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Debt Dilution and Firm Investment
Joachim Jungherr 1
Immo Schott 2
1Institut d’An`alisi Econ`omica (CSIC), MOVE, and Barcelona GSE
2Universit´e de Montr´eal and CIREQ
1st Catalan Economic Society Conference
Barcelona, May 26, 2017
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Motivation
Big question: Do financial frictions matter for firm
investment?
Standard models: short-term debt only
Empirically, most firm debt is long-term debt:
for the average U.S. corporation, 67% of total debt does
not mature within the next year
This paper:
introduces long-term debt (and a maturity choice) into a
standard model of firm financing and investment
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Preview of Results
Main result:
firms with outstanding long-term debt do not internalize
all potential costs of default
they increase leverage and default risk
⇒ ”Debt Dilution”
debt dilution reduces investment and output
We show this:
analytically (2-period model)
quantitatively (dynamic model)
empirically (using firm-level Compustat data)
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Outline
1. Introduction
2. 2-period Model
3. Dynamic Model
4. Empirical Results
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Outline
1. Introduction
2. 2-period Model
3. Dynamic Model
4. Empirical Results
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Setup
2 periods: t = 0, 1
A firm owned by risk-neutral shareholders:
earnings in t = 1:
f (k) − δk + εk
f (k) concave ⇒ diminishing returns
capital k set in t = 0:
idiosyncratic earnings shock ε uncertain
E[ε] = 0
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt
Definition
Debt: A bond is a promise to pay one unit of the num´eraire
good together with a coupon payment c at the end of t = 1.
firm can raise funds in t = 0 by selling a number ∆b of
new bonds at market price p
total funds raised in t = 0 on the bond market: p∆b
Assume that there is an exogenous amount b of bonds
outstanding ⇒ “Long-term” debt
these bonds are otherwise identical to the one-period
bonds sold in t = 0 and due in t = 1
total stock of debt in t = 1: b + ∆b ≡ ˜b
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt & Capital
Firm chooses capital k in t = 0:
firm sells new bonds and gets ∆bp
shareholders inject equity e
k = e + p ∆b
Benefit of debt:
total stock of debt in t = 1: ˜b = b + ∆b
coupon payments ˜bc are tax-deductible
Shareholder net worth q at the end of t = 1:
q = k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b]
debt lowers tax payment by τc˜b
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Limited Liability & Timing
Definition
Limited Liability: Shareholders are free to default in t = 1
and leave the firm to lenders for liquidation. A fraction ξ of
firm assets is lost in this case.
Timing:
t=0 Given b, the firm chooses k, e, and ˜b = b + ∆b
t=1 ε is realized.
This determines net worth q.
The firm decides whether to default.
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Firm Problem
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Firm Problem
t = 1: Default threshold ¯ε: q = 0
⇔ k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Firm Problem
t = 1: Default threshold ¯ε: q = 0
⇔ k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0
t = 0: Firm problem given b:
max
k,e,∆b,˜b,ε
− e +
1
1 + r
∞
ε
[k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε
s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0
k = e + p ∆b
˜b = b + ∆b
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Creditors’ Problem
We have assumed that fraction ξ of firm assets is lost in case
of default
Here: ξ = 1 ⇒ liquidation value of the firm is zero
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Creditors’ Problem
We have assumed that fraction ξ of firm assets is lost in case
of default
Here: ξ = 1 ⇒ liquidation value of the firm is zero
t = 0: Risk-neutral lenders break even on expectation:
p =
1
1 + r
[1 − Φ(ε)] (1 + c)
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
t = 0: Firm maximizes shareholder value subject to creditors’
break even condition:
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
t = 0: Firm maximizes shareholder value subject to creditors’
break even condition:
max
k,e,˜b,ε,p
− e +
1
1 + r
∞
ε
[k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε
s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0
k = e + p (˜b − b)
p =
1
1 + r
[1 − Φ(ε)](1 + c)
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
t = 0: Firm maximizes shareholder value subject to creditors’
break even condition:
max
k,e,˜b,ε,p
− e +
1
1 + r
∞
ε
[k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε
s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0
k = e + p (˜b − b) ⇒ e = k − p (˜b − b)
p =
1
1 + r
[1 − Φ(ε)](1 + c)
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
t = 0: Firm maximizes shareholder value subject to creditors’
break even condition:
max
k,e,˜b,ε,p
− e +
1
1 + r
∞
ε
[k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε
s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 ⇒ ˜b = G(¯ε, k)
k = e + p (˜b − b) ⇒ e = k − p (˜b − b)
p =
1
1 + r
[1 − Φ(ε)](1 + c)
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
t = 0: Firm maximizes shareholder value subject to creditors’
break even condition:
max
k,e,˜b,ε,p
− e +
1
1 + r
∞
ε
[k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε
s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 ⇒ ˜b = G(¯ε, k)
k = e + p (˜b − b) ⇒ e = k − p (˜b − b)
p =
1
1 + r
[1 − Φ(ε)](1 + c) ⇒ p = H(¯ε)
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
t = 0: Firm maximizes shareholder value subject to creditors’
break even condition:
max
k,e,˜b,ε,p
− e +
1
1 + r
∞
ε
[k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε
s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 ⇒ ˜b = G(¯ε, k)
k = e + p (˜b − b) ⇒ e = k − p (˜b − b)
p =
1
1 + r
[1 − Φ(ε)](1 + c) ⇒ p = H(¯ε)
⇒ This problem can be re-written in terms of k and ¯ε
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
Simplification: c = r
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Equilibrium
Simplification: c = r
Consolidated problem in t = 0 given b:
max
k,ε
− k + [1 − Φ(ε)]
p
(˜b − b)
∆b
+
1 − τ
1 + r
k
∞
ε
[ε − ε] ϕ(ε)dε
subject to: ˜b = G(¯ε, k)
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: First Order Conditions
Two First Order Conditions:
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: First Order Conditions
Two First Order Conditions:
Capital k:
−1
Marginal
cost of
capital
+ [1 − Φ(ε)]
∂G(¯ε, k)
∂k
Marginal increase
in value of debt
+
1 − τ
1 + r
∞
ε
[ε − ε] ϕ(ε) dε
Marginal increase
in expected dividend
= 0
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: First Order Conditions
Two First Order Conditions:
Capital k:
−1
Marginal
cost of
capital
+ [1 − Φ(ε)]
∂G(¯ε, k)
∂k
Marginal increase
in value of debt
+
1 − τ
1 + r
∞
ε
[ε − ε] ϕ(ε) dε
Marginal increase
in expected dividend
= 0
Threshold value ¯ε:
[1 − Φ(ε)] (1 − τ)k
τc
1 + (1 − τ)c
Marginal tax benefit of ¯ε
− ϕ(¯ε)(1 + c)(˜b − b)
Marginal increase in
expected costs of default
internalized by the firm
= 0
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt Dilution
Choice of threshold value ¯ε:
marginal increase in total expected costs of default
ϕ(¯ε)(1 + c)˜b
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt Dilution
Choice of threshold value ¯ε:
marginal increase in total expected costs of default
ϕ(¯ε)(1 + c)˜b
firm only internalizes the loss in value of newly issued
bonds: ∆b = ˜b − b
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt Dilution
Choice of threshold value ¯ε:
marginal increase in total expected costs of default
ϕ(¯ε)(1 + c)˜b
firm only internalizes the loss in value of newly issued
bonds: ∆b = ˜b − b
marginal increase in expected costs of default
internalized by the firm
ϕ(¯ε)(1 + c) (˜b − b)
∆b
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt Dilution
Choice of threshold value ¯ε:
marginal increase in total expected costs of default
ϕ(¯ε)(1 + c)˜b
firm only internalizes the loss in value of newly issued
bonds: ∆b = ˜b − b
marginal increase in expected costs of default
internalized by the firm
ϕ(¯ε)(1 + c) (˜b − b)
∆b
firm disregards that by increasing ¯ε it also reduces
(”dilutes”) the value of previously issued bonds b
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt Dilution
Proposition
The default rate Φ(¯ε) is increasing in b.
the higher is b, the lower is the fraction of total default
costs internalized by the firm
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt Dilution
Proposition
For b > b, capital k is falling in b.
b =
(1 − τ)k f (k)
k − f (k)
1 + (1 − τ)c
.
