The Miller And Modigliani Capital Structure Irrelevance Theorem Finance Essay

The miller And Modigliani Capital Structure Irrelevance Theorem Finance Essay depraved to Modigliani and Miller (1958, MM hereafter), Capital Structure is non irrelevant when we choose a satisfying with a dividend pay appear policy. This article extends the MM upper-case letter bodily body social organization theorem by relaxing the full payout self-reliance and introducing retention policy. The theoretical graphemeing raises that it is practicable to verify the theorem when we enjoin an investor who exchanges his initial holding for an new(prenominal)wise portfolio constitute of usage and investment. The a posteriori analysis of this current approach is ground on a data set of the USA galvanizing Utilities and rock oil companies for the purpose 1990-1998. The results submit that the relationships betwixt supplement and household pry are signifi potbellytly affected by the slosheds payout proportion.1. IntroductionMiller and Modiglianis (1958) irrelevanc y theorem is whiz of the beta and puzzling issues in modern corpo locate finance theory 1, which has ch on the wholeenged the handed-down view2, that an optimum leverage exists. The main source of the puzzle stems from the fact that pecuniary research dont seem to explain the secure financing behaviour as we start to pay off the MM theory with the evidence(Myers 1984, Gordon1994, Rajan and Zingales1995). The MM theorem(proposition I) has shown that under a perfect mart supposal the market place place appreciate of any mansion is independent of its roof structure (Stulz2006). This fundamental proposition evidently indicates that the cleverness of investors to engage in personal or homemade leverage is qualified to ensure that corporate leverage in itself aliveness non modify the derive market esteem of the unwavering 3. In other spoken communication, the theorem provides conditions under which arbitrage by individuals keeps the take to be of the truehearted d epend simply on cash full point generated by the investment policy. Literature about the validness of the MM-proposition is discussed about whether investors coffin nail au soticly accomplish the required conditions of the arbitrage method without changing the overall hold dear of the necktie. In this context, many authors defy shown the inadequacy of the theorem when inconstants that deal with the real world are introduced.Following the seminal paper of MM (1958), about theories commit been put forward in corporate finance to lenify the shortcomings of the irrelevancy theorem with inconsistents that explain the star signs superior of capital structure. match to the previous debate, upbraiding against this theorem can be grouped in devil types of arguments on the one hand, there are papers which deal with the limitations of the arbitrage conditions on the other hand, there are studies which analyze the exercise of market imperfections on the familys choice of capital structure. Despite the importance of these interventions, we none that all of the limitations deal with the explicit assumptions utilise by MM, but no(prenominal) deals with the critiques of the MMs implicit assumptions. More recently, DeAngelo and DeAngelo (2006, DD hereafter) have challenged MMs irrelevance dividend policy. Dealing with this alternative of profits as in full administrated, these authors have showed the irrelevance of the MM dividend irrelevance theorem when MMs assumptions are relaxed to allow retention. As DeAngelo and DeAngelo(2006, rogue 294) wrote When MMs assumptions are modified to allow retention with the NPV of investment policy fixed, a menage can reduce its value by paying out less than the full leave value of FCF, and so Payout policy matters and Investment policy is non the sole determinant of value . According to DD(2006), the MMs irrelevance theorem forces firms to choose only among dividend policies that distribute the full prese nt value of degage cash flow(FCF) to shareholders. Distributions below the totality of mesh are ruled out by the implicit surmisal.Dealing with this alternative of fully-distributed hire, MM(1958) used the homogeneous guessing in the development of the irrelevance of capital structure.. As pointed by the authors .as impart become clear later, as long as management is presumed to be acting in the best engagements of the convey-takingholders, retained earnings can be regarded as equivalent to a fully subscribed, pre-emptive issue of common stock. Hence, for present purposes, the division of the stream mingled with cash dividends and retained earnings in any period is a mere detail. MM, 1958 p266. However, MM(1958) failed to recognize