Topics in Contract Theory Lecture 6. Separation of Ownership and Control

Transcription

1 Leonardo Felli 16 January, 2002 Topics in Contract Theory Lecture 6 Separation of Ownership and Control The definition of ownership considered is limited to an environment in which the whole ownership of a company is concentrated in the hands of a unique party. Recall that is never optimal to share ownership (joint ownership is dominated). In reality ownership is however often shared among a number of agents (shareholders). In this situation (publicly held company) the control of the company is in the hands of an individual (manager or CEO) that may not be the owner. 1

2 The natural question: Topics in Contract Theory 2 how is it possible to rationalize this allocation of ownership and control? We are going to derive an incomplete contract framework in which in equilibrium there will be sharing of ownership: one individual retains cash flow rights, and releases control of the company; a different individual acquires the control of the company. The contractual incompleteness that leads to this type of framework generates an inefficiency that differs from the hold-up problem.

3 Topics in Contract Theory 3 This inefficiency is associated with the non-contractibility of an aspect of the preferences of the individual who has control (residual rights). This aspect of the preferences is known as private benefits from control. There exists a collection of perks, benefits, status associated with having the residual rights on a company. These are very difficult benefits to dispose of by means of a contract and therefore are transferred only when the (residual rights) control is transferred. These benefits differs from the transferable value of the company that usually corresponds to the expected present discounted value of all future profits of the company.

4 Topics in Contract Theory 4 Consider first a simple model involving two parties: an entrepreneur and a raider. Assume that the entrepreneur is the incumbent owner of the company. In his hands the value of the transferable value of the company is V E while the private benefits that the entrepreneur gets from the company is B E. The total value of the company is: V E + B E The raider is interested in acquiring the company. In the raider s hands the transferable value of the company is V R while the raider s private benefits are B R.

5 Topics in Contract Theory 5 The total value of the company in the hands of the raider is: V R + B R We first consider a simple transaction in which E and R meet to negotiate a contract for the transfer of the company (if they so desire). We assume that the contract can specify the transfer of any percentage µ, µ [0, 1], of the shares of the company. The owner of a share of the company is entitled to cash flow rights on the company: the corresponding share of the tradable value of the company V h, h {E, R}. The owner of a share of the company may also be entitled to control rights on the company: a vote to decides on the company activity.

6 Topics in Contract Theory 6 Assume that a majority rule is used to take a decision on the company activity. The residual rights of control on the company reside with the shareholder(s) that have the majority of the shares of the company that have control rights. The percentage of (all the) shares of the company that represent the majority of the shares with control rights is known as the control stake of the company. Let α be the control stake of the company. If every share of the company is entitled to a vote α could be equal to 50% of the shares plus one share of the company. If instead half of the company shares have control rights and half of the company share have only cash flow rights then α is half of the company shares with control rights plus one of these shares.

7 Topics in Contract Theory 7 Therefore the individual who owns the control stake α of the company obtains the private benefits B h, h {E, R}, from the control of the company. For simplicity we assume that the bargaining process between the entrepreneur and the raider is a simple cooperative split. Let S be the lowest possible price that the entrepreneur (the seller of the company) is willing to accept. Let B be the highest price that the raider (the buyer of the company) is willing to pay.

8 Topics in Contract Theory 8 Then: Trade occurs if and only if B > S The trading price is: ψ B + (1 ψ) S The payoff to E after the trade is: ψ B + (1 ψ) S The payoff to R after the trade is: B ψ B + (1 ψ) S = (1 ψ) (B S)

9 Topics in Contract Theory 9 Result 1. (Zingales 1995) There is no need to separate cash flow rights and control rights of a company if an entrepreneur owns the entire company when facing a raider. The sale of the company is efficient. Proof: Assume that E decide to trade and transfer the ownership of the entire company µ = 1 to R. Given the value of the company to E and R we obtain that S = V E + B E, B = V R + B R In other words the payoff to E is: ψ (V R + B R ) + (1 ψ) (V E + B E )

10 Topics in Contract Theory 10 Then trade occurs if and only if ψ (V R + B R ) + (1 ψ) (V E + B E ) > (V E + B E ) or (V R + B R ) > (V E + B E ) which proves efficiency. Assume now that only a percentage µ α of the shares of the company is traded between E and R. Then the highest price that R is willing to pay is: B = µ V R + B R The lowest price that E is willing to accept is: S = V E + B E (1 µ)v R

11 Topics in Contract Theory 11 The total trading price for the µ shares is then: ψ (µ V R +B R )+(1 ψ) [V E +B E (1 µ) V R ] = = µ V R (1 ψ) V R +ψ B R +(1 ψ) (V E +B E ) The payoff to E is then (1 µ)v R +µv R (1 ψ)v R +ψ B R +(1 ψ)(v E +B E ) = ψ (V R + B R ) + (1 ψ) (V E + B E ) Clearly the payoffs to E and to R are the same for every value of µ α which concludes the proof. Consider now the possibility that E could go public on the stock market before meeting R for the trade of the company.