For b < b, capital k is increasing in b.
the higher is b, the higher is ¯ε
ambiguous effect of higher ¯ε on capital:
lower effective tax rate ⇒ higher capital
lower bond price ⇒ higher cost of capital ⇒ lower capital
for b > b, the second effect dominates
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
2-period Model: Debt Dilution
Proposition
If k is falling in b, leverage ˜b/k is increasing in b.
if k is falling in b, higher ¯ε implies higher debt ˜b and
therefore higher leverage
if k is increasing in b, this may or may not hold
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Outline
1. Introduction
2. 2-period Model
3. Dynamic Model
4. Empirical Results
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Setup
Definition
Short-term Debt: In period t, the firm can sell a short-term
bond. This is a promise to pay 1 + c in period t + 1.
t: firm receives pS ˜bS
t+1: firms pays (1 + c)˜bS
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Setup
Definition
Long-term Debt: In period t, the firm can sell a long-term
bond. A fraction γ of this bond matures each period. This is a
promise to pay γ + c in period t + 1, (1 − γ)(γ + c) in period
t + 2, (1 − γ)2
(γ + c) in period t + 3, etc. ...
t: firm receives pL˜bL
t+1: firms pays (γ + c)˜bL
t+2: firms pays (1 − γ)(γ + c)˜bL
t+3: firms pays (1 − γ)2
(γ + c)˜bL
t+4: etc.
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Setup
Definition
Floatation cost on the bond market:
η [˜bS
t + (˜bL
t − bt)]
The firm pays η for each bond sold on the bond market
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Equilibrium
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Equilibrium
Firm maximizes shareholder value subject to creditors’ break
even condition:
firm cannot commit to future actions
firm must take future firm policy as given
time-consistent policy
Markov Perfect equilibrium
Equilibrium
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Parametrization
Variable Description Value Target/Source
r riskless rate 0.0309
δ depreciation 0.391 Capital-output ratio 2.07
γ repayment rate 0.1283 Long-term debt share 67.4%
c debt coupon r
τ tax rate 0.3 Hennessy and Whited (2005)
σε st.dev. earnings 0.6275 Leverage 27.2%
α decr. returns 0.9 Blundell and Bond (2000)
η floatation cost 0.0109 Altinkilic and Hansen (2000)
ξ default cost 0.62 Credit spread 2.30%
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Policy Functions
0 200 400
Defaultrate
0
0.02
0.04
0.06
0.08
Default Rate Φ(ε)
0 200 400
Capital
1200
1300
1400
1500
1600
Capital policy k
Long-term Debt outstanding b
0 200 400
Leverage
0
0.2
0.4
0.6
Leverage (˜bS
+ ˜bL
)/k
Long-term Debt outstanding b
0 200 400
Output
600
650
700
750
Output y
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Policy Functions
0 200 400
Spread
0
0.02
0.04
0.06
Short-term Bond Spread
0 200 400
Spread
0
0.02
0.04
0.06
Long-term Bond Spread
Long-term Debt outstanding b
0 200 400
Long-termDebt
0
200
400
600
Stock of Long-term Debt ˜bL
Long-term Debt outstanding b
0 200 400
ShareofLong-termDebt
0.6
0.7
0.8
0.9
Share of Long-term Debt
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Maturity Choice
Trade-off between short-term and long-term debt (LTD):
LTD saves floatation costs on the bond market
but LTD also creates debt dilution in the future
⇒ higher default risk in the future
Higher future default risk hurts the firm:
lower price of LTD sold today!
default risk convex in b
incentive to reduce LTD as b increases
Higher future default risk also hurts the holders of previously
issued LTD b:
higher b means less of the total cost of LTD is
internalized by the firm!
incentive to increase LTD as b increases
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Outline
1. Introduction
2. 2-period Model
3. Dynamic Model
4. Empirical Results
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Empirical Analysis
One measure of debt dilution is the OLD-Share, the ratio of
LTD outstanding b to total debt ˜bS
+ ˜bL
:
OLD-Share =
b
˜bS + ˜bL
Theoretical prediction: the OLD-Share is...
... positively correlated with leverage and default risk
... negatively correlated with capital
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Empirical Analysis
Empirical test:
firm-level data from Compustat 1984-2014
Moody’s Default & Recovery Database 1988-2014
excluding financial firms and utilities
Convert the panel into a cross-section of firms: for firm j we
use...
average of firm j’s OLD-Share in year t, t + 1, t + 2, ...
average of firm j’s leverage in year t, t + 1, t + 2, ...
etc.
