1. Chapter 6 Corporate Restructuring Theory

2. A. A Theory of Reverse Leverage Buy Out

3. Assumption
a. Managers know only the expected value of its performance. Outside investors have a prior probability distribution on this expected value. Firms’ realized performance is revealed when it goes public.
b. Two period 1 and 2, privately held firms can go public at end of either period. All managers have the same discount factor β. Market pays m per dollar of expected per-period earnings.
c. A firm with expected per-period earnings μ. Managers observe period 1 earnings x. and decide whether to go public. If they decide to sell, they report x. If they wait, they report x and realized earnings in period 2, z.
d. β and m are common knowledge. Managers know μ, but market has only a prior distribution on μ, ρ (μ). Per-period earnings distribution f (x; μ). Market pays dollar amount s (x) if go public in period 1 and s (x, z) if in period 2.

4. Model Managers choice at the end of period 1, Action Payoff Managers
sell
wait

5. Proposition I
The managers decision rule: “ Sell at the end of period 1 if x＞h (μ), where h is some upward-slope function or cutoff curve; otherwise sell in period 2.” x
x = 2μ
Not possible
x = h (μ)
Sell
Wait μ

6. Implications a. For x = h (μ), the manager is indifferent
between waiting and selling.
i.e.
b. At IPO, firm reveals information to market about
quality.
If manager sells in period 1
If manager sells in period 2
c. As β decrease, x = h (μ) shifts to the right. i.e. a
more impatient manager has a lower selling
threshold in terms of period 1 realized earnings.
d. Good firms with higher μ are more likely to sell
in the first period than lower bad firms.

7. B. A Theory of Corporate Spin-offs

8. (A) Assumptions
1.Risk-neutral agents：the board, the incumbent, division manager, the rival and passive investors.
2.Firm with two divisions(1,2). Set up by incumbent management.(I) Incumbent invests all his wealth, W1, controls f% of equity, remaining equity held by passive investors.
3. Four dates, t=0,1,2,3
t=0
Board decides to spin-off or not
t=1
Board decision is announced publicly with plan
t=3
If a rival has appeared, a control contest takes place.
t=2
Rival appears/
Does not appear

9. (B)Model 1.The incumbent
(a)obtains both security benefits and private benefits
And,
(b)Exerts two effect levels：normal (ni) or diligent (di)
(c)Incurs a personal cost C(ei), C(ei=ni)=0 and C(ei=di)=c>0
And, C(eq)= C(e1) + C(e2)
(d)Objective function：
-Max expected value of control benefits and security benefits
-Min personal cost
-Vote management team in control contest

10. 2.The rival
(a) rival appear prob, ψ and no rival appear prob, 1-ψ.
(b) rival invests WR
(c) Object function to max personal private benefit. Vote himself
3. The division manager
(a) No wealth, with Prob. β
(b) Objective function to max personal private benefit.
4.Firm valuation

11. 5. The Board
Objective function max combined firms long-term equity value
6. Passive investors and control contest
(a) Passive investors vote for better manager.
(b) Incumbent with normal effect obtain zero vote in firm 2.
(c) Incumbent with normal effect obtain all vote in firm 1.
(d) Rival obtain all vote in firm2.

12. (C)Equilibrium
1.Proposition I (Spin-off where the incumbent relinquishes control of firm 2)
Let private benefits of firm 2 be small, PI2<P. Then
(a) The board chooses to spin off firm 2.
(b) The incumbent choose to maintain control of firm 1 follow the spin-off and work normally. The incumbent relinquishes control of firm 2 to the division manager.
(c) If rival appears offer spin-off, the incumbent invests all his wealth in firm 2 and a control contest take place. In control contest, both the passive investors and incumbent vote for the rival, so that the rival win control of firm2. If rival does not appear, the incumbent and division manager maintain control of firm 1 and 2, respectively.

13. 2. Proposition II.(Spin-off where the incumbent maintain control of both firms)
Let the private benefits of firm 2 be large, PI2≧ P. If incumbent is poorer at managing firm 2 than rival.
(a) The board chooses to spin-off division 2.
(b) The incumbent maintains control of both firms following the spin-off and work normally to managing both firms.
(c) If a rival appear subsequent to the spin-off, the rival invests all his wealth in firm 2, and a control contest takes place. In the control contest, all the passive investors vote for the rival, so the rival wins firm 2. If no rival appears, the incumbent maintains control of both firms.

14. 3. Proposition III：(Spin-off followed by no take-over)
Let the private benefits of firm 2 be large, PI2 ≧ . If the incumbent is better at managing firm 2 than rival.
(a) The board chooses to spin-off firm 2.
(b) The incumbent maintains control of both firms following the spin-off. He works normally in managing firm 1 and diligently in managing firm 2.
(c) If a rival appears following spin-off, the rival invests all his wealth in firm 2 and control contest takes place. In control contest, all the passive investors vote for the incumbent, so that the incumbent controls firm 2. The incumbent maintain control of both firms regardless of the appearance of the rival.

15. 4. Proposition IV ：( Announcement Effect)
(a) If incumbent derive either large private benefit in firm 2 (PI2 ≧ ) or incumbent relinquishes control of one firm to division manager, the announcement of a spin-off results in a positive announcement effect.
(b) The magnitude for the above announcement effect is increasing in the potential rival’s ability and in the probability of the rival’s arrival.
(c) When the incumbent relinquishes control of one firm to a division manager, the magnitude of the announcement effect is increasing in the division manager’s ability.
(d) The announcement effect is increasing in the difference in the incumbent’s management abilities across the two decision, n1- n2
(e) The announcement effect is increasing in the size of firm 2 as a fraction of the size of the joint firm.

16. 5. Proposition V ：( Long-term equity value changes)
There is a long-term increase in the combined equity value if a takeover takes place.
If neither firm resulting from a spin-off experience a takeover, the long-term changes in the combined equity value are non positive.
The magnitude of long-term equity value changes in increasing in the difference in the incumbent management ability across the two divisions, if any firm resulting from the spin-off experiences a takeover.