that proposition I implies that firms distribute all their cash flow to shareholders without paying any assistance to their retention policy. This paper constitutes a new extended proof of the MM theorem by not asking the hypothesis of earni ngs as fully distributed. We pass on show that it is possible to verify the theorem when we venture an investor who exchanges his initial holding for a mix of habit and investment. The rest of the paper is organized as follows in the next section, we demonstrate the irrelevance of the MMs capital structure irrelevance when earnings are not fully distributed. We propose the misfortune of extending of the MM theorem. Furthermore, we show that the twain firms are not forced to distribute their full earnings and the irrelevance is hold in the charge of the mix of investment and consumption. discussion section III describes the data set, introduces the methodology, examines the hypothesis of the variables and investigates whether the empirical Modigliani-Miller capital structure irrelevance is influenced by dividend payout proportion. Section IV provides some concluding remarks.2. How do we reconcile MMs capital structure irrelevant theorem with the firms payout choice?2.1 The fai lure of the MM theorem when earnings are not fully distributed.As indicated by Rubinstein (2003), the law of the saving of investment value of MM(1958) was anticipated by many studies (Fisher (1930), Williams5 (1938), Durand (1952) Morton (1954) for examples) but none of these authors have used arbitrage mechanism to prove the invariance of the be of capital under changes in leverage. The MMs theorem demonstrates that under certain hypothesis of market conditions, the value of the firm is independent of its debt- uprightness ratio and is given by capitalizing the pass judgment final payment generated by its assets. This model can be expressed asfor any firm j in class k (1)Where V stands for the market value of the firm, S for the market value of its common shares, D for the market value of its debts, X for its anticipate earnings forwards interest on its assets, for the capitalization rate appropriate to its class.The analysis of the MMs arbitrage stairs shows the implicit hy pothesis of full payout ratio which plays a crucial position in the model. The MMs capital structure irrelevance theorem constrains firms to distribute all of their earnings. In particular, we note that the validity of the proof developed by MM is based on this implicit assumption. MM(1958) consider (see MM(1958) pageboys 269-270 ) the return of the investor Y as a fraction of the cyberspace income lendable (X-rD for levered firm and X for unlevered firm) for the stockholders.(2)Where is the return of the investor before arbitrage transition, L is levered firm and U is Unlevred firm and is fraction of the total outstanding shares own by the investor. Obviously, MM(1958) confuse artificially return of the investor(dividend return) and force out income which should be distributed between dividend and retention. MM(1958 page 266) assert that the division of the stream between cash dividends and retained earnings in any period is a mere detail.When we derive the MM capital structu re theorem for firms that are not distributing all their earnings as dividends, it follows a non-adequacy of the arbitrage operations, a non-proof of the irrelevance model. send back I shows the 2 cases used by MM(1958) when we introduce a level of payout different from 100%. Therefore, when we use the kindred arbitrage as MM(1958), we moldiness then admit that the two firms distribute all the available income to verify the leverage irrelevance proposition. As result be shown later, this assumption can modify the validity of the MM theorem. To justify this thesis, we suppose the akin steps of the MM kickoff proposition but with a splendid loss here we suppose that firms are not constrained to distribute all of their earnings. This means that we introduce in the arbitrage reasoning the payout ratio (PR) as a new variable. slacken I below shows that MM theorem is not sustain. The difference between returns (before and after arbitrage operations) is not the analogous as show ed by MM (1958). panel I. The irrelevance of the MM capital structure irrelevance when payout ratio is different from 100% start opening night VL VU south possibility VU VLFirst put the initial return of the investor YL encourage actArbitrage process Sold his initial deserving of the firm L Borrows an additional amount dL with the same interest rate r Acquired new shares of the firm usold his initial terms of the firm UAcquired new shares of the firm LAcquired new bonds b of the firm LThird interpret the