Dependence of the multiplier in the transaction on the magnitude of the buyer multiplier

We use a multivariate OLS regression setting to determine the impact of acquirer valuation on deal premium and deal multiple. We run the regression of takeover premium on a set of variables that represent acquirer valuation, a set of control variables such as target valuation, deal characteristics, target and acquirer financial characteristics and macroeconomic and industry characteristics. To account for possible differences in deal premium and deal multiple across various industries, we include in a set of control variables monthly GICS Level 2 industry multiples provided by S&P 500 set of indices.

For the first sample we build the following regression:

2.1.1 Dependent variable

Deal premium is the percentage difference between acquirer offer price per share over target share price 30 days before the announcement date. Such definition of the premium is consistent with numerous previous studies (Alexandridis, 2013; Bruslerie, 2013; Davis and Madura, 2017; Lai, 2019). Other approach is to measure the cumulative abnormal return (CAAR) on target's stock over particular window around deal announcement. However, we want to find out the relationship between acquirer valuation and the consideration actually paid in the form of deal premium or deal multiple, that is why we use the first approach. Premiums are used in its natural log form in the regression.

In the following paragraphs we describe how independent and control variables are calculated and state positive (+) or negative (-) expected signs in the brackets consistent with hypotheses developed in the first chapter.

2.1.2 Independent variables

Here and thereafter we provide calculation of acquirer and target valuation metrics together. Acquirer valuation metrics are used as independent variables in our regression representing the primary area of interest. Target valuation metrics are used together with acquirer valuation metrics and serve as control variables. Acquirer P/BV (+) and Target P/BV (-) is the market-to-book ratio where market capitalization is taken 30 days before the announcement date, book value of equity is taken at the last reporting period prior to the takeover announcement. We use two variations of this multiple in a set of regressions: P/BV and normalized P/BV which is P/BV divided by P/BV of GICS Level 2 S&P 500 Index during the month preceding the month of deal announcement.

Acquirer P/V (+) and Target P/V (-) is the market-to-value ratio where market capitalization is taken 30 days before the announcement date, fundamental value of equity is the predicted value from ordinary least squares (OLS) regression where market capitalization is regressed on the set on company fundamentals and year and industry dummy variables (described further).

To measure value-generating potential we use Acquirer ROE/CoE (-) and Target ROE/CoE (+) which is the ratio of return on equity which is taken at the last reporting period prior to the takeover announcement over industry cost of equity calculation (described further).

Acquirer Growth/P (-) and Target Growth/P (+) is the ratio of value of growth opportunities over the market capitalization 30 days before the announcement date. Value of growth opportunities is backed out using fundamental value and value of assets in place (described further).

2.1.3 Control variables

Deal characteristics. Stake acquired (+) is the equity stake acquired in an M&A deal. Form of payment (+) is the dummy variable that is equal to 1 if consideration paid by an acquirer was in the form of cash, 0 if in the form of stock of mixed payment. Unsolicited offer (+) is the dummy variable that is equal to 1 if an acquirer made an unsolicited offer to a target meaning a target was not actively searching for a buyer and 0 otherwise, serving as a hostility proxy.

Target and acquirer financial characteristics. Target (-) and acquirer (+) size is the natural logarithm of target's market capitalization 30 days before the announcement date. Target (?) and acquirer (-) leverage is the ratio of target's total debt at the last reporting period to the market capitalization 30 days before the announcement date. Target (-) and acquirer (+) cash and other liquid assets (% of total assets) is the ratio of target's cash and short-term investments to total assets at the last reporting period. Target 52-Week High (-) is the ratio of 52-week high stock price to stock price 30 days before deal announcement.

Macroeconomic and industry characteristics. Same industry dummy (?) is equal to 1 if GICS Level 2 code is the same for target and acquirer and 0 otherwise. To account for market-wide misvaluation we use normalized S&P index P/E (-) which is the ratio of S&P 500 Index P/E during the month of deal completion to the average value of S&P 500 Index P/E during 2010-2019. To account for industry-wide valuation we use target (-) and acquirer (+) industry multiples P/BV and P/Earnings during the month of deal announcement. Target (+) and acquirer (-) industry ROE is ROE of respective target and acquirer GICS Level 2 S&P 500 Indices during the month of deal announcement. Target (-) and acquirer (-) industry cost of equity which is calculated using monthly yield-to-maturity of the S&P U.S. Treasury Bond 10-Year Index as the risk-free rate from Bloomberg database, yearly historical implied US equity risk premiums from Damodaran website and 5-year weekly raw betas of GICS Level 1 set of indices against S&P Index from Bloomberg database.

For the second sample of deals with private targets we build the following regression:

Dependent variable: deal normalized multiple

Deal normalized multiple is the ratio of deal P/BV multiple to GICS Level 2 S&P 500 Industry P/BV multiple during the month of deal completion. Deal P/BV is the ratio of implied equity value to book value of equity at the last reporting period before deal announcement. Implied equity value is the total consideration paid to target shareholders.

Independent variables in the subset of deals with private targets include only variables concerning acquirer valuation: acquirer P/BV, P/Value, ROE/CoE and Growth/P. Control variables are the same as within the first subset with several exceptions: target and acquirer size is the natural logarithm of target's total assets instead of market capitalization, target and acquirer leverage is the ratio of total debt to total equity at the last reporting period, target 52-Week High is not calculated.

