Agency Costs and the Size Discount: Evidence from Acquisitions

Many scholars have found a negative relationship between a firm’s size and its value, as measured by Tobin’s q. This result is called the size discount. There are hypotheses about why the size discount exists, but none have been rigorously empirically tested. This paper argues that the size discount is created by the inability of shareholders to minimize agency costs in larger companies. Statistical tests suggest that the size discount only appears in large firms with managers that impose excessive agency costs upon their shareholders. Empiricists who use Tobin’s q to proxy for growth opportunities may need a different proxy.


INTRODUCTION
Many researchers have empirically documented a negative relationship between the size of a fi rm and its relative value, as measured by Tobin's q. 1 In fact, a negative correlation between size and value appears over and over in the fi nance and accounting literature. This relationship has come to be called a size discount, because larger fi rms are relatively less valuable than smaller fi rms. It is one of the most common yet unexplained phenomena in fi nancial data. The presumption has been that size proxies for variation in growth opportunities or systematic differences between large and small fi rms. 2 However, no empirical evidence testing such presumptions exists.
The purpose of this paper is to determine what drives the empirically-observed size discount. Both a review of prior studies and the following empirical analysis suggest that the cause of the size discount is the inability of shareholders to minimize agency costs in larger companies. The evidence throughout shows that larger fi rms are relatively less valuable than smaller fi rms, which is due to the weakening of internal and external corporate governance mechanisms as fi rms grow larger.
In order for agency costs to explain the size discount, two conditions must hold. First, shareholders of smaller fi rms must be able to reduce agency costs more effectively than shareholders of larger fi rms. Second, there must be a signifi cant size discount for the subset of fi rms with high agency costs, but no size discount for the subset of fi rms with low agency costs. 3 In other words, a size discount should only be imposed upon a large fi rm's shareholders when an intolerable level of agency costs is present. Ultimately, if shareholders cannot discipline a manager who is imposing unnecessary agency costs, the fi rm must be less valuable.
The existing empirical evidence suggests that shareholders of smaller fi rms are able to reduce agency costs more effectively than shareholders of larger fi rms. Past studies have shown that larger fi rms are less likely to have a blockholder, to pass a meaningful proxy proposal, to have an effective board of directors, and to be acquired than smaller fi rms. All together, the evidence in the corporate fi nance literature provides ample support for the hypothesis that agency costs are harder to control in larger fi rms.
The analysis in this paper seeks to determine if there is a signifi cant size discount for the subset of fi rms with high agency costs, but no size discount for the subset of fi rms with low agency costs. Logically, if the manager's interests are well aligned with those of the shareholders, then the effectiveness of the disciplinary mechanisms is irrelevant to the value of the fi rm. On the other hand, when the manager has an incentive to destroy shareholder wealth, the effectiveness of the disciplinary mechanisms plays a large role in determining the value of the fi rm.
The empirical analysis in this paper primarily focuses on bad bidders, in the context of Mitchell and Lehn (1990). By defi nition, bad bidders are fi rms that undertake acquisitions that result in a decrease in shareholder wealth. For each company in the sample, the change in shareholder wealth is measured by the abnormal change in stock price around the announcement of a takeover. Therefore, the sample used in this paper is composed only of fi rms that made an acquisition attempt.
Bad bids offer a nice starting point because they provide a simple measure of the agency costs borne by the shareholders. Acquisitions are unique events in that they provide a clear example of how one decision made by the CEO affects shareholder wealth. When a manager makes an acquisition that results in an increase in the fi rm's stock price, the executive is properly fulfi lling her/his duties of maximizing shareholder wealth. On the other hand, when a manager undertakes an acquisition that results in a decrease in stock price, agency costs are imposed upon the fi rm's owners. A negative announcement-period return is a direct agency cost, because it results in an immediate loss of wealth to shareholders and because self-interested shareholders would not undertake an acquisition that resulted in a decrease in their own wealth. Therefore, the announcement-period abnormal returns that are calculated for each fi rm directly measure the agency costs that managers of bad bidder fi rms are imposing upon their shareholders.
Bid quality is measured within a sample of acquirers that made a takeover bid in the period from 1980-2000. This sample contains 9,434 fi rm-years, each representing a separate year in which a fi rm attempted an acquisition. Firms are split into a high agency costs subsample and a low agency costs subsample, as determined by the abnormal returns around the announcement of an acquisition. The results of regression analysis show that size and q are signifi cantly negatively correlated for bad bidders, but not for good bidders. In other words, a size discount exists for the fi rms in the high agency costs subsample, but not for those in the low agency costs subsample.
A similar test is performed to determine if the size discount is as signifi cant for single segment fi rms as it is for diversifi ed fi rms. The results show a size discount in both the undiversifi ed and diversifi ed subsamples. While the scale of the size discount is different between the two groups, it is negative and signifi cant for both. The evidence suggests that this particular systematic difference between large and small fi rms is not responsible for the size discount.
The robustness of these results is tested using the Gompers, Ishii, and Metrick (2003) G-Index as a separate measure of agency costs. In theory, this measure of corporate governance should proxy for the level of agency costs within a fi rm. The more pro-management governance provisions that the fi rm has in place, the more likely the managers are to impose excessive agency costs. While the G-index only provides an indirect measure of agency costs, it is available for more fi rms than is acquisition data. The results of this secondary analysis reiterate the prior fi ndings. The evidence suggests that the size discount only exists in fi rms with high agency costs. In total, the theory and evidence provided in this paper offer support for a size discount, created by the inability of corporate control mechanisms to effectively discipline managers of larger fi rms. This paper is particularly timely in light of recent studies. Evidence that managers of larger fi rms impose higher agency costs through value-reducing acquisitions comes from Moeller, Schlingemann, and Stulz (2004) and Offenberg (2009). Both studies demonstrate that announcement-period returns are negatively correlated with size. In other words, larger fi rms are more likely to be bad bidders than smaller fi rms. Their results highlight the fact that managers of larger fi rms impose higher acquisition-based agency costs upon their shareholders than managers of smaller fi rms. Yermack (2006) looks at the correlation between the use of corporate jets and the change in shareholder wealth. The author describes personal aircraft use as a source of agency costs between shareholders and managers, and by far the most costly fringe benefi t enjoyed by major company CEOs. Yermack hypothesizes that CEOs who impose agency costs on their shareholders in the form of corporate jets may just as easily impose far more damaging agency costs as well. More directly to the point of the present study, the author fi nds that personal aircraft use and a broader consumption of perquisites increases as fi rm size increases.
The remainder of this paper is organized as follows: the fi rst section provides a more thorough review of the relevant corporate fi nance literature about the size discount and past studies that relate size and the effectiveness of corporate governance mechanisms. The next segment describes the data and methodology of

