The effect of product differentiation on strategic
financing decisions.
Richard Fairchild
University of Bath
School of Management
Working Paper Series
2004.07
This working paper is produced for discussion purposes only. The papers are expected to be
published in due course, in revised form and should not be quoted without the author’s
permission.
1
University of Bath School of Management
Working Paper Series
University of Bath School of Management
Claverton Down
Bath
BA2 7AY
United Kingdom
Tel: +44 1225 826742
Fax: +44 1225 826473
http://www.bath.ac.uk/management/research/papers.htm
2004
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Enterprises
2004.06
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Assessing the context, nature, and extent of MNEs’ Backward
knowledge transfer to Chinese suppliers
2004.07
Richard Fairchild
The effect of product differentiation on strategic financing
decisions.
2
The effect of product differentiation on strategic financing decisions.
Richard Fairchild
E-mail: [email protected]
Abstract.
In a model of duopoly Bertrand competition in differentiated products, rival firms may use the
debt level strategically to soften price competition and increase profits. The equilibrium
choice of debt level depends on the degree of differentiation, and the firms’ short-term and
long-term incentives. At maximum product differentiation, the rivals always use zero debt. As
differentiation (and market power) reduces, firms may be induced to increase the debt level to
keep prices high. At low levels of differentiation (high levels of competition), firms may
return to low debt levels, as the predation effect dominates.
1. Introduction.
Financial and industrial economists have increasingly recognised the interaction between
product market competition and financing decisions of firms. A firm may use financial
leverage strategically to affect a rival’s behaviour. There are two main modelling approaches;
limited liability models and deep purse, or predation, models. In limited liability models,
firms pursue policies that transfer wealth from debt holders to equity holders. Hence, firms
have an incentive to set high debt levels. Under Cournot quantity competition (Brander and
Lewis 1986), firms with higher debt levels compete more aggressively by increasing output
and profit at their rivals’ expense. Under Bertrand price competition (Showalter 1995) rivals
can use debt financing to soften price competition. Therefore, the limited liability models
predict a positive relationship between market power and debt.
©Richard Fairchild 2004
3
In the deep purse or predation models (Brander and Lewis 1986; Bolton and Scharfstein
1990), an unlevered firm can enter a market to steal market share from a highly levered firm,
or even drive it into bankruptcy. Therefore, in contrast to the limited liability models, the
predation models predict a negative relationship between market power and debt.
Empirical tests of these models have provided mixed results.
Some researchers find a
negative relationship ( Titman and Wessels 1988; Chevalier 1995; Barclay et al 1995; Rajan
and Zingales 1995; Barclay and Smith 1996), while others find a positive relationship
(Krishnawamy et al 1992, Phillips 1995, Michaelas et al 1999; and Rathinsamy et al 2000).
Pandey (2000) finds a non-linear (cubic) relationship.
Recognition of these conflicting theoretical and empirical results has motivated development
of the model in this paper. We present a new theoretical approach which analyses the effects
of the degree of market power on equilibrium debt levels. We base our model on the analysis
of Dasgupta and Titman (1998), in which long-term debt softens price competition by
inducing the rivals to focus on short-term pricing decisions. We develop a model of duopoly
Bertrand competition in differentiated products, in which rival firms may use the debt level
strategically to soften price competition and increase profits. The equilibrium choice of debt
level depends on the degree of differentiation, and the firms’ short-term and long-term
incentives. At maximum product differentiation, the rivals always use zero debt. As
differentiation (and market power) reduces, firms may be induced to increase the debt level to
keep prices high. At low levels of differentiation (high levels of competition), firms may
return to low debt levels. Hence, our results support Pandey’s finding of a non-monotonic
relationship.
©Richard Fairchild 2004
4
2. The Model.
Consider a financial structure/product pricing game played under duopoly competition. At
date 0, the firms simultaneously choose their financial structures. At date 1, the rivals
simultaneously set product prices. At this stage, they face Bertrand price competition in
differentiated products. The firms then operate in the product market over two periods (date 1
and date 2). The players are risk-neutral, and the risk-free rate is zero.
