Market Valuation and Merger Waves
Matthew Rhodes-Kropf and S. Viswanathan
The Journal of Finance, 2004


•One of the puzzles in finance is why there are periods when mergers are plentiful and other periods when merger activity is much lower.
•The periods of high merger activity seem to be correlated with high market valuations. Moreover, firms tend to use stock in these high activity/high stock markets periods as an “acquisition currency”.
•Mergers involving securities are inherently different from cash takeovers as they involve valuation problems.
•The authors propose a model in which private information on both sides can lead rationally to increase stock merger activity that is correlated with market valuation.

The Model

•The basic model of a merger is a second price auction (strategically equivalent to an English auction)
•There are n risk-neutral firms with synergistic values for the target firm bid in the auction.
•There is a risk neutral target firm T, which considers the bids and decides whether to accept an offer.
•A bidding firm, firm i, has a private value Vi for the target: Vi = XT (1 + si)
Where, the synergy component, si >-1, maybe positive or negative
•Synergies and the merger values are iid, drawn from a distribution Fs(s) and contain a common and firm specific factor.
•The target and the market do not know the true value of each bidder firm, Xi, but they observe the market value of each firm Mi>0.
Where Xi = Mi (1-εi)(1- ρ)
The market value does not necessarily equal Xi because it is possible that the market has misvalued the assets. There are two types of misvaluation market-wide (ρ) and firm specific (εi ). Where εi and ρ are drawn with zero mean from Fε(ε) and Fρ(ρ) and are independent.
•Target firm has a market Value MT. where XT = MT (1+ εi)(1- ρ).
•Although each firm knows if they undervalues or overvalued, they do not know εi or ρ. Each bidder obtains information about the target and the other bidder through MT, Mi, Xi and Vi.
•The authors assume that adverse selection and SEC insider information rules prevent managers from buying and selling their own undervalued or overvalued stock in large enough quantities to restore efficient pricing.
•All firms must bid using only their own equity. An equity bid consist of an offer of fraction αi of the joint firm. After the auction, if the bid is accepted, the total firm value will be Xi + Vi. However, since the target and the market know neither Xi nor Vi, they will rationally value any offer at
E [ αi (Xi + Vi) | ΦT] and E [ αi (Xi + Vi) | ΦM]

•The authors assume that fiduciary responsibility rules require the target to accept only the offer with the highest expected value (>XT).

II Equity Auction with Misvalued Stock

•In a second-price auction with equity bids, firms bid by standing a fraction α of the join firm that they will give to the owners of the target firm.
•The scoring rule is a function of the target’s private information and all the firms’ bids and stock prices, Zi = g (αi, Mi, ΦT)
Where the firm with the highest Z wins the auction.

•In a second-price auction the winning firm pays a fraction that equals the lowest fraction they could have bid and just tied the second highest bidder.

•Lemma 1 shows that all bidders will bid the largest fraction that they would ever be willing to pay.

B.Choosing the winner
•How will the target choose the winner (the equilibrium scoring rule)?
•The target must award the firm with the highest score
•The target ‘s estimate of any firm’s value is E[Xi | Mi, XT, MT)
•After the bids, the target updates his expectation of Xi and must decide the probability that the firm is overvalued versus the probability that the firm has a large synergy.
•The largest score should be assigned to the offer with the highest expected value, where, Zi = g (αi, Mi, ΦT) = E[Vi | Mi, ΦT].
•Lemma 2 shows that the only information that the target needs to rank the bids is
( αi / (1- αi)) * Mi


•Because of market-wide misvaluation, the sufficient statistics used by the target are not independent..
•The target learns something about the synergies from looking at his own misvaluation, and from looking at all of the bids.
•I can be shown that

E[Vii,MiT] =

XT*E [(1+ si) | (1+ si) / ((1- ρ) (1+ εi)), ((1+si) (1+ εj)) / ((1+ sj) (1+ εi)) for all i ≠ j,
and, ((1+ εi) (1+ εT)) / (1+ εi)]

Lemma 4 shows that (1+si) and (1+si) /((1- ρ) (1+ εi)), ((1+si) (1+ εj)) / ((1+sj) (1+ εi)) and ((1+ εi) (1+ εT)) / (1+ εi)affiliated.

•Affiliation essentially means that the expectation of (1+si) increases with any of the sufficient statistics.

III Mergers

•XT is the target’s reservation price and the target’s acceptance rule is simply to accept any offer such that

E[Vi | αi ,Mi, ΦT] > XT or

E [(1+si) | (1+si) / ((1- ρ) (1+ εi)), ((1+si) (1+ εj)) / ((1+sj) (1+ εi)) for all i ≠ j,

and, ((1+εi) (1+ εT)) / (1+ εi)] > 1

Theorem 1: Stock mergers are more likely to occur in overvalued markets that in undervalued markets.

•If the market is overvalued, high ρ, then the target is more likely to overestimate the synergies, even though he can see that his own price is affected by the same overvaluation because he still underestimates the market-wide misvaluation.

•On average, overvalued firms or firms with large synergies win takeover battles and undervalued targets are purchased.

•The fact that a merger occurs provide information about the true value of the target and the bidding firm.

•On the announcement of a stock merger the target’s and the acquirer’s market price could rise or fall. If the target’s reservation price does not bind then the market price of the second highest bidder fall.

•The market expects that the winning firm to be overvalued, the target to be undervalued, and that the synergies to be small or that competition gave most of the synergies to the target.

•It appears that takeovers destroy value. However, the stocks move not because any firm is destroying value by merging, but because in an attempt to create value, they are revealing information about what their price should have been.

IV. Mergers Waves

•The model begins at time zero with prices and realization of each variable. Then at each of m sequential time periods, an auction occurs for an acquisition candidate. Each firm has only one chance to merge. After each auction, market prices react to observed information. They assume that the event merger or not merger and all bids are observed al the end of each period. At the end of m periods, true values are revealed.

Definition 1: A merger wave is defined as a sequence of time periods (two or more) in which the probability of a merger occurring is above the unconditional expected probability of a merger.

Theorem 2 : A high enough realization of the market-wide misvaluation, ρ, will cause a merger wave, even though given a merger in the first period, the market reduces prices until in expectation, there is no market-wide misvaluation left in prices.

•A large realization of ρ will begin a merger wave. However, the merger will occur only if the market stays overvalued.
•Overvaluation that causes a merger wave may not be fully corrected by a market rationality updates. Each subsequent merger signal less and less information about market-wide overvaluation, as the market increases its expectations about a common synergy factor. Hence, the first merger leads to a significant downward revision in the market index, but subsequent mergers do not move the index as much. Therefore, a merger wave may be followed by a market crash when participants learn information about the synergies that leads them to question the gains from the entire sequence of mergers.


•Even fully rational participants make mistakes. Their decision turns out to be the wrong decision ex post even it was correct ex ante. When the market is overvalued, the target rationally reduces the expected value of a given stock offer, and thus, the target values correctly on average. However, the target is more likely to overvalue the offer the greater the market overvaluation is even though the target’s own stock is affected by the same market overvaluation. Thus, market overvaluation increases the chance that a merger occurs. Therefore, a wave can occur due to misvaluation even if there is no underlying reason for mergers. The impacts of misvaluation are significant.

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