The Size Discount
The negative correlation between size and q is observed repeatedly throughout the fi nance literature. Perhaps the most widely cited of these articles is Lang and Stulz (1994). Their study of diversifi cation considers over 600 fi rms in 1984. The result of interest is derived by estimating a regression of q on a number of explanatory variables, including the ratio of R&D to total assets, a diversifi cation dummy, and fi rm size.
Their results show a negative correlation between size and q: as fi rms grow larger they become relatively less valuable. Robustness of this result is emphasized in Daines (2001), who studies the relationship between q and the state of incorporation over 47,000 fi rm-years. The results of his regressions clearly show the coeffi cient on size is negative and signifi cant. This fi nding has been documented in international studies, such as Claessens, Djankov, Fan, and Lang (2002), which show a signifi cantly negative relationship between size and relative value in eight Asian economies.
A number of authors (Demsetz, 1983) have argued that these results may be subject to an endogeneity bias. It may, in fact, be the case that fi rm size and q are determined simultaneously to maximize value. Therefore, an observed relationship between these variables may refl ect an optimal level, rather than a static correlation. Recent studies have attempted to explore this potential bias. Himmelberg, Hubbard and Palia (1999) use fi rm fi xed effects to reexamine the results in studies such as Morck, Shleifer, and Vishny (1988) and McConnell and Servaes (1990). Coles, Lemmon, and Meschke (2007) reconsider the same literature, but specify a structural model of the fi rm that alleviates the endogeneity problem and allows for better analysis of the relationship between fi rm size and q. Both of these articles fi nd that size is negatively correlated to relative value even after controlling for endogeneity. At least within the universe of Compustat fi rms, there does not seem to be an endogenous connection between fi rm size and fi rm value.

