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Small Business Economics
Published in: Small Business Economics 1/2019

02-04-2018

Contracts for venture capital financing with double-sided moral hazard

Authors: Hui Fu, Jun Yang, Yunbi An

Published in: Small Business Economics | Issue 1/2019

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Abstract

Using a Nash bargaining approach, we analyze the financing contract between the entrepreneur and the venture capitalist with double-sided moral hazard in a start-up enterprise. Our results show that there exists an optimal contract set between the entrepreneur and the venture capitalist, in which all contracts achieve an identical second-best social state. Within the optimal contract set, there exists continuum of joint debt-equity financing. The pure equity financing contract exists in the optimal contract set when the ratio of total social surplus to the amount of investment is greater than a threshold.
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Appendix
Available only for authorised users
Footnotes
1
Throughout the paper, we use the phrases “optimal effort” and “equilibrium effort” interchangeably.
 
2
With complete information when efforts are observable and verifiable, the entrepreneur and the VC would be compensated by their respective actual effort. In this case, their optimal effort levels are determined by the following condition:
\( \underset{L,K}{\max}\kern0.5em \gamma S\left(L,K\right)=\gamma \left({R}_{\varepsilon }+c\sqrt{LK}-F-\frac{L^2}{2\eta }-\frac{K^2}{2\theta}\right), \)
where γ = αα(1 − α)(1 − α) is a constant and S(L, K) is the gross social surplus that deducts from the project output the initial investment and effort costs of both parties. To find the optimal effort levels, we take the first-order condition, which gives \( \Big\{{\displaystyle \begin{array}{l}{L}^{\ast }=\frac{c}{2}{\theta}^{\frac{1}{4}}{\eta}^{\frac{3}{4}}\\ {}{K}^{\ast }=\frac{c}{2}{\theta}^{\frac{3}{4}}{\eta}^{\frac{1}{4}}\end{array}}\operatorname{} \).
 
3
Throughout the paper we use the terms “agreed effort” and “expected effort” interchangeably.
 
4
Lemma 1 describes the ideal yet inexecutable entrepreneurial contract form, and Proposition 1 presents the executable contract set (which nests the ideal contract) by introducing conditional social surplus. Only if conditional and actual social surplus are equal, the project output is shared in the same fashion between the ideal contract and the executable contract. The contract is fair in the sense that both parties are compensated by the actual cost of effort. The fairness of contracts in this context is more specific than that discussed in literature such as Fairchild (2011b) who relates it more generally to reciprocity, empathy, and trust.
 
5
In Figure 4 the following assumptions are made regarding the transfer payment: \( T\left(\widehat{L},\widehat{K}\right)=1.5\times \alpha F=0.15 \) in \( M\left({H}_1^{\ast}\right) \), \( T\left(\widehat{L},\widehat{K}\right)=\alpha F=0.1 \) in \( M\left({H}_2^{\ast}\right) \), \( T\left(\widehat{L},\widehat{K}\right)=0.5\times \alpha F=0.05 \) in \( M\left({H}_3^{\ast}\right) \), and\( T\left(\widehat{L},\widehat{K}\right)=0\times \alpha F=0 \) in \( M\left({H}_4^{\ast}\right) \).
 
6
The subset \( M\left({H}_4^{\ast}\right) \) excludes the scenarios when α is between 0.83 and 0.99 because of the negative social surplus (the transfer payment is out of its boundary). Such scenarios are not in the optimal contract set by definition.
 
7
The subset \( M\left({H}_3^{\ast}\right) \) excludes the scenarios when α is between 0.91 and 0.99 because of the negative social surplus.
 
8
Generally, in subsets M(H1*) and M(H3*), the relationships shown in Fig. 4 are not necessarily linear, and the share of social surplus received by the entrepreneur is usually (but not always) greater than the share of project output.
 
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Metadata
Title
Contracts for venture capital financing with double-sided moral hazard
Authors
Hui Fu
Jun Yang
Yunbi An
Publication date
02-04-2018
Publisher
Springer US
Published in
Small Business Economics / Issue 1/2019
Print ISSN: 0921-898X
Electronic ISSN: 1573-0913
DOI
https://doi.org/10.1007/s11187-018-0028-2

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