Partial Acquisition Strategies for Business Combinations

Partial Acquisition Strategies for Business CombinationsAuthor(s): Asim RoySource: Financial Management, Vol. 14, No. 2 (Summer, 1985), pp. 16-23Published by: Wiley on behalf of the Financial Management Association InternationalStable URL: http://www.jstor.org/stable/3665151 .

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Partial Acquisition Strategies for

Business Combinations

Asim Roy

Asim Roy is a member of the faculty of the Decision and Information Systems Department, College of Business, Arizona State University, Tempe, Arizona.

I. Introduction In a business combination, how much of the stock

should be acquired is an important strategic decision that has received little attention in the financial literature. For a transaction to qualify as a legal business combination, a firm only needs to acquire a majority of the voting shares of the target firm. Often, however, the benefits from combination can be gained by pur- chasing less than a majority of the shares, even though the transaction will not qualify as a formal legal combination.' In the rest of the paper, the term "business combination" is used in this extended sense where less

The author wishes to thank the referees for many valuable suggestions and criticisms that improved this paper significantly.

'In this paper the terms "business combination" and "acquisition" are used interchangeably to imply both a merger (where 100% of the target firm's stock is bought and a single corporate entity results) and an acquisition (where 100% or less of the target firm's stock is bought and both the buying and selling firms maintain their separate identities). As explained later in section II.B, the terms are also used to imply situations where no acquisition of stock takes place, but cooperative arrangements have been agreed to by the firms.

than a majority (even zero percent) of the shares can be bought. A business combination, therefore, offers a unique growth opportunity to a firm since it can gain control of (or arrange to use) needed assets at a choice of investment levels; such a choice is not available under internal growth strategies where a full investment is required. This paper explores the implication of a partial acquisition on the net economic benefit for the acquirer. Existing theory creates the impression that if there is net economic benefit in an acquisition (i.e., the two firms are worth more together than separate because of synergies) and if the price is right (i.e., no net loss occurs), then the acquirer should acquire 100% of the target firm, since that will maximize its gain. The paper shows the fallacy of this notion, in general, and demonstrates that, sometimes, less than a full acquisition will maximize the gain for the acquirer.

Crucial to the acquisition model developed here is the treatment of synergy. The critical step is to identify the different components of synergy by their originat- ing firms, that is, to identify whether they come from the acquiring or target firm. That means the acquirer

16



ROY/PARTIAL ACQUISITION STRATEGIES

should separate the additional cash flows that will accrue directly on its side from the ones that will accrue directly to the target firm.

The literature provides very little guidance to a financial manager in the area of partial acquisitions, even though many partial acquisitions take place in real life. The existing acquisition analysis frameworks or models (see Myers [7], Rappaport [8], Larson and Gonedes [5], Cunitz [1], and Weston [10]) do not include partial acquisition possibilities; all assume a 100% stock purchase for analysis purposes.

In addition to investigating the impact of partial acquisitions on the net economic benefit for the acquirer, the paper also derives the maximum price to pay for an acquisition, which could be higher than what is normally shown in the literature. The acquisition model is based on a cash-for-stock exchange. The model also ignores all tax implications for the acquiring and selling firms. In Section II, the classification and exploitation of synergy are further explained. The equation for the net economic gain for the acquirer is also derived there. Section III illustrates the behavior of the net gain function under different acquisition levels and acquisition prices. Section IV determines the optimum acquisition fraction for a given acquisition price. Section V explores the case when the acquisition price varies with the acquisition level. Section VI examines the target firm's gain. In Section VII, the maximum acquisition price is determined.

II. Net Economic Benefit Under Synergistic Effects and Partial Acquisition A. Division of Synergies

Synergistic effects have been discussed extensively in the literature related to mergers and acquisitions. Empirical evidence shows (see Haugen and Langetieg [4], Mandelker [6], Shad [9]) that acquisitions do gen- erate net economic benefits, but that the selling firms capture most of the gain. The economic benefits occur in a number of ways which are succinctly summarized by Dodd and Ruback [2]. These stem from such factors as monopoly power (Ellert [3]), increased production efficiency (Mandelker [6]), economies of scale, and economies of scope. This paper classifies synergies from two different perspectives:

(i) Whether or not the effects are obtained only by additional investment from the acquirer; such investments are assumed to occur at the time of acquisition.