Firm Size and Governance Mechanisms
The purpose of this section is to document evidence in the corporate fi nance literature regarding the ability of corporate governance mechanisms to reduce agency costs in larger fi rms. There are many corporate control mechanisms at shareholders' disposal, should the fi rm's management begin to impose intolerable agency costs. Shareholders may appoint a board of directors that exercises more authority over the executives. They may buy a large block of stock, so as to gain greater control over the fi rm. They may instigate proxy proposals, to change the governance of the fi rm. Also, shareholders may rely on the market for corporate control to step in and remove self-serving managers. An extensive literature has documented the role of each of these devices in disciplining wayward leadership. 4

Boards of Directors
There is some existing theory and evidence that boards of directors become weaker monitors as fi rms become larger. Lipton and Lorsch (1992) and Jensen (1993) argue that a larger board of directors may be less effective. Both cite various reasons why this might be the case, such as free-rider problems, slower decision making, less candid discussions, and biases against risk-taking. Yermack (1996) fi nds that smaller boards are more successful at governing, as measured by the association between board size and fi rm value. His fi ndings also show evidence that as companies grow bigger, boards grow bigger. The conclusion that can be drawn from his analysis is that larger fi rms have larger and thereby less effective boards of directors.
The key role of the board is to hire and fi re managers to best suit the interests of the shareholders. Therefore, one may also observe the effectiveness of the board of directors in their decisions to fi re poorly performing managers. If boards are successful at disciplining managers, then one should observe an increase in turnover following poor performance. Denis, Denis, and Sarin (1997) show in their work that CEOs are less likely to lose their jobs in larger fi rms. This can be interpreted as further evidence that boards become less effective monitors as fi rms grow larger.

Blockholders
A number of studies have shown that shareholders benefi t when the fi rm has a blockholder. Denis, Denis, and Sarin fi nd that the likelihood of top-executive turnover is higher for fi rms with an outside blockholder. Mikkelson and Ruback (1985), as well as Shome and Singh (1995), show increases in stock prices due to block formations. Mikkelson and Partch (1989) explain that acquisitions are more likely to be completed if the fi rm has an outside blockholder. Meanwhile, Bertrand and Mullainathan (2001) provide evidence that CEO pay is less likely to be based on luck when the fi rm has an outside blockholder. Collectively, these results suggest that an outside blockholder can perform a signifi cant monitoring function. Without such monitoring, managers may impose undue agency costs upon the fi rm's shareholders.
Intuitively, one would expect larger fi rms to be less likely to have a blockholder than smaller fi rms. After all, fewer investors can afford to buy 5% of Walmart than 5% of Winnebago 5 . Agrawal and Knoeber (1996) provide empirical evidence that the probability of a fi rm having a blockholder is decreasing in the size of the fi rm. In other words, shareholders of larger fi rms are less likely to enjoy the benefi ts of having a blockholder to mitigate agency costs.

Proxy Proposals
According to the rules of the SEC, any shareholder of record may submit a proxy proposal to the board of directors to be voted upon by the other shareholders. This feature of corporate governance gives every shareholder a voice in how his or her investment is managed. However, once approved, the proposal must be considered for adoption by the board, but they are in no way bound by it. As such, there is only a limited probability of inducing change in an undisciplined management team via proxy proposal. Bizjak and Marquette (1998) focus on shareholder proposals to revise or rescind poison pills. They fi nd increases in fi rm value following adoption of poison pill-related propositions. This serves as evidence that the shareholder proposal system is effective as an external corporate control mechanism. However, their results also reveal an interesting size disparity: they fi nd a negative coeffi cient on the size variable. This result indicates that it is harder to pass a shareholder proposal through a larger fi rm. In sum, the evidence suggests that the proxy proposal process is an effective means by which to cause changes in corporate governance, with the effectiveness weakening as fi rms grow larger.

Acquisitions
There are a number of theories explaining why larger fi rms are more diffi cult to acquire. Palepu (1986), and Baker and Kennedy (2002) argue that transaction costs associated with an acquisition increase as the size of the target increases. Manne (1965) suggests that antitrust laws may prevent bigger companies from becoming the target of an acquisition -government regulators have been successful at preventing businesses with a large market share from buying other fi rms in the same industry that also hold a considerable market share. Managers may also choose to only make small acquisitions because they are less risky. Empirical evidence in papers such as Moeller, Schlingemann, and Stulz (2004) and Travlos (1987) has shown a negative correlation between the relative size of an acquisition and the announcement period abnormal return for large fi rms. All else equal, a December 2010 J. econ. fi nance adm. sci., 15(29), 2010 6 By forcing fi rms to have data in Compustat after the last acquisition, data for 289 acquisitions made by 217 fi rms are lost. Of those, only two are made by companies that are not already included in the sample. 7 The key results of this study are indifferent to estimating the parameters of the market model with an equal-weighted index rather than a value weighted index. Similarly, using a shorter event window to calculate the cumulative abnormal returns, [-2, 2], does not change the sign nor the significance of the results that establish the main fi ndings of the paper.
manager is less likely to be fi red by disappointed investors when the fi rm purchases smaller targets.
Empirical studies have shown that larger fi rms are less likely to be acquired. Palepu (1986), Berger and Ofek (1996), Harford (1999), and Offenberg (2009) fi nd a negative correlation between size and the probability of becoming a target with US-based fi rms. In a sample of UK-based fi nancial services fi rms, Thompson (1997) also fi nds that larger fi rms are less likely to be acquired.

