# Bidder incentives for informed trading before hostile tender offer announcements.

In these circumstances, the bidding firm has an incentive to tip arbitrageurs, so that shareholders with the lowest private tendering costs own the shares necessary for the bidder to obtain a controlling interest. Inside information creates the opportunity for arbitrageurs to offer uninformed shareholders a price sufficient to induce them to sell. The low private tendering costs of arbitrageurs reduce the minimum successful bid price if the arbitrageurs buy the pivotal share that grants a controlling interest. If, however, arbitrageurs do not purchase the pivotal share, the minimum successful bid price is once again determined by the reservation price of the original pivotal shareholder. In that case, tipping does not lower the cost of the acquisition for the bidder.Target firm management has similar incentives to exploit the differences in shareholders' valuations of the shares arising from private tendering costs. Bagwell (1991) shows that the cost of a takeover to a potential acquirer is increased if the target firm repurchases shares because shareholders with the lowest reservation prices tender first. Thus, a share repurchase leaves the target firm in the hands of shareholders with higher reservation prices, increasing the cost of acquiring the controlling share to subsequent bidders. Tipping arbitrageurs and others with low private tendering costs works in a similar way, but to the advantage of the bidder. If arbitrageurs buy the pivotal share, the bidder's cost of acquiring a controlling interest decreases.

We present a model of a bidding firm's incentive to tip arbitrageurs when there are constraints on the acquisition of shares prior to disclosing information about a bid. The Williams Act amendments to the Securities Exchange Act of 1934 impose just such a constraint. As shown below, the incentive for the bidding firm to leak information prior to announcement depends on 1) the amount of dilution the bidder anticipates (the back-end price imposed by the legal system), 2) the degree to which the back-end price of the offer embeds any stock price increase arising from the additional trading by arbitrageurs prior to announcement, 3) the private tendering costs of the pivotal share, and 4) the size of the bidder's toehold.

The model suggests that the incentive for pre-announcement tipping is negatively related to the degree of expropriation allowed by the legal system. If the legal system allows the bidder to expropriate all of the improvement due to the takeover from minority shareholders, the bidder will not tip because arbitrageurs will be unwilling to purchase a controlling interest. The bidder's incentive to tip is also negatively related to the degree to which the back-end price embeds any pre-announcement run-up because this increases the Cost of the bid. Because the bidder cannot control the amount of informed trading once information is released,(1) if the bidder knows that pre-announcement trading will cause the back-end price to rise sufficiently that the deal becomes unprofitable, it will not tip arbitrageurs. In general, a bidder has more incentive to tip prior to announcement the higher the private tendering costs of the pivotal shareholder and the smaller the bidder's toehold in the target firm's shares.

Since arbitrageurs, who are likely to have lower tendering costs, will tender at a lower price than shareholders with higher private tendering costs, some

value-increasing bids that would otherwise fail succeed in the presence of informed trading. As a result, informed trading enables more value-increasing bids to occur. This benefit has led some to argue that definitions of illegal insider trading should exclude the tipping of arbitrageurs prior to tender offers (Jensen (1986)). In addition, informed trading prior to announcement does not enable value-decreasing bids to occur because arbitrageurs will not buy shares in anticipation of a bid if the bid price will be less than the current market price of the share.

I. The Importance of Private Tendering Costs in Tender Offers

For a tender offer to succeed, a bidder must offer a price for the target firm's stock that is sufficient to induce a controlling fraction of the target's shareholders to tender. This means that the bid price must exceed the value of the stock to the target firm shareholder if that shareholder does not tender, plus any private costs of tendering. The existence of private tendering costs is consistent with the observation that some shareholders fail to sell their shares into a tender offer even at a substantial premium over market price (Brown and Ryngaert (1992) and Comment and Jarrell (1987)).

For example, suppose a share is worth $1 under incumbent management but $2 under the bidder. Assume that complete dilution is possible, in the sense that the bidder may buy out minority shareholders at the pre-bid price. If private tendering costs (taxes and other transaction costs) are $0.75 per share, then existing shareholders will tender only to a bid of at least $1.76 per share (assuming all shareholders are identical), because tendering requires them to give up a share worth $1 and incur $0.75 in transaction costs. Now, assume arbitrageurs have private tendering costs of only $0.50 per share. If arbitrageurs own the pivotal share that gives the bidder a controlling interest, the bidder may succeed with a bid of only $1.51.

A. Private Tendering Costs and the Supply of Target Shares

Private costs of tendering are costs incurred when target firm shareholders tender their shares. One type of tendering cost is the cost of obtaining and evaluating information about the offer. Romano (1987) cites high information costs as the reason small shareholders fail to tender into value-increasing bids. These shares are sometimes referred to as "sleeping shares." Institutional shareholders, however, are likely to have low transaction and information costs, especially on a per share basis (Stulz, Walkling, and Song (1990)).

A second type of private tendering cost is taxes. If a shareholder never plans to sell the shares, the tax cost of tendering is the gross capital gains tax. If the shareholder plans to sell the shares in the future, however, the tax cost of tendering is the incremental tax burden incurred because the capital gains tax must be paid sooner than anticipated. In either case, different shareholders incur different tax consequences from tendering (Bradley, Desai, and Kim (1988) and Stulz, Walkling, and Song (1990)). For example, tax-exempt institutional holders or active traders may not incur taxes as a result of tendering (Brown and Ryngaert (1992)). Even if all taxpayers are subject to the same marginal tax rate, the tax paid on shares tendered will differ as the tax basis (the purchase price of the stock) differs.

Differential private costs of tendering affect the supply schedule of target firm shares faced by the bidder. In a world with homogeneous expectations and zero transaction costs, the supply of shares in the target firm would be perfectly elastic at the current market price. Private tendering costs that differ among shareholders, however, create an upward-sloping supply curve.(2)

Arbitrageurs, because they assemble large blocks of stock and routinely invest in takeover targets, are likely to have low transaction and information costs, especially on a per share basis. Consequently, the release of information to arbitrageurs may reduce the private tendering costs of the pivotal share, thereby increasing the bidder's profit. This is consistent with arguments by Herzel and Katz (1987), Romano (1987), and Weston, Chung, and Hoag (1990), who suggest that investment bankers tip arbitrageurs so that stock will be in "friendly hands." Shareholders who have lower private costs of tendering are more likely to tender to a value-increasing bid.