We build on the model of Dasgupta and Titman (1998). In deciding on their date 1 prices, the
firms face the following trade-off. The short-term date 1 price affects the firms’ market
shares. Assuming that there is a certain customer ‘stickiness’ (customers buying from one
firm in date 1 tend to buy from that same firm in date 2), the date 1 price affects date 1 and 2
profits. The higher the date 1 price, the higher the date 1 profits, but also the lower the market
share, and the lower the date 2 profits. In deciding on date 1 prices, the firms face this tradeoff between date 1 and date 2 profits. In addition, firms face price competition from each
other. In summary, there are two forces driving prices down; Bertrand price competition, and
the firms’ desire for long-term market share.
Increasing long-term financial leverage softens price competition by inducing firms to focus
on short-term pricing and profits. Since they are less interested in future market share, they
compete less aggressively in short-term prices.
The period 1 industry demand function is Q = 2[α − p ], where Q is the quantity demanded
and p is the price. The period 1 demand function for firm i is
qi = α − pi + γ [ p j − pi ].
©Richard Fairchild 2004
(1)
5
where γ represents the degree of differentiation between firm i and firm j. Increasing γ
reflects reducing product differentiation (and, therefore, reducing market power), which
implies that firm i can capture greater market share by undercutting firm j. When γ = 0,
each firm has a local monopoly, and the pricing decision of one firm has no effect on the
quantity demanded from the other firm.
We assume ‘no-switching’ of customers between date 1 and date 2; the quantity of customers
buying from firm i in period 1, qi , buys from the same firm in period 2. Hence, each firm
has a local monopoly in period 2, and the quantity demanded in period 2 from firm i is
q2 = qi . Note that this implies that customers who did not buy from either firm in date 1 drop
out of the market completely at date 2.
The firms face date 2 demand uncertainty. With equal probability, all customers have one of
two possible reservation prices; P2 > 0, or zero. Since each firm has a local monopoly in date
2, each firm can charge the customers their date 2 reservation price. We assume zero costs of
production. Therefore, each firm’s date 2 profit is either q2 P2 = qi P2 or zero, with equal
probability. Hence, at date 1, firm i' s expected period 2 profits are ∏ 2 = qi
P2
. Firm i' s
2
period 1 profit is ∏1 = pi qi .
Since players are risk-neutral and the risk-free rate is zero, the value of firm i can be written
as Vi = ∏1 + ∏ 2 . That is,
Vi = qi ( pi +
P2
).
2
©Richard Fairchild 2004
(2)
6
Define the rivals’ security issue as S i and S j respectively. For simplicity, we allow each firm
to choose from one of two possible levels of long-term debt D. Each firm can either choose
an all-equity (zero debt) structure; S i = E , or each firm can choose a “high-debt” structure
with date 2 repayment value Si = D = qi P2 . In summary, S i , S j ∈ {E , D}.
We solve the financial contracting/pricing game by backward induction.
3. Pricing Decisions for given debt levels.
Firstly, take the date 0 financial contracts Si , S j as given, and solve for the firms’ equilibrium
prices pi ( Si , S j ), and p j ( S j , Si ). . In order to do so, we substitute qi from equation (1) into
equation (2) to obtain;
Vi = αpi − pi + γpi p j − γpi + (α − pi + γ [ p j − pi ])
2
2
P2
.
2
(3)
If both firms have chosen the all-equity contract at date 0 ( D = 0), they set date 1 prices to
maximise (3), taking the other firm’s price as given. We obtain the equilibrium prices by
solving ∂Vi / ∂Pi = 0, and recognising that, in equilibrium, pi * = p j * .
If both firms issue high debt level D = qi P2 , they set date 1 prices to maximise the expected
value of date 1 equity;
∏ i = αpi − pi + γpi p j − γpi .
2
©Richard Fairchild 2004
2
(4)
7
We obtain the equilibrium prices by solving ∂ ∏ i / ∂Pi = 0, and recognising that, in
equilibrium, pi * = p j * .