Summary
As fi rms grow larger, there are fewer chances to have a blockholder or to be acquired entirely, shareholders are less likely to pass meaningful proxy proposals, and the boards of directors become weaker. Collectively, these fi ndings provide evidence that shareholders of larger fi rms are not able to reduce agency costs as effectively as shareholders of smaller fi rms. This result is necessary to support the main hypothesis of this paper, that the size discount is a product of agency costs. However, the main hypothesis can only be true if the size discount is only imposed upon larger fi rms with an intolerable level of agency costs. The remainder of this paper provides empirical evidence that only larger companies with high agency costs bear a size discount.

DATA
In this article, agency costs are measured by the quality of the acquisitions that a fi rm makes. To that end, the sample in the present study is drawn from the SDC Platinum mergers and acquisitions database, over the 21-year period from 1980 through 2000. In creating this sample, a number of criteria are employed. First, for an acquisition to be a part of the sample, the acquirer must be included in the CRSP/Compustat merged database at the end of the fi scal year before and after the acquisition 6 . These two years of data are necessary to calculate all the variables employed in this study, which are described in detail later in this section. Furthermore, the total dollar amount offered as the purchase price for the target must be at least 1% of the book value of the acquirer as of the fi scal year-end immediately preceding the announcement. Applying this 1% relative size screen helps ensure that abnormal returns are caused by the event in question and not random noise in the data. At the fi scal year-end following its last acquisition, the acquirer must have at least $25 million in assets, after adjusting for infl ation. In addition, the acquirer must be attempting to increase its ownership in the target to a level greater than 50%. Acquirers with primary SIC codes in fi nancial (SIC 6000-6999) and utility industries (SIC 4910-4940) are excluded from the sample. A download of data from SDC provides 13,338 usable acquisitions over the period from 1980-2000.
The quality of each individual acquisition attempt is measured with a cumulative abnormal return (CAR), which is calculated using the market model over the event window ranging from fi ve days before the announcement through two days after, [-5,2] 7 . This window was chosen because it has been shown to produce signifi cant announcement-period abnormal returns in past studies of acquisitions, such as in Travlos (1987), Bradley, Desai, and Kim (1988), and Hubbard and Palia (1995). The parameters for the market model are estimated using a value-weighted market index over a 200-day window ending six days before the announcement. Firms are eliminated from the sample if they did not have suffi cient data available on CRSP to estimate at least a 100-day market model.
In this study, the quality of each bidder is measured by the net effect on shareholder wealth of all acquisitions attempted within a fi scal year 8 . As a result, the dataset that is used in the following analysis is composed of observations, rather than just acquisitions, where an observation combines a year's-worth of acquisitions by one fi rm into one data point. As such, from the sample of 13,338 acquisitions downloaded from SDC Platinum, the resulting dataset yields 9,434 fi rm-years. Table 1 shows a summary of the sample. For each year, the number of acquisitions, the number of observations, the average size of the acquirers, and the average Tobin's q are reported. The pattern of acquisitions over time mirrors that described in the literature, with a run-up toward the later end of the 1980s, followed by an even sharper spike in activity in the late 1990s. There are two important time trends to note here. First, the acquirers' decrease is size over time, after adjusting for infl ation. Second, the mean relative value of fi rms increases over time. These time trends indicate that proper controls for time must be included in the analysis that follows.
The quality of the bidder for each observation is measured by compounding CARs from all acquisitions made by the fi rm over a single fi scal year. Compounding returns creates one variable that measures the impact of the fi rm's total acquisition activity on shareholder wealth. Therefore, the primary variable of interest in much of the analysis that follows is the compound CAR (CCAR), where: where CAR 1 is the CAR from the fi rst acquisition made by a fi rm in the fi scal year, CAR 2 is the CAR from the second acquisition, and so on. The resulting compound CAR variable is the measure of bid quality, and therefore the measure of agency costs, used throughout the analysis. Firms with a negative CCAR for a given fi scal year are presumed to have imposed an intolerable level of agency costs upon their shareholders, and, as such, are labeled bad bidders. Firms with a positive CCAR, for a given year, are presumed to be well managed, and are labeled good bidders.
Financial and diversifi cation data are drawn from the Compustat database. All fi nancial data are adjusted for infl ation, using 1980 as the base year. Tobin's q is calculated as in Daines (2001) by dividing the sum of market value of common equity and book value of debt and preferred stock by the book value of assets. The quotient is estimated as of the end of the fi scal year immediately following the acquisition, which allowed for the value of the new entity to be included. To ensure that the correlation between size and q is not biased throughout the analysis, fi rm size is measured using the natural log of sales as of the end of the fi scal year immediately following the acquisition 9 .

