Strategic decentralization, bargaining, and transfer pricing in supply chain efficiency

Strategic decentralization, bargaining, and transfer pricing in supply chain efficiency

In vertical relationships, underinvestment problems can arise because sunk ment costs are ignored in ex post negotiation However, the delegation of bargaining rights to the upstream manager coupled with stock options makes the sunk invest-ment costs relevant costs from the manager's perspective The sunk investment costs are now reversible depending on his exercise decision Thus, under option-based com-pensation, the relevant investment costs create the upstream manager's bargaining power and thereby increase transaction price in negotiation The resulting increased transaction price improves the upstream profit and the improved return on invest-ment induces greater investment by the upstream firm Despite the higher induced transaction price, the downstream firm's profit can also improve because the greater induced investment enhances the viability of the supply chain Such supply chain gains also naturally translate into gains in consumer surplus

invest-The second essay investigates the role of decentralization and vertical licensing

in a durable goods market A monopolist in a durable goods market faces an investment problem in its R&D decision because it cannot commit to a value of

over-a new investment in the future which mover-akes its own product obsolete This pover-a-per demonstrates that decentralization and vertical licensing can help address the

pa-overinvestment problem and increase a firm's profit An internal conflict caused by decentralization is a natural commitment tool for the monopolist to keep its invest-ment level down However, decentralization can also lower the investment too far In such cases, permitting vertical licensing from the R&D division to a potential rival enables the firm to better manage its investment level The competition induced

by vertical licensing decreases the downstream division's profit but the advantage to the R&D division from added investment and an expanded market dominates The result implies that often observed decentralization and licensing across rivals can be

a means of overcoming the time inconsistency problem in a firm's R&D activities The third essay shows the role of decentralization in coordinating market com-petition and vertical efficiency There are many circumstances in which manufactur-ers provide inputs to wholesale customers only to subsequently compete with these wholesale customers in the retail realm Such dual distribution arrangements com-monly suffer from excessive encroachment in that the manufacturer's ex post retail aggression is harmful ex ante because it undercuts potential wholesale profits This paper demonstrates that with dual distribution, a manufacturer can benefit from decentralized control and the use of transfer prices above marginal cost Though these arrangements often create coordination concerns, a moderate presence of such concerns permits the manufacturer to credibly convey to its wholesale customer that

it will not excessively encroach on its retail territory This, in turn, permits the ufacturer to reap greater wholesale profits We also note that this force can point to

man-a silver lining in man-arm's length (pman-arity) requirements on trman-ansfer pricing in thman-at they can solidify commitments to a particular retail posture

Strategic Decentralization, Bargaining, and Transfer Pricing in Supply Chain

Efficiency

A Dissertation Presented to the Faculty of the Graduate School

of Yale University

in Candidacy for the Degree of Doctor of Philosophy

by Dae-Hee Yoon

Dissertation Director: Professor Shyam Sunder

December 2008

UMI Number: 3342736

Copyright 2008 by Yoon, Dae-Hee

All rights reserved

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Contents

Abstract i Dedication 1 Acknowledgements 2

2 Using Stock Options t o Make Sunk Costs Decision-Relevant:

Alle-viating the Upstream Underinvestment Problem 16

2.1 Model 21 2.2 Benchmark: Integration 23

2.3 Non-Integration 26

2.3.1 The Short Run 27

2.3.2 The Long Run and Pareto Gain 31

2.4 Example 37 2.5 Conclusion 40

3 Decentralization and Vertical Licensing: Mitigating the

overinvest-ment problem in a durable goods market 42

3.1 Setup 48 3.1.1 Model 48

3.1.2 Benchmark: The First-Best Solution 50

3.2 Centralization 52

3.3 Decentralization 53

3.4 Licensing and Duopoly 56

3.4.1 Horizontal Licensing under Centralization 57

3.4.2 Vertical Licensing under Decentralization 58

3.4.3 Endogenous Upgrade Level 62

3.5 Example 64 3.6 Conclusion 66

4 Friction in Related Party Trade when a Rival is also a Customer 1 67

4.1 Model 71 4.2 Results 72 4.2.1 Centralization 72

5 Conclusion 91

6 Appendices 94

6.1 Appendix A: Proofs of Propositions in Chapter 2 94

6.2 Appendix B: Proofs of Propositions in Chapter 3 102

6.3 Appendix C: Proofs of Propositions in Chapter 4 107

List of Figures

1.1 Nash Bargaining Solution 11

2.1 The Sequence of Events 27

2.2 The Sequence of Events in the Long Run 31

2.3 The Investment Levels 38

2.4 Profit of the Upstream Firm 38

2.5 Profit of the Downstream Firm 39

2.6 Pareto Gain 39

3.1 The Sequence of Events 50

3.2 The Sequence of Events under Vertical Licensing 59

3.3 The Investment Levels 64

3.4 The Firm's Profit 64

3.5 Endogenous Upgrade and the Firm's Profit 65

4.1 The net benefit of decentralization in terms of wholesale profit (top),

retail profit (bottom), and total profit (middle) as a function of k 79

4.2 The net gain from the decentralization as a function of the bargaining

power 86

List of Tables

2.1 Example 38

To my parents

Acknowledgements

I am sincerely grateful to Professor Shyam Sunder He guided my doctoral study

as both a course advisor and a thesis advisor from beginning to end He always encouraged me to challenge unknown areas with new ideas I am also deeply indebted

to Professor Brian Mittendorf Without his encouragement and help, I would not have made it through the difficult periods during my doctoral study I am very grateful to him for guiding my study and mentoring me