B. Alternatives to Tipping Arbitrageurs Prior to Announcement

To induce arbitrageurs to purchase target firm shares, a bidder must offer them a share of the potential profits from the bid. Thus, it might seem preferable for the bidder simply to increase its ownership of target shares prior to announcement. Absent constraints on the amount of stock purchased by the bidder prior to announcement of the bid, a risk-neutral bidder will purchase the requisite number of shares at each target firm shareholder's reservation price.(3)

Of course, legal constraints limit the stock that bidders may acquire in any firm without disclosure. The Williams Act amendments to the Securities Exchange Act of 1934 require anyone who acquires 5% or more of the stock of a firm to report his holdings and intentions to the SEC within ten days of acquisition. During this ten-day period, the purchaser may acquire more stock on the open market, but once the report is filed, no additional open market acquisitions are allowed. If a bidder encourages stock ownership by other friendly hands, it need not trigger the disclosure role.(4) In the model developed here, it is this legal constraint that gives a bidder the incentive to tip prior to announcement.

In addition, purchasing shares prior to a tender offer may be more difficult than securing financing to complete an offer. To buy a large fraction of target shares before a tender offer, the bidder requires cash; to make a tender offer, the bidder need obtain only a commitment for cash if the offer is successful. For a lender, financing the purchase of shares in the open market prior to an offer presents much greater risk, because the tender offer may fail. Financing the acquisition of shares to complete a conditional tender offer is less risky, because it is contingent upon receipt of sufficient shares to complete the offer. If the tender offer succeeds, the assets of the target can also be used as collateral. Hence, financing is available at lower cost if the bidder initiates a tender offer rather than purchases a toehold.

II. The Model

Suppose that [V.sub.0] is the per share value of a firm under incumbent management. A bidder contemplates a conditional, two-tier hostile tender offer.(5) [V.sub.1] is the per share value of the firm under the bidder; [V.sub.1] [greater than] [V.sub.0]. That is, the completed tender offer will transfer control to economic agents who increase the value of the target's assets.(6) Assume that the number of shares in the target firm, N, is fixed and that control requires 0.5N shares. (Notation is summarized in Table 1.)

For simplicity, assume that there are no rivals in the bidding process, that there is no uncertainty, and that the bidder has acquired a toehold in the target firm of [Alpha]N shares, [Alpha] [less than] 0.5. Assume also that making a bid entails no costs other than acquisition of the shares. Although costs such as legal and investment banking fees reduce the level of the bidder's profits, they do not affect the relationships among the other variables of interest. For simplicity, these costs are assumed to be zero. In addition, assume that both the bidder and the arbitrageurs know the private tendering costs of target firm shareholders and that target shareholders incur the same transaction costs in selling to the arbitrageurs that they do in tendering to the bidder. Assume also that arbitrageurs have lower tendering costs than do other shareholders. For convenience, these costs are set to zero.

To overcome the free-rider problem noted by Grossman and Hart (1980), a bid must be front-end loaded. Shareholders who tender must receive more than those who fail to do so. In this model, the bidder offers a conditional two-tier bid in which the front-end price, B, exceeds the back-end price, [V.sub.b]. The back-end price can be interpreted in two ways: either as the price at which minority shareholders are bought out in a clean-up merger or as the market price of the minority shares after the bid (and after any dilution by the majority shareholder).

The front-end price of the winning bid thus depends on the degree to which the bidder can expropriate the value of the minority shares.(7) The legal system usually constrains the degree of expropriation allowed. Appraisal statutes protect minority shareholders from exploitation by the majority (Bradley, Desai, and Kim (1988)). In addition, fair price laws may require that the back-end price be no less than the front-end price. Even if B and [V.sub.b] are nominally the same, if interest rates are positive, the time lag between the receipt of the front-end payment and the back-end payment ensures that the bid is nevertheless front-end loaded. Thus, in this model, the back-end price, [V.sub.b], is assumed to be fixed by the legal system rather than by the bidder, and the minimum back-end price is assumed to be the value of the firm under incumbent management, [V.sub.b] [greater than or equal to] [V.sub.0].

The front-end price must also compensate for the private costs of tendering. This creates a supply curve for target firm shares as shown in Figure 1. Let [t.sub.i] represent the per share private tendering costs of the ith share; [t.sub.i] is an increasing function of i. Assume that transaction costs are zero for all shares held by the bidder. This corresponds to the segment 0 - [Alpha]N in Figure 1. Holders of other shares may have positive private tendering costs, corresponding to segment [Alpha]N - N in Figure 1. To induce these shareholders to tender, the bidder must offer at least [V.sub.b] + [t.sub.i] + [Epsilon], i = [Alpha]N + 1, ..., N, where [Epsilon] represents the minimum increment over the back-end value necessary to induce these shareholders to tender.(8) (In the numerical examples in Table 2, [Epsilon] = $0.01.)

For the tender offer to succeed, the bidder must offer a price that is sufficient to induce a controlling interest, (0.5 - [Alpha])N shares, to tender. Let c represent the share that grants a controlling interest. Let [t.sub.c] represent the private tendering costs of the controlling 0.5Nth share. The minimum price sufficient to gain control is thus B = [V.sub.b] + [t.sub.c] + [Epsilon].

A. The Bidder's Willingness to Pay for Control

The bidder's willingness to pay for control is determined by the amount of dilution the bidder anticipates, as well as the toehold purchased by the bidder and the value of the firm to the bidder. The more dilution the bidder anticipates, the larger the gain from acquiring control of the target and, hence, the greater the willingness to increase the first-tier price of a bid. Similarly, the larger the toehold or the greater the value of the target to the bidder, the greater the willingness to increase the first-tier bid price.