If firm i has chosen the all-equity contract, and firm j has chosen the high debt contract at
date 0, we solve ∂Vi / ∂Pi = 0, and ∂ ∏ j / ∂Pj = 0, to obtain equilibrium prices.
Therefore, the equilibrium prices for each combination of Si , S j ∈ {E , D} are given in lemma
1.
Lemma 1: The equilibrium prices for given Si , S j ∈ {E , D} are;
a) pi * ( E , E ) = p j * ( E , E ) =
α − 0.5(1 + γ ) P2
.
2+γ
b) pi * ( D, D ) = p j * ( D, D ) =
α
2+γ
.
2α + 3γα − 0.5γ (1 + γ ) P2
2α + 3γα − (1 + γ ) 2 P2
c) pi * ( E , D ) =
, p j * ( D, E ) =
.
2
3γ 2 + 8γ + 4
3γ + 8γ + 4
i) If γ = 0, firm i' s equilibrium price is independent of firm j ' s security choice. Further,
debt provides a higher price than equity; pi * ( D, D ) = pi * ( D, E ) > pi * ( E , D ) = pi * ( E , E ).
ii) If γ > 0, debt softens price competition. Further, each firm’s equilibrium price depends on
the other firm’s equilibrium price;
pi * ( D, D ) > pi * ( D, E ) > pi * ( E , D ) > pi * ( E , E ).
©Richard Fairchild 2004
8
Note that, the highest equilibrium prices occur when both firms issue debt. The lowest
equilibrium prices occur when both firms issue equity. If firm j issues equity, firm i can
commit to a higher price by setting debt, but this price is lower than when both firms issue
debt.
Now move back to date 0 to solve for the rivals’ equilibrium financial contracts.
4. The firms’ simultaneous choice of debt levels.
The rivals choose date 0 financial contracts Si , S j ∈ {E , D}, to maximise firm value, given the
other firm’s choice of debt level. In doing so, each firm recognises that its own choice, and
that of its rival, will affect date 1 prices, as given by lemma 1.
In order to solve for the equilibrium date 0 financial contracts, we substitute the equilibrium
prices given in lemma 1 for each pair of debt levels into (1) to obtain equilibrium quantities.
We then substitute equilibrium prices and equilibrium quantities into (2) to obtain equilibrium
firm values Vi ( S i , S j ) and V j ( S j , S i ) for each pair of debt levels. Finally, we solve for the
date 0 debt levels by finding the Nash equilibria of the normal form game.
Lemma 2: The firm values for given S i , S j ∈ {E , D} are;
a) Vi ( E , E ) = [
α + γα + 0.5(1 + γ ) P2 α − 0.5(1 + γ ) P2 P2
][
+ ]
2+γ
2+γ
2
b) Vi ( D, D ) = [
α + γα α
P
][
+ 2]
2+γ 2+γ
2
©Richard Fairchild 2004
9
c) Vi ( E , D ) = [
3γ 2α + 5γα + 2α + (1 + γ ) 3 P2 − 0.5γ 2 (1 + γ ) P2 2α + 3γα − (1 + γ ) 2 P2 P2
+ ],
][
3γ 2 + 8γ + 4
2
3γ 2 + 8γ + 4
d) Vi ( D, E ) = [
3γ 2α + 5γα + 2α − 0.5γ (1 + γ ) 2 P2 2α + 3γα − 0.5γ (1 + γ ) P2 P2
+ ].
][
3γ 2 + 8γ + 4
2
3γ 2 + 8γ + 4
Therefore, firm i' s best response functions, given S j = E or S j = D, are
Vi ( D, E ) − Vi ( E , E ) =
αP2 [1.5γ 4 + 2.5γ 3 + γ 2 ] − P2 2 (1 + 5γ + 9γ 2 + 7.25γ 3 + 2.75γ 4 + 0.5γ 5 )
,
(3γ 2 + 8γ + 4) 2
αP2 [1.5γ 4 + 2.5γ 3 + γ 2 ] − P2 2 (1 + 5γ + 9γ 2 + 7γ 3 + 2.25γ 4 + 0.25γ 5 )
,
Vi ( D, D ) − Vi ( E , D ) =
(3γ 2 + 8γ + 4) 2
respectively.
