Post on 22-Jun-2020
Corporate Finance:Capital structure and corporate control
Yossi Spiegel
Recanati School of Business
Grossman and Hart, BJE 1980
“Takeover Bids, the Free-Rider Problem, and the Theory of the Corporation’’
Corporate Finance 3
The free rider problem� The timing:
� Consider an individual equityholder with equity participation α
� Let γY be the prob. that the raid succeeds if the equityholder tenders and and γN if he does not tender. The equityholder will tender iff
Period 1 Period 2
The firm is establishedby an entrepreneur and is worth X
A raider appears and can increase valueby R; the raider makes a tender offer X+P
( ) ( )[ ] ( ) ( )[ ]4444 34444 214444 34444 21
t tenderDon'Tender
11 XRXXPX NNYY γγαγγα −++≥−++
Corporate Finance 4
The free rider problem
� Suppose that each individual equityholderis atomistic ⇒ γY = γN= γ
� The condition for tendering:
� The raider’s profit:
� The raider gets nothing and will not ride if the ride requires a cost C!
( ) ( )[ ] ( ) ( )[ ] { {t tenderDon'Tender
t tenderDon'Tender
11 RPXRXXPX ≥⇒−++≥−++444 3444 21444 3444 21γγαγγα
( ) ( ) 0
Paymentpayoffpost Ex
≤−=+−+ PRPXRX4342143421
Corporate Finance 5
Toeholds
� The minimal P to induce atomistic equityholders to tender is R
� If the raider has a fraction β in the firm to begin with then his payoff is
� The takeover will take place iff βR > C, where C is the cost of takeover
( ) ( )( ){
RXRXRX βββ =−−+−+eoverAbsent takover with takePayoff
14444 34444 21
Corporate Finance 6
Dilution
� If the takeover succeeds, the raider can “steal” φ from the firm (φ is implied by the firm’s charter)
� The condition for tendering:
� The raider’s payoff
� The takeover will succeed iff φ > C
( ) ( )[ ] ( ) ( )[ ] { 3214444 34444 21444 3444 21t tenderDon'
Tendert tenderDon'Tender
11 φγφγαγγα −≥⇒−+−+≥−++ RPXRXXPX
( ) CCRXRX −=−−+−+ φφ43421321
Paymentpayoffpost Ex
Corporate Finance 7
Probabilistic C
� Suppose that C ~ [0, ∞) according to F(C)
� The takeover succeeds with prob. F(φ)
� The firm’s value ex ante:
( ) ( )( ) ( )( ) ( ) {φ
φφφφ−
+=−++=R
PFXXFPXFV 1
Corporate Finance 8
The optimal choice of φ
� F.O.C for φ:( ) ( )( ) ( )
{( )( )
( ) 10'
P decreased fromcost Marginal
takeoverofprob increased from
benefit Marginal
=−⇒=−−= φφφ
φφφφ RF
fFRfV
43421
φ
1
φ* R
( )( )
( )φφφ
−RF
f
Stulz, JFE 1988
“Managerial Control of Voting Rights: Financing Policies and the Market for
Corporate Control’’
Corporate Finance 10
The model
� The timing:
� The raider has benefits of control B~[0, ∞)
� To take over the firm the raider needs ½ of the equity
� The raider can try to acquire shares from outsiders. The supply of shares is (1-α)S(p), where S’(p) > 0 (more outsiders submit shares when p is higher)
Stage 0 Stage 2
The firm is established,the entrepreneur keeps equity α and issues 1-αto outsiders
A raider shows up andmay offer p to acquire ½ of the shares
Stage 1
Cash flow X is realized irrespective of the takeover
Corporate Finance 11
Takeover
� To induce a takeover, p needs to be
� p’(α) > 0: α↑ ⇒ p↑
1/2
p
(1-α)S(p)
P(α)
( ) ( ) ( )αα pppS =⇒=−2
11
α↑
Corporate Finance 12
Takeover
� The raider will take over iff B ≥ p(α) ⇒the prob. of takeover is 1-F(p(α))
� The entrepreneur’s payoff:
( ) { ( )( ) ( ) ( )( )( ) ( )[ ]
( )( ) ( ) ( )( )( ) ( )αααα
αααααα
ppFpFBX
ppFXpFBXY
E
E
−−++=
−+−++=
11
11
shares Soldbenefits Privateshares Retained
44444 344444 2143421
Corporate Finance 13
The optimal choice of α� F.O.C for α:
� When α → ½, then (1-α)S(p) = ½ iff S(p) → 1 ⇒ p → ∞ and F(p) → 1:
( ) ( ) ( )[ ] ( )( ) ( )
( ) ( )( )( ) ( ) ( )( )( ) ( )
0
1'11
'1'
effectQuantity shares sold of price on theEffect
takeoverof prob. on theEffect
=
−−−−+
−−=
444 3444 214444 34444 21
44444 344444 21
ααααα
ααααα
ppFppF
ppfpBY E
( ) ( ) ( )( ) ( ) 021'212
2121' <
−=
∞=
ppfp
BY E
321
Corporate Finance 14
The optimal choice of α
� When α = 0:
� If p’(0) > p(0) then y’(0) > 0 so α* > 0
( ) ( )[ ] ( )( ) ( ) ( )( )( ) ( ) ( )( )( ) ( )
( )[ ] ( )( ) ( ) ( )( )( ) ( ) ( )( )00'010'00
0010'010'000'
effect Ownershipeffect Price takeoverof prob. on theEffect
pppFppfpB
ppFppFppfpBY
E
E
−−+−=
−−−+−=44 344 21444 3444 214444 34444 21
Israel, JF 1991
“Capital Structure and the Market for Corporate Control: The Defensive Role of Debt Financing”
Corporate Finance 16
The model
� The timing:
� The value of the firm under the entrepreneur is 0
� The value of the firm under the raider is R ~[0, ∞) with mean ER
� If a takeover takes place, R is split between the entrepreneur and the raider in proportions γ and 1-γ
Stage 0 Stage 2
The firm is establishedby an entrepreneur and issues debt with face value D
A raider shows up andmay takeover the firm
Stage 1
Cash flow X is realized and debt is due
Corporate Finance 17
Analysis
� All-equity firm:
� The raider comes, takes over the firm and pays γER
� Leveraged firm:
� The raider takes over the firm iff R > D and pays the entrepreneur γ(R-D)
� If R < D there is no takeover; since the firm is worth 0 under the entrepreneur, debtholdersreceive nothing
Corporate Finance 18
The choice of debt
� The value of the firm:
� The f.o.c for D:
( ) ( ) ( ) ( )4342144 344 21
DebtEquity
∫∫∞∞
+−=DD
RDdFRdFDRDV γ
( ) ( ) ( ) ( )
( ) ( )( ) ( )0
11
'
=
+−−−=
++−= ∫∫∞∞
DDfDF
DDfRdFRdFDVDD
γ
γ
Corporate Finance 19
The choice of debt
� Rewriting f.o.c:
� At the optimum,� D* > 0
� D* < ∞
� Comparative stats:� γ↑ ⇒ D↓
( )( )
( ) γ−=≡−
11
DDHDF
DDf
Corporate Finance 20
Illustrating the first-order conditions
D
DH(D)
1-γ
D*
Corporate Finance 21
Illustrating the model
R1
Rf(R)
Df(R)
D
γRf(R)