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Empirical Results: Leverage
OLS Leverage Leverage Leverage Leverage
(Industry FE) (low Z-score) (high Z-score)
OLD-Share 0.0470*** 0.0654** 0.0222*
(3.83) (3.31) (2.12)
Tobin’s q 0.0273*** 0.0278*** 0.0456*** 0.0148
(6.42) (6.64) (7.46) (1.70)
Profitability -0.171*** -0.172*** -0.0796** -0.0291
(-8.20) (-8.43) (-2.77) (-0.76)
Tangibility 0.253*** 0.243*** 0.282*** 0.118***
(6.59) (6.19) (5.47) (4.01)
Firm age -0.00413*** -0.00411*** -0.00323*** -0.00280***
(-7.66) (-7.75) (-3.38) (-5.60)
log Sales 0.0146*** 0.0121*** 0.0112** 0.0156***
(7.51) (6.30) (3.04) (6.81)
adj. R2
0.2524 0.2557 0.2344 0.3025
N 5118 5115 2556 2559
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Empirical Results: Default
Logit Default Default Default Default
(Industry FE) (low Z-score) (high Z-score)
OLD-Share 0.529* 0.830** -0.345
(2.14) (2.76) (-0.66)
Leverage 3.989*** 3.922*** 3.421*** 3.470***
(11.55) (11.45) (8.04) (4.65)
Tobin’s q -1.237*** -1.238*** -1.026*** -1.112***
(-6.29) (-6.30) (-4.29) (-3.52)
Profitability -1.407*** -1.528*** -0.861* -4.906***
(-4.04) (-4.53) (-2.27) (-5.10)
Firm age 0.00323 0.00408 0.0107 0.0150
(0.35) (0.43) (0.89) (0.85)
log Sales 0.429*** 0.410*** 0.421*** 0.379***
(11.25) (10.39) (9.67) (4.67)
Pseudo R2
0.2096 0.2114 0.2377 0.1638
N 5118 5115 2556 2559
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Empirical Results: Asset Growth
OLS ∆ log Assets ∆ log Assets ∆ log Assets ∆ log Assets
(Industry FE) (low Z-score) (high Z-score)
OLD-Share -0.0697*** -0.0868*** -0.0524***
(-7.43) (-4.91) (-4.58)
Leverage -0.0810*** -0.0725*** -0.0264 -0.0442
(-5.23) (-4.75) (-1.47) (-1.52)
Tobin’s q 0.0339*** 0.0342*** 0.0251*** 0.0401***
(6.46) (6.56) (3.40) (3.98)
Profitability 0.183*** 0.189*** 0.148*** 0.184**
(7.65) (8.00) (4.92) (2.74)
Firm age -0.00646*** -0.00638*** -0.00675*** -0.00640***
(-9.18) (-9.07) (-6.64) (-6.92)
log Sales 0.00556** 0.00871*** 0.01000** 0.00435
(2.73) (4.47) (3.14) (1.88)
adj. R2
0.0830 0.0964 0.0299 0.1425
N 5116 5114 2555 2559
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Outline
1. Introduction
2. 2-period Model
3. Dynamic Model
4. Empirical Results
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Conclusion
Summary of results:
we introduce long-term debt (and a maturity choice) into
a standard model of firm financing and investment
debt dilution increases default risk and leverage, and
reduces investment and output
Room for policy (work in progress):
debt dilution is a time-inconsistency problem
future firm behavior affects price of long-term bonds sold
today
this is not internalized by the firm in the future
policy options: seniority for LTD, ban of LTD, limit for
LTD, limit for leverage, ...
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Conclusion
Thank you!
