Bolton Chen Wang (2009) (Presentation PPT. a Unified Theory of Tobin's Q, Corporate Investment,...
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Transcript of Bolton Chen Wang (2009) (Presentation PPT. a Unified Theory of Tobin's Q, Corporate Investment,...
A unified theory of Tobin’s q,corporate investment, financing,
and risk management
Patrick Bolton, Columbia, CEPR, and NBER
Hui Chen, MIT
Neng Wang, Columbia and NBER
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The Economist, Nov. 22-28, 2008
Model Design
! constant investment opportunity (with a benchmark qtheory)
! constant financing opportunity
! the interaction
Model Sketch: PhysicalProduction
! capital accumulation:
dKt = (It ! !Kt)dt
! output:dYt = Kt (µdt + "dZt)
! cost of investing:
(It + G(It, Kt)) dt.
! adjustment cost G(I,K) = g(I/K)K, where
g(i) =#
2i2.
Model Sketch
! Dynamics for cash W : dWt = change in cash =! CF from operations (production)
! + CF from investing (i.e. (r ! !) Wtdt)! + CF from financing! ! payout
! Precautionary motive for holding cash
! Cost of holding cash: $
! Can pay out cash to investors at any time: 1 for 1
Model Sketch
! Dynamics for cash W : dWt = change in cash =! CF from operations (production)! + CF from investing (i.e. (r ! !) Wtdt)
! + CF from financing! ! payout
! Precautionary motive for holding cash
! Cost of holding cash: $
! Can pay out cash to investors at any time: 1 for 1
Model Sketch
! Dynamics for cash W : dWt = change in cash =! CF from operations (production)! + CF from investing (i.e. (r ! !) Wtdt)! + CF from financing
! ! payout
! Precautionary motive for holding cash
! Cost of holding cash: $
! Can pay out cash to investors at any time: 1 for 1
Model Sketch
! Dynamics for cash W : dWt = change in cash =! CF from operations (production)! + CF from investing (i.e. (r ! !) Wtdt)! + CF from financing! ! payout
! Precautionary motive for holding cash
! Cost of holding cash: $
! Can pay out cash to investors at any time: 1 for 1
Model Sketch
! Dynamics for cash W : dWt = change in cash =! CF from operations (production)! + CF from investing (i.e. (r ! !) Wtdt)! + CF from financing! ! payout
! Precautionary motive for holding cash
! Cost of holding cash: $
! Can pay out cash to investors at any time: 1 for 1
Model Sketch
! Dynamics for cash W : dWt = change in cash =! CF from operations (production)! + CF from investing (i.e. (r ! !) Wtdt)! + CF from financing! ! payout
! Precautionary motive for holding cash
! Cost of holding cash: $
! Can pay out cash to investors at any time: 1 for 1
Model Sketch
! Dynamics for cash W : dWt = change in cash =! CF from operations (production)! + CF from investing (i.e. (r ! !) Wtdt)! + CF from financing! ! payout
! Precautionary motive for holding cash
! Cost of holding cash: $
! Can pay out cash to investors at any time: 1 for 1
Model Sketch
! Option to liquidate! collect lK from capital and W from cash account
! Option to issue external equity! fixed cost! variable cost
! Credit line! credit limit: cK! interest rate: r + "
Model Sketch
! Option to liquidate! collect lK from capital and W from cash account
! Option to issue external equity! fixed cost! variable cost
! Credit line! credit limit: cK! interest rate: r + "
Model Sketch
! Option to liquidate! collect lK from capital and W from cash account
! Option to issue external equity! fixed cost! variable cost
! Credit line! credit limit: cK! interest rate: r + "
Four (optimally divided) regions
! payout region
! cash region (w > 0)
! credit region (w < 0)
! equity financing (liquidation) region
Solution sketch
! Firm value maximization: P (K, W )
! Homogeneity: P (K, W ) = p(w)"K where w = W/K
! Economics: stochastic balanced capital accumulationwith financial frictions
Solution sketch
! Firm value maximization: P (K, W )
! Homogeneity: P (K, W ) = p(w)"K where w = W/K
! Economics: stochastic balanced capital accumulationwith financial frictions
Solution sketch
! Firm value maximization: P (K, W )
! Homogeneity: P (K, W ) = p(w)"K where w = W/K
! Economics: stochastic balanced capital accumulationwith financial frictions
Solution Sketch
! Investment first-order condition:
marginal cost of production =PK(K, W )
PW (K, W )
! marginal value of liquidity (marginal cost of funds):PW (K, W ) = p!(w)
Value and Investment
! firm value-capital ratio p(w):
rp(w) = (i(w)! !) (p (w)! wp! (w))
+ ((r ! $)w + µ! i(w)! g(i(w))) p! (w)
+"2
2p!! (w) .
! investment-capital ratio:
i(w) =1
#
!p(w)
p!(w)! w ! 1
".
Average and marginal q
! Optimal composition of the balance sheet: W and K
! Average q:
qa(w) =P (K, W )!W
K= p(w)! w
! Marginal q:
qm(w) =dP (K, W )
dK= qa(w)! (p!(w)! 1) w
Average and marginal q
! Optimal composition of the balance sheet: W and K
! Average q:
qa(w) =P (K, W )!W
K= p(w)! w
! Marginal q:
qm(w) =dP (K, W )
dK= qa(w)! (p!(w)! 1) w
Average and marginal q
! Optimal composition of the balance sheet: W and K
! Average q:
qa(w) =P (K, W )!W
K= p(w)! w
! Marginal q:
qm(w) =dP (K, W )
dK= qa(w)! (p!(w)! 1) w
Parameter Values
risk-free rate r = 6%mean productivity shock (risk-neutral) µ = 18%volatility of productivity shock " = 9%rate of depreciation ! = 10.07%adjustment cost # = 1.5liquidation value l = 0.9cash-carrying cost $ = 1%proportional financing cost % = 6%fixed financing cost & = 1%
! Benchmark: iFB = 15.1% and qFB = 1.23.