We also build the auxiliary regression to break down target and acquirer market value of equity into value of assets in place, value of growth opportunities and misvaluation. To do this we adopt methodology applied by Bekkum (2011) based on Miller and Modigliani (1961) who determined that firm fundamental equity value (PF) can be partitioned into the value of a firm's assets in place (VAIP) and the present value of future investments in growth opportunities (VGO):

Market value (P) is the sum of fundamental equity value (PF) and misvaluation component (XSP):

To estimate fundamental equity value of the firm we adopt methodology used by Rhodes-Kropf et al. (2005) and Bekkum (2011). Fundamental equity value in this methodology is the predicted value from ordinary least squares (OLS) regression where market capitalization is regressed on the set on company fundamentals and year and industry dummy variables. It is derived from the following regression:

Where P is the target market capitalization 30 days before deal announcement, Book is the book value at the last reporting period prior to deal announcement, NI is the absolute value of net income at last reporting period, I the dummy variable for negative income that allows to include negative observations in the sample, LEV is the ratio of target's total debt at the last reporting period to the market capitalization 30 days before the announcement date, CoE is industry cost of equity calculated as described earlier in section 2.1.3. Control variables. Year and industry dummies are used to control for differences in coefficients across time and different industries.

To estimate value of assets in place () we use economic profit model assuming no growth rate and constant discount rate. We take ROE, cost of equity and book value of equity at last reporting period:

Value of growth opportunities is backed out using fundamental value and value of assets in place:

Misvaluation component (XSP) is difference between market capitalization and fundamental value:

Using this method, we can expand our analysis of influence of acquirer Price/Book on deal premium and multiple and include such ratios as Price/Value where Value if fundamental equity value to capture company misvaluation, VGO/market capitalization to capture growth potential and ROE/CoE to capture value-generating potential.

Table 1 presents summary of dependent, independent and control variables used in regressions and hypotheses testing.

Table 1. Summary of variables

Variable name	Variable type	Calculation
Deal premium	Dependent	Offer price per share/ target share price 30 days before the announcement date
P/BV deal multiple	Dependent	Consideration paid/ target book value of equity at the last reporting period
P/BV deal multiple normalized	Dependent	P/BV deal multiple / GICS Level 2 S&P 500 Industry P/BV during the month of deal completion
Acquirer P/BV Target P/BV	Independent Control	Market capitalization 30 days before the announcement date/ book value of equity at the last reporting period prior to the takeover announcement
Acquirer P/BV normalized Target P/BV normalized	Independent Control	P/BV / P/BV of GICS Level 2 S&P 500 Index during the month preceding the month of deal announcement
Acquirer P/V Target P/V	Independent Control	Market capitalization 30 days before the announcement date / fundamental equity value (fitted value in the regression of market cap on fundamental characteristics)
Acquirer growth opportunities/ P Target growth opportunities/ P	Independent Control	(Fundamental equity value-Value of assets in place)/ Market capitalization 30 days before the announcement date
Acquirer ROE/CoE Target ROE/CoE	Independent Control	ROE at the last reporting period/ Cost of equity Cost of equity = YTM of S&P U.S. Treasury Bond 10-Year Index + S&P 500 Index GICS Level 1 industry beta * Implied equity risk premium (Damodaran data)
Acquirer size Target size	Control Control	Natural log of market capitalization 30 days before the announcement date
Acquirer leverage Target leverage	Control Control	Public targets: total debt at the last reporting period / market capitalization 30 days before the announcement date Private targets: total debt at the last reporting period / book value of equity at the last reporting period
Acquirer cash/assets Target cash/assets	Control Control	Cash &ST investments/ total assets at the last reporting period
Target % of 52-week High (%)	Control	Target stock price 30 days before the announcement date / 52-week high stock price
Stake acquired	Control	Equity stake acquired in the M&A deal
Unsolicited offer dummy	Control	1 - if bid was unsolicited 0 - otherwise
Cash payment dummy	Control	1 - if consideration was paid in cash 0 - if paid in stock or mixed
Industry relatedness dummy	Control	1 - if GICS 2 Level industry codes of target and acquirer coincide 0 - otherwise
Market-wide overvaluation	Control	S&P 500 Index P/E at the deal announcement month / S&P 500 Index P/E average 2010-2019
Industry valuation	Control	P/BV of GICS Level 2 S&P 500 Index during the month of deal announcement
Industry ROE	Control	Mean ROE of companies in GICS Level 2 S&P 500 Index during the month of deal announcement
Industry CoE	Control	YTM of S&P U.S. Treasury Bond 10-Year Index + S&P 500 Index GICS Level 1 industry beta * Implied equity risk premium (Damodaran data)

Source: author's analysis

2.2 Data overview

Data on completed M&A deals was obtained from S&P Capital IQ database. Data on industry multiples, S&P Index P/E, betas, US risk-free rates and equity risk premiums was obtained from the Bloomberg database. First sample includes 923 completed M&A deals in the US announced between 1st of January 2010 and 31st of December 2019. We applied following criteria to the sample:

M&A announced date: 01.01.2010-31.12.2019

Transaction status: closed

Target country of incorporation: USA

Buyer company type: public

Target company type: public

Transaction value: > $10 mln

Percent sought: > 50%

Target stock 1-month premium (%): between 0 and 200

Acquirer and target financials: market capitalization and book value of equity at last reporting period are not unknown

We take M&A deals conducted during the last 10 years since this period is relatively less studied by the scholars and present the period after the Financial crisis of 2007-2008. Some researchers (Ching, 2019) call the period from 2010 till present the seventh merger wave which is characterized by growing US GDP, low interest rates, low unemployment, expansion of stock multiples at the financial market together with growing corporate profits. We look at successfully closed transactions because we want to find out the relation between the actually paid price as measured by deal premium or deal multiple and acquirer and target valuation and withdrawn deals might have different relation between these characteristics. We look at transactions conducted with targets incorporated in the US, firstly, to ensure comparability of results with the existing research, secondly, because we want to compare results between samples with public and private targets and the US data will ensure higher data availability and more reliable conclusions resulting from bigger sample. As we want to measure relation between target and acquirer valuation and deal premium in the first sample, we require both acquirer and target to be public companies at the M&A closing date. The minimum transaction value is $ 10 mln since data on smaller deals is scarcer and less reliable. We explore deals where majority stake was acquired to ensure that deal premium and deal multiple include premium for control. We include the criteria for target stock 1-month premium to be greater than zero percent to exclude deals with financially distressed targets and fire sale and less than 200 percent to exclude corrupted data and special situations with financially distressed targets.

