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




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




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




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

! 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

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

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w !

A. firm value-capital ratio: p(w)

)

)

first-bestliquidationl + w

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B. marginal value of cash: p!(w)

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cash-capital ratio: w = W/K

C. investment-capital ratio: i(w)

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D. investment-cash sensitivity: i!(w)


Optimal Financing

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!m(! = 1%)

w(! = 1%)"

! w(! = 0)


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Dynamic hedging

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A. hedge ratio: !(w)

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B. investment-capital ratio: i(w)

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C. firm value-capital ratio: p(w)

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D. marginal value of cash: p!(w)

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Risk & return

! Conditional ':

'(w) =("

"m

p!(w)

qa(w) + w,

Idiosyncratic volatility and beta

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D. conditional beta: !(w)/!FB

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Credit line

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!m(c = 0.2)

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Investment and q

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A. average q and marginal q

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B. investment and q

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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

bolton chen wang (2009) (presentation ppt. a unified theory of tobin's q, corporate investment,...

Documents

cash w

cash account

cost of investing

r model sketch

fixed cost

variable cost

r wtdt

operations production