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Predicting Australian Takeover Targets:
A Logit Analysis
Maurice Peat*
Maxwell Stevenson*
* Discipline of Finance,
School of Finance,
The University of Sydney
Abstract
Positive announcementday adjusted returns to target shareholders in the event of a
takeover are well documented. Investors who are able to accurately predict firms that
will be the subject of a takeover attempt should be able to earn these excess returns. In
this paper a series of probabilistic regression models were developed that use financial
statement variables suggested by prior research as explanatory variables. The models,
applied to insample and outofsample data, led to predictions of takeover targets that
were better than chance in all cases. The economic outcome resulting from holding a
portfolio of the predicted targets over the prediction period are also analysed.
Keywords: takeovers, targets, prediction, classification, logit analysis
JEL Codes: G11, G17, G23, G34
This is a draft copy and not to be quoted.
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1. Introduction
In this paper our aim is to accurately predict companies that will become takeover
targets. Theoretically, if it is possible to predict takeovers with accuracy greater than
chance, it should be possible to generate abnormal returns from holding a portfolio of
the predicted targets. Evidence of abnormal returns of 20% to 30% made by
shareholders of firms on announcement of a takeover bid is why prediction of these
events is of interest to academics and practitioners alike.
The modelling approach adopted in this study was based on the discrete choice
approach used by Palepu (1986) and Barnes (1999). The models were based on
financial statement information, using variables suggested by the numerous theories
that have been put forward to explain takeover activity. The performance of the
models was evaluated using statistical criteria. Further, the predictions from the
models were rated against chance and economic criteria through the formation and
tracking of a portfolio of predicted targets. Positive results were found under both
evaluation criteria.
Takeover prediction studies are a logical extension of the work of Altman (1968)
who used financial statement information to explain corporate events. Early studies by
Simkowitz and Monroe (1971) and Stevens (1973) were based on the Multiple
Discriminant Analysis (MDA) technique. Stevens (1973) coupled MDA with factor
analysis to eliminate potential multicollinearity problems and reported a predictive
accuracy of 67.5%, suggesting that takeover prediction was viable. Belkaoui (1978)
and Rege (1984) conducted similar analyses in Canada with Belkaoui (1978)
confirming the results of these earlier researchers and reporting a predictive accuracy
of 85% . Concerns were raised by Rege (1984) who was unable to predict with similar
accuracy. These concerns were also raised in research by others such as Singh (1971)
and Fogelberg, Laurent, and McCorkindale (1975).
Reacting to the wide criticism of the MDA method, researchers began to use
discrete choice models as the basis of their research. Harris et al. (1984) used probit
analysis to develop a model and found that it had extremely high explanatory power,
but were unable to discriminate between target and nontarget firms with any degree
of accuracy. Dietrich and Sorensen (1984) continued this work using a logit model
and achieved a classification accuracy rate of 90%. Palepu (1986) addressed a number
of methodological problems in takeover prediction. He suggested the use of statebased
prediction samples where a number of targets were matched with nontargets
3
for the same sample period. While this approach was appropriate for the estimation
sample, it exaggerated accuracies within the predictive samples because the estimated
error rates in these samples were not indicative of error rates within the population of
firms. He also proposed the use of an optimal cutoff point derivation which
considered the decision problem at hand. On the basis of this rectified methodology,
along with the application of a logit model to a large sample of US firms, Palepu
(1986) provided evidence that the ability of the model was no better than a chance
selection of target and nontarget firms. Barnes (1999) also used the logit model and a
modified version of the optimal cutoff rule on UK data. His results indicated that a
portfolio of predicted targets may have been consistent with Palepu’s finding, but he
was unable to document this in the UK context due to model inaccuracy.
In the following section the economic explanations underlying takeover activity
are discussed. Section 3 outlines our takeover hypotheses and describes the
explanatory variables that are used in the modelling procedure. The modelling
framework and data used in the study is contained in Section 4, while the results of
our model estimation, predictions, classification accuracy and portfolio economic
outcomes are found in Section 5. We conclude in Section 6.
2. Economic explanations of takeover activity
Economic explanations of takeover activity have suggested the explanatory
variables that were included in this discrete choice model development study. Jensen
and Meckling (1976) posited that agency problems occurred when decision making
and risk bearing were separated between management and stakeholders1, leading to
management inefficiencies. Manne (1965) and Fama (1980) theorised that a
mechanism existed that ensured management acted in the interests of the vast number
of small noncontrolling shareholders2. They suggested that a market for corporate
control existed in which alternative management teams competed for the rights to
control corporate assets. The threat of acquisition aligned management objectives
with those of stakeholders as managers are terminated in the event of an acquisition in
order to rectify inefficient management of the firm’s assets. Jensen and Ruback
(1983) suggested that both capital gains and increased dividends are available to an
1 Stakeholders are generally considered to be both stock and bond holders of a corporation.
2 We take the interests of shareholders to be in the maximization of the present value of the firm.
4
acquirer who could eliminate the inefficiencies created by target management, with
the attractiveness of the firm for takeover increasing with the level of inefficiency.
Jensen (1986) looked at the agency costs of free cash flow, another form of
management inefficiency. In this case, free cash flow referred to cash flows in excess
of positive net present value (NPV) investment opportunities and normal levels of
financial slack (retained earnings). The agency cost of free cash flow is the negative
NPV value that arises from investing in negative NPV projects rather than returning
funds to investors. Jensen (1986) suggested that the market value of the firm should
be discounted by the expected agency costs of free cash flow. These, he argued, were
the costs that could be eliminated either by issuing debt to fund an acquisition of
stock, or through merger with, or acquisition of a growing firm that had positive NPV
investments and required the use of these excess funds. Smith and Kim (1994)
combined the financial pecking order argument of Myers and Majluf (1984) with the
free cash flow argument of Jensen (1986) to create another motivational hypothesis
that postulated inefficient firms forgo profitable investment opportunities because of
informational asymmetries. Further, Jensen (1986) argued that, due to information
asymmetries that left shareholders less informed, management was more likely to
undertake negative NPV projects rather than returning funds to investors. Smith and
Kim (1994) suggested that some combination of these firms, like an inefficient firm
and an efficient acquirer, would be the optimal solution to the two respective resource
allocation problems. This, they hypothesised, would result in a market value for the
combined entity that exceeded the sum of the individual values of the firms. This is
one form of financial synergy that can arise in merger situations.