EMPIRICAL ANALYSIS
This section focuses on the empirical relationship between size, q, and agency costs in the sample. Table 2 begins by summarizing some of the more interesting features of the sample. The fi rst column shows the average size of the fi rms, as measured by the infl ation-adjusted natural log of sales. The fi rst panel shows the mean for the entire sample, while the second panel breaks the sample into groups defi ned by the headings «Good Bidders» and «Bad Bidders». Table 2 shows that good bidders are signifi cantly smaller fi rms than bad bidders, with the average natural log of sales of 19.93 for the former and 20.17 for the latter. This fi nding agrees with past results in Loderer and Martin (1997), as well as Moeller, Schlingemann, and Stulz (2004), who also fi nd that large fi rms tend to be bad bidders. In addition to bid quality, there are also signifi cant differences between good and bad bidders in profi tability, research intensity, and the timing of their bids. It is important to control for these differences when measuring the size discount in the analysis that follows.
The third panel of Table 2 also shows the difference in size between diversifi ed and undiversifi ed fi rms. The results show that diversifi ed fi rms are signifi cantly larger and have smaller values of q. This suggests that diversifi cation is worth studying as a possible systematic difference between larger and smaller fi rms that may create the size discount. It is interesting to note that the calculated value of q for the diversity subsamples refl ects the diversifi cation discount. Single-segment fi rms have an average q of 2.15, but the average is only 1.75 for diversifi ed fi rms; the difference is statistically signifi cant. Table 3 presents a pair-wise correlation matrix for several of the key variables in the analysis. This offers a fi rst glimpse at the correlations that will be analyzed more thoroughly later in this paper. The most important result to highlight in Table 3 is the relationship between q and size. The purpose of this paper is to study what drives the negative correlation between size and q that has been observed in other datasets, and this correlation coeffi cient (-0.0862) demonstrates that such a relationship exists in this data as well. It is also interesting to note that there is no economically or statistically signifi cant pair-wise correlation between q and the CCAR. Whenever a fi rm's stock price varies, the market value Vol. 15, Nº 29 J. econ. fi nance adm. sci., 15(29), 2010 of assets also varies forcing a change in q. Across all fi rm-years, the value of q does not appear to be infl uenced by the quality of the fi rms' acquisitions.
To study the sensitivity of the relationship between size and value, fi xed effects OLS regressions are estimated with q as the dependent variable, and size as an independent variable. Fixed effects are by fi rm to control for fi rm-specifi c variation in q. A collection of other known predictors of q are incorporated as explanatory variables. The return on assets is included to control for any correlation between size and profi tability, as dis-cussed in Hall and Weiss (1967). More profi table fi rms should have higher levels of q. The ratio of research and development to sales also serves as a control variable, as Kallunki et al. (2009) document a positive correlation between the level of R&D and relative value. Palepu (1986) argues that measures of liquidity and leverage are likely to indicate whether a fi rm is an attractive target: more liquid fi rms are hypothesized to be more valuable and more indebted fi rms should be less valuable. To that end, ratio of cash to sales (liquidity) and the ratio of debt to equity (leverage) are included in the regression as well. There is a dummy variable for Tobin's q is represented by the variable q. Size measures the natural log of the infl ation-adjusted level of sales. CCAR is the compounded cumulative abnormal returns around the announcement of all acquisitions in a given fi rm-year. The 1980s variable is a dummy set equal to one if the fi rm-year was in the period from 1980-1989. The fi rst panel shows data for all 9,434 fi rm years in the sample. The second panel splits fi rm-years into two subsamples based on the quality of the fi rm's acquisitions. The Good Bidders group considers fi rm-years in which the compound CCAR is positive. The Bad Bidders group only considers fi rm-years in which the compound CCAR is negative. The third panel splits fi rms into subsamples based on diversity. Single Segment fi rms are those that report one business segment in Compustat, while Multiple Segment fi rms report more than one segment. There are fewer fi rm years in the third panel due to data availability. P-values reported in the second and third panels measure the signifi cance of a two-tailed t-test for the difference of means. fi rm-years that occurred in the period from 1980-1989, as authors such as Holmstrom and Kaplan (2001) have argued that there were fundamental differences in the takeover markets of the 1980s and 1990s, which may have impacted the fi rm's CCAR 10 .
Preliminary regressions are presented in Table 4. The purpose of this fi rst regression is to document that the size discount exists in this dataset, even after controlling for common determinants of q. The fi rst column shows the expected relationship between size and q, with the second column reporting that the coeffi cient on size is negative and signifi cant at -0.066. This is the size discount: as fi rm size increases, relative value decreases. The control variables discussed above are employed in the second model. Each of these variables has a signifi cant impact upon q, but the size discount is similar, with the coeffi cient on size at -0.062. The results in Table 4 make it apparent that the size discount exists in this sample.
To study whether the size discount varies based upon a variation in agency costs, fi rms are split into a low agency costs subsample labeled Good Bidders and a high agency costs subsample marked Bad Bidders. The results are reported in Table 5.
In the Good Bidders subsample, there is no size discount. The coeffi cient on the size variable is positive but not signifi cantly different from zero. On the other hand, a size discount does appear in the Bad Bidders subsample. The size variable carries a signifi cant coeffi cient of -0.095. This is the main fi nding of this study. A signifi cant size discount exists for fi rms suffering high agency costs, but no similar discount appears for fi rms not burdened by agency costs. These results suggest that agency costs may be a substantial component of the size discount.  To ensure that there is a significant difference between the coeffi cients on the size variables in these two models, an additional regression is estimated in the third column of Table 5 that uses an interaction term. This variable is constructed by multiplying size by a good bidder dummy, which takes the value of one if the fi rm-year had a positive CCAR. The interaction term measures the difference in the size discount between good and bad bidders, or how much less a good bidder is discounted by the market. The results in the third column show that the coeffi cient on the interaction term is positive and signifi cant at 0.109, indicating that the size discount is greater for bad bidders than for good bidders. In other words, large bad bidders have signifi cantly lower values of q than small bad bidders, but large good bidders have similar levels of q to small good bidders. Fuller, Netter, and Stegemoller (2002), amongst others, show that the method of payment (stock vs. cash), the organizational form of the target (public vs. private), whether or not the deal was a tender offer,   and other deal characteristics have an impact on the acquirer's announcement-period abnormal return. It is important to note that no controls are included in the analysis to account for these characteristics of the acquisition. They are intentionally omitted because abnormal returns are being used as an explanatory variable. The abnormal returns are attempting to capture the change in shareholder wealth. Shareholders do not care if they have lost wealth in an acquisition because of the method of payment: they only care that they have lost wealth. As such, including any controls that dilute the impact on shareholder wealth of the managers' decisions is counterproductive.