The maximum amount the bidder will pay for a controlling interest in the firm is the difference between the value of the target to the bidder if the bid succeeds and the value of the toehold it already owns if the bid fails. If the bidder wins, it obtains the value of its 50% stake in the firm plus the proceeds from dilution of the minority shares:

0.5N[V.sub.1] + 0.5N([V.sub.1] - [V.sub.b]) = N([V.sub.1] - 0.5[V.sub.b]) (1)

If the bid fails, the bidder retains the value of its toehold under incumbent management, [Alpha]N[V.sub.0]. The maximum amount the bidder will pay in total for a controlling interest of (0.5 - [Alpha])N shares is the difference between these two values:

N([V.sub.1] - 0.5[V.sub.b] - [Alpha][V.sub.0]) (2)

Therefore the maximum price that the bidder would pay per share in the first tier, B[prime], is given by

B[prime] = ([V.sub.1] - 0.5[V.sub.b] - [Alpha][V.sub.0])/(0.5 - [Alpha]) (3)

The bidder will make an offer and win when B[prime] [greater than] [V.sub.b] + [t.sub.c]. That is, when

[Alpha]([V.sub.1] - [V.sub.0]) + (1 - [Alpha])([V.sub.1] - [V.sub.b]) [greater than] (0.5 - [Alpha])[t.sub.c] (4)

The bidder can win when the gain on its toehold plus the amount it can expropriate from all other shareholders is more than what the bidder must pay in the higher front-end bid price necessary to overcome the pivotal shareholder's private tendering costs.

B. The Arbitrageurs' Decision

A bidder will leak information to arbitrageurs about an impending bid only if the bidder expects arbitrageurs to buy enough stock prior to announcement so that the private tendering costs of the pivotal share will be reduced and profits from the bid will be increased. Arbitrageurs will buy shares only if they expect to sell those shares at a profit. Together, these two conditions constrain the minimum successful bid price and determine the number of shares that arbitrageurs will buy prior to announcement. The profit to the arbitrageurs is affected by the amount of dilution the bidder can impose on minority shareholders, the value of the target under incumbent management, and the private tendering costs of the original shareholders who hold a controlling interest. Consequently, the minimum successful bid price and the number of shares that arbitrageurs will buy depend on these variables as well.

Recall that the back-end price of the bid is determined by the legal system. While statute typically requires valuation of the shares exclusive of any gain engendered by expectation of the takeover,(9) in practice the courts may embed a portion of the pre-announcement run-up in the back-end price. Because pre-announcement trading by the arbitrageurs will induce a ran-up in the target's price prior to announcement as the arbitrageurs move up the supply curve, the back-end price imposed in the presence of tipping, [[V.sub.b].sup.*] may exceed the back-end price imposed in its absence, [V.sub.b]. Thus, [V.sub.0] [less than or equal to] [V.sub.b] [less than or equal to] [[V.sub.b].sup.*].(10)

If n shares are tendered, (0.5 - [Alpha])N/n will be taken up at the first-tier price, B; the remaining fraction will be taken up at the second-tier price, [[V.sub.b].sup.*]. Prior to announcement, informed arbitrageurs are willing to buy and tender share i if

[Mathematical Expression Omitted]

where [t.sub.i] is the private tendering cost of the uninformed shareholder holding share i. That is, arbitrageurs will buy the ith share if the expected increase in the value of the share is greater than the premium that must be paid to acquire the share.

As seen from Inequality (5), the greater the dilution that can be imposed on minority shareholders (the lower the back-end price, [[V.sub.b].sup.*], the fewer shares the arbitrageurs will buy. On the other hand, if pre-announcement trading by arbitrageurs is embedded in the back-end price, arbitrageurs will buy more shares in the target. If the increase in the back-end price due to tipping is sufficiently large, bidders will not find it profitable to tip.

The arbitrageurs will buy exactly (0.5 - [Alpha])N shares if

[Mathematical Expression Omitted]

That is, if

B = [V.sub.0] + [t.sub.c] + 2[Epsilon]. (6)

The smallest bid that the bidder can make that will induce the arbitrageurs to buy the pivotal share is then B = [V.sub.0] + [t.sub.c] + 2[Epsilon], because the arbitrageurs must pay at least [V.sub.0] + [t.sub.c] + [Epsilon] to the original shareholders to induce them to sell a controlling interest.

To induce the arbitrageurs to tender their shares, the front-end price must also be higher than the value of shares retained by the arbitrageurs if they fail to tender. Hence, the lowest first-tier bid price, [B.sup.*], that can succeed in the presence of informed trading is given by

max [[[V.sub.b].sup.*] + [Epsilon], [V.sub.0] + [t.sub.c] + 2[Epsilon]] (7)

Note that no arbitrageur needs to observe the purchases of other arbitrageurs to determine whether to purchase shares; the market price of the stock provides sufficient information. Once the shares are purchased, the arbitrageur will tender them because a shareholder is always better off tendering into a conditional front-end loaded bid.

The pre-announcement purchase of shares by arbitrageurs shifts the supply curve as shown in Figure 2. Notice that the supply curve is discontinuous at [Alpha]N + n, where n represents the number of shares purchased by the arbitrageurs. Only if ([Alpha]N + n) is at least 0.5N (the number of shares required for control) will the purchase of shares by the arbitrageurs increase the profitability of the bid to the bidder. If ([Alpha]N + n) is less than 0.5N, the minimum successful first-tier bid price is still determined by the private tendering cost of the original pivotal shareholder.(11) Consequently, the bidder will tip only if it knows that arbitrageurs will buy a controlling interest.

C. Bidder's Profit Maximization Decision

A profit-maximizing bidder will choose to tip arbitrageurs and others with low private costs of tendering only when the gain from doing so outweighs the cost. The gain from tipping comes from the reduction in the private tendering costs of the pivotal share. The cost of tipping is the increase in the back-end price that arises because of increased trading in shares of the target firm prior to announcement.(12) To determine whether to tip arbitrageurs, the bidder compares the profits from the transaction that occur with tipping and without tipping.