Another form of financial synergy is that which results from a combination of
characteristics of the target and bidding firms. Jensen (1986) suggested that an
optimal capital structure exists, whereby the marginal benefits and marginal costs of
debt are equal. At this point, the cost of capital for a firm is minimised. This
suggested that increases in leverage will only be viable for those firms who have free
cash flow excesses, and not for those which have an already high level of debt.
Lewellen (1971) proposed that in certain situations, financial efficiencies may be
realized without the realization of operational efficiencies. These efficiencies relied
on a simple Miller and Modigliani (1964) model. It proposed that, in the absence of
corporate taxes, an increase in a firm’s leverage to reasonable levels would increase
the value of the equity share of the company due to a lower cost of capital. By a
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merger of two firms, where either one or both had not utilised their borrowing
capacity, would result in a financial gain. This financial gain would represent a
valuation gain above that of the sum of the equity values of the individual firms.
However, this result is predicated on the assumption that the firms need to either
merge or be acquired in order to achieve this result.
Merger waves are well documented in the literature. Gort (1969) suggested that
industry disturbances are the source of these merger waves, his argument being that
they occurred in response to discrepancies between the valuation of a firm by
shareholders and potential acquirers. As a consequence of economic shocks (such as
deregulation, changes in input or output prices, etc.), expectations concerning future
cash flow became more variable. This results in an increased probability that the value
the acquirer places on a potential target is greater than its current owner’s valuation.
The result is a possible offer and subsequent takeover. Mitchell and Mulherin (1996),
in their analysis of mergers and acquisitions in the US during the 1980s, provided
evidence that mergers and acquisitions cluster by industries and time. Their analysis
confirmed the theoretical and empirical evidence provided by Gort (1969) and
provided a different view suggesting that mergers, acquisitions, and leveraged
buyouts were the least cost method of adjusting to the economic shocks borne by an
industry.
These theories suggested a clear theoretical base on which to build takeover
prediction models. As a result, eight main hypotheses for the motivation of a merger
or acquisition have been formulated, along with twenty three possible explanatory
variables to be incorporated predictive models.
3. Takeover hypotheses and explanatory variables
The most commonly accepted motivation for takeovers is the inefficient
management hypothesis.3 The hypothesis states that inefficiently managed firms will
be acquired by more efficiently managed firms. Accordingly,
H1: Inefficient management will lead to an increased likelihood of acquisition.
Explanatory variables suggested by this hypothesis as candidates to be included in the
specifications of predictive models included:
1. ROA (EBIT/Total Assets – Outside Equity Interests)
3 It is also known as the disciplinary motivation for takeovers.
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2. ROE (Net Profit After Tax / Shareholders Equity – Outside Equity Interests)
3. Earnings Before Interest and Tax Margin (EBIT/Operating Revenue)
4. EBIT/Shareholders Equity
5. Free Cash Flow (FCF)/Total Assets
6. Dividend/Shareholders Equity
7. Growth in EBIT over past year, along with an activity ratio,
8. Asset Turnover (Net Sales/Total Assets)
While there are competing explanations for the effect that a firm’s undervaluation
has on the likelihood of its acquisition by a bidder, there is consistent agreement
across all explanations that the greater the level of undervaluation then the greater the
likelihood a firm will be acquired. The hypothesis that embodies the impact of these
competing explanations is as follows:
H2: Undervaluation of a firm will lead to an increased likelihood of acquisition.
The explanatory variable suggested by this hypothesis is:
9. Market to book ratio (Market Value of Securities/Net Assets)
The Price Earnings (P/E) ratio is closely linked to the undervaluation and
inefficient management hypotheses. The impact of the P/E ratio on the likehood of
acquisition is referred to as the P/E hypothesis:
H3: A high Price to Earnings Ratio will lead to a decreased likelihood of acquisition.
It follows from this hypothesis that the P/E ratio is a likely candidate as an
explanatory variable for inclusion in models for the prediction of potential takeover
targets.
10. Price/Earnings Ratio
The growth resource mismatch hypothesis is the fourth hypothesis. However, the
explanatory variables used in models specified to examine this hypothesis capture
growth and resource availability separately. This gives rise to the following:
H4: Firms which possess low growth / high resource combinations or,
alternatively, high growth / low resource combinations will have an increased
likelihood of acquisition.
The following explanatory variables suggested by this hypothesis are:
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11. Growth in Sales (Operating Revenue) over the past year
12. Capital Expenditure/Total Assets
13. Current Ratio (Current Assets/Current Liabilities)
14. (Current Assets – Current Liabilities)/Total Assets
15. Quick Assets (Current Assets – Inventory)/Current Liabilities
The behaviour of some firms to pay out less of their earnings in order to maintain
enough financial slack (retained earnings) to exploit future growth opportunities as
they arise, has led to the dividend payout hypothesis:
H5: High payout ratios will lead to a decreased likelihood of acquisition.
The obvious explanatory variable suggested by this hypothesis is:
16. Dividend Payout Ratio
Rectification of capital structure problems is an obvious motivation for takeovers.
However, there has been some argument as to the impact of low or high leverage on
acquisition likelihood. This paper proposes a hypothesis known as the inefficient
financial structure hypothesis from which the following hypothesis is derived.
H6: High leverage will lead to a decreased likelihood of acquisition.
The explanatory variables suggested by this hypothesis include:
17. Net Gearing (Short Term Debt + Long Term Debt)/Shareholders Equity
18. Net Interest Cover (EBIT/Interest Expense)
19. Total Liabilities/Total Assets
20. Long Term Debt/Total Assets
The existence of Merger and Acquisition (M&A) activity waves, where takeovers
are clustered in wavelike profiles, have been proposed as indicators of changing
levels of M&A activity over time. It has been argued that the identification of M&A
waves, with the corresponding improved likelihood of acquisition when the wave is
surging, captures the effect of the rate of takeover activity at specific points in time,
and serves as valuable input into takeover prediction models. Consistent with M&A
activity waves and their explanation as a motivation for takeovers is the industry
disturbance hypothesis:
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H7: Industry merger and acquisition activity will lead to an increased likelihood
of acquisition.
