corporate finance: debt renegotiation - tau · corporate finance 4 bank debt restructuring y <...

Corporate Finance:Debt renegotiation

Yossi Spiegel

Recanati School of Business

Gertner and Scharfstein, JF 1991

A Theory of Workouts and the Effects of Reorganization Law

Corporate Finance 3

The model

� The timing:

� The dist. of X is f(x) and the CDF is F(X)

� The mean of X is

Period 0 Period 2

The firm has a cash flow Y < B+DThe firm can restructure its debt

The firm needs to pay Bto a bank and qD to bondholdersThe firm can invest I ina project

Period 1

The firm needs to pay (1-q)D to bondholdersThe project yields X~[0,∞)

∫∞

=0

)(ˆ XXdFX

Corporate Finance 4

Bank debt restructuring� Y < I+B+qD ⇒ without restructuring the firm cannot invest

� The firm must raise I+B+qD-Y in period 1 in order to cover I

� The Trust Indenture Act of 1939 requires debtholders unanimity to change the interest, principal, or maturity of pubic debt ⇒ renegotiation of public debt is very hard

� Bank debt restructuring:� the bank gives the firm cash worth I+B+qD-Y so the firm can meet all its

obligations in period 1� the face value of the new bank’s debt is higher to ensure that the bank makes a

profit

� Simplifying assumption: bankruptcy occurs in period 2 iff

� This is a simplifying assumption since the face value of the new bank debt is actually higher

( )4342144 344 21debt publicdebtBank

1 DqYqDBIZX −+−++≡<

Corporate Finance 5

Bank debt restructuring – period 2

� Solvency: X > Z

⇒ The firm and the bank split X–(1-q)D

� Bankruptcy: X < Z

⇒ X

( ) YDBIDqYqDBIZ −++=−+−++≡4342144 344 21debt Publicdebtbank New

1

XZ

YqDBI −++

XZ

Dq)1( −

New bank debt

Public debt

Corporate Finance 6

Condition for bank restructuring

( )( ) ( )4434421

43421444 3444 21

4444 34444 21

ing)restructur(absent bankruptcy

under 1 periodin payoffoutflowcash extra 1 Period

solvencyin payoff 2 Period

bankruptcyin payoff 2 Period

0

)(1

)(

B

Z

Z

LYDB

BYqDIXdFDqX

XXdFZ

YqDBI

≡+

≥−+−−−+

−++

∫

∫

∞

( )( ) ( ) D

Z

Z

ZDq

LYDB

DYY

DB

BqDIXdFDqX

XXdFZ

ZYqDBIX

−≡+

−=−+

≥+−−−+

−−+++

∫

∫

∞

−−

)(1

)(0

/)1(

444 3444 21

Corporate Finance 7

The bank will agree to restrcture B:

� The condition for restructuring:

� VD-LD is positive or negative

( ) ( ) D

Z

Z

LXDdFqXXdFZ

DqqDIX −−+

−+≥−

=

∞

∫∫44444444 344444444 21

ingrestructurunder debt public of value the V

0

D

)(1)(1ˆ

43421321

debt publicoTransfer t

NPVExpected

ˆDD LVIX −≥−

Corporate Finance 8

Investment with bank debt

� Invest iff:

� We can have underinvestment (debt overhang) or overinvestment (asset substitution)

DD LVIX −≥−ˆ

InvestDon’t invest

0

Investment is efficientNo investment is efficient

IX −ˆ

VD-LD>0:

InvestDon’t investVD-LD<0:

Corporate Finance 9

The effect of public debt maturity

� The value of debt under resructuring:

� VD = D if q = 1

� How does q affect VD?