return of the investor YUFinal stand forDifference of earningsY= YU -YLInterpretationsIt is not possible to verify the MM results when we introduce the hypothesis of payout ratio different from 100%, the difference of returns political campaignament depend on the all components of the equation. When we pose PRL=PRU=1, it is easy to obtain the same difference of returns as MM(1958)orNotes Using the MM formulation, we consider two firms L and U, for which the expected retu rn is the same XL = XU = X. companionship U is financed entirely by stock SU and high society L by stock SL and debt D. The market value of each firm is then VU = SU and VL = SL + D, We denote PRL and PRU the payout ratios of the levered and unlevered firms (MM 1958 suppose PRL = PRU = 100% all expected return is distributed).sL =SL, sU =SU denote the value of shares owned respectively by an investor in the levered and unlevered firm with a fraction2.2 The possibility of extensionThe two firms are not obliged to distribute all their income the mix of investment and consumption solution.The object of this section is to show that it is possible to demonstrate MMs proposition I without the hypothesis of earnings are fully distributed. In other words, we present an extension of the MM capital structure theorem for the case in which firms are allowed to have a payout policy. To prove this new proposition, we suppose the same hypothesis used by MM (1958), draw that earnings are not ful ly distributed. Using the MM formulation, we consider two firms U, L for which the expected return is the same XL = XU = X. Company U is financed entirely by stock SU and familiarity L by stock SL and debt D. The market value of each firm is then VU = SU and VL = SL + D.* matter 1 we suppose the value of the levered firm VL , to be greater than that of the Unlevered firm VU ( ).We denote respectively, PRL and PRU the payout ratios of the levered and unlevered firms (MM 1958 page 269) suppose PRL = PRU = 100% all expected return is distributed). First stage (initial return) consider an investor who owns sL dollars value of the stock in the company L representing a fraction of the total outstanding shares SL, where sL= SL. His return YL can be written as(3)The return from this portfolio, denoted by YL, will be a fraction of the income distributed for the stockholders of company L, which equals the multiplication of the payout ratio PRL by the difference between to total return X a nd the interest charge r DL. Where, r is the interest rate which the firm pays on its debt D. Second comprise (Arbitrage process) now suppose that an individual investor who adjusts his own personal leverage in order to increase his profits. He makes the following operations(a ) Sold his worth sL of the company L and he divided it as follows (i) he partly invested an amount IU = PRL.sL (which equals IU=PRLSL) in acquiring shares (ii) he consumes the remainder CL= (1-PRL)SL. where sL= IU + CL .(b) Borrowed an additional amount .(c) Acquired an amount of the shares of the company U. He could so by using the amount IU from the sales of his initial holding and the amount d from borrowing. Third Stage (the new return) the income of the investor ((i) who holds sU dollars worth of the shares of the company U (ii) and who must pay interest of personal debt d would be(4) Last Stage Arbitrage profit Comparing (4) with (3) we obtain(5)Thus, under this approach we can distinguish two situati onsFirst situation If PRU= PRL = 1 then we check the same result as obtained by MM (1958 page 270).(6)Second situation We can also verify the same result of MM(1958 page 270) without the hypothesis of PRU = PRL = 1, we can simply choose PRU = 1, composition the payout ratio of the levered firm PRL is likely to vary between 0% and 100%, we get then(7)From equation (7), we conclude that as long we must verify, so that it pays shareholders of corporation L to sell their investments, by this means decreasing SL and hence VL, and supercede them with a mix of consumption and portfolio investment, which contains shares of the unlevered firm and personal debt, thereby ripening SU and thus VU. This arbitrage process will be finished when sense of balance restores the stated equalities between the set of the two firms.