An industry relative ratio of takeover activity is suggested by this hypothesis:
21. The numerator is the total bids launched in a given year, while the
denominator is the average number of bids launched across all the industries in
the ASX.
Size will have an impact on the likelihood of acquisition. It seems plausible that
smaller firms will have a greater likelihood of acquisition due to larger firms
generally having fewer bidding firms with the resources to acquire them. This gives
rise to the following hypothesis:
H8: The size of a firm will be negatively related to the likelihood of acquisition.
Explanatory variables that can be employed to control for size include:
21. Log (Total Assets)
22. Net Assets
4. Data and Method
The data requirements for the variables defined above are derived from the
financial statements and balance sheet date price information for Australian listed
companies. The financial statement information was sourced from the AspectHuntley
data base which includes annual financial statement data for all ASX listed companies
between 1995 and 2006. The database includes industry classifications for all firms
included in the construction of industry relative ratios. Lists of takeover bids and their
respective success were obtained from the Connect4 database. This information
enabled the construction of variables for relative merger activity between industries.
Additionally, stock prices from the relevant balance dates of all companies were
sourced from the AspectHuntley online database, the SIRCA Core Price Data Set and
Yahoo! Finance.
4.1 The Discrete Choice Modelling Framework
The modelling procedure used is the nominal logit model, made popular in the
bankruptcy prediction literature by Ohlson (1980) and, subsequently, in the takeover
prediction literature by Palepu (1986). Logit models are commonly utilised for
dichotomous state problems. The model is given by equations [1] to [3] below.
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[3]
The logit model was developed to overcome the rigidities of the Linear
Probability Model in the presence of a binary dependent variable. Equations [1] and
[2] show the existence of a linear relationship between the logodds ratio (otherwise
known as the logit Li) and the explanatory variables. However, the relationship
between the probability of the event and acquisition likelihood is nonlinear. This
nonlinear relationship has a major advantage that is demonstrated in equation [3].
Equation [3] measures the change in the probability of the event as a result of a small
increment in the explanatory variables, .
When the probability of the
event is high or low, the incremental impact of a change in an explanatory variable on
the likelihood of the event will be compressed, requiring a large change in the
explanatory variables to change the classification of the observation. If a firm is
clearly classified as a target or nontarget, a large change in the explanatory variables
is required to change its classification.
4.2 Sampling Schema
Two samples were used in the model building and evaluation procedure. They
were selected to mimic the problem faced by a practitioner attempting to predict
takeover targets into the future.
The first sample was used to estimate the model and to conduct insample
classification. It was referred to as the Estimation Sample. This sample was based on
financial data for the 2001 and 2002 financial years for firms that became takeover
targets, as well as selected nontargets, between January, 2003 and December, 2004.
The lag in the dates allows for the release of financial information as well as allowing
for the release of financial statements for firms whose balance dates fall after the 30th
June. Following model estimation, the probability of a takeover offer was estimated
for each firm in the entire sample of firms between January, 2003 and December,
2004 using the estimated model and each firm’s 2001 and 2002 financial data. Expost
predictive ability for each firm was then assessed.
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A second sample was then used to assess the predictive accuracy of the model
estimated with the estimation sample data. It is referred to as the Prediction Sample.
This sample includes the financial data for the 2003 and 2004 financial years, which
will be used in conjunction with target and nontarget firms for the period January,
2005 to December, 2006. Using the model estimated from the 2001 and 2002
financial data, the sample of firms from 2005 and 2006 were fitted to the model using
their 2003 and 2004 financial data. They were then classified as targets or nontargets
using the 2005 and 2006 data. This sampling methodology allows for the evaluation
of exante predictive ability rather than expost classification accuracy. A
diagrammatic explanation of the sample data used for both model estimation and
prediction can be found below in Figure 1, and in tabular form in Table 1.
Figure 1 Timeline of sample data used in model estimation and prediction
Table 1 Sample data used in model estimation and prediction
Sample Financial Data Classification Period
Estimation Sample 2001 and 2002 2003 and 2004
Prediction Sample 2003 and 2004 2005 and 2006
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For model estimation, a technique known as statebased sampling was used.
Allison (2006) suggested the use of this sampling approach in order to minimise the
standard error of the estimated parameters when the dependent variable states were
unequally distributed in the population. All the target firms were included in the
estimation sample, along with an equal number of randomly selected nontarget firms
for the same period. Targets in the estimation sample were randomly paired with the
sample of nontarget firms for the same period over which financial data was
measured.4
4.3 Assessing the Estimated Model and its Predictive Accuracy
Walter (1994), Zanakis and Zopounidis (1997), and Barnes (1999) utilised the
Proportional Chance Criterion and the Maximum Chance Criterion to assess the
predictions of discriminant models relative to chance. These criteria are also
applicable to the discrete choice modelling exercise that is the focus of this study and,
accordingly, are discussed more fully below.
4.3.1 Proportional Chance Criterion
To assess the classification accuracy of the estimated models in this study, the
Proportional Chance Criterion was utilized to assess whether the overall
classifications from the models were better than that expected by chance. This
criterion compared the classification accuracy of models to jointly classify target or
nontarget firms better than that expected by chance. Although the criterion does not
indicate the source of the classification accuracy of the model (that is, whether the
model accurately predicts targets or nontargets), it does allow for the comparison
with alternative models. A simple Zscore calculation formed the basis of a joint test
of the null hypothesis that the model was unable to jointly classify targets and nontargets
better than chance. Under a chance selection, we would expect a proportion of
targets and nontargets to be jointly equal to their frequencies in the population under
consideration. The null and alternative hypotheses, along with the test statistic are
given below.
H0: Model is unable to classify targets and nontargets jointly better than chance.
H1: Model is able to classify targets and nontargets jointly better than chance.
4 This approach differs from matched pair samples where targets are matched to nontargets on the basis of
variables such as industry and/or size.
