Venture Capital Financing with Staged Investment, Agency Conflicts and Asymmetric Beliefs Yahel ...

156 Pages·2005·0.65 MB·English

Venture Capital Financing with Staged Investment, Agency
Conflicts and Asymmetric Beliefs
A Thesis
Presented to
The Academic Faculty
by
Yahel Giat
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
School of Industrial and Systems Engineering
Georgia Institute of Technology
December 2005
Venture Capital Financing with Staged Investment, Agency
Conflicts and Asymmetric Beliefs
Approved by:
Dr. Steve Hackman, Advisor
School of Industrial and Systems Engineering
Georgia Institute of Technology
Dr. Ajay Subramanian, Co-Advisor
Department of Risk Management and Insurance
Georgia State University
Dr. Shijie Deng
School of Industrial and Systems Engineering
Georgia Institute of Technology
Dr. Loren Platzman
School of Industrial and Systems Engineering
Georgia Institute of Technology
Dr. Craig Tovey
School of Industrial and Systems Engineering
Georgia Institute of Technology
Date Approved: November 17, 2005
Maya,
Sheli — Shelach.
Moriah, Yitzhar, Efrat and Reut,
Gidlu LeYiraat Shamayim.
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ACKNOWLEDGEMENTS
I am grateful and obliged to my advisors, Steve Hackman and Ajay Subramanian, for their
relentless efforts and their impressionable advice.
I am indebted to Dan Peled who introduced me to the world of research.
I appreciate the wonderful faculty of the School of Systems and Industrial Engineering. In
particular, Paul Griffin, Pinar Keskinocak and Gunter Sharp who made my learning and
teaching experience pleasurable and interesting.
I thank Steve Hackman, Ajay Subramanian, Shijie Deng, Paul Griffin, Pinar Keskinocak,
Loren Platzman and Craig Tovey — my thesis proposal and/or thesis defense committee
members — for their valuable comments.
Finally, I thank Steve Hackman for this wonderful period in my life.
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TABLE OF CONTENTS
DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
II LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 Staging Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Contract structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3 VC Oversight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 Bargaining Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.5 Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Theoretical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Staging Investment . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Managerial Incentives . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Asymmetric Information and Beliefs . . . . . . . . . . . . . . . . . 24
2.2.4 VC Oversight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.5 Bargaining Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.6 Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
III THE BASIC MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.1 The evolution of the termination value . . . . . . . . . . . . . . . . 32
3.1.2 VC-EN interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 The EN’s Optimal Effort in Period T for a Given Contract . . . . . 36
3.2.2 The VC’s Choice of Contract in Period T . . . . . . . . . . . . . . 37
3.2.3 The Inductive Step . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
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3.3 Properties of the Equilibrium in Each Period . . . . . . . . . . . . . . . . . 40
3.3.1 VC’s Objective Function . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Equilibrium Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.1 Symmetric Attitudes towards Risk and Symmetric Beliefs about
Project Quality (Full Symmetry) . . . . . . . . . . . . . . . . . . . 46
3.4.2 Perfect Information . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4.3 Imperfect Information, Asymmetric Beliefs and Asymmetric Risk
Attitudes - The Actual Scenario . . . . . . . . . . . . . . . . . . . . 48
3.5 Sensitivity of Equilibrium Dynamics. . . . . . . . . . . . . . . . . . . . . . 51
3.5.1 Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5.2 Asymmetry in beliefs . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5.3 Cost of effort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.6 Project Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.7 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
IV ANALYSIS OF RISK — A TWO-PERIOD MODEL . . . . . . . . . . 66
4.1 Risk and Continuation Value . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Risk and Project Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
V NUMERICAL ANALYSIS AND RESULTS . . . . . . . . . . . . . . . . 78
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 The Core Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.2.1 Computing the deterministic path . . . . . . . . . . . . . . . . . . . 80
5.2.2 Computing the termination triggers . . . . . . . . . . . . . . . . . . 80
5.2.3 Computing the model’s results . . . . . . . . . . . . . . . . . . . . . 84
5.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3.1 Data driven parameters . . . . . . . . . . . . . . . . . . . . . . . . 84
5.3.2 Calibrated parameters . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.3 The Base Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4.1 Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4.2 Labor and Capital Substitution . . . . . . . . . . . . . . . . . . . . 96
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VI SHIFTING THE BARGAINING POWER . . . . . . . . . . . . . . . . . 102