I also would like to thank Professor Rick Antle for serving on the committee and giving me his insights for my research I appreciate Professor Jiwoong Shin for his kind advice and encouragement I would like to thank Professor Anil Arya for his advice and coauthoring the third paper of this thesis

I also thank Professors Jacob Thomas, Frank Zhang, and Merle Ederhof for their advice and help during my doctoral study

Finally, I would like to dedicate this thesis to my father and mother Without their sacrifice and support, I could not have pursued my doctoral study Their love enabled me to complete this thesis and the doctoral study

Chapter 1

Introduction

In a modern business, a product is an output of efforts of numerous parties such as employees, managers, suppliers, shareholders and so on Among the parties, suppliers are an integral part of the business process, because their efforts and investments have large impacts on lower costs and higher qualities of final products To procure inputs with lower costs and higher qualities from suppliers, manufacturers make various attempts, such as recognition of best suppliers and sharing production and marketing information

However, a manufacturer and a supplier are two independent entities with ent objectives Each of these entities focuses on maximization of its own profit rather than supply chain efficiency As a result of the different objectives, their bargaining process for procurement contract cannot avoid conflicts which can cause inefficiency

differ-in supply chadiffer-ins

To mitigate the inefficiency in supply chains, various contracts such as a term contract based on contingencies, joint venture, and co-investment have been developed but none of them are complete solutions For instance, the long term contract is often not feasible because the contingencies for the long-term may not be

long-identifiable or contractible In the absence of complete solutions to the supply chain inefficiency, this thesis shows that accounting can provide substitutes for various contracts between a supplier and a buyer through a manager's compensation and an organizational structure

This thesis consists of three essays The first essay shows how a manager's pensation affects an investment hold-up problem and supply chain efficiency by in-creasing a supplier's bargaining power A supplier's delegation of bargaining to a manager with stock options transforms sunk investment costs into relevant costs from a manager's perspective because the sunk investment costs are now reversible depending on his exercise decision The relevant costs increase a manager's bar-gaining power in the negotiation with a buyer and thereby a transaction price and

com-a supplier's profit increcom-ase The improved trcom-anscom-action price increcom-ases the supplier's investment level and can achieve Pareto gain in the supply chain In this supply chain, the manager's option-based compensation is a substitute for a complex con-tract which protects a supplier from a buyer's opportunism and enhances supply chain efficiency

The second essay investigates the role of decentralization and vertical licensing in

a durable goods market A durable good monopolist faces an overinvestment lem because it cannot commit to the optimal level of investment over time due to time inconsistency problem Its new investment creates a new demand but at the same time it makes an old product obsolete If consumers anticipate the arrival of a new product through the rational expectation of the investment level, they are less willing to pay for the initial product Thus, the firm's overall profitability decreases under the investment for a new innovation In this overinvestment problem, decen-tralization based on a negotiated transfer pricing between divisions causes conflicts which lower the investment level Also, vertical licensing from the upstream division

prob-to a rival allows a firm prob-to transform a market structure from a monopoly prob-to a duopoly and thereby a firm can better manage the investment levels over time

The third essay shows that decentralization can be a device of coordinating petition in a market Under decentralization, a transfer price above marginal costs is induced by competing objectives of each related party The double marginalization reduces the downstream profit but it increases the upstream profit by providing a concession to a rival firm: a rival is more willing to pay for the input from the up-stream Then, a firm's profit increases because the gains from the wholesale profit dominate the costs of transfer pricing distortion in retail markets

com-The remainder of this chapter explains the related literature in decentralization, supply chains, strategic delegation, and bargaining

1.1 Decentralization

The effect of decentralization in an organization and a market has been largely tigated Holmstrom (1984) shows that decentralization is more compelling form of a principal's precommitment to a mechanism than centralization with communication Schwartz and Thompson (1986) emphasize the role of commitment of decentraliza-tion in the context of entry deterrence In their research, decentralization is employed for an incumbent firm to preempt rational entry in its market because a newly cre-ated division can duplicate a new entrant's strategy while freely competing against each other Melumad and Reichelstein (1987) show that without communication, delegation is preferred to centralization for the principal's interest On the other hand, when communication between the agent and the principal exists, the perfor-mance of decentralization is equivalent to that of centralization under only some special conditions Melumad and Mookherjee (1989) show that decentralization can

inves-be used for a government to commit to an audit strategy In this setting, delegation

of an audit policy to a manger enables the government to commit to an audit policy

ex post Melumad, Mookherjee, and Reichelstein (1995) compare the performance

of delegation with that of centralization in the presence of an intermediate agent They show that the additional incentive problem in the three-tier hierarchy can be mitigated by sufficient monitoring of an intermediate agent's contribution to the joint output and a specific sequence of contracting