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If the statistic is significant, we reject the null hypothesis and conclude that the
model can classify target and nontarget firms jointly better than chance.
4.3.2 Maximum Chance Criterion
While the Proportional Chance Criterion indicated whether a model jointly
classified target and nontarget firms better than chance, it did not indicate the source
of the predictive ability. However, under the Maximum Chance Criterion, a similar
test of hypotheses does indicate whether a model has probability greater than chance
in classifying either a target or a nontarget firm. The Zscore statistic to test the null
hypothesis that a model is unable to classify targets better than chance is given below.
It is based on the Concentration Ratio defined by Powell (2001) that measures the
maximum potential chance of correct classification of a target, or the proportion of
correctly classified targets from those firms predicted to be targets.
H0: Model is unable to classify targets better than chance.
H1: Model is able to classify targets better than chance.
In order to assess the classification accuracy of the models in the Estimation and
Prediction Samples, these two criteria were used. The focus of this study was on the
use of the Maximum Chance Criterion for targets, as it assessed whether the number
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of correctly predicted targets exceeded the population of predicted targets.5 The
Concentration Ratio was the ratio advocated by Barnes (1999) for maximising returns.
4.3.3 Industry Relative Ratios
Platt and Platt (1990) advocated the use of industry relative variables to increase
the predictive accuracy of bankruptcy prediction models on the pretext that these
variables enabled more accurate predictions across industries and through time. This
argument was based on two main contentions. Firstly, average financial ratios are
inconsistent across industries and reflect the relative efficiencies of production
commonly employed in those industries. The second is that average financial ratios
are inconsistent throughout time as a result of variable industry performance due to
economic conditions and other factors. Platt and Platt (1990) argued that firms from
different industries or different time periods could not be analysed without some form
of industry adjustment. In this study both raw and industry adjusted financial ratios
were used to determine the benefits of industry adjustment.
There are four different model specifications. One was based on raw financial
ratios for the single year prior to the sample period (the Single Raw Model). Another
was based on averaged raw financial ratios for the two years prior to the acquisition
period (the Combined Raw Model). A third specification was based on industry
adjusted financial ratios for the single year prior to the sample period (the Single
Adjusted Model), while the fourth was based on averaged industry adjusted financial
ratios for the two years prior to the sample period (the Combined Adjusted Model).
The purpose of using averages was to reduce random fluctuations in the financial
ratios of the firms under analysis, and to capture permanent rather than transitory
values. This approach was proposed by Walter (1994).
Most researchers used industry relative ratios calculated by scaling firms’
financial ratios using the industry average defined by equation [4] below. Under this
procedure all ratios were standardised to unity. Industry relative ratios such as ROA
or ROE that were greater than unity indicated industry overperformance, while those
less than unity were consistent with underperformance. Problems were encountered
when the industry average value was negative. In this case, those firms that
underperformed the industry average also had industry relative ratios greater than one.
This was the result of a large negative number being divided by a smaller negative
5 That is, the ratio A11/TP1 in Table 2.
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number. Additionally, those firms that overperformed the negative industry average
ratio, but still retained a negative financial ratio, had a ratio less than one. This
ambiguity in the calculation of industry relative ratios had implications for those
models in this study that included variables with negative industry averages for some
ratios. This problem may explain the inability of researchers in the recent literature to
accurately predict target and nontarget firms that utilised industry adjustments and
may have caused the Barnes (1999) model to predict no takeover targets at all.
An alternative methodology was implemented to account for negative industry
averages. Equation [5] below uses the difference between the individual firm’s ratio
and the industry average ratio, divided by the absolute value of the industry average
ratio. As a result all ratios are standardised to zero rather than one. Problems relating
to the sign of the industry relative ratio are also corrected. Underperformance of the
industry results in an industry relative ratio less than zero, with overperformance
returning a ratio greater than zero. This approach is similar to the variable scaling
methods widely documented in the Neural Network prediction literature. It was used
for the two models based on industry relative variables with industry adjustment
based on the 24 industry classification from the old ASX.
4.4 Calculation of Optimal Cutoff Probabilities for Classification
In the case of a logit model, predictive output for an input sample of the
explanatory variables is a probability with a value between 0 and 1. This is the
predicted probability of an acquisition offer being made for a specific firm within the
prediction period. What is needed is a method to convert these predicted probabilities
of an acquisition offer into a binary prediction of becoming a target or not. These
methods are known as optimal cutoff probability calculations and two main
methodologies were implemented in this study.
4.4.1 Minimisation of Error Probabilities (Palepu, 1986)
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In order to understand the calculation of the optimal cutoff probability, what is
needed is an understanding of Type 1 and Type 11 errors. A Type 1 error occurs when
a firm is predicted to become a takeover target when it does not (outcome A01 in
Table 2 below), while a Type 11 error occurs when a firm is predicted not to become
a target but actually becomes a target (outcome A10). Palepu (1986) assumed that the
cost of these two types of errors were identical. To calculate the optimal cutoff
probability, he used histograms to plot the predicted probabilities of acquisition offers
for targets and nontargets separately on the same graph. The optimal cutoff
probability which minimised the total error rate occurs at the intersection of the two
conditional distributions. Firms with predicted probabilities of acquisition offers
above this cutoff were classified as targets and those with probabilities below the cutoff
classified as nontargets.
Table 2 An outcome matrix for a standard classification problem
Predicted Outcome
Actual Outcome NonTarget (0) Target (1) Total
NonTarget (0) A00 A01 TA0
Target (1) A10 A11 TA1
Total TP0 TP1 T
4.4.2 Minimisation of Error Costs (Barnes, 1999)
Palepu (1986) assumed equal costs of Type 1 and Type 11 errors. However, it has
been suggested that, due to investment being less likely in predicted nontargets, the
cost of investing in the equity of a firm which did not become a takeover target (Type
1 error) was greater than the cost of not investing in the equity of a firm that became a
takeover target (Type 11 error). Accordingly, Barnes (1999) proposed minimisation of
the Type 1 error in order to maximise returns from an investment in predicted targets.