1. Profits without Tipping

Profits to the bidder are equal to the value of the firm under the bidder's management less the cost of purchasing a controlling interest at the first-tier price, B; the cost of purchasing the remaining shares not in the toehold at the second-tier price, [V.sub.b]; and the opportunity cost of holding a toehold that could otherwise be sold into the market. That is, without tipping, profits to the bidder are given by:

N[[V.sub.1] - (0.5 - [Alpha])B - 0.5[V.sub.b] - [Alpha][V.sub.0]] (8)

After announcement, the lowest first-tier price B that will induce a sufficient number of the original shareholders to tender in the absence of tipping is [V.sub.b] + [t.sub.c] + [Epsilon]. If the bid succeeds without tipping, profits to the bidder would be

N[[V.sub.1] - (1 - [Alpha]) [V.sub.b] - (0.5 - [Alpha])([t.sub.c] + [Epsilon])] - [Alpha]N[V.sub.0] (9)

A profit-maximizing bidder that does not tip will make a tender offer only if profits are positive, i.e.,

[V.sub.b] [less than] [[V.sub.1] - (0.5 - [Alpha])([t.sub.c] + [Epsilon]) - [Alpha][V.sub.0]]/(1 - [Alpha]) (10)

If Inequality (10) does not hold, the tender offer will not be profitable for the bidder in the absence of tipping.

2. Profits with Tipping

When the bidder tips, it must offer arbitrageurs a price sufficient to induce them to buy the controlling share. Thus, the minimum successful first-tier bid price in the presence of tipping, [B.sup.*], must be at least [V.sub.0] + [t.sub.c] + 2[Epsilon]. To overcome the free-rider problem, the bidder must front-end load the offer so that [B.sup.*] is at least [[V.sub.b].sup.*] as well.

To determine whether the bidder tips, it is useful to examine two cases based on the relationship between [V.sub.0] + [t.sub.c] + [Epsilon] and [[V.sub.b].sup.*], the second-tier price in the presence of tipping.

Case 1. [[V.sub.b].sup.*] [greater than] [V.sub.0] + [t.sub.c] + [Epsilon]

In this case, the back-end price determined by the legal system is higher than the minimum price necessary to induce arbitrageurs to buy a controlling interest. Thus, the winning first-tier price, [B.sup.*], will be [[V.sub.b].sup.*] + [Epsilon]. The bidder's profits with tipping are then:

N[[V.sub.1] - (1 - [Alpha])[[V.sub.b].sup.*] - (0.5 - [Alpha])[Epsilon]] - [Alpha]N[V.sub.0] (11)

The first term is the gain to the bidder from the tender offer. The last term represents the opportunity cost of the toehold shares.

The increase in profits due to tipping in Case 1 is given by the difference between Equations (11) and (9) or

[Delta (difference)][[Pi].sub.1] = N[(0.5 - [Alpha])[t.sub.c] - (1 - [Alpha])([[V.sub.b].sup.*] - [V.sub.b])] (12)

Tipping will increase the bidder's profits if this expression is positive; that is, if:

([[V.sub.b].sup.*] - [V.sub.b]) [less than] [(0.5 - [Alpha])/(1 - [Alpha])][t.sub.c] (13)

In this case, for tipping to be profitable for the bidder, the increase in the back-end price induced by tipping the arbitrageurs must be less than the private tendering costs of the marginal shareholder, weighted by a function of the bidder's toehold. (Of course, it is also necessary that profits, given by Equations (9) or (11), depending on whether tipping occurs, be positive for the bid to occur.)

This is illustrated by example 1 in Table 2. Row 1 shows profits to the bidder when tipping does not occur, assuming a back-end price of $1.52, the minimum back-end price applicable to Case 1 given the parameters in Table 2. As long as Inequality (13) holds, the bidder will tip. Here, if tipping occurs, the back-end price can rise to $1.75, and profits to the bidder will still increase because tipping reduces the private tendering costs of the pivotal share and the first-tier price decreases accordingly (Row 2). However, if the back-end price rises to $1.76 (Row 3), Inequality (13) is violated, and tipping decreases the bidder's profits. Hence, the bidder will not tip. If the bidder tips, the number of shares purchased by arbitrageurs is determined by Inequality (5).

In the special case in which tipping does not increase the back-end price of the bid, so that [[V.sub.b].sup.*] = [V.sub.b], tipping will always increase profits because it decreases the first-tier price without increasing the back-end price. See example 2, Table 2.

Equation (12) can be used to explore the relationship between the incentive to tip and the parameters of the model. It is easy to see that [Delta][Delta (difference)][[Pi].sub.1]/[Delta][t.sub.c] [greater than] 0. That is, the higher the tendering costs of the pivotal share, the greater the incentive to tip.

One can also show that [Delta][Delta (difference)][[Pi].sub.1]/[Delta][Alpha] = N[[[V.sub.b].sup.*] - [V.sub.b] - [t.sub.c]]. It is clear from Equation (13) that when tipping is profitable this expression is negative. That is, the incentive to tip decreases with increases in the toehold. In addition, [Delta][Delta (difference)][[Pi].sub.1]/[Delta]([[V.sub.b].sup.*] - [V.sub.b]) = - (1 - [Alpha])N, which is negative. The incentive to tip also decreases when the second-tier price embeds a greater amount of any pre-announcement price run-up.

Case 2. [[V.sub.b].sup.*] [less than or equal to] [V.sub.0] + [t.sub.c] + [Epsilon]

In this case, the back-end price determined by the legal system is less than the minimum price necessary to induce arbitrageurs to buy a controlling interest. Consequently, the bidder must offer a first-tier price sufficient to induce arbitrageurs to buy the pivotal share; [B.sup.*] = [V.sub.0] + [t.sub.c] + 2[Epsilon]. The desire to induce arbitrageurs to buy the pivotal share provides one explanation why bidders may offer a large premium in the first-tier bid price.(13)

The bidder's profits from tipping in Case 2 are then

N[[V.sub.1] - 0.5([V.sub.0] + [[V.sub.b].sup*]) - (0.5 - [Alpha])([t.sub.c] + 2[Epsilon])] (14)

The increase in profits from tipping in Case 2 is given by the difference between Equations (14) and (9):

[Delta (difference)][[Pi].sub.2] = (1 - [Alpha])N[V.sub.b] - 0.5N[[V.sub.b].sup.*] - (0.5 - [Alpha])N([V.sub.0] + [Epsilon]) (15)

Tipping will increase the bidder's profits if the difference between Equations (14) and (9) is positive; that is, if:

([[V.sub.b].sup.*] - [V.sub.b]) [less than] [(0.5 - [Alpha])/0.5]([V.sub.b] - [V.sub.0] - [Epsilon]) (16)

[TABULAR DATA FOR TABLE 2 OMITTED]

In this case, for tipping to be profitable for the bidder, the increase in the back-end price induced by tipping arbitrageurs must be less than the difference between the second-tier price when the bidder does not tip and the value of the firm under incumbent management, weighted by a factor that depends on the bidder's toehold.

