Distribution of Profits from a Commercial Real Estate Object between Investor and Developer

Suppose that a developer initiates an investment project to build and operate a commercial real estate object, invests his own funds and, because they are insufficient, attracts an investor. The operation of the object will presumably generate a profit stream to be shared between the project participants. Suppose that each project participant specifies his requirements for the cost recovery, namely, the discount rate of income stream (the minimum acceptable return on investment) and the maximum acceptable payback period. The use of the investor’s funds imposes an obligation on the developer to fulfill the investor’s requirements on investment return. Developer would like to get rid of this obligation as early as possible. In addition, each project participant has an interest in reducing his payback period. Therefore, minimizing the maximum of the investor’s and the developer’s cost-recovery times (if their costrecovery requirements are met) ensures that the interests of the project participants were aligned. The project can only be realized if there exists a profit-sharing scheme meeting both participants’ cost recovery requirements. In typical profit-sharing schemes, participants’ shares are constant over time and either proportional to participants’ contributions or provide simultaneous cost recovery. We propose to consider a participant’s profit share as a step function of time, with jumps at the moment of his cost recovery and at the moment of his partner’s cost recovery. Such problem statement has not, to our knowledge, been considered before. The problem reduces to the conditional maximization of two nonlinear differentiable functions of one variable. The article justifies an algorithm that either solves the problem or reveals its insolvability. The proposed approach broadens the range of situations in which an acceptable to both participants profit sharing scheme can be found, thus broadening the set of implementable projects.

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