From Table 2, it can be seen that the minimisation of Type 1 error is equivalent to the
minimisation of the number of incorrectly predicted targets, A01, or alternatively, the
maximisation of the number of correctly predicted targets, A11. It follows that, a cutoff
probability is needed to maximise the number of predicted targets in a portfolio
that became actual targets. This involved maximisation of the ratio of A11 to TP1 in
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Table 2. Figure 2 below is an idealized representation of the Type 1 and Type 2 errors
associated with the Palepu and Barnes cutoff probability methodologies.
As the purpose of this paper was to replicate the problem faced by a practitioner,
unawareness of the actual outcomes of the prediction process was assumed. Further,
Figure 2 Idealized Palepu and Barnes Cutoff Probabilities
the probabilities that companies will become targets were derived from a prediction
model estimated using estimation data on known targets and nontargets. The
companies for which these probabilities are calculated comprised the Prediction
Sample (recall Table 1).
For the calculation of the optimal cutoff probability according to Palepu, a
histogram of predicted acquisition offer probabilities for targets and non targets was
created from the Estimation Sample, and followed the error minimisation procedure
detailed above in section 4.4.1. To calculate the optimal cutoff under the Barnes
methodology outlined in section 4.4.2, the ratio of A11/ TP1 for all cutoff probabilities
between 0 and 1 was calculated to determine the maximum point. A simple grid
search from 0 to 1 in increments of 0.05 was used.
The classification and prediction accuracies under these two methods of
calculating cutoff probabilities was compared for all four models considered in this
study.
NonTargets
Targets
Estimated Acquisition Offer Cutoff Probabilities for NonTargets and Targets
PALEPU CUTOFF
BARNES CUTOFF
Type 2
Error
Type 1
Error
Relative Frequency of NonTargets and Targets
Targets
NonTargets Targets
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5. Results
5.1 Multicollinearity Issues
An examination of the correlation matrix and Variance Inflation Factors (VIFs) of the
Estimation Sample indicated that five variables needed to be eliminated. They are
listed in Table 3. That these variables should contribute to the multicollinearity
problem was not a surprise considering the presence of the large number of potential
explanatory variables measuring similar attributes suggested by the hypothesised
motivations for takeover. These variables have correlation coefficients that exceeded
0.8 or VIFs that exceeded 10. Exclusion of these five variables eliminated significant
correlations in the Variance/Covariance matrix, along with reduction of the VIF
values of all the remaining variables to below 10. The resultant reduced variable set
was used in the backward stepwise logit models estimated and reported in the
following subsection.
Table 3 Variables Removed Due to Multicollinearity
ROE (NPAT/Shareholders Equity – Outside Equity Interests)
FCF/Total Assets
Current Ratio (Current Assets/Current Liabilities)
(Current Assets – Current Liabilities)/Total Assets
Total Liabilities/Total Assets
5.2 Backward Stepwise Regression Results
Using the remaining variables after controlling for multicollinearity, backward
stepwise logistic regressions were performed for each of the four model
specifications. Consistent with the methodology of Walter (1994), the significance
level for retention of variables in the analysis was set at 0.15. The results for these
models that were estimated using a common set of target and nontarget firms are
presented in Tables 4 to 7, with the results for the combined adjusted model in Table
7 described in more detail in the following subsection.6
The backward stepwise analysis for this model required seven steps, eliminating
six of the fifteen starting variables, while retaining nine significant variables. These
6 Detailed results for each of the models represented in Tables 4 to 7 are available from the authors on request.
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Table 4 Backward Stepwise Results for Single Raw Model
Variable Parameter
Estimate Prob > Chi Sq
Intercept 13.14 ( Chi Sq
Intercept 0.58 (0.02)
Asset Turnover (Net Sales/Total
Assets) 0.59 (0.03)
Capital Expenditure/Total Assets 0.34 (0.07)
Dividend Payout Ratio 0.22 (0.07)
Long Term Debt/Total Assets 0.21 (0.11)
Ln (Total Assets) 12.07 ( Chi Sq
Intercept 12.36 ( Chi Sq
Intercept 0.04 (0.92)
ROA (EBIT/Total Assets – Outside Equity
Interests) 0.28 (0.09)
Asset Turnover (Net Sales/Total Assets) 0.54 (0.05)
Capital Expenditure/Total Assets 0.69 (<0.01)
Quick Assets/Current Liabilities
(Current Assets – Inventory)/Current Liabilities 0.93 (0.02)
Dividend Payout Ratio 0.34 (0.02)
Long Term Debt/Total Assets 0.32 (0.07)
Merger Wave Dummy 0.59 (0.06)
Ln (Total Assets) 13.34 (<0.01)
Net Assets 0.21 (0.07)
results provided evidence concerning six of the eight hypothesised motivations for
takeover discussed previously in Section 3.
The growth resource mismatch hypothesis was only significant in the two adjusted
models. This suggested that growth should be measured relative to an industry
benchmark when attempting to discriminate between target and nontarget firms.
5.3 Classification Analysis
While the analysis of the final models was of theoretical interest, the primary aim of
this paper was to evaluate their classification accuracy. For the purposes of
classification, the models were reestimated using the Estimation Sample with all
variables included. The complex relationships between all the variables were assumed
to provide us with the ability to discriminate between target and nontarget firms.
Using financial data from 2001 and 2002, the models were estimated on the basis of
62 targets matched with 62 nontargets where the targets were identified between
January, 2003 and December, 2004. Following estimation of the model, an insample
fit was sought for the entire sample of the 1060 firms reporting 2001 and 2002
financial data. To proceed with classification, we derived a cutoff probability using
20
the methods of Palepu (1986) and Barnes (1999). The graph presented in Figure 3
focuses on the combined adjusted model and the Palepu cutoff point. Using a bin
range of 0.05, it showed the histograms required for the calculation of the cutoff
probability using the Palepu methodology was approximately 0.675. This is the
probability corresponding to the highest point of intersection of the plots of the
estimated acquisition probabilities for target and nontarget companies.
Figure 3 Cutoff Calculations using the Palepu methodology and 0.05 histogram
bin increments.
Table 8 Summary of optimal cutoff probabilities for all models under both
methodologies.