Consider example 4 in Table 2. Profits to the bidder without tipping are shown in Row 8, assuming an exogenous back-end price of $1.20. Even if tipping increases the back-end price from $1.20 to $1.37, as in Row 9, it still increases the bidder's profits because the front-end price decreases sufficiently that Inequality (16) is not violated. If, however, the back-end price rises to $1.38, Inequality (16) is violated, so that tipping would reduce the bidder's profits.

The special case where [V.sub.b] = [V.sub.0] is illustrated in example 5. In this case, Inequality (16) reduces to the condition that tipping will increase the bidder's profits only if [[V.sub.b].sup.*] [less than] [V.sub.0]. Since [V.sub.0] [less than or equal to] [V.sub.b] [less than or equal to] [[V.sub.b].sup.*], this condition will never hold, and the bidder will never tip. In example 5, when [V.sub.b] = [[V.sub.b].sup.*] = [V.sub.0], tipping reduces profits because the extra round of transactions increases the first-tier price by [Epsilon].

It is clear from Equation (15) that, in Case 2, the incentive to tip is independent of the tendering costs of the marginal share (although whether a bidder faces Case 2 rather than Case 1 depends on [t.sub.c]). In Case 2, [Delta][Delta (difference)][[Pi].sub.2]/[Delta][Alpha] = N[[V.sub.0] - [V.sub.b] + [Epsilon]]. This derivative is negative when [V.sub.b] [greater than] [V.sub.0] + [Epsilon]. That is, in most cases, the incentive to tip decreases with increases in the bidder's toehold.

III. Distributional and Efficiency Implications

We show below that, in this model, tipping redistributes the gain from a tender offer. In addition, it enables the success of some value-increasing bids that would otherwise fall.

A. Division of Gains from a Tender Offer

If the bidder does not tip arbitrageurs prior to announcement, total profits to the original target shareholders are the difference between the value of (0.5 - [Alpha])N shares taken up at the first-tier bid price plus the 0.5N shares taken up at the second-tier bid price and the value of those (1 - [Alpha])N shares under incumbent management, plus the private tendering costs incurred by the shareholders. That is, shareholder profits are:

N[(1 - [Alpha])([V.sub.b] - [V.sub.0]) + (0.5 - [Alpha])([t.sub.c] + [Epsilon])] - [summation of] [t.sub.i] where i = [Alpha]N + 1 to [Alpha]N + n (17)

In a world with no tipping, the total gain from the tender offer is the sum of the gain to the bidder, given in Equation (9), and the gain to the original shareholders:

N[[N.sub.1] - [V.sub.0]] - [summation of] [t.sub.i] where i = [Alpha]N + 1 to [Alpha]N + n (18)

The total gain from the tender offer is the increase in the value of the target minus the tendering costs incurred by the shareholders.

The total gain from the tender offer if the bidder tips arbitrageurs prior to announcement is the sum of the gains to the bidder, the original shareholders, and the arbitrageurs. Recall that in Case 1 arbitrageurs will tender n shares in total; (0.5 - [Alpha])N shares are taken up in the first tier at [B.sup.*] = [[V.sub.b].sup.*] + [Epsilon] and the remaining, shares, [n - (0.5 - [Alpha])N], are taken up in the second tier at [[V.sub.b].sup.*]. Total receipts for the arbitrageurs are then n[[V.sub.b].sup.*] + (0.5 - [Alpha])N[Epsilon]. The cost to acquire these shares from the original shareholders is given by

n[V.sub.0] + [summation of] ([t.sub.i] + [Epsilon]) where i = [Alpha]N + 1 to [Alpha]N + n (19)

In Case 1, the arbitrageurs' profits are given by:

[Mathematical Expression Omitted]

To calculate profits to the original shareholders one must consider their tendering behavior. In Case 1, the first-tier and second-tier prices differ only by [Epsilon]. Consequently, no shareholder with tendering costs greater than [Epsilon] will tender; thus, only shares held by the arbitrageurs are tendered. The n shares sold by the original shareholders to the arbitrageurs prior to announcement are each sold for [Epsilon] more than the shareholder's reservation price; thus, in total, they earn n[Epsilon]. The N - n - [Alpha]N shares not sold to the arbitrageurs will receive the back-end price, [[V.sub.b].sup.*]. In Case 1, when the bidder tips arbitrageurs, the total gains to the original shareholders are then:

(N - n [Alpha]N)([[V.sub.b].sup.*] - [V.sub.0]) + n[Epsilon] (21)

If the bidder's profits, shown in Equation (11), are summed with those of the arbitrageurs (Equation (20)) and the original shareholders (Equation (21)), it is clear that total gains from the tender offer are unchanged if tipping occurs. Tipping merely redistributes these gains away from the original shareholders to the bidder and arbitrageurs.

In Case 2, arbitrageurs buy prior to announcement and then tender exactly enough shares to give the bidder a majority. Arbitrageurs buy no more than (0.5 - [Alpha])N shares because the maximum back-end price is [V.sub.0] + [t.sub.c] + [Epsilon] in Case 2. It would not be profitable for an arbitrageur to buy more shares because what the arbitrageur would have to pay to induce the c + 1st share to sell is greater than or equal to the first-tier price. The arbitrageurs sell (0.5 - [Alpha])N shares in the first tier at [V.sub.0] + [t.sub.c] + 2[Epsilon]. The cost to acquire these shares is given in Equation (19). Thus, in Case 2, the arbitrageurs' profits from the bid are given by:

(0.5 - [Alpha])N([t.sub.c] + [Epsilon]) - [summation of] [t.sub.i] where i = [Alpha]N + 1 to 0.5N (22)

Shareholders who do not sell to the arbitrageurs are those for whom [t.sub.i] [greater than] [t.sub.c]. These shareholders would receive [V.sub.0] + [t.sub.c] + 2[Epsilon] - [t.sub.i] if they tender and [[V.sub.b].sup.*] if they do not. Unless [Epsilon] is large, these shareholders will not find it profitable to tender.(14) (Here [Epsilon] is assumed to be small.) Thus, in this model, only the shares held by arbitrageurs are tendered. The gains to the original shareholders are then:

90.5 - [Alpha] N[Epsilon] + 0.5N([[V.sub.b].sup.*] - [V.sub.0]) (23)

The bidder's profits are shown in Equation (14). Again, summing the profits to the original shareholders, the bidder, and the arbitrageurs shows that tipping does not affect the total profits from the successful tender offer, merely their distribution.