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
Dynamic Model: Equilibrium
Firm maximizes shareholder value subject to creditors’ break
even condition:
V (b) = max
k,e ,˜bS ,˜bL,¯ε,pS ,pL
−e
+
1
1 + r
∞
¯ε
q + V ((1 − γ)˜bL
) ϕ(ε)dε + Φ(¯ε) V (0)
s.t.: q = k − ˜bS
− γ˜bL
+ (1 − τ)[kα
− δk + εk − c˜bS
− c˜bL
]
¯ε : q + V ((1 − γ)˜bL
) = V (0)
k = e + pS ˜bS
+ pL
(˜bL
− b) − η(˜bS
+ ˜bL
− b)
pS
=
1
1 + r
[1 − Φ(¯ε)] (1 + c) + Φ(¯ε)
(1 − ξ)˜q
˜bS + ˜bL
pL
=
1
1 + r
[1 − Φ(¯ε)] γ + c + (1 − γ) pL
(1 − γ)˜bL
+ Φ(¯ε)
(1 − ξ)˜q
˜bS + ˜bLGo back
Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results

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Debt dilution and firm investment

  • 1. Debt Dilution and Firm Investment Joachim Jungherr 1 Immo Schott 2 1Institut d’An`alisi Econ`omica (CSIC), MOVE, and Barcelona GSE 2Universit´e de Montr´eal and CIREQ 1st Catalan Economic Society Conference Barcelona, May 26, 2017 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 2. Motivation Big question: Do financial frictions matter for firm investment? Standard models: short-term debt only Empirically, most firm debt is long-term debt: for the average U.S. corporation, 67% of total debt does not mature within the next year This paper: introduces long-term debt (and a maturity choice) into a standard model of firm financing and investment Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 3. Preview of Results Main result: firms with outstanding long-term debt do not internalize all potential costs of default they increase leverage and default risk ⇒ ”Debt Dilution” debt dilution reduces investment and output We show this: analytically (2-period model) quantitatively (dynamic model) empirically (using firm-level Compustat data) Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 4. Outline 1. Introduction 2. 2-period Model 3. Dynamic Model 4. Empirical Results Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 5. Outline 1. Introduction 2. 2-period Model 3. Dynamic Model 4. Empirical Results Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 6. 2-period Model: Setup 2 periods: t = 0, 1 A firm owned by risk-neutral shareholders: earnings in t = 1: f (k) − δk + εk f (k) concave ⇒ diminishing returns capital k set in t = 0: idiosyncratic earnings shock ε uncertain E[ε] = 0 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 7. 2-period Model: Debt Definition Debt: A bond is a promise to pay one unit of the num´eraire good together with a coupon payment c at the end of t = 1. firm can raise funds in t = 0 by selling a number ∆b of new bonds at market price p total funds raised in t = 0 on the bond market: p∆b Assume that there is an exogenous amount b of bonds outstanding ⇒ “Long-term” debt these bonds are otherwise identical to the one-period bonds sold in t = 0 and due in t = 1 total stock of debt in t = 1: b + ∆b ≡ ˜b Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 8. 2-period Model: Debt & Capital Firm chooses capital k in t = 0: firm sells new bonds and gets ∆bp shareholders inject equity e k = e + p ∆b Benefit of debt: total stock of debt in t = 1: ˜b = b + ∆b coupon payments ˜bc are tax-deductible Shareholder net worth q at the end of t = 1: q = k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] debt lowers tax payment by τc˜b Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 9. 2-period Model: Limited Liability & Timing Definition Limited Liability: Shareholders are free to default in t = 1 and leave the firm to lenders for liquidation. A fraction ξ of firm assets is lost in this case. Timing: t=0 Given b, the firm chooses k, e, and ˜b = b + ∆b t=1 ε is realized. This determines net worth q. The firm decides whether to default. Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 10. 2-period Model: Firm Problem Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 11. 2-period Model: Firm Problem t = 1: Default threshold ¯ε: q = 0 ⇔ k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 12. 2-period Model: Firm Problem t = 1: Default threshold ¯ε: q = 0 ⇔ k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 t = 0: Firm problem given b: max k,e,∆b,˜b,ε − e + 1 1 + r ∞ ε [k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 k = e + p ∆b ˜b = b + ∆b Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 13. 2-period Model: Creditors’ Problem We have assumed that fraction ξ of firm assets is lost in case of default Here: ξ = 1 ⇒ liquidation value of the firm is zero Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 14. 