(ii) Whether the additional cash flows are reflected on the acquiring or the target firm's side.

A few examples will clarify this classification scheme. For instance, when two firms having marketing strengths in two different geographic areas combine, they may very well exploit each other's marketing power to their mutual benefit. This may not involve additional investment, and the effects of increased sales should show up on both sides. If, on the other hand, two firms combine to exploit their respective technological strengths to develop new products, they may require additional investment to obtain new equipment and facilities. Synergistic effects derived from horizontal or vertical combinations may be similarly classified. A vertical combination may reduce the need for a large inventory of a raw material, since that would be supplied by the acquired subsidiary. Thus, the acquirer gains from cost reductions and savings in working capital without additional investments. Hori- zontal integrations can reduce the pressure of competi- tion and result in higher and stable prices, benefiting both sides without additional costs. A horizontal inte- gration may also result in cost savings from joint utili- zation of facilities. As these examples indicate, our classification of synergy is a simple one, and is an integral part of all acquisition analysis to practitioners.

B. Capturing Synergy Synergies between two firms can be captured by (i) one firm gaining effective control over the other

through majority stock ownership (singly or jointly with others); and

(ii) cooperative arrangements between the firms, such as marketing arrangements, joint ventures, etc.

In the first case, when control is required to capture synergies, the acquirer would need to buy a minimum number of shares of the target firm (say a percent, which could be less than 50% if there are other shareholders of the target firm who will cooperate with the acquirer to form a majority). In the second case, when control is not required to capture the synergies, no shares need be bought. However, in both cases, the acquirer has the choice of buying more shares than the required minimum of a percent, where a = 0 when cooperative arrangements are involved and 0 < a -< 50% when control is needed. It is assumed that in neither case would the synergies change (increase or decrease) if more than the minimum share is bought.

Even though it's a misnomer to refer to some cooperative arrangements, where no shares are bought, as

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FINANCIAL MANAGEMENT/SUMMER 1985

"acquisitions" or "business combinations" (though they represent a combination of efforts by the two firms), the paper uses these terms in this extended sense. Therefore, the acquisition model presented here also explores the economic impact of buying any fraction of the target firm when cooperative arrangements are feasible and sufficient by themselves to capture the synergies.

C. Net Economic Benefit to the Acquirer in a Partial Acquisition

If a subsidiary is partially owned, the parent firm receives only the corresponding fraction of the subsid-

iary's value. However, in an accounting sense, the

acquirer is entitled to the full benefit of any synergistic effects that are not shared. One has to be cautioned that the preceding statement refers only to the allocation of values in a definitional sense and not to their actual sharing between the firms, which is determined by the acquisition price and the acquisition fraction. That is, we are referring to the ex-post rather than the ex-ante distribution of the economic gain here.

Let a = minimum fraction of shares required to

capture the synergies; 0 - a -< 0.5; A = price to be paid in cash for 100% of the

target firm; if a fraction of the target firm is bought, a proportional price is

paid; X = fraction to be acquired of the target

firm, where a < X < 1.0; VA, VB = pre-acquisition values of the acquiring

and target firms, respectively; AV^, AVB = additional values, post-acquisition, ac-

cruing to the acquiring and target firms, respectively, because of synergies that do not require any additional investment;

AVA, AVLB = additional values, post-acquisition, accruing to the acquiring and target firms, respectively, because of synergies that do require an additional investment of amount I at the time of acquisition;

GA = gain (or loss) in value from the acquisition for the acquirer's original shareholders.