B. Tipping Enables Value-Increasing Bids to Succeed

Private tendering costs may cause value-increasing bids to fail. For example, assume that a share is worth $1 under incumbent management but $1.50 under the bidder, and that the bidder may buy out minority shareholders at $1.30. If private tendering costs for existing shareholders are $0.50 per share, then existing shareholders will tender only to a bid of at least $1.81 per share (B = [V.sub.b] + [t.sub.c] + [Epsilon]). However, from Equation (3), the bidder's maximum per share first-tier bid price is $1.77. Consequently, a value-increasing bid will fail due to the presence of private tendering costs. As shown below, some value-increasing bids that fail in the absence of informed trading succeed if arbitrageurs are tipped before announcement. As a result, informed trading before announcement enables more value-increasing bids to succeed.

From Section II, a tender offer will fail in the absence of tipping if the bidder's maximum willingness to pay, B[prime], is less than the bid that induces the pivotal shareholder to tender. That is, the bid will fail if B[prime] [less than] [V.sub.b] + [t.sub.c] + [Epsilon], where B[prime] is given by Equation (3). Given the need to overcome tendering costs, the bidder may not be willing to bid enough to win even if [V.sub.1] [greater than] [V.sub.0].

Because tipping may increase the back-end price, [[V.sub.b].sup.*], the bidder's maximum willingness to pay for the controlling shares if arbitrageurs are tipped, [B[prime].sup.*], is given by

[B[prime].sup.*] = ([V.sub.1] - 0.5[[V.sub.b].sup.*] - [Alpha][V.sub.0])/(0.5- [Alpha]) (24)

In this case, as long as the bidder's willingness to pay is at least as great as the minimum acceptable bid, the bidder can win with tipping. That is, the bidder can win if [Mathematical Expression Omitted]. Thus, the following two inequalities jointly define the conditions under which tipping enables the success of bids that would fail in the absence of tipping:

B[prime] [less than] [V.sub.b] + [t.sub.c] + [Epsilon], and

[B[prime].sup.*] [greater than] max [[V.sub.0] + [t.sub.c] + [Epsilon], [[V.sub.b].sup.*]] (25)

In Case 1, max [[V.sub.0] + [t.sub.c] + [Epsilon], [[V.sub.b].sup.*]] = [[.V.sub.b].sup.8]. By substituting Equation (3) for B[prime] and Equation (24) for [B[prime].sup.*] in the inequalities in (25), value-increasing bids that succeed with tipping but fail in its absence are defined in terms of a range of exogenous back-end prices. Employing the assumption that [[V.sub.b].sup.*] [greater than or equal to] [V.sub.b], these bids occur when:

[Mathematical Expression Omitted]

The lower limit of the inequality details when a bid fails in the absence of tipping, the upper limit when a bid succeeds with tipping.

Example 3 in Table 2 illustrates this point. Even if the back-end price rises from $1.60 to $1.78, tipping reduces the front-end sufficiently that a bid that is not profitable without tipping is profitable if tipping is allowed.

In Case 2, [V.sub.0] + [t.sub.c] + [Epsilon] [greater than] [[V.sub.b].sup.*]. In this case, a bid succeeds with tipping if [B[prime].sup.*] [greater than] [V.sub.0] + [t.sub.c] + [Epsilon]. Substituting for B[prime] and [B[prime].sup.*] as above, tipping enables bids that would fail without it if:

[Mathematical Expression Omitted]

The lower limit, the condition under which a bid fails in the absence of tipping, is the same as that in Equation (26). The upper limit indicates when a bid succeeds with tipping in Case 2.

Consider the basic parameters of Table 2 ([V.sub.1] = $1.75, [V.sub.0] = $1, [Alpha] = 0.05, N = 1,000, [Epsilon] = $0.01). In the absence of tipping, if the back-end price is $1.30 and [V.sub.1] falls to $1.50, the bid will be unprofitable (Equation (9)). Yet, if the bidder tips in this same situation, this bid becomes profitable even if the back-end price rises to $1.51 because the front-end price has decreased sufficiently (Equation (14)).

C. Value-Decreasing Bids

While we show that tipping arbitrageurs prior to announcement enables some value-increasing bids to succeed that would otherwise fail, a related question is whether informed trading prior to announcement allows some value-decreasing bids to succeed.

Conditional two-tier tender offers are coercive; once the bid is announced, target shareholders will tender if the first-tier price, B, is greater than the second-tier price, [V.sub.b], even if B is less than the current market price of the stock, [V.sub.0]. Thus, in the absence of any opposition, a value-decreasing bid, [V.sub.1] [less than] [V.sub.0], could succeed. Bradley, Desai, and Kim (1988), however, demonstrate that target management is always able to structure an offer to repurchase shares that dominates any value-decreasing bid.

The same result holds in the presence of pre-announcement informed trading. In the model developed here, there is no uncertainty. Both the bidder and the arbitrageurs know the supply schedule of shares in the target firm. The arbitrageurs also know the bidder's per share value of the target, [V.sub.1]. If [V.sub.1] were less than [V.sub.0] (a value-decreasing bid) and the back-end of the bid were required to be at least [V.sub.1], then the bidder's maximum first-tier price would be less than [V.sub.0]. Arbitrageurs would not purchase any shares because they would not pay the current market price, [V.sub.0], for a share that they know will be purchased at something less. As a result, tipping arbitrageurs prior to announcement will not change the result of Bradley, Desai, and Kim (1988) that all successful tender offers will be value-increasing.

