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Optimal Value Declaration in "Buy-Sell" Situations

Author

Listed:
  • Yigal Gerchak

    (Department of Management Sciences, Faculty of Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1)

  • J. David Fuller

    (Department of Management Sciences, Faculty of Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1)

Abstract

Buy-Sell "Shotgun" clauses call for a partner who wishes to discontinue a partnership to declare a value for the business, and for the other partner to then buy her out or sell to her at this value. The resulting decision model for an expected utility maximizing individual, who is uncertain of the business' valuation by the partner, is analyzed. This model is also applicable to a "divide and choose" fair division method, as well as some historical tax/customs schemes, and is more general than comparable bidding/auctions models. After showing that the optimal declaration is always between the declarer's valuation and the fractile of the subjective distribution corresponding to the share owned, we show that the optimal declaration is always increasing in the valuation, and for a risk-neutral declarer also increasing in the share owned. We prove that the more risk-averse the declarer, the closer is the optimal declaration to the valuation, and the higher the probability that the partner who values the business more will end up owning it. Finally, we relate the optimal declaration to the degree of uncertainty concerning the partner's valuation.

Suggested Citation

  • Yigal Gerchak & J. David Fuller, 1992. "Optimal Value Declaration in "Buy-Sell" Situations," Management Science, INFORMS, vol. 38(1), pages 48-56, January.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:1:p:48-56
    DOI: 10.1287/mnsc.38.1.48
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    Cited by:

    1. Wang, Haijun & Tan, Jie & Guo, Shuojia & Wang, Shenhao, 2018. "High-value transportation disruption risk management: Shipment insurance with declared value," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 293-310.
    2. Athanassoglou, Stergios & Brams, Steven J. & Sethuraman, Jay, 2008. "Minimizing regret when dissolving a partnership," MPRA Paper 12776, University Library of Munich, Germany.
    3. Haan, Marco A. & Heijnen, Pim & Schoonbeek, Lambert & Toolsema, Linda A., 2012. "Sound taxation? On the use of self-declared value," European Economic Review, Elsevier, vol. 56(2), pages 205-215.
    4. Miguel A. Costa‐Gomes & Yuan Ju & Jiawen Li, 2019. "Role‐Reversal Consistency: An Experimental Study Of The Golden Rule," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 685-704, January.

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