The values for VA, AV^, AVA', VB, AVB, and AVB' are assumed to be non-negative and estimated by ac-

quirer's management. Since the acquirer shares the subsidiary's value, its

net gain (or loss) in value for a cash acquisition is given by

GA = AVA + A V, +

X(VB + AVB + AVB) - XA - I,

or

G = AVA + AV' -

I + X(VB + AVB + AVB' - A), (1)

where

XA = actual price to be paid for X fraction of the target firm,

X(VB + AVB + AV B) = value accruing to the acquirer from fractional own-

ership of the target firm, and

AVA + AV^A = value accruing directly to the acquirer, in the accounting sense, that is not shared with the minority (or majority) shareholders of the re- sulting subsidiary.

In Section V, the case in which the acquisition price A varies with the acquisition level is explored. One could similarly explore cases when the synergistic effects are a function of the acquisition level, but it is not done in this paper. One also could view synergies in a different way based on Equation (1): those that have a value to the acquirer independent of the percentage ownership (i.e., AVA and AVAI) and those that depend on the percentage ownership (AVB and AV,').

III. Illustration

Suppose that Firm A, a manufacturer of peripheral computer equipment, is interested in buying Firm B, another growing peripheral manufacturer. Firm A is based primarily in the U.S., while Firm B is based primarily in Japan. Firm A's main products are CRT terminals and modems, while Firm B primarily manu- factures printers and hard discs. Firm A views Firm B as a good acquisition candidate since it can exploit Firm B's established sales and marketing staff in Japan to increase its market share there. Firm B will also benefit significantly since its sales in the U.S. will be increased through Firm A's vast sales network. Their joining would also give them a stronger product line to market. Firm A wants to analyze this acquisition for different acquisition prices. It assumes that no extra investment would be required to realize the synergistic sales benefits. Firm A's management estimates Firm B's pre-acquisition value at $20 million (VB = $20

18




million). The estimated value of additional sales of Firm A's products in Japan is $9 million (AVA = $9 million) and the estimated value of additional sales of Firm B's products in the U.S. is $7 million (AVB = $7 million). According to existing acquisition models, the maximum price Firm A can pay for Firm B would be

VB + AVB + AVA = 20 + 7 + 9 = $36 million.

The models implicitly assume that, for any price less than $36 million, there would be net economic benefit for the acquirer, and its gain would be maximized by a full acquisition. Exhibit 1 shows the net benefits for Firm A, for different acquisition fractions and acquisition prices, calculated using Equation (1), assuming a minimum purchase of 50% of Firm B's stock is required to gain control over it.

The results in Exhibit 1 are quite contrary to the conventional analysis. For the low price of $25 million, the analysis shows that conventional wisdom is right: that is, Firm A should buy 100% of Firm B to maximize its gain. However, for the purchase price of $35 million (which is less than the maximum price of $36 million by conventional analysis), it shows that Firm A would gain the most by acquiring just 50% of Firm B rather than 100%. Observe also that less would be invested ($17.5 million at 50% versus $35 million at 100%) for more benefit ($5 million at 50% versus only $1 million at 100%). The comparison is more interesting when the acquisition price is $40 million. According to the conventional analysis, Firm A should not buy Firm B at this price. However, Exhibit 1 shows positive benefits for Firm A if say, 50% of Firm B is bought, though there would be a net loss at 100%. Thus Firm A can still make a profitable acquisition at that price if it buys approximately the minimum required fraction of Firm B.

Observe that for certain acquisition prices, the net benefit for the acquirer increases when the acquisition level is reduced, whereas for certain other prices the

Exhibit 1. Net Gain (or Loss) in Value, G^, for Different Acquisition Fractions and Acquisition Prices

Acquisition Acquisition Price (A)

Fraction (X) A = $25M A = $35M A = $40M

X = 100% 1 -4 X = 85% 10.7 2.2 -2.05 X = 75% 10.5 3 -0.75 X = 60% 10.2 4.2 1.2 X = 50% 10 5 2.5

opposite is true. Also, when more is gained through lower acquisition levels, one is actually investing less for more value.