Diversifi cation
If the size discount is due to diversifi cation in large fi rms, then it should be apparent in a subsample of diversifi ed companies, but not in a subsample of singlesegment entities. To test this proposition, fi rms are split into subsamples and fi xed-effects regressions of the determinants of q are re-estimated, with the results presented in Table 6. The fi rst column shows the fi ndings for diversifi ed fi rms. As expected, the size coeffi cient has a negative and signifi cant value, refl ecting the size discount. However, this is also true for nondiversifi ed fi rms. While the scale of the discount is less for single segment companies versus multi-segment fi rms (-0.065 vs. -0.124), the signifi cance is still apparent. The third column estimates a separate regression, which includes all fi rm-years and uses an interaction term to determine the signifi cance of the difference of the size discounts. This interaction term, which multiplies size by a dummy variable set equal to one if the fi rm has multiple segments, measures how much larger the coeffi cient on the size variable is for diversifi ed fi rms versus nondiversifi ed fi rms. It is interesting to note that the coeffi cient on the interaction term suggests that the size discount is dependent upon the diversity of the fi rm. In other words, large diversifi ed fi rms exhibit less of a size discount than large undiversifi ed fi rms, but smaller diversifi ed fi rms bear more of a size discount than smaller undiversifi ed fi rms. In total, the results presented in Table 6 suggest that the size discount is present and signifi cant even after controlling for diversifi cation.
As a further test, a diversifi cation dummy was inserted into the regressions previously estimated in Table  5. Again, the dependent variable is the fi rm's Tobin's q, and the result of interest is the coeffi cient on the size variable. To be thorough, the discrete variable used to measure agency costs in the model in Table 5 was replaced with a continuous measure. More specifi cally, the Good Bidder Dummy is replaced with CCAR.
The fi rst and second columns of Table 7 show the coeffi cient estimates of a regression with fi rms split into a Good Bidder sample and a Bad Bidder sample. Size bears a negative and signifi cant coeffi cient for bad bidders, once again indicating the presence of a size discount. However, the coeffi cient on size for good bidders is positive and insignifi cant. The results suggest that the size discount only affects the relative value of bad bidders, but not good bidders. Finally, the third column reintroduces the interaction term that measures the signifi cance of the difference between the size discount in good and bad bidders. The coeffi cient on the interaction term is again positive and signifi cant (0.097), suggesting that the size discount has less of an impact on the value of good bidders than bad bidders, even after controlling for the diversifi cation discount.

