Instrumentos

Thus far we have considered an exogenous takeover premium which we believe to be a good model of a contested takeover in which the bid price is forced above the level an individual bidder would bid in the absence of competing buyers. Nonetheless, numerous takeover offers are characterised by only one bidder.

This section studies the case of the takeover premium being strategically set by a Bidder with no competitors. Hence, the Bidder makes an offer maximizing his expected profit, which is the product of the surplus from the takeover and the probability that the takeover takes place. Suppose that the Bidder’s value of the target company isW > V. The game proceeds as in the benchmark setting with the

only difference that, at t = 0, the offer P solves the following bidder optimisation problem: max P∈[V,W]{Π = (W −P)β(θ ∗_{(P))} (2.12)} = max P∈[V,W] {Π = (W −P) Φ (√τθ[θ∗(P)−y])}

whereθ∗(P) is implicitly characterised by equation (2.9). We assume that the bid- ding firm shares the same information set as the market makers – this prevents market participants seeking to make inferences as to the target Board’s entrench- ment from the bidder’s bid price.13 We assume P ∈[V, W] for analytical simplicity and for realism. Nonetheless, in principle an offer P < V can be optimal if the Board have expected entrenchment y < 0. This would be the case after political pressure urging a sale for example. We omit those cases where the target Board is keen to be replaced. The takeover offer determines both the Bidder’s surplus if the takeover succeeds and the probability that this occurs. The following Lemma characterises the solution to the Bidder’s problem:

Lemma 23 Suppose the Bidder’s value for the target company is sufficiently large, i.e. W −V > y− κδ

2 + p

π/2τθ. Then, Π in (2.12) is quasiconcave and has an interior maximum at the optimal bidP∗ which is implicitly characterised by:

P∗ =W −[1−κδ∆ϕ(∆ [θ ∗_(P∗_{)−y])] Φ} √_τ θ[θ∗(P∗)−y] √ τθϕ √ τθ[θ∗(P∗)−y] (2.13)

Proof. See Technical Appendix.

For analytic solutions we restrict to the case in which the surplus available is large enough. This allows us to show that the Bidder’s profit function is quasi- concave. The Lemma implies that the optimal bid always satisfiesθ∗(P∗) > yand

13

Other papers in the literature of takeovers have assumed that shareholders have better infor- mation than the Bidder. Ekmekci and Kos(2016) argue that this can be thought of as a reduced form of a model in which the Bidder has some information, yet this information is public.

therefore, the probability that the takeover succeeds conditional on an offer being made is above one half.

This is a complicated setting which makes analysis difficult. Nonetheless we can establish a number of comparative statics results with respect to the expected level of the Board’s resistance,y.

Proposition 24 With a strategic Bidder:

1. The equilibrium bid priceP is increasing in the prior expected level of takeover resistance;

2. The probability the takeover succeeds falls in the prior expected level of resis- tance;

3. The stock price during the offer period is affected in an ambiguous direction by the prior expected level of takeover resistance.

Proof. The proofs of parts 1 and 2 are contained in the Technical Appendix. The proof of part 3 is by virtue of the numerical example in Figure2.3.

The Proposition indicates the Bidder responds to increases in the prior ex- pected level of takeover resistance with a bigger bid premium. This increase in the offer is designed to counter the expected takeover defence and to do enough to en- courage the sophisticated shareholders to pressure the Board to agree to the bid. Nonetheless, the positive effect of a higher bid on the probability of a takeover is ultimately insufficient to outweigh the negative impact of a sufficiently great level of Board resistance. Hence the takeover becomes less likely.

Figure2.3plots both the endogenous takeover bid P∗ and the interim stock priceM as a function of the Board’s expected typeyfor a given numerical example. It is possible to see that the takeover premium increases monotonically in response to a stronger expected defence, conforming to result 1 of Proposition 24. It is also possible to see that the price of the stock in the offer period, M, presents an

V = 10 11 12 13 14 W = 15 0 2 4 6 8

y

Figure 2.3: Optimal takeover bid P∗ and the corresponding interim period stock priceM as a function of takeover resistancey.

The takeover premium isP∗−V whereas the spread from which risk-arbitrageurs aim to make profit isP∗−M. Parameter values areW = 15,V = 10,τε= 4,τθ= 5,κ=.75 andδ=.4.

inverted-U shape relationship with the expected takeover resistance. As we consider ever higher levels of the Board’s expected resistance, it is not possible for the increase in the bid price to rise sufficiently to maintain the probability of takeover success. As a result the probability of offer acceptance eventually falls and so the price of the stock during the offer period ultimately collapses.