IV. Optimum Acquisition Fraction for the Fixed Price Case

The question addressed now is: Given an acquisition price, how much of the target firm should one buy in order to maximize the net benefit? Since net gain GA is a linear function of the acquisition fraction X, the gain would be maximized at one of the boundaries of the feasible range of X (a% - X - 100%) depending on the direction of the slope. From Equation (1), the slope of the linear function GA is equal to (VB + AVB + AVBI - A).

The following three cases occur and determine the corresponding optimal acquisition levels:

A. Case 1 A* = A = VB + AVB + AVEB (zero slope).

A* is called here the "critical price" for the acquisition: it is the price at which the slope of the GA function is zero. It depends only on the pre-acquisition value of the target firm and the synergies on its side. When the critical price is paid, the net gain for the acquirer is independent of the acquisition level. Therefore, the acquirer would be better off spending the minimum for the same gain; that is, it should buy an interest of only a percent in this case. At the critical price, the net gain is

GA = AVA + AV,A - I.

Another interpretation of the critical price is that it is the price that allocates to each firm the synergies on its side. For the illustration in Section III, the critical price is $27 million (A* = 20 + 7 = $27 million).

B. Case 2

VB + AVB + AVB' > A (positive slope), or A* > A.

In this case, the net gain for the acquirer would be maximized by a full acquisition, since the gain increases with X. In other words, if the acquisition price is less than the total value to be gained from the target firm, then it's a good deal and one should buy the whole firm. This was the case for the $25 million acquisition price in the previous illustration. Even when there is no synergy, 100% of a target firm should be acquired at a bargain price.

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Exhibit 2. Net Economic Benefit as a Function of the Acquisition Fraction X for Different Acquisition Prices

GA 4

AVA + AVAI

CASE 2

Case I (Critical Price) - I

CASE 3

100%

MAXIMUM PRICE

C. Case 3

VB + AVB + AVBI < A (negative slope), or A* < A.

Here, the net gain for the acquirer would be maximized only when the minimum fraction a of the shares is acquired, since the gain decreases with increasing X. It means that, if the acquisition is overpriced (com- pared to the critical price), then one should buy only the minimum required interest in the firm. This was the case for the $35 and $40 million acquisition prices in the previous illustration. One should, however, make sure that the net gain, GA, is non-negative. This brings up the issue of maximum price to pay for an acquisition, which is addressed in Section VII.

Explicit conditions have now been derived for when it is optimal to acquire either fully or partially. Exhibit 2 shows the behavior of the net gain function for the different cases. Observe that it is never optimal (even for the critical price case) to acquire at any level other than a or 100%. The optimal acquisition level is an extreme point solution for the fixed price case.

V. Optimum Acquisition Fraction for the Variable Price Case

In many acquisitions, the acquiring firm has to pay a higher price for a larger share of the target firm. These are situations where certain shareholders will not tender their shares till a higher price is offered. It is, of course, difficult to express the acquisition price in a form that exactly accounts for this phenomenon. How- ever, simple functional forms, such as linear or quadratic functions, might capture the essence of this phenomenon and be used in the acquisition analysis. This paper examines the linear and quadratic price functions to show how the acquisition strategy differs from the fixed price case.

A. Linear Price Function Let's say the acquisition price A is expressed as

A = AO + bX fora <- X < 1.0.

Substituting this expression for A in Equation (1) and solving for X from G' = 0, the optimal acquisition

1.-i I_ * _w

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Exhibit 3. Net Gain for Firm A as a Function of the Acquisition Fraction X for Two Different Linear Price Functions

GA

10.5 -

10 .

9.5

9

50%

Xopt = 62.5%

I----I- - A = 22 + 4X

A = 25 + 2X

<op+ -50 t\

9.375

i i I 4 4 62.5% 75%

-10.5

- 10

-9

X -

100%

fraction Xopt is obtained as

Xopt (VB + AVB + AVB') - AO

2b

B. Quadratic Price Function Let's say the acquisition price A is expressed as

A = Ao + bX + cX2 for a - X - 1.0.