Also, a supply chain is another form of decentralization and many papers have

examined the effect of decentralization in distribution channels Desai et al (2004)

find that having a retailer in the distribution channel helps a manufacturer improve profit under some conditions in a durable good market In detail, they show that under two-part prices the wholesale price should be higher than the manufacturer's marginal cost to cope with the durable good problem Balasubramanian and Bhard-waj (2004) examine the benefit of decentralization in the presence of multiple decision variables: price and quality Decentralization allows each division to focus on price and quality respectively without spillover effect and the firm can choose a proper level of quality which maximizes its profit Arya and Mittendorf (2006a) show that

in a durable good market channel discord can mitigate the overproduction problem

1.2 Supply Chains and Its Implication for

Account-ing

While the accounting research on divisional relationships in a firm (e.g., transfer pricing and capital budgeting) has been extensively done, the role of accounting information in supply chains has been overlooked until recently

One may think that the results in divisional relationships are just analogous to the

issues in supply chains But it is not necessarily the case The important difference

between supply chains and divisional relationships is goal congruence In divisional relationships, a divisional manager's payoff is aligned with a firm's goal and the decision making can be coordinated with relative ease via compensation and transfer pricing by headquarters On the other hand, supply chains consist of two independent firms and each firm has its own objective The different objectives cause conflicts between firms and the conflicts often lead to inefficiency such as underinvestment problems in supply chains (Williamson 1979, 1985) But the conflicts cannot be as readily controlled as in divisional relationships The two independent entities make

it difficult to coordinate mechanisms such as managers' compensation and transfer pricing for supply chain efficiency For the coordination, they need to go through a complex negotiation process, which causes another conflict Therefore, the solutions

in divisional relationship cannot be simply applied to the issues in supply chains For that reason, we need to examine the role of accounting separately in the context

of supply chains

Only a few papers have investigated the role of accounting in supply chains jan and Baiman (2002) investigate the effect of information sharing in buyer-supplier relationships They show that a buyer's information sharing of innovation can en-hance production efficiency, but it can also induce a supplier's misappropriation of the shared information Such a trade-off determines the level of information exchange

Ra-in supply chaRa-ins Kulp (2002) analyzes the determRa-inants and effects of the use of two alternative inventory management systems in supply chains: a traditional system and

a Vendor Managed Inventory (VMI) system The result shows that the reliability of

a retailer's acounting information and a manufacturer's ability to capture the shared information affect the performance of the VMI Arya and Mittendorf (2006c) inves-tigate the role of accounting earnings fixation in a vertical relationship They show

that the higher demand of downstream under earnings fixation increases the rents

of upstream which lift the investment incentive, thereby mitigating an investment hold-up problem On the other hand, this thesis investigates the role of accounting information in mitigating conflicts in supply chains via a manager's compensation and an internal organizational structure, which has not been examined before

1.3 Strategic Delegation

Since Schelling (1960) first stressed the notion of strategy of conflict, many papers (e.g., Vickers (1985), Fershtman and Judd (1987), and Sklivas (1987)) have exam-ined the benefit of strategic delegation in competition between rivals Vickers (1985) examined the role of strategic delegation in various situations and suggested the po-tential implication in horizontal competition and vertical relationships Fershtman and Judd (1987) and Sklivas (1987) show that the strategic choice of compensation changes a manager's behavior and, as a result, the firm's profit can be affected in hor-izontal competition In quantity competition, a manager becomes more aggressive

as a result of the strategic choice of incentives On the other hand, in price tition the manager becomes less aggressive as a result of the strategic compensation and a firm's profit improves Alles and Data (1998) show that in decentralized firms transfer prices should exceed marginal costs when considering strategic interaction

compe-in duopolistic price competition In their paper, the cost-plus transfer price compe-induces

a marketing manager to set a price higher, thereby mitigating market competition Similarly, Gox (2000) analyzes that a publicly observable commitment to an ab-sorption costing system can be a strategic device to achieve softened competition in duopoly

1.4 Bargaining in Supply Chains

Bargaining is prevalent in everyday life and it is prominent in business Employment contracts, mergers and acquisitions, and especially procurement contracts are all the result of bargaining To predict the equilibrium of this common practice, economists have searched extensively for bargaining models and the optimal strategy for the negotiation process In the past several decades, numerous bargaining models have been developed and examined, but the Nash bargaining solution (Nash 1950, 1953)

is still the most commonly employed model in economic research The model is very general without strong assumptions, and unlike other models with multiple equilibria, it generates a unique solution by using simple intuitions In the next section, I explain the detailed formulation of the Nash bargaining solution