Optimal Cutoff Methodology
Probabilities Palepu Barnes
Single Raw Model 0.725 0.85
Single Adjusted Model 0.725 0.90
Combined Raw Model 0.850 0.95
Combined Adjusted Model 0.675 0.95
The optimal cutoff probabilities derived by using both the Barnes and Palepu
methodologies for all four models are reported in Table 8. The optimal cutoff
21
probabilities calculated using the Barnes methodology were significantly larger than
the cutoffs calculated under the Palepu methodology for all models.7
Table 9 below shows the outcome of the application of all of four models to the entire
Estimation Sample based on a cutoff derived under the Barnes approach. Included in
this table are the outcome matrices for each of the models. An outcome of 0 indicated
that the firm was not a target or was not predicted to be a target in the sample period.
A value of 1 indicated that a firm was predicted to be, or become a target in the
sample period. On the basis of these outcome matrices, a number of performance
measures were generated.
The first measure was the Concentration Ratio. This is a measure of Predictive
Accuracy measure of the model and corresponds to the Maximum Chance Criterion.
It is the proportion of actual targets that formed the portfolio of predicted target firms
for each of the models and was represented by the ratio A11/TP1 from the outcome
matrix depicted previously in Table 2. The next measure indicated the expected
accuracy under a chance selection of takeover targets within the sample period
(TA1/T). It measured the extent to which the model exceeded the accuracy expected
under a chance selection and quantified the Proportional Chance Criterion. The last
measure is a measure of the accuracy of the model relative to chance and is calculated
by dividing the first ratio by the second and then subtracting unity. All three measures
were expressed as a percentage. An examination of the statistics corresponding to
these measures for all four models in Table 9 indicated that, for the estimation sample
with a Barnes cutoff, the combined raw model was the most accurate. Of the 80 firms
that this model predicted to become takeover targets in the estimation period, 19
actually became targets. This represented a prediction accuracy of 23.75%. When
taken relative to chance, this accuracy exceeded the benchmark by 305%.
For the purpose of comparison, the classification results for the cutoff
probabilities calculated using the Palepu cutoff points are presented in Table 10. As
was the case when the Barnes methodology was used to determine the cutoff values
for classification, the Palepu approach realised similar results. The combined raw
model was again the most accurate model for prediction with a predictive accuracy of
19.59% and a relative to chance figure of 234.3%. However, as was the case for all
four models, the use of this cutoff probability approach significantly reduced the
7 As is noted in following tables, this is an explanation for the smaller number of predicted targets under this
methodology.
22
Table 9 Outcome Matrices for all models for classification of Estimation
Sample (Barnes cutoff probability)
ESTIMATION SAMPLE
Predictive Accuracy
Single Raw Model (Cutoff = 0.85
probability) †† Chance Accuracy
Actual Outcome
Predicted
Outcome Relative to Chance
0 1 Total
0 874 124 998 97.00% 94.15% 3.03%**
1 27 35 62 22.01% 5.85% 276.24%**
Total 901 159 1060
Single Adjusted Model (Cutoff
probability = 0.90) ††
Actual Outcome
Predicted
Outcome
0 1 Total
0 906 88 994 96.18% 94.13% 2.18%**
1 36 26 62 22.81% 5.87% 288.59%**
Total 942 114 1056
Combined Raw Model (Cutoff
probability = 0.95) ††
Actual Outcome
Predicted
Outcome
0 1 Total
0 935 61 996 95.60% 94.14% 1.55%**
1 43 19 62 23.75% 5.86% 305.29%**
Total 978 80 1058
Combined Adjusted Model (Cutoff
probability = 0.95) ††
Actual Outcome
Predicted
Outcome
0 1 Total
0 938 56 994 95.33% 94.13% 1.27%*
1 46 16 62 22.22% 5.87% 278.54%**
23
Total 984 72 1056
†† Indicates that the overall predictions of the model are significantly better than chance at the 1%
level of significance according to the Proportional Chance Criterion.
** Indicates that the prediction of targets or non targets individually is significantly greater than chance
at the 1% level of significance according to the Maximum Chance Criterion.
* Indicates that the prediction of targets or non targets individually is significantly greater than chance
at the 5% level of significance according to the Maximum Chance Criterion.
Table 10 Outcome Matrices for all models for classification of Estimation
Sample (Palepu cutoff probabilty)
ESTIMATION SAMPLE
Predictive
Accuracy
Single Raw Model (Cutoff probability = 0.725) †† Chance Accuracy
Actual Outcome Predicted Outcome
Relative to
Chance
0 1 Total
0 812 186 998 97.83% 94.15% 3.91%**
1 18 44 62 19.13% 5.85% 227.01%**
Total 830 230 1060
Single Adjusted Model (Cutoff probability = 0.725)
††
Actual Outcome Predicted Outcome
0 1 Total
0 787 207 994 97.52% 94.13% 3.60%**
1 20 42 62 16.87% 5.87% 187.39%**
Total 807 249 1056
Combined Raw Model (Cutoff probability = 0.85) ††
Actual Outcome Predicted Outcome
0 1 Total
0 840 156 996 97.22% 94.14% 3.27%**
1 24 38 62 19.59% 5.86% 234.30%**
Total 864 194 1058
Combined Adjusted Model (Cutoff probability =
0.675) ††
Actual Outcome Predicted Outcome
24
0 1 Total
0 749 245 994 97.53% 94.13% 3.61%**
1 19 43 62 14.93% 5.87% 154.34%**
Total 768 288 1056
†† Indicates that the overall predictions of the model are significantly better than chance at the 1%
level of significance according to the Proportional Chance Criterion.
** Indicates that the prediction of targets or non targets individually is significantly greater than chance
at the 1% level of significance according to the Maximum Chance Criterion.
Concentration Ratio and, therefore, the classification accuracy of the models under
the Maximum Chance Criterion. Interestingly, while the Palepu methodology did
improve the correct classification of targets accurately predicted (A11), in doing so, it
also predicted a large number of nontarget firms to become targets (A01).