* Case 2 we suppose the value of the unlevered firm VU , to be larger than that of the Levered one VL ( ). First stage The return of the investor who holds sU dollars of shares of company U representing a fractionof the total outstanding stock SU . Where(8)The return from this portfolio denoted by YU will be a fraction of the income distributed to shareholders of the unlevered firm U. Second stage suppose that the investor exchanges his initial holding in U by another portfolio in the levered firm L. The arbitrage process with consumption behaviour will take the following form the investor sold his worth of company U and divided it as follows(i) He invested partially of the shares of the company L(ii) He invested also of bonds of the company L(iii) The remainder will be consumed.From IL and IB , we can write respectively Third stage The return of the investor (i) who holds IL dollars worth of the shares of the company L (ii) and who holds IB dollars worth of bonds of the company L.(9) Last stage Arbitrage profit comparing YL (from 9) with YU (from 8) we obtain(10)In order to get a profi tabulate arbitrage opportunity for the investor, we must consid er a positive difference of returns. Analysing equation (10), we can good formulate two possibility of payout ratioIn the first, if we suppose a full earning model for the two firms (PRL = PRU = 1), therefore we will obtain the same results as showed by MM(1958) (page 270). According to this situation, equation (10) can be written as(11)In the second, the MMs results can also be obtained if we just assume a full earnings for levered firm PRL= 1 while the payout ratio of the unlevered firm PRU is likely to vary between 0% and 100% implying that the firm can use a payout policy, which is not restricted to full earnings. much(prenominal) a representation is written as(12)In this context, it is also principal(prenominal) to show that as we must obtain , hence it pays the shareholders of company U to sell their holdings and substitute them with a mix of consumption and portfolio investment, which contains shares and bonds. If, all investors in firm U will accomplish the three stages b elow, decrease the value of the unlevered firm U and increase the price of the levered firm L. This switching process will be over when equilibrium restores the stated equalities between the determine of the two firms.From these demonstrations (case 1 and case 2) we can conclude that we are not compelled to suppose that the two firms distribute all of their returns. In other words we can make arbitrage process merely by considering that the price firm (levered firm L in the first case and unlevered firm U in the second case) has a payout ratio PR which is not restricted to be 100% of the earnings. The table below summarizes the theoretical findings.Table II the MMs arbitrage and the payout hypothesisConditionsConclusionsMMs arbitrage conditions without dividend payoutMMs(1958) irrelevance theoremMMs arbitrage conditions with a payout ratioFailure of the MMs proofMMs arbitrage conditions with a payout ratio and consumption hypothesisProof of the MMs irrelevance theorem(Extension)3. The Empirical AnalysisThe previous part of this paper provides a new extension of the relationship between firm value and capital structure when the firm has a payout policy. In this section, we attempt some possible empirical tests. The central issue is, whether or not the leverage ratio affects firm value when earnings are not fully distributed?.Modigliani and Miller (1958) have taken two judges of 43 electric automobile utilities during 1947-1948 and 42 embrocate companies during 1953. The data are provided respectively by two studies chaired by Allen (1954) and Smith (1955) and they regardd the weighted modal(a) court of capital (wacc) concord to the financial leverage of the firm. The regression form of the model was(13)Where wacc is the weight cost of capital approximated by X /V , here X is the expected return net of taxes, V is the market value of all securities and the financial leverage of the firm cardd by the ratio D/V, where D is the market value of Bonds and preferred stock. The results of the tests (as shown MM(1958page 282) are favourable to Modigliani and Miller (1958)s hypothesis. The values of the correlations coefficients are small and not statistically evidentiary. Weston (1963) criticizes Modigliani-Miller empirical result. In particular, he assumes that the lack of assemble of capital structure on the overall value of the firm is due to deficiency of the approach to take account of other factors that may be influencing the firms cost of capital. Contrary to MM, the author shows in the empirical tests that leverage is correlated blackballly with firm value in the comportment of the hypothesis of earnings growth.3.1 Data and MethodologyIn order to conduct an empirical analysis similar to MMs, we have collected data on the same spheres from the same country as done by Modigliani and Miller 1958. The data we use are annual standardized financial cultivation of US firms observed in the period 1990-1998. Our sample is formed by two sub samples from