1.4.1 Nash Bargaining

The Nash bargaining solution is based on the subtle concept of cooperation, which means that "the two individuals are supposed to be able to discuss the situation and agree on a rational joint plan of action, an agreement that should be assumed to be enforceable." (Nash, 1953) The important negotiation device in the Nash bargaining solution is the threat based on the disagreement point, which is the payoff in the event of negotiation failure Thus the disagreement points and the set of feasible payoffs available to both players jointly decide the negotiation outcome for the two parties

Nash (1953) shows the unique bargaining solution using two approaches: the negotiation model and the axiomatic method The axiomatic approach is commonly used, and the explanation of the Nash bargaining solution in this section follows this

approach According to Myerson (1991), the bargaining problem is defined by (F, v),

where F is a subset of R 2 , which is closed and convex and v = (t>i, v<f) is a vector in

R 2 1 Additionally,

F n {(x 1 ,x 2 ) | xi > vi and x 2 > v 2 } (1)

is nonempty and bounded F stands for the set of feasible payoff allocation, and v

stands for the disagreement point In this formulation, the bargaining problem is

defined as a problem of finding a solution function (f> (F, v), where

The axioms for the Nash bargaining solution are as follows

Axiom 1 (Strong Efficiency) <f> (F, v) is an allocation in F, and, for any x in F, if x >

4> (F, v), then x = (/) (F, v)

Axiom 2 (Individual Rationality) </> (F, v) > v

Axiom 3 (Scale Covariance) For any numbers Ai, A2,7l5 and 72 such that Ai > 0

and\ 2 > 0, ifG = {(Ai^i + ^ lt X 2 x 2 + 72,) I (xi,x 2 ) e F} andw = (Ai^i + 7X, X 2 v 2 + 72) ,

then 0 (G, w) = (Ai0x (F, v)+'y 1 , A202 (F, v) + 72)

Axiom 4 (Independence of Irrelevant Alternatives) For any closed convex set G,

ifGQFandcj) (F, v) € G, then (p (G, v) = (f> (F, v)

Axiom 5 (Symmetry) If v\ = v2 and {{x 2 ,x x ) | (xi,x 2 ) G F}, then <\> x (F,v) =

<t> 2 (F,v)

Axiom 1 implies that the bargaining solution should be feasible and Pareto

effi-cient Axiom 2 suggests that each player should get a payoff which is greater than

^ n this section, I follow a notation in Myerson (1991)

the disagreement point Axiom 3 indicates that the real outcome is not changed by order preserving linear transformations of the utilities Axiom 4 means that deleting feasible alternatives which are not chosen, should not affect the bargaining solution Axiom 5 implies that if bargaining positions of players 1 and 2 are symmetric in the bargaining, the bargaining solution is also symmetric The Nash bargaining solution satisfies these axioms and generates one unique solution by the maximization of the product of the two parties' incremental profit as follows

Figure 1.1: Nash Bargaining Solution

Based on the disagreement points (vi, v 2 ), two parties decide the negotiation outcome (xi,x 2 ) = ( ^ , ^ ) by the notions of symmetry and efficiency At the point, the Nash product {x\ — fi) (x2 — ^2) is also maximized

One common question for the Nash bargaining solution is why it uses the uct to get the negotiation outcome instead of simply splitting the total surplus by half The idea of splitting the total surplus by half is based on the egalitarian so-lution which distributes equal gains to two bargainers In this interpersonal utility approach, the axiom of scale covariance is generally violated because the interper-sonal comparison does not have decision-theoretic significance (Myerson 1991) The Nash bargaining solution is a synthesis of the egalitarian solution and the utilitarian solution which maximizes the sum of two persons' utility Then, under only some conditions, the egalitarian solution is the same as the Nash bargaining solution by corresponding to the utilitarian solution

prod-If the players are asymmetric in their bargaining strengths, the two persons gaining problem can be generalized to a nonsymmetric Nash bargaining solution by

bar-dropping the axiom of symmetry Then, the positive number a and /3 (0 < a, (3 < 1)

imply each party's bargaining power and the Nash product is defined as follows

The buyer is a monopolist in the final market with a linear demand function (p =

a — bq) and it purchases intermediate goods from a supplier The supplier produces

the intermediate goods at constant marginal cost c Then, the upstream firm's profit

IS

while the downstream firm's profit is

Through the bargaining process, the two parties decide the transaction price t

and the supplier has bargaining power p and the buyer has bargaining power 1 — p

Backward induction is used to get the equilibrium First, the buyer decides the

Second, based on the quantity and price, the two parties negotiate the transfer price

by maximizing the Nash product

Then, the equilibrium outcomes are

,'a-c\ (a-c)(2 — p) a + c (a - c\ _

The equilibrium outcomes maximize the Nash product, that is, total surplus, and

allocate the surplus to each party according to the bargaining power As we see in

the result, the transaction price becomes larger as the supplier's bargaining power

(p) increases Accordingly the quantity decreases and the external price increases,

thereby causing the double marginalization problem As the supplier's bargaining

power becomes larger, the double marginalization problem becomes more severe

be-cause the buyer responds to the increase of the transaction price by decreasing the

external quantity which causes the price increase

According to the equilibrium outcomes, each party's profit is as follows:

