How firm boundaries and relatedness jointly affect diversification value: trade-offs between governance and flexibility

Abstract

Diversification involves ongoing decisions about firm boundaries and relatedness. We develop a theoretical model that uses a real-option framework combined with optimal mechanism design to analyze how choices of boundaries and relatedness affect firm performance in the face of tradeoffs between governance and flexibility. We find that: (1) optimal boundaries and relatedness are substitutes in determining firm performance; (2) the association between relatedness, the most commonly studied aspect of diversification, and firm performance is indeterminate; (3) the substitution between relatedness and boundaries declines as noise in internal communication increases; (4) variation in relatedness has greater impact than boundary size when headquarters can pick multiple winners; and (5) as the internal market for information becomes more efficient, the lower the value of relatedness in combination with small boundaries. The general conceptual implication of these points is that corporate governance interacts with firm relatedness and boundaries in generating diversification performance.

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source about projects, i.e., more efficient internal information market (c). a Firm value as a function of relatedness and boundaries under noisy signals (P3). b Firm value as a function of relatedness and boundaries under multiple winner picking (Proposition 4). c Firm value as a function of relatedness and boundaries under a change in the allocation mechanism (P5)

Fig. 5

Notes

  1. 1.

    Firm boundary (N) indicates the number of investment opportunities (projects) that HQ considers. HQ chooses N out of the population of product lines, brands, distribution channels, locations, customer segments, value chain as well as industries. Therefore, N can become very large (e.g. P&G, Google, business groups).

  2. 2.

    HQ commits to its solution, which remains optimal in three situations. First, our model can represent a repeated game between HQ and its divisions. Using the Folk theorem (Fudenberg and Maskin 1986), we can achieve any feasible and individually rational payoff if both HQ and PMs are sufficiently patient. In this case, deviating from the commitment is not optimal. Second, if HQ and PMs have identical time preferences, non-cooperative bargaining produces a Bayesian equilibrium in which a mechanism exists and produces the same allocation (Fudenberg and Tirole 1991). Third, if HQ commits to outside investors about processes that specify capital allocation, HQ can change the allocation rule only with the approval of its board; such a change is undesirable to all participants of the game. The notion of mechanism design and HQ’s commitment to it corresponds to the idea of constitution writing (Bower 1970), in which a key role of the top management team is to define and manage the organization’s structural rules.

  3. 3.

    Risk aversion of HQ (more generally, HQ’s utility function) does not affect optimal resource-allocation qualitatively because we can transform a risk-aversion valuation problem into a risk-neutral valuation (Sakhartov and Folta 2014).

  4. 4.

    We treat all projects equally, without giving special allocation to any project ex-ante. In addition, the model excludes information that does not influence the incentives of PMs and HQ. For example, if we introduced external shocks to projects and designed resource allocation conditional on the shocks, an asymmetrical equilibrium would arise; this is an equilibrium because exogenous shocks do not destroy incentive compatibility. Introducing prior information instead of external shocks leads to the same results. We abstract away such situations because they are straightforward. Furthermore, if shocks or prior information are assigned to projects with equal chance a priori (a maximum-entropy approach), we return to a symmetric equilibrium.

  5. 5.

    Our truth-telling approach conforms to the VCG mechanism in two ways. First, both investigate how to allocate a given amount of internal resources to N agents. Second, the solutions are similar; as in the VCG family, our approach assigns a mechanism designer to pay a player the function of values of the other players.

  6. 6.

    We define relatedness as input commonality. In turn, since any production function that matches inputs and outputs is one-to-one, input commonality generates output commonality.

  7. 7.

    William McKnight, the chair of 3 M’s board. https://hbr.org/2013/08/the-innovation-mindset-in-acti-3.

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Kang, H., Burton, R.M. & Mitchell, W. How firm boundaries and relatedness jointly affect diversification value: trade-offs between governance and flexibility. Comput Math Organ Theory (2020). https://doi.org/10.1007/s10588-020-09316-7

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Keywords

  • Diversification theory
  • Firm boundaries
  • Relatedness
  • Real options
  • Agency theory
  • Mechanism design