12 Topics in Contract Theory 12 We assume that in this case E can exchange a minority stake of the company in exchange for cash. Assume that the market is fully rational and forecasts that the raider will acquire the company and the company will then have the transferable value V R. Therefore the market will pay for a minority stake (1 µ) of the company the price (1 µ) V R In this case, it is possible for E to find optimal separating the cash flow rights and the control rights of the company.

13 Topics in Contract Theory 13 Result 2. (Zingales 1995) Trade occurs only if and only if (V R + B R ) > (V E + B E ) in other words it is efficient. Full separation of cash flow rights and control rights of a company µ = α is optimal when V R > V E and E can go public before facing the raider. Proof: Assume that E goes public and obtains price (1 µ) V R from selling the minority stake 1 µ on the market.

14 Topics in Contract Theory 14 E now only owns a percentage µ α of the shares of the company and this is traded between E and R. The highest price that R is willing to pay is: B = µ V R + B R The lowest price that E is willing to accept is now : S = µ V E + B E The total trading price for the µ shares is then: ψ (µ V R + B R ) + (1 ψ) (µ V E + B E ) The payoff to E before going public is now: ψ (V R + B R ) + (1 ψ)[µ V E + B E + (1 µ) V R ] = ψ (V R +B R ) + (1 ψ)(v E +B E ) + + (1 ψ) (1 µ) (V R V E )

15 Topics in Contract Theory 15 Therefore E chooses µ so as to solve the following problem: max µ s.t. ψ (V R + B R ) + (1 ψ)(v E + B E ) + 1 µ α + (1 ψ) (1 µ) (V R V E ) The solution to the problem above is: µ = α V R > V E µ = 1 V R < V E Therefore if V R V E then trade occurs if (V R + B R ) > (V E + B E )

16 Topics in Contract Theory 16 If instead V R > V E then trade occurs if ψ (V R + B R ) + (1 ψ)(v E + B E ) + + (1 ψ) (1 α) (V R V E ) > (V E + B E ) or: [1 α(1 ψ)] (V R V E ) > ψ (B E B R ) This condition is satisfied if and only if (V R + B R ) > (V E + B E ) Notice that in the environment we just analyzed either we have full separation of cash flow right and control rights, µ = α, or we have no separation of cash flow rights and control rights, µ = 1.

17 Topics in Contract Theory 17 Consider now a situation in which facing a raider there exists two potential buyers instead of a single raider. Let these buyers be: buyer 1, tradable value of the firm V 1 ; buyer 2, tradable value of the firm V 2. We assume that: V 2 > V 1 V E Assume also for simplicity B E = 0. Consider first the case in which neither buyer has private benefits from control.

18 Topics in Contract Theory 18 Assume further that when facing these two buyers E decides to auction off the company to the highest bidder. This is the optimal selling procedure in the event that the bidders have private information on the value of the company in their hands. For simplicity we analyze the case where however all parties have symmetric information. Result 3. (Cornelli and Felli 2001) Full separation of cash flow rights and control rights of a company µ = α is optimal when E faces more than one potential buyer, and buyers do not have private benefits from control. The trade of the company is efficient.

19 Topics in Contract Theory 19 Proof: Assume that a stake µ of the company µ α is auctioned off. The two buyers valuations are: B 1 = µ V 1, B 2 = µ V 2 The equilibrium of the auction is such that bidder 2 obtains µ shares at the price µ V 1 The payoff to E is then: µ V 1 + (1 µ) V 2 Therefore E chooses the stake to auction off solving the following problem: max µ s.t. µ V 1 + (1 µ) V 2 1 µ α The solution is then µ = α Buyer 2 gets the company so efficiency arises.

20 Topics in Contract Theory 20 Consider now the case in which we allow bidders to re-trade the stake of the company they get in the auction (a common value component in the bidders valuations). Two periods: Period 1: auction as above. Period 2: trade among bidders. The trade among bidders occurs only if the company is bought by bidder 1 then bidder 1 is the seller and bidder 2 the buyer. Let S 1 be the lowest price the seller (bidder 1) is willing to accept. Let B 2 be the highest price at which the buyer (bidder 2) is willing to buy the company.

21 Topics in Contract Theory 21 We assume that in stage 2: with probability ψ the seller makes a take-it-orleave-it offer to the buyer, with probability (1 ψ) the buyer makes a takeit-or-leave-it offer to the seller. Result 4. (Cornelli and Felli 2001) Full separation of cash flow rights and control rights of a company µ = α is optimal when E faces more than one potential buyer, buyers do not have private benefits from control, and they can retrade the stakes of the company. The trade of the company is efficient.

22 Topics in Contract Theory 22 Proof: Assume that only the stake µ of the company is auctioned off in period 1. The reservation values of the two bidders are: B 2 = µ V 2, S 1 = µ V 1 Hence the price the seller (bidder 1) is able to obtain in period 2 is µ [ψv 2 + (1 ψ)v 1 ]. This is the seller s (bidder 1 s) willingness to pay in the auction of the control stake of the firm.