There is a total of 1038 completed deals (with transaction value of more than $ 10 mln and acquired stake more than 50%) between public acquirers and public targets during the examined period in the USA where consideration offered to shareholders is known. Applying further criteria to target stock premium and availability of acquirer and target financials decreases our sample to 923 deals.

Second sample includes 345 completed M&A deals in the US announced between 1st of January 2010 and 31st of December 2019. We applied following criteria to the sample:

M&A announced date: 01.01.2010-31.12.2019

Transaction status: closed

Target country of incorporation: USA

Buyer company type: public

Target company type: private

Transaction value: > $10 mln

Percent sought: > 50%

Acquirer financials: market capitalization and book value of equity are not unknown

Target financials: book value of equity at last reporting period is not unknown

There is a total of 4128 completed deals (with transaction value of more than $ 10 mln and acquired stake more than 50%) between public acquirers and private targets during the examined period in the USA where consideration offered to shareholders is known. The most restrictive criteria applied to second subset is availability of target book value of equity at last reporting period. We need this data to construct deal multiple P/BV, however, availability of private target financials is limited. That is why our second sample consists of 359 completed deals.

2.3 Descriptive statistics

First sample includes 923 completed M&A deals in the US announced between 1st of January 2010 and 31st of December 2019. From Table 2 we see that sectors with highest M&A activity during the chosen period are Financials (34% of total deals), IT (19%), Healthcare (15%) and Consumer (8%). High M&A activity in the financial sector was a response to intense competition from banks and non-banks, decelerating loan growth and necessity to carry out cost savings that would free up money for technology spending. Scale becomes more important as banks compete in a technology arms race. High M&A activity in IT sector was caused by the increasing importance of mobile technology, emergence of cloud computing and by the fact that companies' ever-increasing reliance on data analytics motivates confident firms to perform as acquirers at the M&A market. Factors behind high M&A activity in healthcare sector are strong demographic tailwinds such as overall population aging, sector's recession resistance, large addressable sub-markets, high industry fragmentation, innovation, and adoption of technology to address quality and efficiency demand. We also notice that sector structure is different for cash and stock deals: in the subsample of cash deals highest amount of deals is in IT sector (28%), healthcare (25%) and financials (11%), while in the subsample of stock deals highest amount of deals is in the financials (51%), IT (12%) and energy (10%).

Table 2. Number of announced deals distributed across sectors and years public (0) and private (1) targets

Source: author's calculations

From Table 3 we see that median deal premium decreased from 49% in 2010 to 37% in 2019 while P/E multiple of S&P 500 Index increased from 15.4x in 2010 to 20.0x in 2019 consistent with the hypothesis that higher stock market valuation leads to lower deal premiums. While in 2010 highest deal premiums were paid in financial sector (64%), IT (54%) and Healthcare (52%), in 2019 leaders changed- Healthcare (46%), Industrials (40%), Energy (40%)- while median premiums across all industries decreased.



Table 3. Median deal premiums across sectors and years (public targets)

Source: author's calculations

From the summary statistics in Table 4 for the first sample of deals between public acquirers and public targets in 2010-2019 we see that average deal premium was 42%: in stock deals average premium is 37% while in cash deals average deal premium is 48% consistent with hypothesis that deal premiums in cash deals are higher due to immediate tax implications for target shareholders. Average stake acquired is 99% consistent with our criteria to analyze deals where more than 50 percent stake was acquired to ensure that all deal premiums include control premiums and we do not have to control specifically for it. 43% of deals are cash deals while 57% of deals involve either stock or mixed form of consideration. Considering target and acquirer valuation we notice that targets have on overage higher P/BV and P/Value multiple, higher growth opportunities and lower value-generating potential than acquirers. It can be caused by the fact that targets find themselves on overage at the growth stage of life cycle which is characterized by high growth (and growth expectations embedded in multiples) and some of the targets are yet to reach profitability. We also notice that 81% of the deals were carried out in the same industry meaning the period from 2010 to 2019 was characterized by industry consolidations rather than conglomerate building and business diversification.

Second sample includes 359 completed M&A deals in the US announced between 1st of January 2010 and 31st of December 2019. Sectors with highest M&A activity during the chosen period are Financials (23%), Industrials (19%), IT (13%) and Healthcare (12%). Sectors with highest normalized P/BV deal multiples in 2019 include Consumer staples (3.1x), IT (1.9x) and Healthcare (1.4x) while sectors with lowest deal multiples include Industrials (0.7x) and Materials (0.98x).