Examination of the best response functions Vi ( D, E ) − Vi ( E , E ) and Vi ( D, D ) − Vi ( E , D )
reveals the following;
Lemma 3: The equilibrium security issuance is as follows;
a) If γ = 0, Vi ( D, E ) − Vi ( E , E ) = Vi ( D, D ) − Vi ( E , D ) = −
2
P2
. Firm i' s dominant strategy is
16
to issue equity. By symmetry, this is also firm j' s dominant strategy. Hence, the equilibrium
is {Si = S j = E}.
©Richard Fairchild 2004
10
b) Vi ( D, D ) − Vi ( E , D ) > Vi ( D, E ) − Vi ( E , E ), ∀γ > 0.
If Vi ( D, D ) − Vi ( E , D ) > Vi ( D, E ) − Vi ( E , E ) ≥ 0, the equilibrium is {Si = S j = D}.
If Vi ( D, D ) − Vi ( E , D ) ≥ 0 > Vi ( D, E ) − Vi ( E , E ), the multiple equilibria are {Si = S j = D},
and {Si = S j = E}.
If 0 > Vi ( D, D ) − Vi ( E , D ) > Vi ( D, E ) − Vi ( E , E ), the equilibrium is {Si = S j = E}.
Examination of the best response functions Vi ( D, E ) − Vi ( E , E ) and Vi ( D, D ) − Vi ( E , D )
reveals that the equilibria depend on product differentiation γ , the firms’ long term incentives
(affected by P2 ), and the firms’ short-term incentives (affected by α ). For simplicity, we take
the firms’ short-term and long-term incentives as given, and focus on the effects of γ on the
equilibria.
We solve using the parameter values α = 3,500 and P2 = 1,000.
We consider product
differentiation in the interval γ ∈ [0,6]. This ensures that equilibrium prices are non-negative
for any combination of securities; pi ( Si , S j ) ≥ 0, p j ( Si , S j ) ≥ 0 ∀Si , S j ∈ {E , D}. Diagram 1
demonstrates firm i' s best response functions; Vi ( D, D ) − Vi ( E , D ) (the upper line), and
Vi ( D, E ) − Vi ( E , E ) (the lower line).
We obtain our main result (this relationship is demonstrated in diagram 2);
©Richard Fairchild 2004
11
Proposition 1: For the parameter values α = 3,500 and P2 = 1,000, the equilibrium is
{Si = S j = E} ∀γ ∈ (0,1.5]; {Si = S j = E} and {Si = S j = D} ∀γ ∈ (1.5,1.8]; {Si = S j = D}
∀γ ∈ (1.8,5]; and {Si = S j = E} and {Si = S j = D} ∀γ ∈ (5,6].
Therefore, for these parameters, the relationship between market power and debt is nonmonotonic (as in Pandey 2000). This is affected by a combination of the limited liability and
predation effects. In the low range of γ (that is, high differentiation/high market power) the
limited liability effect dominates. That is, the rivals use debt to soften price competition.
However, note that debt and market power are substitutes. At maximum differentiation (local
monopolies; γ = 0), the rivals do not need to issue debt to soften price competition. As
differentiation reduces, the rivals increase debt (debt substitutes for market power in softening
price competition).
When differentiation reduces sufficiently, there are multiple equilibria. Now the predation
effect dominates (a firm with low debt can steal market share by setting a lower price than a
firm with high debt), thus driving debt down.
©Richard Fairchild 2004
12
Increase in value
due to issuing debt
Firm i's security reaction functions: alpha =
3500, P2 = 1000.
100000
50000
0
0
-50000
1
2
3
4
5
6
-100000
Gamma
Diagram 1.
Effect of Product Differentiation on Equilibrium
Debt Levels
3500000
Debt Level.
