Of the DCF-method for real estate valuation under uncertainty

S. A. Smolyak (), Vadim Arkin and Alexander Slastnikov ()

Economics of Contemporary Russia, issue 3

Abstract: We offer a mathematical model for estimating the market value of a property comprised of a building and a land parcel. For these purposes, we apply an unconventional version of the discounted cash flow analysis, the highest and best use principle, as well as notions utilized in the theory of real options. In doing so, we take into account the income tax paid by the owner of the property and ad valorem expenses (for example, the property tax) - as part of the costs associated with the use of the property. Therefore, the cash flows used in the valuation of property are post-tax. The input information for appraising the market value of the property includes the market value of underlying land plot and the net income that property generates as of the valuation date (net of ad valorem expenses). However, the values of these inputs subsequent to the date of valuation are unknown, and their dynamics is modelled by random processes of the geometric Brownian motion. Solutions to the model indicate that the value of building depends on the value of the land on which it is located, the corresponding dependence being a nonlinear one. Thus, if the ratio of income from the property use to the value of the land plot does not exceed a certain threshold, the value of the building must be zero (that is, the value of the overall property must coincide with the value of the land plot). We present some examples of application for the proposed method. Of course, the market value of the property depends likewise on the parameters of those random processes that describe the dynamics of income from the property use and the market value of the land. In one example we show how the values of these parameters can be evaluated on the basis of the price data on several comparable properties.

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