Substituting this expression for A in Equation (1) and solving for X from GA' = 0, the optimal acquisition fraction Xopt is obtained as

Xopt

2b + /4b2 + 12c(VB + + AV + AVB - AO) (3)

2(VB + AVB + AVB - A0)

C. Observations on the Variable Price Cases Unlike the fixed price case, the variable price cases

can have an interior optimal solution for the acquisition

fraction. One also may obtain a solution to Xopt from Equation (2) or Equation (3) that is outside its feasible range. In such instances, the feasible optimal solution would be the nearest extreme point. That is, if Xop, > 1, then set Xopt= 1; if Xopt < a, then set Xop = a.

Based on the example in Section III, Exhibit 3 shows the net gain for Firm A assuming two different linear price functions. For the price function, A = 22 + 4X, the optimal acquisition fraction is 62.5% (an interior solution). For the other price function, A = 25 + 2X, the optimal acquisition fraction is 50%. The price function, A = 22 + 4X may be interpreted to mean that if only 50% of Firm B is to be acquired, the acquisition price would be (22 + 2)/2 = $12 million, but if 100% is to be acquired, the acquisition price is not just double (i.e., $24 million), but somewhat more ($26 million).

If the price function for the example is A = 22 + 2X + X2/6 (quadratic), then the optimal acquisition fraction Xop, is 0.91.

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I I




VI. Gains for the Stockholders of the Target Firm

The gains for the stockholders of the target firm can be determined by classifying these stockholders into two groups:

(i) Group A- the minority (or maybe the majority) shareholders of the target firm after the partial acquisition; this group is (1- X) percent of the original stockholders of the target firm who did not sell their stock; and

(ii) Group B - this group consists of the X percent of the original stockholders who sold their shares to the acquiring firm.

Let GRA and GRB be the total gains for the groups A and B respectively. Then,

GRA = (I-X) (AVB + AVB), (4)

and

GRB = X(A-VB). (5)

Empirical evidence shows that the target firm gets on an average a 20% premium (Shad [9]), and during the past decade it has actually been in the 40 to 70%

range. Suppose that the selling stockholders of the

target firm (Group B) will want a Y percent premium. The corresponding acquisition price then is determined from the relation

X(A-VB) = XYVB,,

or

A= (1+Y)VB. (6)

Equation (6) gives an obvious result. When evaluating acquisitions, one might define feasible pricing strate-

gies such that the selling stockholders get at least a Y

percent premium. For the minority shareholders

(Group A) to receive the same premium, the amount of

synergy required on the target firm's side is shown by the following equation:

AVB + AV,B = YVB. (7)

Hence, if AVB + AVB < YVB, the Group A stockholders earn a lesser premium than Group B stockholders. And unlike the selling stockholders (Group B), Group A has no mechanism (such as the acquisition price) to leverage their premium. Hence, in gener-

al, the premiums earned by the two groups will be different in a partial acquisition.

The conditions of Section VI can be reinterpreted here. If AVB + lAVB < YVB, then in a full acquisition, the acquirer will be paying a higher premium to Group A than what they can get from their synergy. So it is

optimal in this case to acquire the minimum, and vice versa.

VII. Maximum Price for an Acquisition: Fixed Price Case

Let Amax be the maximum price to pay for the target firm. The notion of the maximum price is one that will not dilute the current wealth position of the acquirer's shareholders. In Exhibit 2, observe that there will be

many prices that produce zero gain, since many of the downward sloping price curves cross the X-axis. It is assumed here that the net gain (AVA + AV,' - I) at the critical price is positive. Of the price curves cross-

ing the X-axis, it is obvious that the one intersecting the X-axis at X = a will produce the highest price. Thus, Amax is determined from Equation (1) by setting GA 0 and X = a (assuming a > 0), and solving for A, which gives

Amax = [(AVA + AVA - I) +

a (VB + AVB + AVB')]/a. (8)

For the previous example, the maximum price is $45 million from Equation (8) (for a = 0.5), which is much more than the $36 million maximum price one obtains by conventional analysis. If the synergistic effects of AVA, AVA', and AVB' are absent, then the maximum price from Equation (8) would be the same as the one from conventional analysis. Hence, the

higher maximum price can be paid only when those

synergies exist. Observe that the maximum price is

paid only to a percent of stockholders of the target firm.