3000000
2500000
2000000
1500000
1000000
500000
0
0
1
2
3
4
5
6
Differentiation Parameter
Diagram 2.
©Richard Fairchild 2004
13
Conclusion.
We have developed a financial contracting model in which firms use debt strategically to
soften Bertrand price competition. Our main result is that, when firms have local monopolies,
they both issue equity in equilibrium. As differentiation reduces, firms substitute debt for
equity in order to soften price competition (limited liability effect). When differentiation
reduces sufficiently, the predation effect dominates, and the debt level is driven down.
Our simple approach provides a good basis for future theoretical and empirical research. We
have analysed the effects of the differentiation parameter γ on equilibrium debt levels for
particular long-term and short-term parameters P2 and α . Development of the model will
analyse the effect of these parameters on the equilibria. Furthermore, we have only considered
two possible debt levels (high or zero). We may develop this model to include more debt
levels, at the expense of tractability (see, for example, Fairchild (2004), who includes zero,
medium and high debt levels). Furthermore, future research will examine the impact of
agency costs, and sequential predation (as in Bolton and Scharfstein 1990) in this model.
©Richard Fairchild 2004
14
References:
Bolton, P., and Scharfstein D., 1990. A Theory of predation based on agency problems in
financial contracting. American Economic Review. 93-106.
Barclay, M.J. and Smith, C.W., 1996. On financial architecture: leverage, maturity and
priority. Journal of Applied Corporate Finance 8 (4), 4-17.
Barclay, M.J., Smith, C.W., and Watts, R.L. 1995. The determinants of corporate leverage
and dividend policies. Journal of Applied Corporate Finance 7 (4), 4-19.
Brander, J.A., and Lewis, T.R., 1986. Oligopoly and financial structure: the limited liability
effect. American Economic Review 956-970.
Chevalier, J., 1995. Capital structure and product-market competition: empirical evidence
from the supermarket industry. American Economic Review; 415-435.
Dasgupta, S, and Titman, S.,
1998. Pricing Strategy and Financial Policy. Review of
Financial Studies; 705-737.
Fairchild, R. 2004. Potential product market competition, financial structure, and actual
competitive intensity. Mimeo, SSRN database.
Grullon, G; Kanatas, G., and Kumar. P., 2002. Financing decisions and advertising: an
empirical study of capital structure and product market competition. Mimeo, SSRN database.
©Richard Fairchild 2004
15
Krishnawamy, C.R., Mangla, I. And Rathinasamy, R.S. 1992. An empirical analysis of the
relationship between financial structure and market structure. Journal of Financial and
Strategic Decisions, 5 (3), 75-88.
Michaelas, N., Chittenden, F. and Poutziouris, P. 1999. Financial policy and capital structure
choice in U.K. SMEs: empirical evidence from company panel data.
Small Business
Economics, 12, 113-130.
Pandey, I.M. 2002. Capital structure and market power interaction: evidence from Malaysia.
Mimeo, SSRN database.
Philllips, G. 1995. Increased debt and industry product markets: An empirical analysis.”
Journal of Financial Economics 189-238.
Rajan, R. G. and Zingales, L. 1995. What do we know about capital structure? Some evidence
from international data, Journal of Finance 50 (5), 1421-1460.
Rathinasamy, R.S., Krishnaswamy, C.R. and Mantipragada, K.G. 2000. Capital structure and
product market interaction: an international perspective. Global Business and Finance Review
5 (2), 51-63.
Showalter, D.
1995 Oligopoly and financial structure: comment.
American Economic
Review. 647-653.
©Richard Fairchild 2004
16
Titman, S. and Wessels, R. 1988. The Determinants of Capital Structure Choice. Journal of
Finance, 43 (1) 1-19.
©Richard Fairchild 2004
17
University of Bath School of Management
Working Paper Series
Past Papers
University of Bath School of Management
Claverton Down
Bath
BA2 7AY
United Kingdom
Tel: +44 1225 826742
Fax: +44 1225 826473
http://www.bath.ac.uk/management/research/papers.htm
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