(a - c)2(2 - p)2

The sum of two firms is

, which is the supply chain efficiency The supply chain efficiency is smaller than

the first-best outcome under integration ( ^ )• The result implies that the supply

chain suffers from double marginalization as long as p > 0, that is, when there is a

conflict in the bargaining

Example 1 Demand function is p = 2 — q, c = 1, and p = \ Then, the equilibrium

outcomes are as follows:

1.5 Organization of Dissertation

The following chapters examine the role of strategic delegation, transfer pricing and bargaining in enhancing supply chain efficiency Chapter 2 examines how strategic delegation coupled with stock options increases a firm's bargaining power using sunk costs Chapter 3 investigates the role of decentralization and vertical licensing in overcoming the overinvestment in a durable goods market Chapter 4 shows that the friction due to decentralization can be a way of coordinating market competition and vertical efficiency Chapter 5 concludes this thesis

C h a p t e r 2

Using Stock Options t o Make

Sunk Costs Decision-Relevant:

Alleviating t h e U p s t r e a m

U n d e r i n v e s t m e n t P r o b l e m

Recent corporate scandals have focused considerable attention on issues of corporate governance The conventional wisdom is that effective governance entails aligning the incentives of managers with those of shareholders A case in point is the drum-beat of criticism directed towards the use of stock options and pressure to shift incentive compensation toward restricted stock (e.g., Meulbroek (2001), Hall and Murphy (2002, 2003)) In contrast, this paper demonstrates that the misalignment

of incentives wrought by stock options can be an effective means of gaining traction

in bargaining, which, in turn, can actually benefit shareholders and supply chain efficiency in the long-run

Since Schelling (1960) first introduced the strategy of conflict, many papers (e.g.,

Fershtman and Judd (1987), and Sklivas (1987)) have examined the benefit of gic delegation in horizontal competition between rivals Unlike the previous studies, this paper shows that in a vertical relationship stock options can be a natural de-vice of delegation for strategic bargaining by utilizing a designed conflict between an owner and a manager

strate-In a vertical relationship, an investment hold-up problem usually arises because the investments made by the upstream party are sunk before price and quantity are negotiated in detail At the negotiation stage, sunk costs are ignored and thus the transaction price will not fully include the investment cost As a result, the investment level of the upstream party becomes lower than the optimal level This hold-up problem translates into an inefficiency in the supply chain

In this research, I examine how an upstream manager's compensation, in ular stocks or options, affects the investment hold-up problem The analysis may shed light on the relative benefits of each form of compensation Stocks and options have been used as popular forms of contingent payment, but we still do not fully understand under what circumstances each kind of contingent payment performs better

partic-The model consists of an upstream firm and a downstream firm partic-The upstream firm is specialized in the development of a new product and the downstream firm is specialized in mass production and/or dissemination of the product One example is the relationship between a research company which develops a new drug candidate and a pharmaceutical company which commercializes the candidate The upstream (the research company) has an investment project that develops a new product If the upstream succeeds in the project, it sells the product to the downstream (the pharmaceutical company) and the downstream sells it in the external market The feasibility of the new project depends on the level of investment made prior to product

viability At the outset, the two parties cannot specify the detailed terms of price and quantity should the product eventually be viable, because they naturally cannot precisely describe the specifics of the new product prior to its existence The project itself is the process of building up the specifics and they can describe the product only

ex post (Tirole 1999) Therefore, their up-front contract cannot avoid being general

In this relation-specific investment project, the upstream's bargaining power is weak after the product is developed because the investment cost becomes sunk and the upstream firm is a captive to the downstream firm The downstream then pushes the transaction price down using its bargaining power in the negotiation The upstream firm, anticipating this situation, makes lower investment or walks away from the project at the beginning Thus, an inefficiency in the vertical relationship, often referred to as an investment hold-up problem, arises

Under this circumstance, I show that employing option-based compensation can mitigate the investment hold-up problem, both by creating more bargaining power for the upstream manager and by limiting the downside risk of investment

Options enable the manager to get a higher transaction price in the negotiation by creating more bargaining power Under stock-based compensation, the investment cost is reflected in the manager's payoff regardless of whether the negotiation breaks down or not In other words, the investment cost is sunk at the time of the negotiation because it is not reversible and therefore the transaction price will not reflect the sunk investment cost But under option-based compensation, the investment cost

is not sunk and it is a relevant cost from the manager's perspective because it is now reversible depending on the manager's exercise decision That is, if the manager exercises his options, the investment cost will be reflected in the manager's payoff But if he does not exercise his options, the investment cost is not included in his payoff and thus the investment cost is reversible depending on the manager's exercise

decision Then, the investment cost is no longer a sunk cost and it becomes a relevant cost from the manager's perspective As a result, the relevant investment cost creates more bargaining power for the manager and the manager will get a higher transaction price, one which reflects the investment cost The higher transaction price based on the more bargaining power naturally increases the investment level Adding to the bargaining effect, options protect a manager from the downside risk of investment and induce him to invest more This feature further restores incentives for investment The paper's results show that under option-based compensation, the investment hold-up problem can be mitigated by the higher level of investment and the upstream firm's profit improves under large uncertainty because of the higher transaction price Also, the higher level of investment can improve supply chain efficiency and consumer surplus by enhancing the feasibility of investment