D. Disadvantages of Pre-Announcement Informed Trading

The arguments that bidders have the incentive to tip arbitrageurs prior to announcement and that such informed trading enables more value-increasing bids to occur imply that informed trading enhances society's welfare.(15) However, there are some broader costs to society from informed trading. Ausubel (1990), Bhattacharya and Spiegel (1991), and Manove (1989) show that informed trading may not improve welfare because it engenders a loss of investor confidence that harms both insiders and outsiders. In addition, an agent who can trade in advance in assets whose prices depend on the agent's actions may have an incentive to take value-decreasing actions (Hirshleifer (1971) and Kyle and Vila (1991)). Policy decisions regarding informed trading prior to public announcement must weigh these costs against the gains from enabling more value-increasing bids to succeed.

IV. Conclusion

Informed trading that encourages investors with low private costs of tendering to purchase a controlling interest in a target reduces the minimum successful bid price and increases profits for the bidder. To induce a controlling interest to tender, the bidding firm must offer a price greater than the value of retaining the stock plus the private tendering costs of the pivotal share. Because arbitrageurs are perceived to have low private tendering costs, bidding firms have an incentive to tip arbitrageurs prior to public announcement of a tender offer to alter the ownership structure of the target firm. In the absence of pre-announcement informed trading, some value-increasing tender offers fail because of private tendering costs. As a result, informed trading prior to announcement of a tender offer enables more value-increasing tender offers to occur.

The incentive for bidders to tip arbitrageurs depends on the amount of dilution the legal system will allow, the increase in the back-end price that occurs due to pre-announcement informed trading, the private tendering costs of the share that grants a controlling interest, and the size of the bidder's toehold. These factors create several testable empirical implications.

First, if the bidder is able to fully dilute the value of minority shareholders, it will not tip arbitrageurs prior to announcement. Arbitrageurs will not buy shares in the target if they know that the bidder may expropriate the value of shares taken up in the second tier. Because the legal system often prevents complete expropriation (either through fair price laws, fair price charter amendments, or the appraisal remedy), one implication is that pre-announcement tipping would be negatively related to the degree of expropriation allowed by the legal system. Since this depends on state statute and case law, there should be cross-sectional variation by state and over time.

Second, the bidder's incentive to tip decreases if an increase in the target firm's stock price prior to announcement is embedded in the back-end price. Because this raises the total cost of the bid, less pre-announcement informed trading should be observed when the legal system incorporates pre-announcement price increases in the second-tier price.

Third, the benefit to the bidder from pre-announcement informed trading comes from reducing the private tendering cost of the share that provides a controlling interest. The higher the private tendering costs of this pivotal share, the greater the incentive to tip arbitrageurs. Thus, the incentive to tip arbitrageurs should be negatively related to the degree of institutional ownership in the target firm because greater institutional ownership increases the likelihood that the pivotal share is already held by a shareholder with low tendering costs.

Finally, in most cases, the incentive to tip investors with low private costs of tendering increases with decreases in the bidder's toehold. As a result, one would expect more tipping to occur after the 1968 enactment of the Williams Act, which imposed limits on the size of the toehold a bidder may acquire before revealing its intentions to the public.

1 The term "insider trading" has particular legal connotations. The broader and more neutral term "informed trading" means any trading on material information that is not publicly known.

2 In an empirical study of Dutch auction repurchases, Bagwell (1992) provides evidence that firms face upward-sloping supply curves when repurchasing shares.

3 In theoretical models developed by Chowdhry and Jegadeesh (1994) and Hirshleifer and Titman (1990), the probability of success of a tender offer is positively related to a bidder's toehold. Walkling (1985) presents empirical evidence consistent with this hypothesis. Our model has no uncertainty and abstracts from the effect of the toehold on the probability of success of a given bid. However, profitability of a bid is positively related to the bidder's toehold. In their model, Hirshleifer and Titman (1990) also show that increasing the bid premium increases the probability of success of a tender offer. Such a strategy has no role in the model developed in this paper because the bidder makes only bids that succeed with probability one.

4 Some commentators distinguish between parking and putting stock in friendly hands. The nominal holder of parked stock is understood not to be the owner of the stock and is usually insulated from any gains or losses. Whether putting stock in friendly hands is a violation of Section 14(e) of the Securities Exchange Act of 1934 may depend on the information revealed when the suggestion to buy target shares is made.

5 In other types of control transactions (such as a negotiated merger), the pattern of information release may differ.

6 Bradley, Desai, and Kim (1988) demonstrate that successful tender offers are always value-increasing because target management can always make a counter-offer that dominates a value-decreasing bid.

7 In their theoretical model, Hirshleifer and Titman (1990) show that the probability of success is positively related to the amount of dilution that can be imposed on minority shareholders.

8 Note that for some targets, [t.sub.i] could equal zero for some (or all) of the shares not in the bidder's toehold. Here, [t.sub.i], i = [Alpha]N + 1, ..., N, is assumed to be greater than zero to illustrate the advantages of informing arbitrageurs.

9 Ravid and Spiegel (1990) quote Section 262 of Delaware statute as a typical example: "'...the Court shall appraise the shares, determining their fair value exclusively of any element of value arising from the accomplishment or expectation of the merger....'"

10 The public announcement of a takeover attempt is usually associated with a 25-30% increase in the stock price of the target firm (Jarrell, Brickley, and Netter (1988)). Up to half of this run-up may occur before the announcement (Keown and Pinkerton (1981)). Meulbroek (1992) and Sanders and Zdanowicz (1992) suggest that pre-announcement run-up is a result of informed trading, while Jarrell and Poulsen (1989) argue that much of the run-up is due to non-insider trading activities.

11 This analysis is at variance with an argument by Stulz, Walkling, and Song (1990) that increases in the bidder's toehold or increases in institutional ownership always cause the reservation price of the pivotal share to decline. The reservation price of the pivotal share will change only if the change in ownership structure encompasses that share.

12 The model abstracts from other possible costs of tipping, such as attracting a rival or increases in the cost of additional shares purchased prior to announcement to increase the bidder's toehold.

13 See Fishman (1988) for an alternative explanation of large premiums based on signaling.

14 Share i will be tendered if [V.sub.0] + [t.sub.c] + [Epsilon] - [t.sub.i] [greater than] [[V.sub.b].sup.*]. That is, if [Epsilon] [greater than] 0.5[([[V.sub.b].sup.*] - [V.sub.0]) + ([t.sub.i] - [t.sub.c])].