2-period Model: Creditors’ Problem We have assumed that fraction ξ of firm assets is lost in case of default Here: ξ = 1 ⇒ liquidation value of the firm is zero t = 0: Risk-neutral lenders break even on expectation: p = 1 1 + r [1 − Φ(ε)] (1 + c) Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 15. 2-period Model: Equilibrium t = 0: Firm maximizes shareholder value subject to creditors’ break even condition: Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 16. 2-period Model: Equilibrium t = 0: Firm maximizes shareholder value subject to creditors’ break even condition: max k,e,˜b,ε,p − e + 1 1 + r ∞ ε [k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 k = e + p (˜b − b) p = 1 1 + r [1 − Φ(ε)](1 + c) Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 17. 2-period Model: Equilibrium t = 0: Firm maximizes shareholder value subject to creditors’ break even condition: max k,e,˜b,ε,p − e + 1 1 + r ∞ ε [k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 k = e + p (˜b − b) ⇒ e = k − p (˜b − b) p = 1 1 + r [1 − Φ(ε)](1 + c) Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 18. 2-period Model: Equilibrium t = 0: Firm maximizes shareholder value subject to creditors’ break even condition: max k,e,˜b,ε,p − e + 1 1 + r ∞ ε [k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 ⇒ ˜b = G(¯ε, k) k = e + p (˜b − b) ⇒ e = k − p (˜b − b) p = 1 1 + r [1 − Φ(ε)](1 + c) Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 19. 2-period Model: Equilibrium t = 0: Firm maximizes shareholder value subject to creditors’ break even condition: max k,e,˜b,ε,p − e + 1 1 + r ∞ ε [k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 ⇒ ˜b = G(¯ε, k) k = e + p (˜b − b) ⇒ e = k − p (˜b − b) p = 1 1 + r [1 − Φ(ε)](1 + c) ⇒ p = H(¯ε) Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 20. 2-period Model: Equilibrium t = 0: Firm maximizes shareholder value subject to creditors’ break even condition: max k,e,˜b,ε,p − e + 1 1 + r ∞ ε [k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] ϕ(ε) dε s.t.: ε : k − ˜b + (1 − τ)[f (k) − δk + εk − c˜b] = 0 ⇒ ˜b = G(¯ε, k) k = e + p (˜b − b) ⇒ e = k − p (˜b − b) p = 1 1 + r [1 − Φ(ε)](1 + c) ⇒ p = H(¯ε) ⇒ This problem can be re-written in terms of k and ¯ε Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 21. 2-period Model: Equilibrium Simplification: c = r Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 22. 2-period Model: Equilibrium Simplification: c = r Consolidated problem in t = 0 given b: max k,ε − k + [1 − Φ(ε)] p (˜b − b) ∆b + 1 − τ 1 + r k ∞ ε [ε − ε] ϕ(ε)dε subject to: ˜b = G(¯ε, k) Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 23. 2-period Model: First Order Conditions Two First Order Conditions: Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 24. 2-period Model: First Order Conditions Two First Order Conditions: Capital k: −1 Marginal cost of capital + [1 − Φ(ε)] ∂G(¯ε, k) ∂k Marginal increase in value of debt + 1 − τ 1 + r ∞ ε [ε − ε] ϕ(ε) dε Marginal increase in expected dividend = 0 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 25. 2-period Model: First Order Conditions Two First Order Conditions: Capital k: −1 Marginal cost of capital + [1 − Φ(ε)] ∂G(¯ε, k) ∂k Marginal increase in value of debt + 1 − τ 1 + r ∞ ε [ε − ε] ϕ(ε) dε Marginal increase in expected dividend = 0 Threshold value ¯ε: [1 − Φ(ε)] (1 − τ)k τc 1 + (1 − τ)c Marginal tax benefit of ¯ε − ϕ(¯ε)(1 + c)(˜b − b) Marginal increase in expected costs of default internalized by the firm = 0 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 26. 2-period Model: Debt Dilution Choice of threshold value ¯ε: marginal increase in total expected costs of default ϕ(¯ε)(1 + c)˜b Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 27. 2-period Model: Debt Dilution Choice of threshold value ¯ε: marginal increase in total expected costs of default ϕ(¯ε)(1 + c)˜b firm only internalizes the loss in value of newly issued bonds: ∆b = ˜b − b Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 28. 2-period Model: Debt Dilution Choice of threshold value ¯ε: marginal increase in total expected costs of default ϕ(¯ε)(1 + c)˜b firm only internalizes the loss in value of newly issued bonds: ∆b = ˜b − b marginal increase in expected costs of default internalized by the firm ϕ(¯ε)(1 + c) (˜b − b) ∆b Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 29. 