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3.1 Optimal Contractual Parameters in Period T . . . . . . . . . . . . 103
6.3.2 The inductive step . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.4 Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
VII NON-OBSERVABLE EFFORT . . . . . . . . . . . . . . . . . . . . . . . . 112
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.2 Two-Period Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.3 T-period Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.4 Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
VIIICONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
APPENDIX A — CODE DESIGN . . . . . . . . . . . . . . . . . . . . . . . 130
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
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LIST OF TABLES
1 Risk forces affecting continuation value . . . . . . . . . . . . . . . . . . . . . 69
2 Risk forces affecting project duration . . . . . . . . . . . . . . . . . . . . . . 75
3 Average time between funding for different investment stages . . . . . . . . 85
4 Average number of investment rounds by industry . . . . . . . . . . . . . . 87
5 Investment categorized by return . . . . . . . . . . . . . . . . . . . . . . . . 87
6 The initial feasible regions and base values for the calibrated parameters . . 92
7 Economic results of the calibration process . . . . . . . . . . . . . . . . . . 92
8 The base values for the data driven parameters . . . . . . . . . . . . . . . . 93
9 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
10 Programming parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
11 Multiple experiment parameters. . . . . . . . . . . . . . . . . . . . . . . . . 133
12 Calibrations parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
viii
LIST OF FIGURES
1 Optimal investment function . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2 Optimal risky compensation path for different levels of initial asymmetry . 49
3 Equilibrium investment paths . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Sensitivity of equilibrium investment path to the price of risk. . . . . . . . . 53
5 Sensitivity of equilibrium investment path to the initial asymmetry in beliefs 54
6 Sensitivity of risky compensation to the cost of effort . . . . . . . . . . . . . 55
7 Two period lattice for base numbers and initial technical risk σ2 = 0.1 . . . 71
0
8 Two period lattice for base numbers and initial technical risk σ2 = 0.5 . . . 72
0
9 Two period lattice for base numbers and initial technical risk σ2 = 1 . . . . 73
0
10 Schematic overview of the numerical analysis . . . . . . . . . . . . . . . . . 79
11 Schematic overview of the quality lattice . . . . . . . . . . . . . . . . . . . . 81
12 Expected net firm value vs. initial technical risk . . . . . . . . . . . . . . . 94
13 Date zero continuation value vs. initial technical risk . . . . . . . . . . . . . 94
14 Expected firm duration vs. initial technical risk . . . . . . . . . . . . . . . . 95
15 Expected net firm value vs. market risk . . . . . . . . . . . . . . . . . . . . 96
16 Date zero continuation value vs. market risk . . . . . . . . . . . . . . . . . 97
17 Expected firm duration vs. market risk . . . . . . . . . . . . . . . . . . . . 97
18 Expected net firm value vs. capital elasticity . . . . . . . . . . . . . . . . . 100
19 Date zero continuation value vs. capital elasticity . . . . . . . . . . . . . . . 100
20 Expected firm duration vs. capital elasticity . . . . . . . . . . . . . . . . . . 101
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SUMMARY
Weconsiderariskaverseentrepreneurwhoapproachesadiversifiedventurecapitalist
(VC) for financing of a project with positive potential return. We develop several models
thatcapturekeyfeaturesoftheventurefinancing,includingstagedinvestment,VCoversight
costs and agency conflicts. The contract between the VC and the EN includes risk-free and
pay-performance sensitive compensation. Moral hazard arises because the EN must exert
effort for the project to succeed. Our model is novel in that it also allows for asymmetric
beliefs about project quality due to the EN’s optimism even when the VC and EN face
symmetric information.
WefirstanalyzetheVC-ENrelationshipwhentheVChasbargainingpower. Wecharac-
terizetheequilibriumlevelsforthepay-performancesensitivities,investmentandeffortover
time and show they can be either increasing or decreasing or initially increasing and then
decreasing. We find that asymmetric beliefs and risk aversion have opposite effects on the
VC-EN relationship. When the EN is moderately more optimistic than the VC, he accepts
more risk and exerts more effort and the VC responds with more investment. In contrast,
risk aversion reduces effort and investment. Our model predicts a performance-sensitive
investment policy where critical milestones must be achieved for investment to continue.
Thesemilestonesincreasewiththeriskaversionanddecreasewiththeasymmetryinbeliefs.
Consequently, project duration increases with asymmetric beliefs and decreases with risk
aversion.
Wecalibratethiscoremodeltoempiricaldataandusenumericalanalysistodemonstrate
that the technical and systematic risks have opposite effects. The VC’s payoff and the
project’s value and duration increase with technical risk and decrease with systematic risk.
We analyze the relationship when the EN has bargaining power, and find that the
equilibrium and the corresponding implications for venture financing do change. In this
setting, the negative effects due to risk aversion are more pronounced. We also find that
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