Interestingly, when the uncertainty in a market is modest, even the downstream firm is better off when the upstream firm utilizes option-based compensation One may expect that the downstream would be worse off because of the higher transaction price that ensues, but the results show that the downstream can be better off because the higher level of upstream investment enhances the feasibility of a new product which more than offsets the disadvantage of a higher transaction price Thus, in this case, option-based compensation achieves Pareto improvements in a vertical relationship

There is limited accounting research which examines the effect of sunk costs on

decision making Kanodia et al (1989) show that the sunk cost leads to escalation

behavior when a manager's subsequent action reveals information about a manager's talent The manager's reputation concern prevents a manager from switching his previous decision Also, Hemmer (1996) examines the optimal allocation of sunk capacity costs and joint costs using the linear principal-agent framework On the

other hand, this paper shows that the sunk investment cost can be a good bargaining device for a manager when it is coupled with stock options

Similar to this paper, many papers have examined the relative efficiency of stocks (linear pay) and options (convex pay) Models that point to the incentive benefits of

options include Hirshleifer and Suh (1992), Hemmer et al (2000), Feltham and Wu

(2001), Core and Qian (2002), Lambert and Larcker (2004), Arya and Mittendorf

(2005), and Flor et al (2006) Papers that underscore the benefits of stock are

Meulbroek (2001) and Hall and Murphy (2002) The primary focus of the above papers is on intrafirm incentives In contrast, the present paper investigates the role

of option-based compensation for bargaining in inter-firm relationships

Since Williamson (1979, 1985) first stressed the investment hold-up problem in vertical relationships, many theories have been developed in various contexts to figure out the question As in this paper, Spiegel (1996) proposes alleviating the investment hold-up problem by shifting the bargaining power of the upstream party In Spiegel (1996), the upstream firm uses its capital structure to create bargaining power in subsequent negotiation The higher portion of debt in the capital structure enables the upstream to get a higher transaction price in the negotiation and the underinvest-ment problem is mitigated In a sense, this paper extends Spiegel's bargaining power insight to the realm of managerial compensation and shows that the sunk investment cost can be a negotiation tool under option-based compensation Edlin and Reichel-stein (1995) is another paper which employs the Nash bargaining solution concept

in the investment hold-up problem They introduce a fixed-price contract prior to the investment decision and the prior contract determines the disagreement point in the later renegotiation, thereby affecting the investment incentive The important distinction between their work and this research is that they consider the investment hold-up problem between divisions in a firm while this paper focuses on the relation-

ship between two firms with independent objectives in a supply chain In addition, this paper brings a manager's compensation into play to increase the investment incentive To attenuate the hold up problem, Ndldeke and Schmidt (1995) utilize

an option contract: it gives an upstream firm the right to deliver a fixed quantity

of the good and forms a buyer's contractual payment conditional on the upstream firm's decision On the other hand, this paper uses option-based compensation for the manager of the upstream firm to create bargaining power in the negotiation with the downstream

The remainder of this chapter consists of 5 sections Section 2.1 describes the model Section 2.2 shows a benchmark, the first-best solution in the integrated regime Section 2.3 examines how and when supply chain efficiency is enhanced by option-based compensation Section 2.4 discusses an example Section 2.5 suggests future directions and concludes this chapter

2.1 M o d e l

There are two firms, an upstream firm and a downstream firm The upstream firm has a project developing a new product If the upstream succeeds in bringing the project to fruition, it sells the new product to the downstream The only buyer for the new product is the downstream firm and it is a monopolist in the external market

The product, if successfully developed, has an inverse linear demand, p(q) = a — bq

in the external market

Before the product is developed, there is uncertainty about both its feasibility and its demand in the event of feasibility The feasibility of the project depends on

the level of investment, / , by the upstream firm The probability function, L(I) =

1 — exp(—/) represents the likelihood of project feasibility; L(I) is an increasing,

concave, and twice differentiable function Uncertainty about demand is reflected in

the demand intercept, a The random variable a has a common knowledge density function / ( a ) that is strictly positive on the closed interval [a, a] with mean /j, a and variance a 2a 1 The upstream firm and the downstream firm learn of product demand and feasibility after the investment stage The upstream firm faces constant

marginal production cost, c, c <a After the new product is developed, the two parties negotiate a transaction price, t, and quantity, q

The owner of the upstream firm hires a manager and delegates the decision ing for both investment and negotiation with the downstream firm The upstream

mak-firm has assets in place with a value of M and M > I The owner and the manager are

both risk neutral, and the owner can offer stock-based compensation or option-based compensation Stock-based compensation awards a certain number of shares of stock

to the manager while option-based compensation grants a right to exercise options

for shares at a predetermined strike price, M For simplicity, the total number of firm

shares is also normalized to one The manager's next best compensation

opportu-nity (reservation wage) is U Under stock-based compensation, the manager's payoff,