2-period Model: Debt Dilution Choice of threshold value ¯ε: marginal increase in total expected costs of default ϕ(¯ε)(1 + c)˜b firm only internalizes the loss in value of newly issued bonds: ∆b = ˜b − b marginal increase in expected costs of default internalized by the firm ϕ(¯ε)(1 + c) (˜b − b) ∆b firm disregards that by increasing ¯ε it also reduces (”dilutes”) the value of previously issued bonds b Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 30. 2-period Model: Debt Dilution Proposition The default rate Φ(¯ε) is increasing in b. the higher is b, the lower is the fraction of total default costs internalized by the firm Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 31. 2-period Model: Debt Dilution Proposition For b > b, capital k is falling in b. b = (1 − τ)k f (k) k − f (k) 1 + (1 − τ)c . For b < b, capital k is increasing in b. the higher is b, the higher is ¯ε ambiguous effect of higher ¯ε on capital: lower effective tax rate ⇒ higher capital lower bond price ⇒ higher cost of capital ⇒ lower capital for b > b, the second effect dominates Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 32. 2-period Model: Debt Dilution Proposition If k is falling in b, leverage ˜b/k is increasing in b. if k is falling in b, higher ¯ε implies higher debt ˜b and therefore higher leverage if k is increasing in b, this may or may not hold Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 33. Outline 1. Introduction 2. 2-period Model 3. Dynamic Model 4. Empirical Results Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 34. Dynamic Model: Setup Definition Short-term Debt: In period t, the firm can sell a short-term bond. This is a promise to pay 1 + c in period t + 1. t: firm receives pS ˜bS t+1: firms pays (1 + c)˜bS Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 35. Dynamic Model: Setup Definition Long-term Debt: In period t, the firm can sell a long-term bond. A fraction γ of this bond matures each period. This is a promise to pay γ + c in period t + 1, (1 − γ)(γ + c) in period t + 2, (1 − γ)2 (γ + c) in period t + 3, etc. ... t: firm receives pL˜bL t+1: firms pays (γ + c)˜bL t+2: firms pays (1 − γ)(γ + c)˜bL t+3: firms pays (1 − γ)2 (γ + c)˜bL t+4: etc. Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 36. Dynamic Model: Setup Definition Floatation cost on the bond market: η [˜bS t + (˜bL t − bt)] The firm pays η for each bond sold on the bond market Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 37. Dynamic Model: Equilibrium Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 38. Dynamic Model: Equilibrium Firm maximizes shareholder value subject to creditors’ break even condition: firm cannot commit to future actions firm must take future firm policy as given time-consistent policy Markov Perfect equilibrium Equilibrium Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 39. Dynamic Model: Parametrization Variable Description Value Target/Source r riskless rate 0.0309 δ depreciation 0.391 Capital-output ratio 2.07 γ repayment rate 0.1283 Long-term debt share 67.4% c debt coupon r τ tax rate 0.3 Hennessy and Whited (2005) σε st.dev. earnings 0.6275 Leverage 27.2% α decr. returns 0.9 Blundell and Bond (2000) η floatation cost 0.0109 Altinkilic and Hansen (2000) ξ default cost 0.62 Credit spread 2.30% Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 40. Dynamic Model: Policy Functions 0 200 400 Defaultrate 0 0.02 0.04 0.06 0.08 Default Rate Φ(ε) 0 200 400 Capital 1200 1300 1400 1500 1600 Capital policy k Long-term Debt outstanding b 0 200 400 Leverage 0 0.2 0.4 0.6 Leverage (˜bS + ˜bL )/k Long-term Debt outstanding b 0 200 400 Output 600 650 700 750 Output y Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 41. Dynamic Model: Policy Functions 0 200 400 Spread 0 0.02 0.04 0.06 Short-term Bond Spread 0 200 400 Spread 0 0.02 0.04 0.06 Long-term Bond Spread Long-term Debt outstanding b 0 200 400 Long-termDebt 0 200 400 600 Stock of Long-term Debt ˜bL Long-term Debt outstanding b 0 200 400 ShareofLong-termDebt 0.6 0.7 0.8 0.9 Share of Long-term Debt Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 42. Dynamic Model: Maturity Choice Trade-off between short-term and long-term debt (LTD): LTD saves floatation costs on the bond market but LTD also creates debt dilution in the future ⇒ higher default risk in the future Higher future default risk hurts the firm: lower price of LTD sold today! default risk convex in b incentive to reduce LTD as b increases Higher future default risk also hurts the holders of previously issued LTD b: higher b means less of the total cost of LTD is internalized by the firm! incentive to increase LTD as b increases Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 43. Outline 1. Introduction 2. 