15 This is true to the extent that social welfare is identified with value-increasing bids. It is appropriate if tendering costs consist of tax payments that are merely redistributions. To the extent that tendering costs represent the use of real resources rather than merely wealth transfers, a social welfare measure would need to incorporate these costs.

References

Ausubel, L.M., 1990, "Insider Trading in a Rational Expectations Economy," American Economic Review (December), 1022-1041.

Bagwell, L.S., 1991, "Share Repurchase and Takeover Defense," Rand Journal of Economics (Spring), 72-88.

Bagwell, L.S., 1992, "Dutch Auction Repurchases: An Analysis of Shareholder Heterogeneity," Journal of Finance (March), 71-106.

Bhattacharya, U. and M. Spiegel, 1991, "Insiders, Outsiders and Market Breakdowns," Review of Financial Studies (Vol. 4, No. 2), 255-282.

Bradley, M., A. Desai, and E.H. Kim, 1988, "Synergistic Gains from Corporate Acquisitions and their Division between the Stockholders of Target and Acquiring Firms," Journal of Financial Economics (May), 3-40.

Brown, D.T. and M.D. Ryngaert, 1992, "The Determinants of Tendering Rates in Interfirm and Self-Tender Offers," Journal of Business (October), 529-555.

Chowdhry, B. and N. Jegadeesh, 1994, "Pre-Tender Offer Share Acquisition Strategy in Takeovers," Journal of Financial and Quantitative Analysis (March), 117-129.

Comment, R. and G.A. Jarrell, 1987, "Two-Tier and Negotiated Tender Offers: The Imprisonment of the Free-Riding Shareholder," Journal of Financial Economics (December), 283-310.

Fishman, M., 1988, "A Theory of Preemptive Takeover Bidding," Rand Journal of Economics (Spring), 88-101.

Grossman, S.J. and O.D. Hart, 1980, "Takeover Bids, the Free-Rider Problem, and the Theory of the Corporation," Bell Journal of Economics (Spring), 42-64.

Herzel, L. and L. Katz, 1987, "Insider Trading: Who Loses?," Lloyds Bank Review (July), 15-26.

Hirshleifer, D. and S. Titman, 1990, "Share Tendering Strategies and the Success of Hostile Takeover Bids," Journal of Political Economy (April), 295-324.

Hirshleifer, J., 1971, "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review (September), 561-574.

Jarrell, G.A., J. Brickley, and J.M. Netter, 1988, "The Market for Corporate Control: The Empirical Evidence Since 1980," Journal of Economic Perspectives (Winter), 49-68.

Jarrell, G.A. and A.B. Poulsen, 1989, "Stock Trading Before the Announcement of Tender Offers: Insider Trading or Market Anticipation?," Journal of Law, Economics and Organization (Fall), 225-248.

Jensen, M.C., 1986, "Don't Freeze the Arbs Out," Wall Street Journal (December 3), 26.

Keown, A.J. and J.J. Pinkerton, 1981, "Merger Announcements and Insider Trading Activity: An Empirical Investigation," Journal of Finance (September), 855-869.

Kyle, A.S. and J. Vila, 1991, "Noise Trading and Takeovers," Rand Journal of Economics (Spring), 54-71.

Manove, M., 1989, "The Harm from Insider Trading and Informed Speculation," Quarterly Journal of Economics (November), 823-845.

Meulbroek, L.K., 1992, "An Empirical Analysis of Illegal Insider Trading," Journal of Finance (December), 1661-1699.

Ravid, S.A. and M. Spiegel, 1990, "On Toeholds and Bidding Contests," Unpublished Paper (July).

Romano, R., 1987, "The Political Economy of Takeover Statutes," Virginia Law Review (February), 111-199.

Sanders, R.W. and J.S. Zdanowicz, 1992, "Target Firm Abnormal Returns and Trading Volume Around the Initiation of Change in Control Transactions," Journal of Financial and Quantitative Analysis (March), 109-129.

Stulz, R.M., R.A. Walkling, and M.H. Song, 1990, "The Distribution of Target Ownership and the Division of Gains in Successful Takeovers," Journal of Finance (July), 817-833.

Walkling, R., 1985, "Predicting Tender Offer Success: A Logistic Analysis," Journal of Financial and Quantitative Analysis (December), 461-478.

Weston, J.F., K.S. Chung, and S.E. Hoag, 1990, Mergers, Restructuring, and Corporate Control, Englewood Cliffs, N J, Prentice-Hall.

RELATED ARTICLE: Table 1. Notation

[V.sub.0] = Per share value of target assets under control of incumbent management

[V.sub.1] = Per share value of target assets under control of bidder

N = Total number of shares in target firm

n = Number of shares tendered (equal to number of shares purchased by arbitrageurs)

[Alpha] = Bidder's toehold in target (fraction of total shares)

B = First-tier offer price in the absence of informed trading

[B.sup.*] = First-tier offer price in the presence of informed trading

B[prime] = Maximum first-tier offer price bidder is willing to pay in the absence of informed trading

[B[prime].sup.*] = Maximum first-tier offer price bidder is willing to pay in the presence of informed trading

[V.sub.b] = Second-tier offer price in the absence of pre-announcement informed trading, [V.sub.b] [greater than or equal to] [V.sub.0]

[[V.sub.b].sup.*] = Second-tier offer price in the presence of pre-announcement informed trading, [[V.sub.b].sup.*] [greater than or equal to] [V.sub.b]

[t.sub.i] = Private tendering cost of share i

[t.sub.c] = Private tendering cost of the share that grants a controlling interest

Devra L. Golbe is Professor of Economics at Hunter College of the City University of New York, New York, NY. Mary S. Schranz is Assistant Professor of Finance at Lehigh University, Bethlehem, PA.

Printer friendly Cite/link Email Feedback | |

Author: | Golbe, Devra L.; Schranz, Mary S. |
---|---|

Publication: | Financial Management |

Date: | Dec 22, 1994 |

Words: | 8906 |

Previous Article: | Taxes and the returns to foreign acquisitions in the United States. |

Next Article: | Does targeted investing make sense? |

Topics: |