January Effect
It is widely documented that stock prices tend to rise in the month of January. It is not immediately clear what affect this phenomenon should have on announcementperiod returns to acquirers, nor to the size discount. On one hand, rising prices make targets more expensive, so acquirers may be more likely to overpay. On the other hand, rising stock prices also make the acquirer's equity more valuable as a form of merger consideration, so they may be able to spend less cash to complete the deal.
In unreported t-tests, mean acquirer CARs are 2.03% in January, and 1.16% in the other eleven months of the year. The difference is signifi cant at the 5% level. It appears that buyers do make better deals in January. In order to determine if these deals in January are driving the results in Table 7, the regression (unreported) is estimated without January deals included in the CCAR calculation 11 . The resulting coeffi cient estimates are not substantially different than those reported in Table 7, column 3, both in size and signifi cance. In other words, the key results of this paper are not a by-product of better deal-making in January.

A Note on Growth
As mentioned previously, authors in the past have suggested that the negative correlation between size and Tobin's q is driven by a difference in growth prospects. One way to test the validity of this claim would be to measure q, then measure the change in assets over the next several years and see how well the variation in q predicts the variation in asset growth. The fundamental problem with such a test is the survivorship bias. In the present sample, over 23% of fi rms drop out within three years. On average, these fi rms are signifi cantly smaller and less profi table than the survivors, but tend to make much better acquisitions. It is diffi cult to know the implications of this survivorship bias, but any results drawn from such a sample would have to be interpreted cautiously.

A Note on Bankruptcy
Another systematic difference that has been observed between larger and smaller fi rms is the probability of bankruptcy. In Ohlson (1980), a logit model is used to predict whether a fi rm will fi le for bankruptcy in the period up to twelve months following the end of the fi scal year. In a sample of fi rms covering 1970-1976, larger fi rms were found to be less likely to fi le for bankruptcy. However, these fi ndings were updated in a recent paper by Hillegeist, Keating, Cram, and Lundstedt (2004) (HKCL hereafter), whose dataset covers the exact same period as the present study, from 1980-2000. Their results show the opposite size effect of the original Ohlson study. More specifi cally, HKCL fi nd that as fi rm size increases, the probability of bankruptcy increases.
One interesting test to include in the present study would be to determine if the negative correlation between size and q is driven by bankruptcy costs. To that end, probabilities of bankruptcy are calculated for all of the fi rms in the sample using the updated logit model coeffi cients from the HKCL study. The highest resulting probability of bankruptcy for all fi rm-years in the present sample is approximately 16%. Nearly all of the fi rm-years in this dataset have a less than 10% chance of entering into bankruptcy in the coming year. It appears that all of these fi rms are fi nancially healthy, as would be expected of acquirers. The drawback to this fi nding is that no reasonable tests could be run on the present sample, which includes a probability of bankruptcy as a determinant of Tobin's q, since bankruptcy is such an unlikely occurrence. After all, Ohlson (1980) argues that no fi rm with an estimated probability of bankruptcy under 50% can reasonably be expected to go bankrupt.