Liquidation
! !"!# !"$ !"$# !"% !"%#!"&
$
$"%
$"'
$"(
w !
A. firm value-capital ratio: p(w)
)
)
first-bestliquidationl + w
! !"!# !"$ !"$# !"% !"%#
#
$!
$#
%!
%#
*!
B. marginal value of cash: p!(w)
! !"!# !"$ !"$# !"% !"%#!!"&
!!"(
!!"'
!!"%
!
!"%
cash-capital ratio: w = W/K
C. investment-capital ratio: i(w)
)
)
first-bestliquidation
! !"!# !"$ !"$# !"% !"%#!
#
$!
$#
%!
D. investment-cash sensitivity: i!(w)
cash-capital ratio: w = W/K
Optimal Financing
! !"!# !"$ !"$# !"%$
$"$
$"%
$"&
$"'
!m(! = 1%)
w(! = 1%)"
! w(! = 0)
A. firm value-capital ratio: p(w)
(
(
! = 1%! = 0
! !"!# !"$ !"$# !"%$
$"%
$"'
$")
$"*
B. marginal value of cash: p!(w)
(
(
! = 1%! = 0
! !"!# !"$ !"$# !"%!!"&
!!"%
!!"$
!
!"$
!"%
cash-capital ratio: w = W/K
C. investment-capital ratio: i(w)
(
(
! = 1%! = 0
! !"!# !"$ !"$# !"%!
%
'
)
*
$!
$%
cash-capital ratio: w = W/K
D. investment-cash sensitivity: i!(w)
(
(
! = 1%! = 0
Dynamic hedging
! !"!# !"$ !"$# !"%!$!
!&
!'
!(
!%
!
A. hedge ratio: !(w)
)
)
costly marginfrictionless
! !"!# !"$ !"$# !"%
!!"(
!!"%
!
!"%
B. investment-capital ratio: i(w)
)
)
frictionlesscostly marginno hedging
! !"!# !"$ !"$# !"%$"$
$"%
$"*
$"(
cash-capital ratio: w = W/K
C. firm value-capital ratio: p(w)
)
)
frictionlesscostly marginno hedging
! !"!# !"$ !"$# !"%$
$"#
%
%"#
*
cash-capital ratio: w = W/K
D. marginal value of cash: p!(w)
)
)
frictionlesscostly marginno hedging
Risk & return
! Conditional ':
'(w) =("
"m
p!(w)
qa(w) + w,
Idiosyncratic volatility and beta
! !"# !"$ !"% !"&'
'"#
'"$
'"%
'"&
#
A. firm value-capital ratio: p(w)
(
(
idio vol: 5%idio vol: 15%idio vol: 30%
! !"# !"$ !"% !"&'
'"'
'"#
'")
'"$
'"*
'"%
'"+
B. marginal value of cash: p!(w)
(
(
idio vol: 5%idio vol: 15%idio vol: 30%
! !"# !"$ !"% !"&!!")
!!"#
!!"'
!
!"'
!"#
cash-capital ratio: w = W/K
C. investment-capital ratio: i(w)
(
(
idio vol: 5%idio vol: 15%idio vol: 30%
! !"# !"$ !"% !"&!"%
!"&
'
'"#
'"$
'"%
'"&
cash-capital ratio: w = W/K
D. conditional beta: !(w)/!FB
(
(
idio vol: 5%idio vol: 15%idio vol: 30%
Credit line
!!"# !!"$ ! !"$ !"#!"%
$"$
$"&
$"'
!m(c = 0.2)
! w(c = 0.2)
m(c = 0)"
w(c = 0)"
A. firm value-capital ratio: p(w)
(
(
c = 0.2c = 0
!!"# !!"$ ! !"$ !"#$
$"#
$")
$"*
$"+
B. marginal value of cash: p!(w)
(
(
c = 0.2c = 0
!!"# !!"$ ! !"$ !"#!!"#'
!!"$'
!!"!'
!"!'
!"$'
cash-capital ratio: w = W/K
C. investment-capital ratio: i(w)
(
(
c = 0.2c = 0
!!"# !!"$ ! !"$ !"#!
&
*
%
$#
cash-capital ratio: w = W/K
D. investment-cash sensitivity: i!(w)
(
(
c = 0.2c = 0
Investment and q
!!"# !!"$ ! !"$ !"#$"$%
$"$&
$"$'
$"#
$"##
$"#%
$"#&
$"#'
$"(
cash-capital ratio: w = W/K
A. average q and marginal q
)
)
qa (c = 0.2)qm (c = 0.2)qa (c = 0)qm (c = 0)qFB
!!"# !!"$ ! !"$!"'
!"*
$
$"$
$"#
$"(
cash-capital ratio: w = W/K
B. investment and q
q
)
)
qaqm
qm/p!
i
!!"# !!"$ ! !"$!!"$
!!"!+
!
!"!+
!"$
!"$+
i
Main Results
! Investment first-order equation
marginal cost of investing =marginal q
marginal cost of financing
! financing: no target cash level, target leverage;financing regions:
! payout! cash! credit! equity financing (or liquidation)
Main Results
! Investment first-order equation
marginal cost of investing =marginal q
marginal cost of financing
! financing: no target cash level, target leverage;financing regions:
! payout! cash! credit! equity financing (or liquidation)
Main Results (continued)
! risk management: cash, hedging, and asset sales
! firm value and risk/return: idiosyncratic andsystematic risks
! methodology: tractable dynamic economic framework