Chemla, Gilles

Winter, Ralph

English

Research Papers in Economics

1
Taxes and Corporate Dynamics:
The Product-Market Effect
Gilles Chemla
Dauphine Recherches en Management, CNRS
Imperial College Business School
Ralph Winter
Sauder School of Business, Univ British Columbia
(preliminary and incomplete)2
Motivation
￿ Contribute to our understanding of capital budgeting 
with costly external finance
￿ Examine the effect of perfect product-market 
competition on corporate dynamics
￿ Clarify flaws of traditional capital budgeting methods. 3
Our Starting Point 1
• Costly “round trip” to internal capital. 
→ distinction between internal capital & external finance
Our Proposition: 
• One dollar of internal capital is more valuable in states of 
the world where competitors have little cash.   
• Competitors have little cash 
→ investment in industry capacity low 
→ marginal return to physical capital high 
→ marginal value of low-cost capital (internal capital) high.4
Our Starting Point 2
Therefore: value in being an “industry 
contrarian”: correlated with industry return.
• Effective cost of capital includes covariance 
(project, other projects in the industry) even if 
risk neutral environment. 
• CAPM-like result for industry portfolio of projects5
Related Literature 1
￿ Capital budgeting: Corporate investment guided by rates 
of return available to investors (Brennan, 2003). 
No financial frictions → product market unimportant ( 
Leahy, 1992).
￿ Investment/CF correlation (Gomes, 2001) 
￿ Debt dynamics (Hennessy and Whited, 2005).  
Here  1. Focus on internal versus external cash.
2. Effect of product-market competition.6
Related Literature 2
￿ Corporate finance/product-market competition: Focus on 
strategic interactions: Brander and Lewis (1986), Bolton 
and Scharfstein (1990), Tirole (2006, Ch. 7).
Instead, we focus on perfect product-market competition 
and its effect on corporate decisions in presence of costly 
external finance.7
Model (1): The Product-Market
• Single perfectly competitive product market. 
Inverse demand p = P(X), X aggregate output
• Firm i invests xi 0 in riskless asset, xi j in the jth risky, real asset. 
• 1 dollar invested provides 1 unit of output for one period.
• Cost of producing xij is čj xi j.  Costs čj are functions of a random 
variable ω with cdf f distributed on a compact set.  Stochastic 
constant returns to scale. 
• Stationary distribution of project returns.
• Physical capital is rented or can sell in a perfect market.8
• Each firm is endowed in period 1 with internal capital bi1. Denote 
b1={b11,…,bN1}. Firms enter each period with internal capital in the 
industry, b, inherited from the previous period.  
• In each period, firms issue new equity ei at no cost and pay 
shareholders dividend di that is subject to linear tax rate td. 
• The adjusted amount bi + ei- di invested in xi={xi0,xi1,...xin}
• The product market opens, each firm supplies a quantity xi, and 
the equilibrium price is determined as p=P(∑ijxij).  
• Costs are realized.  Riskless asset earns rf, investment xj earns 
operating cash flow [p(Xt)xij- cjxij]. Corporate tax rate tc
• Personal tax rate tp< tc
Model (2): The Financial Market9
Model (3): The equilibrium
• q(b); the market to book ratio.
• {xi j (), ei(), di()}
• v(b,ω), the next period's market to book ratio given this period's 
amount of internal cash and given the realization of ω (infinite
horizon)
• b′(b, ω), next period's internal cash.
Rational expectations require that v(b, ω) = q(b′(b, ω)).
Recursive competitive equilibrium (Stokey & Lucas 1989). 
Partial equilibrium social welfare:
W’(b) = Maxd, e, xj S(X)+ (1-td )d(b) - e(b)+ [1+ rf(1-tp)]-1E[W(b’(b,ω))]10
Model (4): The Firm’s Program
• Firm i max value to risk-neutral shareholders:
Maxdi, ei, xij (1-td )di(b) - ei (b) +E[v(b′ (b, ω)) bi′(b, ω)]
subject to:
• ∑j xij(b) = bi - di (b) + ei (b)
• di (b), ei (b), xi j(b) ≥ 0
• b′(b,ω) = [p(X(b)) X(b)- ∑j cj (ω)xj (b) ](1-tc)+x0(1+rf(1-tc))]11
Social Planner’s Problem
￿ Social planner's pb has a unique bounded continuous solution. 
￿ Pb with 1 state variable, the aggregate internal equity. 
￿ "Everything aggregates“: Aggregate e, d, x depend only on b