( ) ( )∫∫∞

−+−

+=Z

Z

D XDdFqXXdFZ

DqqDV )(1)(

1

0

0)()(

)()(

0

0

=−−>

−−=∂∂

∫∫

∫∫∞

∞

Z

Z

Z

Z

D

XDdFXZdFZ

DD

XDdFXXdFZ

DD

q

V

Corporate Finance 10

The effect of public debt maturity� q↑ ⇒ VD↑ ⇒ VD - LD↑

� Investment takes place iff:

� Since q↑ ⇒ VD↑, underinvestment is likely when q → 1 (short maturity) and overinvestment is likely when q → 0 (long maturity)

� q↑ exacerbates underinvestment (debt overhang) but alleviate overinvestment (asset substitution)

DD LVIX −≥−ˆ

Bad effect:

Good effect:



0


IX −ˆ


New capital infusions from a new bank or by issuing equity� Invest iff:

� The new cash infusion exacerbates underinvestment (debt overhang) but alleviate overinvestment (asset substitution).

� VD is even higher if the cash infusion is via equity (debt has priority over equity during bankruptcy in period 2)

⇒ The firm will issue debt, not equity (equity subsidizes public debt and is therefore wasteful)

321)(

ˆ

+

−+−≥− BDD LBLVIX

VD-LD>0:

VD-LD<0:



0


IX −ˆ


New senior debt� Suppose the firm can issue in period 1 senior debt with

face value D’ which is due in period 2 (existing debt is not protected by seniority covenants)

� If D’ →∞, the firm always defaults in period 2 so the new senior debtholders will get the entire period 2 cash flow

� Existing debt gets 0 in period 2

⇒ The value of the existing debt is only equal to the period 1 payment qD < VD


New senior debt

� Invest iff:

� The new senior debt alleviates underinvestment (debt overhang) but exacerbates overinvestment (asset substitution).

� Seniority covenants (which prevent the firm from issuing senior debt) are worthwhile if overinvestment is likely (q → 0) but are a bad idea if underinvestment is likely (q → 1)

DLqDIX −≥−ˆ

VD-LD>0:

VD-LD<0:



0


IX −ˆ


Existing public debt is junior to bank debt

� If the firm goes bankrupt in period 1, junior debtholders get [Y-B]+ < LD

� Invest iff:

� When existing debt is junior, underinvestment (debt overhang) is exacerbated (likely when q → 1) but overinvestment (asset substitution) is alleviated (likely when q → 0).

[ ] DDD LVBYVIX −>−−≥− +ˆ

VD-LD>0:

VD-LD<0:InvestDon’t invest


0


IX −ˆ

Public Debt Exchange


Public debt exchange� Suppose the firm can restructure its public debt (despite

the difficulties) through an exchange (tender your old debt and get a new debt or cash)

� The firm faces a cash shortage:

� Timing:� Stage 1: the firm makes TIOLI offer to the bank� Stage 2: the firm offers an exchange of existing public debt

with new public debt due in period 2 whose face value is pD(investors who refuse keep their old securities)

{ 43421

invest and 1 periodin solvent stay

toneededMoney

invest andbankpay

Money to

qDBIYBI ++<<+


Public debt exchange – stage 2� Suppose the bank rejects the TIOLI

� The firm offers an exchange of existing public debt with new senior public debt due in period 2 and with face value pD

� The firm can set p s.t. old debtholders get nothing in period 2

� Suppose that

� If the condition holds, then there exists an equil. in which all public debtholdersaccept

⇒ If the condition holds, the bank gets B if it rejects the TIOLI ⇒ to induce the bank to accept the TIOLI, the firm must offer the bank at least B

{BYqDIXqDBIYX +−≥−⇒≥−−+ ˆˆ

high) is p since 0 is payoff 2 period(their exchange the

reject whosdebtholderof payoff 1 Period

high)set is p sinceeverythingget (they

debtholds public newof payoff 2 period Max.