23 Topics in Contract Theory 23 It is also bidder 2 s winning bid, since µ V 2 > µ [ψv 2 + (1 ψ)v 1 ]. Hence, the payoff to E is: (1 µ)v 2 + µ [ψv 2 + (1 ψ)v 1 ] The stake µ is chosen by E so as to solve: max µ s.t. (1 µ)v 2 + µ [ψv 2 + (1 ψ)v 1 ] 1 µ α The solution to E s problem is therefore µ = α. Notice that once again bidder 2 gets the company therefore efficiency is guaranteed. By auctioning off only the control stake α E can guarantee himself a stake (1 α) of the company at the highest value V 2.

24 Topics in Contract Theory 24 Assume that after the auction a buyer 3, with valuation V 3 > V 2 will want to buy the firm (no discounting). Should E wait for him? If E have not yet sold the firm when buyer 3 appears, they can bargain with this buyer and their proceeds are: ψv 3 + (1 ψ)v E Assume instead that the creditors auction off the firm s control stake in the first period to bidders 1 and 2 and let the winner of this auction bargain with buyer 3. Then the payoff bidder i = 1, 2 expects from bargaining with bidder 3 is α [ψv 3 + (1 ψ)v i ].

25 Topics in Contract Theory 25 The equilibrium bid is then α [ψv 3 + (1 ψ)v 1 ] The revenues from the auction are: (1 α)v 3 + α[ψv 3 + (1 ψ)v 1 ] Notice that even if V 1 = V E the revenues in the second case are higher Result 5. In other words even when the buyer that can maximize the value of the company is not at the auction it is still optimal for E to auction off immediately the minimum control stake of the company.

26 Topics in Contract Theory 26 Let i s ownership, i {1, 2} of the company entail public (transferable) benefits V i and private benefits B i. First consider the case in which public benefits V 1 and V 2 are positively correlated with the private benefits B 1 and B 2 : V 1 < V 2 and B 1 < B 2 Result 6. When public and private benefits from control are positively correlated then full separation of cash flow rights and control rights of a company µ = α is optimal.

27 Proof: In this case Topics in Contract Theory 27 V 2 + B 2 > V 1 + B 1. If only the stake µ is auctioned off, the equilibrium price of the auction is: [µv 1 + B 1 ] The total revenue accruing to E is then: µv 1 + (1 µ)v 2 + B 1 The stake µ is chosen by E so as to solve: max µ s.t. µv 1 + (1 µ)v 2 + B 1 1 µ α It is therefore optimal to auction off the minimum control stake µ = α of the company.

28 Topics in Contract Theory 28 Consider now the case in which the public benefits V 1 and V 2 and the private benefits B 1 and B 2 are negatively correlated: V 1 < V 2 and B 1 > B 2 In this case it might not be optimal to auction off the minimum stake necessary to transfer control α. We can distinguish three cases. Case 1: which implies αv 2 + B 2 > αv 1 + B 1 V 2 + B 2 > V 1 + B 1

29 Topics in Contract Theory 29 In this case regardless of the control stake auctionedoff α µ 1 the company will be allocated to bidder 2. Result 6. The proceeds to E are therefore maximized by auctioning-off the minimum control stake µ = α. Proof: E s problem is then: max µ (1 µ)v 2 + µv 1 + B 1 s.t. 1 µ α The solution to this problem is then: µ = α.

30 Topics in Contract Theory 30 Case 2: αv 2 + B 2 < αv 1 + B 1 and V 2 + B 2 > V 1 + B 1 Notice that in this case: if µ = α is auctioned off the control is obtained by bidder 1 if µ = 1 is auctioned-off the control is obtained by bidder 2. Result 7. In Case 2 it is optimal to separate only partially the cash flow rights and the control rights: µ = µ, α < µ < 1

31 Topics in Contract Theory 31 Proof: There exists a value µ, α < µ < 1, such that: µv 2 + B 2 = µv 1 + B 1 If E sells a stake µ of the company, bidder 2 wins the auction and E s returns are µv 1 + B 1 + (1 µ)v 2 = V 2 + B 2 Then E extracts all the surplus from bidder 2. In this case the entire surplus is extracted since E can equalize the willingness to pay of both bidders by bundling together cash flow rights and control rights. The rest of the tradable value of he company is obtained from the stock market.

32 Topics in Contract Theory 32 Case 3: V 2 + B 2 V 1 + B 1 Notice that if the entire firm is auctioned off bidder 1 obtains the firm. Result 8. In Case 3 it is not optimal to separate the cash flow rights and the control rights of the company: µ = 1 Proof: If a stake µ of the company is auctioned off then bidder 2 gets the company with the bid: (1 µ)v 1 + µv 2 + B 2

33 Then E s problem is: Topics in Contract Theory 33 max µ (1 µ)v 1 + µv 2 + B 2 s.t. 1 µ α The solution to this problem since V 1 < V 2 is: µ = 1 The reason is that by selling less than the entire company E captures part of winning bidder s public value that in this case is the smallest of the two.