The Barnes methodology focused on the maximisation of returns from an
investment in predicted targets. Rather than being focused on the prediction of a large
number of targets accurately, it focused on the improvement in the proportion of
actual targets in the portfolio of predicted targets. Accordingly, there are a smaller
number of targets predicted under the Barnes methodology. As previously noted in
Section 4.3.2, the Barnes methodology coincided more with the spirit of the
Maximum Chance Criterion rather than the Proportional Chance Criterion.
According to the Proportional Chance Criterion, all four models were able to
jointly classify targets and nontargets within the estimation period significantly better
than chance. Further, as revealed by the Maximum Chance Criterion, all models also
classified targets alone significantly better than chance but on an individual basis.
Overall, these results indicated high model classification ability. This was expected
given that all targets in the estimation sample were used in the estimation of the
model parameters.
5.4 Classification in the Prediction Period
The next step of the analysis was to assess the predictive abilities of our models
using the Prediction Sample. Of the total 1054 firms in this sample, 108 became
targets during the prediction period. Panel A and Panel B of Table 11 report the
predictions from the four estimated models using both the Barnes and Palepu cutoff
probability approaches. Under the Barnes cutoff methodology, calculation of the
Concentration Ratio indicated that the combined raw and combined adjusted models
performed best of all of the models. This confirmed the results from the estimation
25
period. The combined adjusted model predicted 125 firms to become targets during
the prediction period, during which 25 actually became targets. Prediction accuracy
was 20%. Under a chance selection, we would have expected only 10.30% of those
companies predicted to become targets to actually become targets. This meant that the
model exceeded a chance prediction by 94.18%. While Walter (1994) was able to
predict 102% better than chance, other studies including that of Palepu (1986) and
Barnes (1999) were unable to achieve this level of accuracy.
Industry adjustment increased predictive ability for both the single and combined
models, suggesting that stability may be achieved through these adjustments.
Furthermore, the combination of two years of financial data also appeared to improve
predictive accuracy. This suggests that this adjustment eliminates random fluctuations
in the financial ratios being used as input to the prediction models.
Table 11 Prediction results for all four models using the Prediction Sample and
both Barnes and Palepu cutoff probabilities
PREDICTION SAMPLE
(Barnes cutoff probabilities)
Panel A
PREDICTION SAMPLE
(Palepu cutoff probabilities)
Panel B
Predictive Chance Relative to
Accuracy Accuracy Chance
Predictive Chance Relative to
Accuracy Accuracy Chance
Single Raw Model
(Cutoff probability = 0.90)
15.09% 10.25% 47.22%*
Single Raw Model
(Cutoff probability = 0.725)
16.83% 10.25% 64.20%*
Single Adjusted Model
(Cutoff probability = 0.95)
15.79% 10.27% 53.75%*
Single Adjusted Model
(Cutoff probability = 0.725)
17.79% 10.27% 73.22%*
Combined Raw Model
(Cutoff probability = 0.85)
17.65% 10.25% 72.29%**
Combined Raw Model
(Cutoff probability = 0.85)
17.51% 10.25% 70.83%**
Combined Adjusted Model †
(Cutoff probability = 0.95)
Combined Adjusted Model
(Cutoff probability = 0.675)
26
20.00% 10.30% 94.18%**
16.77% 10.30% 62.82%**
† Indicates that the overall predictions of the model are significantly better than chance at the 5% level
of significance according to the Proportional Chance Criterion.
** Indicates that the prediction of targets or non targets individually is significantly greater than chance
at the 1% level of significance according to the Maximum Chance Criterion.
* Indicates that the prediction of targets or non targets individually is significantly greater than chance
at the 5% level of significance according to the Maximum Chance Criterion.
The prediction results for the Palepu derived cutoff probabilities are presented in
Table 11 (Panel B). By a comparison of Panel A with Panel B in Table 11, it can be
seen that when the Barnes cutoff probability methodology was used for the single
models, the Concentration Ratio decreased relative to that of Palepu. However, it
improved the ratio for the combined models. This result was reversed when the
Palepu cutoff probability approach was used. Further, given the better performance
of the combined models using the estimated sample, this provided the rationale for the
use of the combined modes and the Barnes methodology to calculate the optimal cutoff
probabilities.
A different variable selection approach was implemented in an attempt to improve
the accuracy of the two best predictive models, namely, the combined raw model and
the combined adjusted model. A number of variables that had been insignificant in all
estimated models were removed and the estimation and classification procedures
repeated on the remaining variable data set.8 The classification results for the
Table 12 Application of improved models to both the Estimation Sample and
Prediction Sample.
ESTIMATION SAMPLE
(Barnes cutoff probabilities)
PREDICTION SAMPLE
(Barnes cutoff probabilities)
Predictive Chance Relative to
Accuracy Accuracy Chance
Predictive Chance Relative to
Accuracy Accuracy Chance
Combined Raw Model ††
Combined Raw Model
8 The variables removed were: Growth in EBIT over the past year, Market to book ratio (Market Value of
Securities/Net Assets), and the Price/Earnings Ratio.
27
(less variables 7,9 and 10)
24.66% 5.86% 320.77%**
(less variables 7,9 and 10)
17.54% 10.25% 71.22%**
Combined Adjusted Model ††
(less variables 7,9 and 10)
24.56% 5.87% 318.34%**
Combined Adjusted Model
(less variables 7,9 and 10)
22.45% 10.30% 118.05%**
†† Indicates that the overall predictions of the model are significantly better than chance at the 1%
level of significance according to the Proportional Chance Criterion.
** Indicates that the prediction of targets or non targets individually is significantly greater than chance
at the 1% level of significance according to the Maximum Chance Criterion.
* Indicates that the prediction of targets or non targets individually is significantly greater than chance
at the 5% level of significance according to the Maximum Chance Criterion.
application of this model to both the estimation and prediction periods are given in
Table 12.
The elimination of variables resulted in significant improvements in the insample
classification accuracy using the estimation sample, with accuracies exceeding chance
by well over 300%. This improvement in classification accuracy was maintained into
the prediction period. The accuracy of the combined adjusted model was 118%
greater than chance. This represented a level statistical accuracy above that reported
by any similar published study in the area of takeover prediction. These results can be
used to refute the claims of Barnes (1999) and Palepu (1986) that models cannot be
implemented which achieved predictive accuracies greater than chance. They further
confirm the results of Walter (1994) while using a wider sample of firms.