4434421


Bank debt restructuring in stage 1

� The restructured bank debt, B’, is senior to public debt

� The firm makes a TIOLI to the bank s.t.:

� Rewriting:

� The bank accepts the TIOLI only if B’ satisfies the above equation

{

ealternativbanks' The

)( ifpayment Cash (-) ifinfusion cash New

2 periodin fullin paid isbank The

'

B' toup dollarsfirst thegetsbank The

'

0

)(')( BqDIYXdFBXXdFB

B

=−−++

+

∞

∫∫ 434214342143421

( )( ) ( )( )∫∫∞

−−−−=−−−+'

'

0

)(')(B

B

XdFqDIYBBXdFBqDIYX


Back to public debt exchange (the bank’s debt remains B)

� Suppose that so the firm can exchange its public debt

� Suppose the firm offers new debt with face value pD (p need not be so high that bankruptcy occurs for sure) - solvency in period 2:

BYqDIX +−≥−ˆ

X

Y-I-B (extra cash from period 1)

Xb

pD (face value of new debt)

X+Y-I-B (cash in period 2)

pD is paid in full


Back to public debt exchange (the bank’s debt remains B)

� Solvency in period 2 (the face value of new debt is pD):

� The value of old public debt:

� The value of new public debt (paid only in period 2):

{( )

44 344 21solvencyin payoff 2 Period

payoff1 Period

)(1∫∞

−+=bX

XDdFqqDOD

( )434214444 34444 21

fullin paid isdebt Publicfullin paidnot isdebt Public

0

)()( ∫∫∞

+−−+=b

b

X

X

XpDdFXdFBIYXND

bXYpDBIXpDBIYX ≡−++≥⇒≥−−+ 43421

1 period fromleft cash Extra


Public debt exchange

� The minimal p needed to ensure acceptance is defined implicitly by ND = OD:

� Reorganizing, p which ensures that public debt can be exchanged, is defined by:

( ) ( )∫∫∫∞∞

−+=+−−+bb

b

XX

X

XDdFqqDXpDdFXdFBIYX )(1)()(0

( ) ( )∫∫∞

−=−−−+b

b

X

X

XDdFpXdFBqDIYX )(1)(0


Summary

� The bank accepts the TIOLI only if B’satisfies:

� Public debtholders accept the public debt exchange only if p satisfies:

( ) ( )∫∫∞

−=−−−+b

b

X

X


( )( ) ( )( )∫∫∞

−−−−=−−−+'

'

0

)(')(B

B

XdFqDIYBBXdFBqDIYX


Exchange or restructure B?

� Equityholders’ payoff:� In a public debt exchange: [X-Xb]

+, where Xb ≡I+B+pD-Y

� In bank debt restructuring: [X-B’-(1-q)D]+

� Exchange is more profitable iff

� We’ll show that this inequality holds by writing B’ = Xb-(1-q)D+ε and showing that ε > 0

{DqXBDqBX

YpDBI

bb )1(')1(' −−>⇒−+<−++


Exchange or restructuring of B?� The condition for bank debt restructuring:

� Recall that B’ ≡ Xb-(1-q)D+ε and Xb ≡ I+B+pD-Y. Then the RHS becomes:

( )( )

( ) ( ) ( )

( )( )∫∫

∫

∫

∞∞−

∞

+−−=

∞

−−=

−+−−+=

−−−

+−−−++−=

−−−−

''

' )1('

'

)(1)(

)(1

)('

BB

b

pDX

B DqxB

X

B

XdFDpXdFDXYBI

XdFqDIYDqYpDBIB

XdFqDIYBB

b

b

b

εε

εε

48476

44444 344444 21

44 844 76

( )( ) ( )( )∫∫∞

−−−−=−−−+'

'

0

)(')(B

B

XdFqDIYBBXdFBqDIYX


Exchange is more profitable� The TIOLI to the bank:

� The condition for public debt exchange:

� Suppose that ε < 0. Then, B’ ≡ Xb-(1-q)D+ε < Xb

⇒ The LHS of the 2nd equation is larger but the RHS of the 1st

equation is larger ⇒ Contradiction!

⇒ ε > 0 ⇒ B’ > Xb-(1-q)D ⇒ exchange is more profitable

( )( ) ( )∫∫∞

−=−−−+b

b

X

X


( )( ) ( )( )∫∫∞

−−=−−−+'

'

0

)(1)(B

B

XdFDpXdFBqDIYX ε

corporate finance: debt renegotiation - tau · corporate finance 4 bank debt restructuring y <...

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