7rm is a(M+(t s —c)q—I) in the event of feasibility and a(M—I), otherwise, where a is the number (percentage) of shares granted and t s is transaction price Under option-

based compensation, the manager's payoff is (3Max {M + (t 0 — c)q — I — M, 0} in the event of feasibility and (3Max{M + 0 — / — M, 0} = 0, otherwise, where (3 is the number (percentage) of option shares granted and t 0 is transaction price.2 In the

1The first-order approach provides interior solutions if and only if a\ > 86 — (/ia — c) 2 This condition will be assumed throughout the following sections

2The optimal a and (3 are derived from the individual rationality (IR) constraint, respectively

as follows: under stock, the IR constraint is a(M + (t — c)q — I) > U and the optimal weight which maximizes the upstream's profit is a* = M+(f^-c)q*-r Under options, the IR constraint is

f3Max {(£ — c)q — 1,0} > U and then /?* = MaxUt*-c)q*-i o> • Throughout the following sections,

the superscript is suppressed and a and /3 are always optimal values Also, with the optimal a and /3, the manager's expected compensation is U under both stock and options and then he is

indifferent to the kind of compensation

event of feasibility, the upstream firm's profit is

and the downstream's profit is 7T2 = (p — t)q Throughout the paper, backward

induc-tion is used to examine the equilibrium behavior of the upstream and downstream firms

Given this setup, I examine both the short run and long run effects of stock and options in a vertical relationship and show under different compensations how the bargaining decision in the short run influences the investment decision in the long run

2.2 Benchmark: Integration

As a benchmark, consider the integrated regime in which the upstream and the downstream comprise a single entity Under the integrated regime, negotiation is moot and there is no investment hold-up problem First, consider the case in which

an owner does not hire a manager and he makes the investment decision The absence of divergent incentives in both negotiation and investment enables the owner

to achieve the first-best solution The first-best solution will be a good benchmark for the non-integrated regime which will be investigated

Using backward induction, the optimal quantity (q) and the resulting price (p)

in the external market solve:

Max q(a — bq — c) — I (1)

Denote the solution to (1) by q*(a) The "c" subscript denotes the integrated

(cen-tralized) solution Given the optimal quantity, the owner decides the investment

level which matches the marginal cost of investment with the marginal return of

investment in the following objective function:

Max f [M + L(I)(p(q* c (a)) - c)q:(a) - 1} f(a)da (2)

Denoting the solution to (2) by /*, the firm's expected profit is

f [M + L(I* c )(p( q ;(a)) - c)q* c {a) - I* c ] f(a)da (3)

The resulting equilibrium outcome in the integrated regime is as reported in Lemma

1 (All proofs are provided in the appendix.)

L e m m a 1 Under the integrated regime, the equilibrium outcomes are:

Q*c(a) = - g j p P(qt{a)) = —g—; and

46

In Lemma 1, the quantity and the price increase as a (the demand intercept)

be-comes greater In the same fashion, I* increases as the expected relative profitability (fi a

-c) of the market increases From the result we can see the effect of demand

uncer-tainty, a 2a , on the investment level As the uncertainty (o^) increases, the firm's

investment level becomes greater The firm's profit is convex in the demand a so

that incremental uncertainty always increases the firm's expected profit, thereby

increasing the investment level

As a next step, consider the outcome if the owner hires a manager and he delegates

decision making for investment to the manager The owner considers contingent

payment based on performance to motivate the manager by making the manager's

payoff in line with his interest As contingent payment, the owner offers

stock-based compensation or option-stock-based compensation By delegating decision making,

divergent incentives are a concern, but the choice of contingent payment can solve

the problem

Regardless of stock or options, the manager's decision of optimal quantity in the

external market is the same as before:

Max q(a — bq — c) — / (4)

q

At the investment stage, each contingent payment makes a difference In

partic-ular, stock-based compensation aligns the manager's payoff exactly with the owner's

interest as in (5) and naturally the manager replicates the owner's decision

Max I a[M + L(I)(p(q*(a)) - c)q*{a) - I]f{a)da (5)

In (5), the manager chooses the investment level, which is the same as /*, the

first-best level of investment

On the other hand, option-based compensation makes the manager focus on the

upside of the project which leads him to choose investment as in (6)

Max I PL{I)Max {M + (p{q*{a)) - c)q*(a) - I - M, 0} f(a)da (6)

Then, under option-based compensation, the manager chooses a level of

invest-ment, which is different from I* Thus, as confirmed in Proposition 1, the owner's

profit is not optimized by the manager's decision making

Proposition 1 Under the integrated regime, the use of stock-based compensation

dominates option-based compensation by replicating the owner's optimal decision making

2.3 Non-Integration

Under the non-integrated regime, the upstream and the downstream parties are

sepa-rate firms The upstream firm makes an investment in a project and the downstream firm buys the new product of the project and sells it in the external market In this non-integrated regime, an investment hold-up problem occurs because the two parties have to negotiate the transaction price after the upstream firm makes the investment