￿ W is increasing in b and ω.
￿ The SP's solution can be implemented as a competitive equilibrium.
￿ The competitive stock market price of internal equity in each period 
is the marginal social value of equity. Same with the product price.12
The One-Period problem 1
￿ Firms invest in the risky project with the lowest 
expected cost only.
￿ As  tp< tc,, firms do not invest in the riskless asset.
￿ If bT is very large, then NPV of every dollar invested 
is zero.
￿ If bT is lower, profit made on dollars of internal 
capital invested.13
The One-Period problem. 
P High bT
P(K1T)
K1T Aggregate output
All output financed with internal capital. Zero profit.14
The One-Period problem. 
P Intermediate bT
P(bT)
bT Aggregate output
Higher price. Profit.15
The One-Period problem. 
P Low bT
P(K2T)
bT K2T< K1T
Profit td on units of output financed with internal capital. 16
The Two-Period Problem
￿ Supply from one firm is perfect substitute to 
supply from another. 
￿ Aggregate internal equity is a sufficient 
statistic for product market prices, Tobin’s q...
￿ Tobin’s q decreases with internal capital in 
the industry.17
The Two-Period problem 2
￿ The value of $1 of internal capital invested in the project is 
higher when competitors’ cost of capital is high. Value of being 
a contrarian.
￿ Firms take into account the correlation between projects and 
the Tobin’s q.
￿ With normal distributions, that collapses to:
E(rj) = rf+ λ λ λ λ cov( cj, ∑ijcj (ω ω ω ω)xij (b))
￿ Firms like projects with low expected costs and with negative 
correlation with product market.18
Notes:
￿ Everything here is derived in a risk-neutral 
environment.
￿ The product market partially completes an 
otherwise incomplete financial market.
The Two-Period Problem 319
￿ Firm value q(b)b, with q() decreasing in b
￿ Equity issues for low levels of internal capital
￿ As internal capital increases, no investment in 
the riskless asset, then xO increases
￿ Dividends for high levels of internal capital
The Infinite Horizon Problem 120
￿ Inventory model of internal capital
The Infinite Horizon Problem 221
Capital Budgeting Implications 1
￿ The value of projects incorporates that each dollar of 
return is an option of either paying a dividend or 
reinvesting. 
￿ Unlike APV or WACC that are inconsistent with simple 
opportunity cost principles :
1. They value project returns as cash, not as internal capital 
with a market price.
2. They treat the investment of $1 of internal equity as $1 
independently of amount of internal equity available and 
of future projects.22
Capital Budgeting Implications 2
1. Unlike APV/WACC, trapped equity effect of 
dividend taxation may increase investment
2. Rational pecking order theory (with riskless debt 
as in Hennessy Whited) where cost of debt is 
higher when capital is scarce in the industry. 23
Risk Management Implications
￿ Firms gain from insurance to transfer wealth from 
next-period states of low q (high b) to states of high 
q (low b).
￿ In equilibrium, the optimal amount of insurance at 
the firm level is irrelevant (like in an M&M world)
￿ The total demand for insurance against a risk 
(summing across all firms in the product market) is 
determined in equilibrium. 24
Empirical Predictions
￿ Investment/cash flow correlation is now well-documented.
Here, we predict that investment by one firm decreases with 
internal capital in competitors.
￿ Capital budgeting rules affected by technological environment 
and product-market competition.
￿ Market value of cash, and, eg, corporate governance. Think 
harder about adequate thresholds, etc.
￿ Rationale for FF factors?
￿ Hedging industry shocks rather than firm shocks25
Conclusion
￿ Product-market matters in a simple risk-neutral 
environment with corporate and personal taxes.
￿ The interactions between capital budgeting and the 
product market may well deserve greater scrutiny.
￿ Capital budgeting has a "home-made" risk-
management feature. 

Taxes and Corporate Dynamics: The Product-Market Effect.

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Taxes and Corporate Dynamics: The Product-Market Effect.

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Research Papers in Economics