From the summary statistics in Table 4 for the second sample of deals between public acquirers and private targets in 2010-2019 we see that average deal P/BV during the chosen period was 9.94x and normalized P/BV was 3.3x which is significantly higher than in the first sample with public targets (5.1x and 1.6x accordingly) and the difference between them is statistically significant. This is consistent with prior findings that state that private targets have higher bargaining power due to their concentrated ownership and less pressure from less informed outside investors. Acquirer's valuation is high based on normalized P/BV of 1.78x and P/Value of 1.37x and higher than for the first sample with public targets (1.5x and 1.3x accordingly) but the difference is not statistically significant. Contrary to the sample with public targets, in the second sample targets have higher value-generating potential than acquirers - ROE/CoE ratio is equal to 2.2 for targets vs 1.36 for acquirers, the difference is statistically significant which might indicate that private targets are generally more mature and profitable and better run, indicated by higher normalized deal multiple. While in the first sample public acquirers appear to buy young, fast-growing, and unprofitable targets, in the second sample acquirers buy more mature, profitable and well-run companies acquisition of which can result in high synergies. The percentage of cash deals in the second sample is lower - 27% in comparison with 43% in the first sample which might indicate that private targets are more willing to accept stock as form of consideration compared to public targets since shareholders of private targets are more willing to accept liquidity to cash out of their illiquid holdings. Acquirer and target leverage and cash/assets is on similar levels with targets having slightly higher leverage and is similar to the sample with public targets. 75% of deals is carried out in the same industry compared to 81% deals in the first sample which goes against prior findings (Capron and Shen, 2007) which state that due to less informational transparency acquirers prefer buying private targets in the same or related industry and public targets when entering new industries. We also notice that public acquirers in the first sample are bigger and more profitable based on ROE/CoE and they acquire on average larger targets. Table 30 -Table 32 in the Appendix to Chapter 2 provide further descriptive statistics on two samples.

Table 4. Descriptive Statistics of two samples (deals with public and private targets)

	Public targets	Private targets
Variable	Obs	Mean	Std.Dev.	Obs	Mean	Std.Dev.
Deal_premium	923	.419	.306
Deal_pbv	882	5.094	13.554	359	9.942	30.395
Deal_pbv_n~m	882	1.659	2.698	359	3.312	11.023
Acq_pbv	912	3.832	10.107	345	5.315	24.055
Acq_pbv_norm	912	1.459	3.841	345	1.776	5.57
Target_pbv	884	5.255	37.936
Target_pbv~m	884	1.945	17.252
Acq_PV	923	1.254	1.604	359	1.37	1.811
Target_PV	920	1.362	2.933
Acq_roecoe	900	1.538	2.485	331	1.166	2.626
Target_roe~e	848	.356	2.896	270	2.204	3.839
Acq_GOMC	900	1.162	1.346	325	1.36	1.516
Target_GOMC	846	1.739	2.059
Stake_acq	923	98.773	6.263	359	98.978	5.8
Cash_payment	923	.429	.495	359	0.27	0.445
Unsolicited	923	.789	.408	359	0.869	0.338
Acq_MC	923	22622.17	50231.02	359	2940.947	15300.34
Target_MC	920	2136.596	5684.503
Acq_assets	923	25057.95	61248.46	359	4014.977	16860.6
Target_ass~s	923	3168.181	10269.46	359	504.496	1386.148
Acq_lev	923	.532	1.059
Acq_lev_1	922	.217	.182	359	0.195	0.21
Target_lev	920	.649	1.55
Target_lev_1	920	.211	.638	221	0.227	0.239
Acq_cash	920	.124	.149	349	0.156	0.182
Target_cash	914	.193	.225	201	0.15	0.204
Target_52_~h	923	.821	.178
Same_ind	923	.811	.391	359	0.747	0.436
SP500_pe	923	18.165	2.464	359	17.648	2.404
SP500_pe_n~m	923	1.019	.138	359	0.99	0.135
Acq_ind_pb~d	923	2.897	2.006	359	3.104	1.865
Acq_ind_pb~m	923	1.058	.657	359	1.173	0.63
Target_ind~d	923	2.952	2.033	359	3.104	1.81
T~d_pbv_norm	923	1.078	.671	359	1.174	0.612
Acq_ind_roe	923	.154	.084	359	0.163	0.079
Target_i~roe	923	.155	.083	359	0.163	0.077
Acq_ind_coe	923	.083	.016	359	0.083	0.015
Target_i~coe	923	.083	.016	359	0.083	0.015

Source: author's calculations



Chapter 3. Empirical results

H1: Buyers with higher Price/Book buy targets with lower Price/Book

We conduct difference of means test (t-test) to test Hypothesis 1 on the sample of deals between public acquirers and public targets. Moreover, we conduct t-test for subsamples of cash and stock deals as we expect difference between Price/Book of buyers and targets might be more significant for stock deals than for cash ones. We use both two-sample t-test with equal and unequal variances (Welch's test).

For all deals null hypothesis saying that difference in means between Target P/BV and Acquirer P/BV is equal to zero is not rejected at 5% significance level and we do not find evidence that buyers with higher Price/Book buy targets with lower Price/Book (Table 5). For cash and stock deals separately null hypothesis about zero difference is also not rejected. We also test for difference in means between normalized by industry mean Price/Book multiples and do not reject null hypothesis. Therefore, although target Price/Book is higher than acquirer Price/Book in all samples, the difference is not statistically significant. Our findings are not consistent with prior findings of Rhodes-Kropf and Viswanathan (2005), Dong et al. (2006), Bekkum (2011).

Table 5. Difference in means tests (t-test) for acquirer and target P/BV

Source: author's calculations

H2: In deals where acquirer P/BV is higher than target P/BV, deal premium is higher than in deals where relationship is opposite

We conduct difference of means test (t-test) to test Hypothesis 2 on the sample of deals between public acquirers and public targets. We create dummy variable Higher_Acq_pbv which equals to 1 if acquirer P/BV is higher than target P/BV and 0 otherwise. We see that although mean premium for Higher_Acq_pbv = 1 is 42.4% while for Higher_Acq_pbv = 0 is 41.7%, the null hypothesis about zero difference in means is not rejected (Table 6). Therefore, we do not find prove that in deals where acquirers have P/BV higher than their targets, deal premiums are higher than otherwise.