At the stage of negotiation, the investment cost is sunk for the upstream firm and the downstream firm, which is aware of this, reduces the transaction price it is will-

ing to pay The upstream, anticipating this consequence, naturally makes a lower investment than is ideal for the supply chain

In detail, the short run case and the long run case are examined separately First, in the short run, the upstream investment level is presumed fixed and only the bargaining decision is under the manager's control Then, the compensation structure determines the supply chain efficiency through the bargaining outcome

only On the other hand, in the long run, both the investment decision and the

bargaining decision are under the upstream manager's control and it is shown how

the manager's investment level is affected by the bargaining outcome

2.3.1 The Short R u n

In the short run, the investment level is hard to adjust so that only the bargaining

decision is influenced by the upstream manager After the feasibility of product

is learned, the manager negotiates with the downstream firm to decide transaction

price Thus, the upstream manager makes a decision for bargaining only and we

can examine the pure bargaining effect of compensation Figure 2.1 describes the

to decide transaction price (t) and quantity (q)

External market price (p)

is realized

Figure 2.1: The Sequence of Events

Stock-Based Compensation

To investigate the effect of stock-based compensation in a vertical relationship, the

optimal price which the downstream decides at the end of the game is determined

first The negotiated transaction price is determined based on the Nash bargaining

solution concept (Nash 1950, 1953) The Nash bargaining solution characterizes

the bargaining process only by the information incorporated in the player's utility

function, the payoff in the event of agreement, and the disagreement points under the

axiomatic approach (Binmore et al 1986) The advantage of employing the Nash

bargaining solution is that the format of negotiation is not restricted and the result

can be easily generalized

The negotiation is made by the downstream firm and the upstream manager

Each party's incremental profit is defined as the difference between the payoff when

the negotiation is successful and the payoff when the negotiation fails as follows:

Downstream firm : [q(a — bq — t)] — 0 = q(a — bq — t);

Upstream manager : [a(M + (t — c)q — I)) — [a (M — I)] — aq(t — c)

In the Nash bargaining solution, the quantity and the transaction price arising from

negotiation maximize the product of their incremental profits from negotiation as

follows:

Max [aq(t - c)] [q(a - bq - t)] (7)

q, t

In the negotiation, the two parties decide the quantity which maximizes their total

profit, and the optimal quantity is

The parties also negotiate the transaction price which decides each party's profit

As we see in (7), the manager's incremental profit from successful negotiation does

not include the investment cost Under stock-based compensation, regardless of

the negotiation outcome, the investment cost is included in the manager's payoff

because his payoff is aligned with the owner's Then, the investment cost is sunk

at the negotiation stage and the transaction price is lower because it cannot recover

the investment cost The alignment of the manager's payoff with the owner's payoff

causes the same investment hold-up In the Nash bargaining solution, the equilibrium

transaction price is

«(<>) = < = + I - 5 - ) 5 S — (9)

As seen in (9), the transaction price does not include the investment cost and the

result implies an investment hold-up problem

The resulting equilibrium outcomes under stock-based compensation are

Next consider option-based compensation, which makes the sunk investment cost a

negotiation tool Under option-based compensation, each party's incremental profit

from trade is defined as follows3:

Downstream firm : [q(a — bq — t)} — 0 = q(a — bq — t);

Upstream manager : [j3Max{M + (t - c)q - I - M, 0}] - 0 = j3 ((t - c)q - I)

Under option-based compensation, the investment cost is reflected in the manager's

payoff if the negotiation is successful and the manager exercises his options But if

the negotiation fails, he does not have to exercise his options and the investment cost

3 I assume throughout that profit from successful negotiation exceeds the investment cost Its

sufficient condition is that a is large enough

is not included in his payoff That is, the investment cost is reversible depending on

the manager's exercise decision Then the investment cost is no longer a sunk cost,

and it becomes a relevant cost from the manager's perspective Therefore, unlike the

case of stock-based compensation, the upstream manager's incremental profit from

the negotiation includes the investment cost, i\ In equilibrium, the relevant

invest-ment cost pushes the downstream to increase the negotiated transaction price The

downstream accepts the increased transaction price because it will profit from the

transaction even if it pays for the investment cost (A breakdown of the negotiation

gives zero profit to the downstream.) As we see in the following Nash product, the

manager's incremental profit considers the investment cost and we can expect that

the negotiated transaction price will increase:

Max [/3 (q(t - c) - I)][q(a - bq - t)] (10)

q, t

From (10), the negotiated quantity is

Based on the negotiated quantity, the two parties negotiate the transaction price

Option-based compensation creates more bargaining power for the manager by

trans-forming the manager's payoff from the owner's and making the sunk cost relevant

in the negotiation This higher bargaining power increases the transaction price as

follows:

q + 3c bl

As we see, the transaction price under option-based compensation increases as the

investment increases Therefore, the transaction price is greater than the price under