the pick outric sector we use 256 companies, and from the oil sector we take 223 companies. These data were obtained from the Worldscope Database (SIC Code 13 and 49). Contrary to Weston(1963), we consider the hypothesis of risk-class can be verified in the oil industry and the electric sector (as supposed by MM 1958).According to MM(1958), a analogue model was constructed to explain the relationship between leverage and the firm value. The variables used in our regressions are constructed (see table III) as the same way as presented by these authors. The corresponding models used by MM(1958) are For ride 1 see MM(1958) page284 (note 38), for model 2,see MM(1958) page282 For mock up 3,see MM(1958) page284 (note 39) For. With regard to the basic capital structure irrelevance theorem to be estimated we propose three regression models as followsModel 1 (14)Model 2 (15)Model 3 (16)Where wacc is the weighted mean(a) cost of capital Leverage 1 first measure of le verage ML1 modified leverage 1 Value the ratio of the firm value , ER earnings ratio DR debt ratio.The purpose of model 1 is to test the piece of leverage (as measured by Debt ratio DR) on firm value, while the Model 2 and model 3 test the effect of leverage (measured by Leverage1) on the cost of capital (measured by WACC). The variable ML1(modified leverage 1) is included in model3 to test the U-shaped hypothesis that the coefficient e of this variable should be significant and positive to confirm the tralatitious view, and not importantly different from zero to confirm the irrelevance theorem.. Note also that tally to our approach the correlation between these variables should be different from zero.To test the validity of the MMs proposition when earnings are not fully distributed, we alternatively estimate all the above regressions in the absence (model MM58 and the model MM58supp) and the presence of the payout ratio. We corroborate this last alternative in two steps In the first step, we test the models for all firms (model MMExt). In the second step, we test the models for subsamples First Quartile sample ( steadys Payout ratio is less than 25%), Second Quartile sample (firms payout ratio is between 25% and 50%), Third Quartile sample (firms payout ratio is between 50% and 75%), and Fourth Quartile sample (firms payout ratio is more than 75%). The tableIII below reports the different measures of variables and their predicted effects.Table III. Measures of variables and predicted signsVariablesSymbolMeasureMM possiblenessOur HypothesisDependants variablesWeighted average cost of capitalWACCX/VFirm value ratioValueV/AThe explanatory variablesFirst measure of leverageLeverage 1D/V naught effect operative effectModified Leverage 1 measureML1D.D/V.SZero effectSignificant effect dinero ratioERX/ADebt ratioDRD/AZero effectSignificant effectPayout ratioPayoutDiv/NINot testedSignificant effectNotes the table reports the different measures of variables where V firm value= market value of equity S +market value of debt D, X Earnings before interest and Taxes (EBIT), A is the value of the total assets, NI net income. ML1 modified leverage 1 measure = (D/V)/(1-D/V). We measure the value of the Debt D by the amount of total liabilities.3.2 Descriptive statisticsAs indicated in Table IV, the descriptive statistics shows that the average value of cost of capital is 5.92% for electric utilities and 4.48% for oil companies6. On average, we have a leverage ratio of 51.79%(37.85%), this measure is 62% (50.2%) when we use total assets as deflator . The average firm has a value ratio of 1,38 for electric utilities which is much weaker than those of oil companies (1,99). For these firms, earnings ratio ranges from 0% to 2.7% for electric utilities (0% to 66% for oil companies). In terms of net income, the average value of payout is more important for electric utilities (45%) ranging from 0% to 99,9%, than those of oil companies (16%). These results show that the division of the stream between cash dividend and retained earnings in any period is not a mere detail as supposed by Modigliani and Miller (1958 page 266). None of firms in the two samples and during the whole period (1990-1998) has distributed the totality of its income. For the normal distribution of the series rough the mean (see table IV), all of the distributions of the variables are not symmetric since their lopsidedness values are different from zero. This conclusion is also verified by the values of the Kurtosis which are quite different from 3.Table IV. Descriptive Statistics of Variables (256 pickric Utilities and 223 Oil Companies)VariablesSampleMeanMinimumMaximumStd. DevSkewnessKurtosisObsWACC pick