Table 6. Difference in means tests (t-test) for deal premium in two groups

Source: author's calculations

H3: Buyer with higher Price-to-Value buy targets with lower Price-to-Value

We conduct difference of means test (t-test) to test Hypothesis 3 on the overall sample of deals between public acquirers and public targets, as well as on subsamples of cash and stock deals. We do not reject null hypothesis about zero difference in means between target and acquirer Price/Value in any test (Table 7). Our finding is not consistent with prior findings of Rhodes-Kropf and Viswanathan (2005), Dong et al. (2006), Bekkum (2011).

Table 7. Difference in means tests (t-test) for acquirer and target P/V

Source: author's calculations

H4: Buyers with less growth opportunities buy targets with more growth opportunities

We conduct difference of means test (t-test) to test Hypothesis 4 on the overall sample of deals between public acquirers and public targets. We reject null hypothesis about zero difference in means and we see that target growth opportunities are significantly higher than growth opportunities of the target (Table 8). Our findings are consistent with Rhodes-Kropf and Viswanathan (2005), Owen and Yawson (2010) and Davis and Madura (2017) and not consistent with Bekkum (2011).

Table 8. Difference in means tests (t-test) for acquirer and target growth opportunities

Source: author's calculations

H5: Buyers with higher value-creating potential (ROE/CoE) buy targets with lower value-creating potential (ROE/CoE)

We conduct difference of means test (t-test) to test Hypothesis 5 on the first sample of deals between public acquirers and public targets and on the second sample of deals between public acquirers and private targets. For the first sample we reject null hypothesis about zero difference in means (Table 9) and we see that ROE/CoE of acquirers is significantly higher than ROE/CoE of targets and that acquirers on average generate positive economic value (mean ROE/CoE is 1.53) while targets on average generative negative economic value - destroy value (mean ROE/CoE is 0.36). Our findings are consistent with life cycle stage theory and studies of Spence (1977), Wernerfelt (1985), Selling and Stickney (1989) and Anthony and Ramesh (1992). However, for the second sample (Table 10) we reject null hypothesis about zero difference in means and we see that ROE/CoE of acquirers is significantly lower than ROE/CoE of targets, and both acquirers and targets generate positive economic value which is consistent with findings of Owen and Yawson, 2010. The difference in test results between two samples might be explained by the fact that private targets are more mature than their acquirers and public targets generating positive economic value.

Table 9. Difference in means tests (t-test) acquirer and target ROE/CoE (public targets)

Source: author's calculations

Table 10. Difference in means tests (t-test) acquirer and target ROE/CoE (private targets)

Source: author's calculations

H6: Private targets receive on overage higher deal multiple than public targets

We conduct difference of means test (t-test) to test Hypothesis 6 to see if difference in means in normalized deal multiple differs from zero for public and private targets. We reject null hypothesis about zero difference in means (Table 11) and we see that mean normalized deal multiple for private targets (3.3x) is significantly higher than for public targets (1.65x). Our findings are consistent with prior study of Ang and Kohers (2001) which state that private targets have higher bargaining power due to their concentrated ownership and absence of less informed outside investors who might pressure company into selling during unfavorable times.

Table 11. Difference in means tests (t-test) for normalized deal multiple (merged sample)

Source: author's calculations

To test hypothesis 7-11 we build 2 kinds of multivariate OLS regressions: first for the first overall sample of deals between public acquirers and public targets with dependent variable being deal premium, second for the overall sample of deals between public acquirers and private targets with dependent variable being normalized deal multiple. Models are tested for heteroscedasticity using Breusch-Pagan test and for multicollinearity using VIF factor (Table 12). In tests for heteroscedasticity where null hypothesis about constant variance of errors is rejected, White robust standard errors are used to combat heteroscedasticity. We also check VIF factor for all regressors and see that since industry and target industry coincide in 83% of deals in first sample and in 75% of deals in second one, VIF factors for regressors such as acquirer and target industry ROE, CoE and P/BV are higher than 10. To combat multicollinearity in regressors we use either acquirer or target industry characteristics as control variables in different versions of regressions. Moreover, since independent variables in our hypotheses are also highly correlated and have VIF factor higher than 10 (Table 13), we build separate regressions with these independent variables (P/BV, P/BV normalized, P/Value, ROE/CoE, Growth opportunities/P) isolating variables of our interest to combat multicollinearity.

Table 12. VIF factor for regressors (public targets)

	VIF	1/VIF
ln Acq pbv	1.647	.607
ln Target pbv	1.895	.528
Stake acq	1.042	.959
1.Cash payment	1.466	.682
1.Unsolicited	1.037	.964
ln Acq MC	3.007	.333
ln Target MC	2.64	.379
Acq lev	1.306	.766
Target lev	1.389	.72
Acq cash	1.444	.693
Target cash	1.677	.596
Target 52 high	1.269	.788
Same ind	1.192	.839
SP500 pe norm	1.332	.751
Acq ind pbv closed	13.047	.077
Target ind pbv clo~d	12.925	.077
Acq ind roe	9.789	.102
Target ind roe	9.603	.104
Acq ind coe	7.081	.141
Target ind coe	7.057	.142
Mean VIF	4.092	.