The combined adjusted model significantly outperformed the other models for
predictive purposes, suggesting that this is the most appropriate model for the
application of logit analysis to predict takeover targets in the Australian context.
5.5 Economic Outcomes
Although the above methodology provided us with a statistical assessment of
model performance, it had nothing to say about the economic usefulness of the model.
Palepu (1986), Walter (1994), and Wansley et al. (1983) all implemented an equally
weighted portfolio technique to assess whether their predictions of takeover targets
were able to earn abnormal risk adjusted returns. The conclusion we drew from the
results of the abovementioned studies was that a positive abnormal return was not
guaranteed from an investment in the targets predicted from these models. The
portfolios of predicted targets in two of these studies were unrealistically large at 91
28
in the case of Walter, and 625 in the case of the Palepu studies. Due to the effect of
transaction costs on returns, practitioners would be likely to limit themselves to
smaller portfolios in the order of 10 to 15 stocks.
To make an economic assessment of the economic usefulness of our modelling
approach, we replicated a modified version of the Palepu (1986) and Walter (1994)
portfolio technique using our predicted targets. Only commonly predicted targets
across all models were included in the portfolio analysis for two reasons. The first
was to reduce the number of stocks to a manageable level, and second, to improve the
ratio of actual targets in the portfolio. Further, we rejected the equally weighted
portfolio approach on the grounds that it was an inefficient strategy for an informed
investor who possessed results from our modelling. We reasoned that such an investor
could most likely take a leveraged position through derivatives.
The portfolio analysed in this study comprised of 13 predicted target firms of
which 5 actually became targets. While this is a good result per se, we sought to
quantify the economic benefit from an investment in these stocks. The portfolio of
predicted targets was held for the entire prediction period of 2005 and 2006 that
constituted 503 trading days. The first column of Table 13 below presents the
percentage of Cumulative Average Abnormal Return (CAAR%) at 20 day intervals
during the prediction period.
Table 13 Cumulative Average Abnormal Returns (CAARs) for the portfolio of
commonly predicted takeover targets for the Prediction Period of 2005
and 2006
Day Portfolio
(13 Stocks)
Actual Targets
(5 Stocks)
Day Portfolio
(13 Stocks)
Actual Targets
(5 Stocks)
CAAR (%) CAAR (%) CAAR (%) CAAR (%)
20 1.38 5.36 280 4.77 29.64
40 2.84 10.50 300 4.67 32.47
60 1.98 5.58 320 3.08 33.53
80 2.53 6.11 340 0.73 31.96
100 5.52 1.15 360 2.89 26.62
120 4.40 25.16 380 5.28 33.72
140 3.06 17.83 400 6.99 32.02
160 4.38 20.70 420 9.78 37.43
180 5.51 24.79 440 11.33 40.22
200 9.90 34.82 460 57.44 46.00
29
220 7.51 34.87 480 58.38 47.27
240 6.40 29.31 500 68.90 52.12
260 5.04 27.71 503 68.67* 50.86^
The full prediction period CAAR of 68.67% was significantly greater than zero at
the 1% level of significance under the Standard Abnormal Return [SAR]
methodology of Brown and Warner (1985). We recognised that these results could
have been potentially driven by actual nontarget firms within the portfolio of
predicted targets. This would suggest that the abnormal return was the result of the
chance selection of overperforming nontarget firms, rather than an accurate
selection of target firms. To answer this question, the same CAAR calculation was
applied to the subportfolio of firms that actually became targets.
The full period CAAR of 50.86% was also significantly greater than zero at the
1% level. This supported the proposition that the CAAR of the portfolio was driven
by the performance of the actual targets within the portfolio.
Table 13 also indicated that the CAAR for the portfolio increased significantly
between days 440 and 460. This result was driven by the extremely positive returns
on the stock ATM which was a nontarget firm predicted by the models to be a target.
After repeating the portfolio analysis with this stock eliminated from the portfolio of
predicted targets, it was found that a significant positive abnormal return of 25%9 was
realized for the entire prediction period.
Another observation from Table 13 was that the CAAR was not positive (nor
significant) for either of the portfolios early in the prediction period. From the second
column of Table 14, the CAAR after 100 days was negative. Further, after 340 days
the CAAR was indistinguishable from zero. The real gains to the portfolio were made
as mergers or acquisitions were announced and completed in the latter stages of 2006,
highlighting the fact that the portfolio had to be held for the entire prediction period in
order to realise the potential available returns.
6. Conclusion
The main finding of this paper was that the combined adjusted model which was
based on averaged, industry adjusted financial ratios across the sample period,
9 t = 9.63
30
emerged as a clear standout with regards to predictive accuracy. Further, the
implementation of industry adjusted data, as described in Section 4.3.3 of this paper,
significantly improved the classification accuracy of all the models bar one that were
analysed in both the estimation and prediction periods. Additionally, this paper
provided evidence that the inclusion of the Barnes methodology for calculation of the
optimal cutoff point significantly improved classification accuracy and enabled the
successful use of logit models to predict takeover targets within the Australian
context. The accuracy of the single best model in this paper exceeded a chance
selection by 118% and represented the highest reported accuracy for a logit model.
Another important finding of this paper resulted from the examination of a
portfolio of predicted targets. We demonstrated that an investment in the predicted
targets, that were common across the logit models, resulted in significant Cumulative
Average Abnormal Returns (CAARs) being made by an investor. Several steps were
undertaken to ensure that this result was robust against returns on predicted nontarget
stocks. This suggests that the abnormal returns made are based on the accuracy of the
predictions common to the logit models analysed in this study rather than any chance
selection. We believe our results provide evidence in favour of the proposition that an
abnormal return can be made from an investment in the commonly predicted takeover
targets from the four logitbased models analysed in this paper.
There is a wealth of evidence in existence that suggests that combining forecasts
from different models improves forecasting ability. This is an obvious direction for
future research and may well be achieved either by a logit and MDA combination, or
through the inclusion of a neural network approach to predict targets.
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