Robustness
To test the robustness of the results, a secondary dataset is constructed with a different measure of agency costs. In this analysis, instead of measuring agency costs with CCAR, they are measured using the G-index presented in Gompers, Ishii, and Metrick (2003). In essence, the G-index assigns one point for each measure employed by a fi rm that reduces shareholder rights. These provisions may include poison pills, classifi ed boards, golden parachutes, and so on. The more anti-shareholder provisions the fi rm has enacted, the higher its G-index score. In theory, managers have a greater opportunity to impose agency costs if they have more such provisions in place. In total, scores can range from 0 to 24. Gompers, Ishii, and Metrick classify fi rms with a score under six as a democracy, and scores over 13 as a dictatorship.
The G-index data is available for a subset of fi rms in the Compustat database. The score is not calculated yearly for each fi rm, so in missing years, the most recent score is used. For instance, if a fi rm received a score of 10 in 1990 and 15 in 1992, it is assumed that it would still receive a 10 in 1991. Summary statistics regarding this subset of data are presented in Table 8. The G-index scores from 1990-2006 are supplemented with fi nancial data from Compustat. The key variables, such as Tobin's q and size, are calculated in the identical manner as that described previously, with the obvious exception of CCAR. Firms in this alternative sample are not required to be acquirers; they must only have a G-index score 12 .
In order to check the robustness of the prior results, the same tests are run using this new measure of agency costs. The regression model employed again uses q as the dependent variable, with size and the G-index as explanatory variables. The results are presented in Table 9. In this analysis, democracies are the functional equivalent of good bidders, as they are both expected to have low agency costs. Similarly, dictatorships are expected to have high agency costs like bad bidders.
The coeffi cients in column 1 suggest that size does not have any explanatory power with q amongst the 12 There is not enough overlap between the sample of acquirers used in the beginning of the paper and the G-Index sample introduced here to combine them into one panel and run meaningful statistical tests. low-agency costs sample, the democracies. To the contrary, size and q are negatively correlated for fi rms with high agency costs, the dictatorships. In the Dictatorships column, the coeffi cient on size is -0.095 and it is signifi cant at the 5% level. These fi ndings echo the results in Table 5. It appears that the size discount is limited to fi rms with high agency costs. The third column of Table 9 combines democracies and dictatorships into one panel. The coeffi cient on the size discount approaches zero, but the interaction term is negative and signifi cant. This result again shows that size and value are only negatively related in fi rms in which it is diffi cult to minimize agency costs. Overall, the fi ndings from the tests in Table 9 support the prior analysis with acquirers. The key result, that the size discount is driven by agency costs, appears to be robust to the measure of agency costs.

CONCLUSIONS
Over the past twenty years, many papers have been published in the accounting and fi nance literature that show a negative correlation between the size and relative value of a fi rm. While it is often assumed that the size discount is due to differences in growth opportunities, there is no published evidence to justify why this relationship exists. The arguments set forth in this paper establish an agency costs-based explanation for the size discount as an alternative to the status quo.
In fact, it is quite likely that the expected growth rates of large and small fi rms are the same. There may be large fi rms with plenty of growth opportunities, such as Google, with their ambitions to enter countless new internet-based markets in the coming years. Similarly, there may be small fi rms with no growth opportunities, such as typewriter manufacturers. Consider further that large fi rms can be viewed as a collection of small fi rms. For example, Microsoft is a company that sells operating systems in one market, network utilities in another market, computer games to a third market, and so on. From this viewpoint, it becomes apparent that the growth opportunities for large fi rms may be no different than those for small fi rms. This paper argues that this size discount is based on the decreasing ability of corporate governance mechanisms to discipline management as fi rms grow larger. This hypothesis is supported by both a wealth of prior research, which documents weaker disciplinary mechanisms, higher agency costs, and lower values of q in larger fi rms, along with the empirical fi ndings presented in this study. The evidence demonstrates that a size discount is apparent in fi rms burdened by high agency costs, but not in fi rms with low agency costs. It also shows that no similar disparity exists between diversifi ed and nondiversifi ed corporations, and is robust to using the G-Index as an alternative measure of agency costs. This article takes a fi rst stab at the hypothesis that agency costs drive the size discount, but leaves many questions unanswered. Further tests with larger, more diverse and international samples are warranted, as are tests with improved measures of agency costs. These provide avenues for future research. This table shows the results of Fama-MacBeth fi xed-effects regressions with Tobin's q as the dependent variable. G is the fi rm's G-Index score in a given fi rm-year. The fi rst column only considers fi rm-years in which G<6. The second column only considers fi rm-years in which G>13. Size is measured with the infl ation-adjusted natural log of sales as of the end of the fi scal year. The S&P500 variable is a dummy set equal to one if the fi rm was a member of the S&P 500 for the given year. Fixed effects are at the industry level.