Source: author's calculations

Table 13. VIF factor for independent variables

	VIF	1/VIF
ln Target pbv	19.597	.051
ln Acq pbv	18.298	.055
ln Target pbv norm	12.998	.077
ln Acq pbv norm	12.139	.082
ln Acq PV	3.088	.324
ln Target PV	2.794	.358
Target GOMC	2.558	.391
Acq roecoe	1.742	.574
Target roecoe	1.7	.588
Acq GOMC	1.637	.611
Mean VIF	7.655	.

Source: author's calculations

For both samples we build set of regressions for overall sample and separately for stock and cash deals. Each regression in the set has different independent variable of interest: acquirer and target P/BV, normalized P/BV, P/Value, ROE/CoE and GO/P.

H7 (a): Higher acquirer P/BV leads to higher deal premium

For the first sample the coefficients by acquirer P/BV and normalized P/BV are positive but not statistically significant at any reasonable level of significance for the overall sample of deals (Table 14). However, for the subsample of stock deals acquirer P/BV and normalized P/BV are positive and significant at 1% significance level. In the subsample of cash deals these regressors have negative signs that are not significant at any reasonable level of significance. Our findings for the overall and cash samples are consistent with prior studies of Dong et al. (2006) and Davis and Madura (2017) who also find the relationship between acquirer P/BV and deal premium to be not statistically significant. Our finding for the stock sample is consistent with the study of Dong et al. (2006) who finds that this relation becomes significant at the 1% level within the stock offer subsample. The fact that acquirer multiple is significant only in stock subsample proves that buyers with higher P/BV are ready to pay higher deal premiums since they have access to relatively cheap stock financing and can pay higher price without destroying value for its shareholders.

We use target P/BV and P/BV normalized as control variables along with acquirer valuation in regressions with public targets. The coefficients by target P/BV and normalized P/BV are negative and statistically significant for the overall sample of deals and stock subsample while not significant for cash subsample of deals. Our findings are consistent with previous studies (Walkling and Edmister, 1985; Comment, Schwert, 1995; Dong et al., 2006; Alexandridis, 2013; Simonyan, 2014; Lai, 2019). It can be argued that undervalued targets receive higher deal premiums because they negotiate more actively, and bidders are willing to pay more to ensure bid success.

Table 14. Regression results (public sample, dependent variable-deal premium)

	All deals	Stock deals	Cash deals
	P/BV	P/BV norm	P/BV	P/BV norm	P/BV	P/BV norm
ln_Acq_pbv	0.059		0.201***		-0.096
	(0.047)		(0.066)		(0.063)
ln_Acq_pbv_norm		0.043		0.171***		-0.076
		(0.048)		(0.064)		(0.063)
ln_Target_pbv	-0.088**		-0.212***		-0.035
	(0.034)		(0.050)		(0.046)
ln_Target_pbv_norm		-0.115***		-0.268***		-0.043
		(0.033)		(0.053)		(0.045)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 31 -Table 33
Obs.	862	862	494	494	368	368
R-squared	0.214	0.216	0.242	0.242	0.215	0.214

Source: author's calculations

We also construct ratio of acquirer P/BV to target P/BV (ln_pbv_ratio) to see if difference between acquirer and target valuation influences deal premium. The coefficient by ln_pbv_ratio is positive and statistically significant at 1% level for stock deals and at 5% level for all deals while proving not significant for cash deals (Table 15). Therefore, we find evidence that acquirer is ready to pay higher premium when his multiple is higher than multiple of a target because he has bigger “buffer” in which he can operate without destroying shareholder value, the effect is more pronounced for stock deals than for overall sample of deals. In case of stock deals acquirer paying with stock that is more highly valued than stock of a target basically means that he attracts financing at lower cost than his rate of return which he receives investing in a target. We compare R2 in regressions with independent variables P/BV, normalized P/BV and ratio of acquirer P/BV to target P/BV and see that regressions with normalized acquirer and target P/BV have the highest R2 of 21.6% and therefore, the highest explanatory power of deal premium.

Table 15. Regression results (public sample, dependent variable-deal premium)

	(1)	(2)	(3)
	All deals	Stock deals	Cash deals
ln_pbv_ratio	0.076**	0.206***	-0.011
	(0.030)	(0.049)	(0.033)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 34
Obs.	862	494	368
R-squared	0.214	0.242	0.206
Standard errors are in parenthesis
*** p<0.01, ** p<0.05, * p<0.1

Source: author's calculations

H7 (b): Higher acquirer P/BV leads to higher deal multiple

For the second sample the coefficients by acquirer P/BV and normalized P/BV are positive are significant at 1% level for overall sample and subsample of stock deals and positive and significant at 5% level for subsample of cash deals (Table 16). We disregard results of cash deals due to too small number of observations and too high R2 in comparison with other regressions. In contrary to the first sample, in the second sample acquirer valuation proves to be significant also for overall sample and cash deals. The difference in results between public and private targets can be explained by difference in dependent variables or by the fact that acquirer valuation serves as a stronger reference point with private targets who do not have their own market valuation than with public targets which have their own market multiples which serve as stronger reference point in deal negotiations. To draw direct comparison of regression results and prove the robustness of results of regressions with normalized deal multiple with private targets, we build regression with normalized deal multiple for public targets in Hypothesis 11 and look at the difference in regression results for public and private targets.

