)11. By dividing corporate taxes by corporate profits a simple measure of effective tax rate is derived as shown in Figure 3. As quite some fluctuations in effective tax rate are observed, it we use the 4-year moving average for all tests, reflecting the inability of companies to predict next year's effective tax rate. These values deviate up to 3 percentage points of the values reported by Yin for the 1995-2000 time period. Admittedly the calculation method used is simplistic, but at the same time is more precise than assuming a flat 30% or 35% corporate tax over the whole period. It must also be noted that postulate 4 can be further refined going forward, as large variations exist 9 See \"Economic Analysis: Despite Rapid Growth, Corporate Tax Receipts Fall Short\" by Martin A. Sullivan on http://www.taxanalysts.com. 10 See table 2.1 of \"Historical Tables, Budget of the United States Government\1. Read \"Understanding the Fed Model, Capital Structure, and Then Some\" It is attached as a PDF file. This is an off-beat paper that contains some interesting, novel ideas and ways of thinking about traditional corporate finance topics. The paper brings together ideas around capital structure, valuation, dividend policy, share repurchases, beta, and leverage for the market as a whole by thinking about what individual managers and investors do. As with any paper, it's a discussion, not gospel. a. Summarize the paper in about 100 words. b. Pick a sub-topic to explore in more detail (300 words). Perhaps replicate an experiment with data or look at one of the referenced papers. Maybe a critique of Timmer or a comparison to textbook theory. Or link this thinking to an analysis of an individual company strategy