out0.059240.000000.290900.031880.2923286.3760992304Oil0.044810.000000.695820.054484.7599342.05262007Leverage1Elect0.517960.015730.994160.17873-0.469253.363652304Oil0.378570.00000.982370.217140.209522.364312007ValueElect1.381550.090879.771120.822685.5198945.787 12304Oil1.991720.14447138.565.4030818.7716397.6152006ERElect0.073530.00000.0276120.041580.777907.942742304Oil0.064180.00000.6643030.066832.10426211.5462007DRElect0.623220.027610.9950660.14891-0.99914.789832304Oil0.502200.00000.99780.22065-0.25932.48472006ML1Elect1.349130.000252169.3466.648017.3645344.9502304Oil0.612980.000023.24541.53468.6309103.962006PayoutElect0.451690.000000.999800.35978-0.155691.404172304Oil0.163810.00000.99910.277211.509673.9064620063.3 The effect of Leverage on the firm value (model 1)The MM(1958)s theorem is confronted with our hypothesis in order to know the crucial effect of payout ratio on the sensitivity of firm value to leverage. If our prediction is true, we should find a significant coefficient of leverage ratio, otherwise the MMs view should be confirmed. As indicated in table V, estimates result shows that coefficients of earning ratio (ER) and debt ratio (DR) are significantly different from zero, which fails to support the MMs view. Since our resul ts, as presented below, demonstrate that the coefficient of debt ratio is significantly negative and contrary to the traditional view. We prefer to give more explanations of this relationship based on the presence of the payout policy. The latter has a negative influence on the two samples (see Model MMExt , table V) which is in the opposite direction as obtained by the cost of capital regressions (see tableVI). There are two main explanations for this resultAccording to Brigham and Gordon(1968), the relationship between stock price and leverage depends on the association between R (return on assets and investment) and i ( the rate of interest which the firm pays on its debt), not on the level of Leverage L. This can be written as(16)Where E is the book value of the common equity per share, k is the rate at which dividend is discounted. It is evident, when R is less than i, the leverage effect on stock price P will be negative. Furthermore, the negative influence of the dividend rat io on the firm value confirms the leverage meet when the return on investment is less than the cost of debt. This means that firms experiencing discredit rate of investment tend to use funds from internal and outer resources to display higher payout ratio.The leverage measure is not the same in Wacc regression, this variable is measured by debt on firm value (D/V), while in firm value regression (Value), the debt ratio is measured by debt on total Assets (D/A). The fact that both variables are divided by different deflators may be affected by a haphazard disturbances of the market value of the firm. This bias correlation is not observed in the firm value regression.According to Modigliani and Miller (1958), the constant term in the previous regression should give more information on the value of the unlevered firm. As shown in table IV below, the estimated coefficient of this variable is not only significantly different from zero, but is quite positive and greatly sexual relatio n to the coefficient of the debt ratio. This conclusion is confirmed for the two samples with large values for the oil companies.Table IV. Directs Pooled Least-Squares Estimates of the effects of leverage on the firm valueCoefficients ofRegressionsSample unremittingERDRPayoutAdRObsMM 58Elect1.893a-0.158a-0.805a0.0252304Oil2.464a-6.730a-0.6680.0482007MM ExtElect1.963a-0.131a-0.466a-0.625a0.0952304Oil2.465a-6.703a-0.642-0.0860.0482007First QuartileElect1.969a-0.133b-0.412c0.005801Oil2.342a-7.490a-0.2860.0521440Second QuartileElect1.465a2.650a-0.554a0.187216Oil1.659a-0.197-0.501a0.033279Third QuartileElect1.206a1.823a-0.249a0.096738Oil1.224a3.229a-0.0550.113207Fourth QuartileElect1.080a1.809a-0.1050.102549Oil7.197a0.983-9.064a0.67672Notes a, b and c indicate significance at the 1%, 5%, and 10% levels respectively.3.4 The effect of leverage on the cost of capital (model 2 and Model 3)According to Modigliani and Millers proposition I the average cost of capital Wacc (Xt/V) should tend to have the same value independently of the degree of leverage MM (1958, page281). In other words, the leverages coefficient parameter in the Wacc regression should be insignificant and statistically equal to zero. The results of the MM model tests are shown in table V (models MM58 and MM58supp). According to this table, the MM hypothesis is only verified in the oil sample, while leverage in the electric utilities has a negative and significant effect (coefficient is equal -0, 1162) on the cost