Table 16. Regression results (private sample, dependent variable-normalized deal multiple)

	All deals	Stock deals	Cash deals
	P/BV	P/BV norm	P/BV	P/BV norm	P/BV	P/BV norm
ln_Acq_pbv	0.405***		0.384***		0.791***
	(0.076)		(0.088)		(0.278)
ln_Acq_pbv_norm		0.394***		0.375***		0.665**
		(0.076)		(0.080)		(0.293)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 35-Table 37
Obs.	190	190	144	144	46	46
R-squared	0.392	0.391	0.349	0.348	0.653	0.638

Source: author's calculations

H8 (a): Higher buyer growth opportunities lead to lower deal premium

For the first sample the coefficients by acquirer GO/P are negative but not statistically significant for the overall sample of deals and stock subsample and positive and not statistically significant for cash subsample of deals (Table 17). Therefore, we reject hypothesis that higher buyer growth opportunities lead to lower deal premium and our findings are not consistent with Kim (2011) and Davis and Madura (2017) who find statistically significant relation between growth opportunities and deal premiums.

We use target growth opportunities as control variable in this regression. The coefficients by target GO/P are positive and statistically significant for the overall sample, as well as for stock and cash subsamples with different levels of significance: 1%, 5% and 10% respectively. Our findings are consistent with prior studies (Davis and Madura, 2015; Davis and Madura, 2017) and can be explained by the fact that targets with higher growth opportunities are more desirable by the acquirers, receive on overage more competitive bids and have higher bargaining power which leads to higher deal premiums.

Table 17. Regression results (public sample, dependent variable-deal premium)

	All deals	Stock deals	Cash deals
	GO/P	GO/P	GO/P
Acq_GOMC	-0.010	-0.017	0.070
	(0.012)	(0.016)	(0.046)
Target_GOMC	0.038***	0.043**	0.032*
	(0.014)	(0.021)	(0.017)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 31 -Table 33
Obs.	817	477	340
R-squared	0.207	0.220	0.202

Source: author's calculations

H8 (b): Higher buyer growth opportunities lead to lower deal multiple

For the second sample the coefficients by acquirer GO/P are also found negative but not statistically significant for the overall sample of deals and stock and cash subsamples (Table 18). Therefore, for private targets we also reject the hypothesis that higher buyer growth opportunities lead to lower deal multiple.

Table 18. Regression results (private sample, dependent variable-normalized deal multiple)

	All deals	Stock deals	Cash deals
	GO/P	GO/P	GO/P
Acq_GOMC	-0.042	-0.039	-0.006
	(0.030)	(0.030)	(0.081)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 38-Table 40
Obs.	178	134	44
R-squared	0.295	0.246	0.582

Source: author's calculations

H9 (a): Higher acquirer P/V (mispricing) leads to higher deal premium

For the first sample with public targets the coefficients by acquirer P/Value are positive and not statistically significant for the overall sample of deals, positive and statistically significant at 5% level for stock deals and negative and negative and statistically significant at 5% level for cash deals. Our findings with respect to overall sample of deals and stock deals are consistent with prior study of Dong et al. (2006), while findings regarding cash deals are not consistent with the prior study. We find evidence that overvalued acquirers are ready to pay on average higher premiums as they have access to relatively cheap stock financing and the relation holds when acquirers use their overvalued stock as means of payment. The negative relation in the cash subsample of deals can be explained by the fact that cheap source of financing in the form of stock makes payment with internal cash resources less attractive for the acquirer and they are not interested in paying higher deal premiums with cash.

Target P/V serves as one of the control variables in this regression. The coefficients by target P/Value are negative and statistically significant at 1% level for the overall and stock samples of deals and negative and not significant for the subsample of cash deals (Table 19). Our findings are consistent with prior study of Dong et al. (2006) and we can state that more overvalued targets have less potential upside in the M&A valuation and acquirers are less likely to offer high premiums if they believe that target is overvalued.

Table 19. Regression results (public sample, dependent variable-deal premium)

	All deals	Stock deals	Cash deals
	P/V	P/V	P/V
Acq_PV	0.033	0.152**	-0.129**
	(0.053)	(0.072)	(0.066)
Target_PV	-0.122***	-0.211***	-0.081
	(0.044)	(0.064)	(0.059)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 31 -Table 33
Obs.	908	516	392
R-squared	0.221	0.238	0.225

Source: author's calculations

H9 (b): Higher acquirer P/V (mispricing) leads to higher deal multiple

For the second sample the coefficients by acquirer P/Value are positive and statistically significant at 5% level for the overall sample, positive and significant at 10% level for stock subsample and positive but not statistically significant for cash subsample (Table 20). We disregard results of cash deals due to too small number of observations and too high R2 in comparison with other regressions. The results are similar to the ones in the sample with public targets with respect to stock deals implying that overvalued acquirers pay higher deal multiple for a target. Since, stock deals make up higher share of all deals in the second sample than in the first sample (73% to 57% accordingly), acquirer P/V becomes significant for the overall sample of deals with private targets.

Table 20. Regression results (private sample, dependent variable-normalized deal multiple)

	All deals	Stock deals	Cash deals
	P/V	P/V	P/V
Acq_PV	0.185**	0.221*	0.104
	(0.094)	(0.121)	(0.184)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in in Table 35-Table 37
Obs.	198	152	46
R-squared	0.296	0.265	0.561

Source: author's calculations

H10 (a): Higher acquirer ROE/CoE leads to lower deal premium

For the first sample of deals with public targets the coefficients by acquirer ROE/CoE are positive and statistically significant at 1% level for the overall and stock samples of deals and positive and not significant for the subsample of cash deals (Table 21). Our findings are not consistent with prior study of Davis and Madura (2017) who find statistically significant negative influence on deal premium. Therefore, we did not find evidence for the fact that if acquirer generates excess returns as measured by ROE/CoE then its shareholders might have less incentives to acquire targets and overpay for them. The positive influence of acquirer ROE/CoE on deal premium can be explained by the fact that that ratio ROE/CoE serves as an indicator for managerial efficiency of acquirer company which means it can realize higher expected synergies from a deal and therefore, pay higher deal premiums.