Let A'ma be the maximum price one could pay for a full acquisition. Then A'max is determined from Equa- tion (1) by setting GA = 0 and X = 1, and solving for A, which gives

A'max = AV + AV,I + VB + AVB + AV, - I. (9)

Thus A'max actually corresponds to the conventional notion of maximum price. For any price strictly between A'ma and Amax, the net economic benefit for the

acquirer would be negative for a full acquisition.

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VIII. Conclusion It has been demonstrated that the acquisition frac-

tion does affect the economic gain for the acquirer. In the fixed price case, depending on the acquisition price, a lower acquisition level will either increase or decrease the net gain. If the acquisition price is less than the critical price, then a lower acquisition level decreases the net gain. So, in this case, it is optimal to buy the whole company to maximize the benefit. On the other hand, if the acquisition price is more than the critical price, then it is optimal to buy just a minimum fraction of the target firm. The optimum fraction to buy, for the fixed price case, is always at one of the extremes of the permissible range for the acquisition fraction, even when the price is equal to the critical price. When the acquisition price is not fixed, but varies with the acquisition level, it has been shown that the optimum acquisition fraction can be an interior solution in the feasible range. Fundamental to the results here is the concept of breaking down the synergy into its components, instead of lumping them together, as is normally done. The paper also derives the maximum price one could pay for an acquisition for the fixed price case. Again, because synergies are treated by components, the maximum price could be higher than what one obtains from conventional analysis.

The ideas presented in this paper should be useful from the practitioner's point of view. The financial manager can now think of paying higher premiums than previously thought. The feasibility of paying higher premiums through lower acquisition levels should also expand the supply of acquisition candi- dates that provide an acceptable return on investment. Note also that, in addition to the acquisition price, the acquisition fraction determines the sharing of the benefits of an acquisition. The acquisition price is largely an external variable in the model, a function of the market mechanism. The acquisition level is largely a management choice. Specific acquisition cases might

digress from this view. That is, the acquisition level might have to be negotiated or reevaluated. For example, a typical case is when some shareholders of the

target firm refuse to sell their shares, preventing a

complete acquisition. Irrespective of the negotiability issue, financial managers now know how the acquisition level, as an instrument of benefit sharing, works for or against them. Such knowledge should be helpful in any negotiation.

References 1. J. Cunitz, "Valuing Potential Acquisitions," Financial Ex-

ecutive (April 1971), pp. 16-28. 2. P. Dodd and R. Ruback, "Tender Offers and Stockholders

Returns: An Empirical Analysis," Journal of Financial Economics (1977), pp. 351-373.

3. J. C. Ellert, "Mergers, Antitrust Law Enforcement and Stockholders Returns," Journal of Finance (1976), pp. 715-732.

4. R. Haugen and T. C. Langetieg, "An Empirical Test for Synergism in Merger," Journal of Finance (September 1975), pp. 1003-1013.

5. K. Larson and N. Gonedes, "Business Combinations: An Exchange Ratio Determination Model," Accounting Re- view (October 1969), pp. 720-728.

6. G. Mandelker, "Risk and Return: The Case of the Merging Firms," Journal of Financial Economics (1974), pp. 303- 336.

7. S. Myers, "A Framework for Evaluating Mergers," in S. C. Myers (ed.), Modern Developments in Financial Manage- ment, New York, Praeger, 1976, pp. 633-645.

8. A. Rappaport, "Strategic Analysis for More Profitable Ac- quisitions," Harvard Business Review (July-August 1979), pp. 99-111.

9. J. S. R. Shad, "The Financial Realities of Mergers," Har- vard Business Review (November-December 1969), pp. 133-146.

10. F. J. Weston, "The Determination of Share Exchange Ra- tios in Mergers," in Alberts and Segall (eds.), The Corpo- rate Merger, Chicago, University of Chicago Press, 1966.

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Partial Acquisition Strategies for Business Combinations

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