2-period Model 3. Dynamic Model 4. Empirical Results Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 44. Empirical Analysis One measure of debt dilution is the OLD-Share, the ratio of LTD outstanding b to total debt ˜bS + ˜bL : OLD-Share = b ˜bS + ˜bL Theoretical prediction: the OLD-Share is... ... positively correlated with leverage and default risk ... negatively correlated with capital Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 45. Empirical Analysis Empirical test: firm-level data from Compustat 1984-2014 Moody’s Default & Recovery Database 1988-2014 excluding financial firms and utilities Convert the panel into a cross-section of firms: for firm j we use... average of firm j’s OLD-Share in year t, t + 1, t + 2, ... average of firm j’s leverage in year t, t + 1, t + 2, ... etc. Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 46. Empirical Results: Leverage OLS Leverage Leverage Leverage Leverage (Industry FE) (low Z-score) (high Z-score) OLD-Share 0.0470*** 0.0654** 0.0222* (3.83) (3.31) (2.12) Tobin’s q 0.0273*** 0.0278*** 0.0456*** 0.0148 (6.42) (6.64) (7.46) (1.70) Profitability -0.171*** -0.172*** -0.0796** -0.0291 (-8.20) (-8.43) (-2.77) (-0.76) Tangibility 0.253*** 0.243*** 0.282*** 0.118*** (6.59) (6.19) (5.47) (4.01) Firm age -0.00413*** -0.00411*** -0.00323*** -0.00280*** (-7.66) (-7.75) (-3.38) (-5.60) log Sales 0.0146*** 0.0121*** 0.0112** 0.0156*** (7.51) (6.30) (3.04) (6.81) adj. R2 0.2524 0.2557 0.2344 0.3025 N 5118 5115 2556 2559 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 47. Empirical Results: Default Logit Default Default Default Default (Industry FE) (low Z-score) (high Z-score) OLD-Share 0.529* 0.830** -0.345 (2.14) (2.76) (-0.66) Leverage 3.989*** 3.922*** 3.421*** 3.470*** (11.55) (11.45) (8.04) (4.65) Tobin’s q -1.237*** -1.238*** -1.026*** -1.112*** (-6.29) (-6.30) (-4.29) (-3.52) Profitability -1.407*** -1.528*** -0.861* -4.906*** (-4.04) (-4.53) (-2.27) (-5.10) Firm age 0.00323 0.00408 0.0107 0.0150 (0.35) (0.43) (0.89) (0.85) log Sales 0.429*** 0.410*** 0.421*** 0.379*** (11.25) (10.39) (9.67) (4.67) Pseudo R2 0.2096 0.2114 0.2377 0.1638 N 5118 5115 2556 2559 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 48. Empirical Results: Asset Growth OLS ∆ log Assets ∆ log Assets ∆ log Assets ∆ log Assets (Industry FE) (low Z-score) (high Z-score) OLD-Share -0.0697*** -0.0868*** -0.0524*** (-7.43) (-4.91) (-4.58) Leverage -0.0810*** -0.0725*** -0.0264 -0.0442 (-5.23) (-4.75) (-1.47) (-1.52) Tobin’s q 0.0339*** 0.0342*** 0.0251*** 0.0401*** (6.46) (6.56) (3.40) (3.98) Profitability 0.183*** 0.189*** 0.148*** 0.184** (7.65) (8.00) (4.92) (2.74) Firm age -0.00646*** -0.00638*** -0.00675*** -0.00640*** (-9.18) (-9.07) (-6.64) (-6.92) log Sales 0.00556** 0.00871*** 0.01000** 0.00435 (2.73) (4.47) (3.14) (1.88) adj. R2 0.0830 0.0964 0.0299 0.1425 N 5116 5114 2555 2559 Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 49. Outline 1. Introduction 2. 2-period Model 3. Dynamic Model 4. Empirical Results Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 50. Conclusion Summary of results: we introduce long-term debt (and a maturity choice) into a standard model of firm financing and investment debt dilution increases default risk and leverage, and reduces investment and output Room for policy (work in progress): debt dilution is a time-inconsistency problem future firm behavior affects price of long-term bonds sold today this is not internalized by the firm in the future policy options: seniority for LTD, ban of LTD, limit for LTD, limit for leverage, ... Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 51. Conclusion Thank you! Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results
  • 52. Dynamic Model: Equilibrium Firm maximizes shareholder value subject to creditors’ break even condition: V (b) = max k,e ,˜bS ,˜bL,¯ε,pS ,pL −e + 1 1 + r ∞ ¯ε q + V ((1 − γ)˜bL ) ϕ(ε)dε + Φ(¯ε) V (0) s.t.: q = k − ˜bS − γ˜bL + (1 − τ)[kα − δk + εk − c˜bS − c˜bL ] ¯ε : q + V ((1 − γ)˜bL ) = V (0) k = e + pS ˜bS + pL (˜bL − b) − η(˜bS + ˜bL − b) pS = 1 1 + r [1 − Φ(¯ε)] (1 + c) + Φ(¯ε) (1 − ξ)˜q ˜bS + ˜bL pL = 1 1 + r [1 − Φ(¯ε)] γ + c + (1 − γ) pL (1 − γ)˜bL + Φ(¯ε) (1 − ξ)˜q ˜bS + ˜bLGo back Introduction 2-period Model Equilibrium Dynamic Model Equilibrium Empirical Results