corporate finance: debt renegotiation - tau · corporate finance 4 bank debt restructuring y <...
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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:
InvestDon’t invest
InvestDon’t invest
0
Investment is efficientNo investment is efficient
IX −ˆ
Corporate Finance 11
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:
InvestDon’t invest
InvestDon’t invest
0
Investment is efficientNo investment is efficient
IX −ˆ
Corporate Finance 12
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
Corporate Finance 13
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:
InvestDon’t invest
InvestDon’t invest
0
Investment is efficientNo investment is efficient
IX −ˆ
Corporate Finance 14
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
InvestDon’t invest
0
Investment is efficientNo investment is efficient
IX −ˆ
Corporate Finance 16
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 ++<<+
Corporate Finance 17
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
Corporate Finance 18
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
Corporate Finance 19
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
Corporate Finance 20
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
Corporate Finance 21
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
Corporate Finance 22
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
XDdFpXdFBqDIYX )(1)(0
( )( ) ( )( )∫∫∞
−−−−=−−−+'
'
0
)(')(B
B
XdFqDIYBBXdFBqDIYX
Corporate Finance 23
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(' −−>⇒−+<−++
Corporate Finance 24
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
Corporate Finance 25
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
XDdFpXdFBqDIYX )(1)(0
( )( ) ( )( )∫∫∞
−−=−−−+'
'
0
)(1)(B
B
XdFDpXdFBqDIYX ε