Target ROE/CoE serves as one of the control variables in this regression. Target value-generating potential measured by ROE/CoE was not found to be statistically significant at any reasonable level of significance. Our finding is consistent with prior study of Madura (2012) who finds influence of target industry ROE not to have statistically significant influence on deal premiums. Negative signs by the coefficients are consistent with prior studies of Almeida, Campello and Hackbarth (2011), Khatami, Marchica and Mura (2015) and Lai (2019) who find negative relation between target profitability and deal premium which can be explained by the fact that financially distressed targets will receive access to capital and resources in acquisition that result into improved synergies for the acquirers.

Table 21. Regression results (public sample, dependent variable-deal premium)

	All deals	Stock deals	Cash deals
	ROE/CoE	ROE/CoE	ROE/CoE
Acquirer_roecoe	0.030***	0.045***	0.003
	(0.010)	(0.013)	(0.016)
Target_roecoe	-0.014	-0.010	-0.013
	(0.010)	(0.018)	(0.010)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 31 -Table 33
Obs.	817	477	340
R-squared	0.211	0.229	0.196

Source: author's calculations

H10 (b): Higher acquirer ROE/CoE leads to lower deal multiple

For the second sample the coefficients by acquirer ROE/CoE are positive for the overall sample and stock subsample but not statistically significant and negative and not significant for cash subsample (Table 22). We see that contrary to the first sample, acquirer ROE/CoE does not have significant explanatory power of deal multiple, implying that acquirer financial characteristics and value-generating ability are less relevant for consideration paid, probably because acquirer of private targets in our sample are smaller and less efficient (measured by ROE/CoE) than acquirers of public targets in the first sample. Target ROE/CoE serves as one of the control variables in this regression. Target value-generating potential measured by ROE/CoE was also not found to be statistically significant at any reasonable level of significance similar to the results in the first sample.

Table 22. Regression results (private sample, dependent variable-normalized deal multiple)

	All deals	Stock deals	Cash deals
	ROE/CoE	ROE/CoE	ROE/CoE
Acquirer_roecoe	0.009	-0.020	0.102
	(0.029)	(0.030)	(0.098)
Target_roecoe	0.012	0.009	0.021
	(0.020)	(0.028)	(0.030)
… Here and thereafter we provide shortened versions of tables with regression results omitting control variables. Full versions of the tables can be found in the Appendix in Table 38-Table 40
Obs.	157	116	41
R-squared	0.328	0.299	0.661

Source: author's calculations

H11: Influence of acquirer P/BV, P/Value, growth opportunities and ROE/CoE on deal multiple is the same for deals with public and private targets

We build multivariate OLS regression on a merged sample with both public and private targets. We incorporate dummy variable Type_target with 0 standing for public target and 1 standing for private target. We also generate interaction variables with dummy variable Type_target. To test whether the estimated parameters for the first sample with public targets are statistically different from the estimated parameters for the second sample with private targets we perform F-test to test that the coefficients on the dummy variable and the interaction term are jointly zero. We reject null hypothesis about coefficients on the dummy variable and the interaction term being jointly zero for all underlying independent variables (acquirer P/BV, P/BV normalized, P/Value, growth opportunities and ROE/CoE) implying that estimated parameters for public targets are significantly different from parameters for private targets (Table 44 in the Appendix to Chapter 3).

From Table 23 and Table 24 we can see that coefficients by Acquirer P/BV and P/BV normalized for deals with private targets are significantly higher (0.405 vs 0.239 and 0.394 vs 0.246) than for public targets implying that acquirer valuation influences deal multiple of private targets more than deal multiple of public targets. This might be explained by the fact that 75% of deals with private targets are carried out by acquirers in the same industry and since a private target does not have market valuation, acquirer valuation and multiples might serve as a strong reference point during negotiations and private targets with their higher bargaining power can push deal multiple towards acquirer multiple (taking into account premium for control). Public targets, on the other hand, have their own market multiples which serve as a stronger reference point in deal negotiations than acquirer valuation, therefore, influence of acquirer multiples on deal multiple for public targets is lower. We also find that acquirer ROE/CoE influence is positive and growth opportunities influence on deal multiple is negative and statistically significant for public targets while not significant for private targets. This can be explained by either smaller sample of deals with private targets or that deal multiple in deals with private targets are driven primarily by target financial characteristics, management, and presence of value-enhancing opportunities. We also see that Acquirer P/BV, normalized P/BV becomes significant for overall sample of deals with public targets when we regress these variables on normalized deal multiple rather than deal premium, whilst with deal premium as dependent variables acquirer valuation was significant only for stock subsample. This might be explained by the fact that deal premiums and normalized deal multiple might show different results as whether consideration paid was too high or not: if, for example, target was highly undervalued compared to industry average, acquirer can pay high deal premium and at the same time deal multiple can stay below industry average. Then, deal premium will show high deal premium and normalized deal multiple will stay below 1 indicating underpayment. If we stick to efficient market hypothesis and assume that stock market values companies fairly on average, then target multiple before the deal must be on average correct, and in this case, deal premium is a better measure of overpayment than normalized deal multiple which can stay below 1 but not necessarily indicate underpayment if target “fair” multiple lies below industry average due to firm specific characteristics (lack of financial transparency, inexperienced management, low stock liquidity, etc.). Therefore, we argue that results of regressions with deal premium provide ultimately more reliable results, however, in the absence of such measure for private targets, we build regressions with normalized deal multiple and compare them across two samples.