Abstract
Abstract The transactional assets pricing approach within valuation theory (TAPA) reviewed in this paper and developed by the authors, now more than a decade ago (MICHALETZ, ARTEMENKOV A. & ARTEMENKOV L., (2007), has found many applications in professional valuation practices dealing with illiquid assets (Leyfer 2006; Andrews 2011)). Consequently, challenges have arisen to ascertain its performance and develop tools, on its basis, which can be employed by valuers in their everyday practice and which are aligned as much as possible with the income approach tools used by them in their professional work. This paper proposes modifications to the standard direct income capitalization technique to align it as closely as possible with the results derivable under the applications of the TAPA basic pricing formula. The authors develop the respective adjustments using the Taylor series expansion and then, using a simulation technique, outline the performance of the resulting modified (“quick”) income capitalization model against the TAPA benchmark. The findings indicate that such a modified (“quick”) income capitalization approach has reasonable accuracy, which makes it amenable to direct usage in valuation practice, given the described assumptions.
Highlights
The structure of this paper is as follows: In Section 1, we review a mathematical formulation for the “transaction equilibrium” and “fair exchange” principles, which are essentially incorporated into the equitable value basis of valuation under the International Valuation Standards (IVS) 2017 edition (IVSC (2017))
There are all kinds of variations in between these two extremes, and we cannot offer any normative theory of portfolio formation7, as we observe that, in many instances and sectors, buyers and sellers of assets follow a diversity of practices with respect to the composition of their investment portfolios
The terminal value of the subject asset at the end of its useful life is zero (refer to Formula (3.5)). After these assumptions are put into Formula (3.8), we arrive at the Inwood formula: PV
Summary
The structure of this paper is as follows: In Section 1, we review a mathematical formulation for the “transaction equilibrium” and “fair exchange” principles (as applied to values-in-exchange situations), which are essentially incorporated into the equitable value basis of valuation under the International Valuation Standards (IVS) 2017 edition (IVSC (2017)). The second opposite view is that the difference in the rates of return is immaterial, and all the avenues of reasonable investment strategies are open for both the buyer and the seller to pursue Both settle for the optimal reinvestments with regard to PV and NOI amounts that agents of their circle deem most rewarding and practicably follow. Making the assumption that both rates are uniform: r s (i) = rb (i) = r( i ) and after appropriate substitutions, we conclude that Formula (1.4) can be simplified and converted into the following: This is the well-known formula always used in DCF analysis/calculations, though its justification is more often formulated axiomatically from the principle of anticipation or the investment worth paradigm (or deduced from the relational definition of discount rate in a static perfect market setting, as in Miller & Modigliani (1961)‘s Formulas (1)-(10) ), rather than from the “transactional equilibrium based view” proposed above, which places Formula (1.5) as a specific case of a more general Formula (1.4) situation. As established in the preceding section, the discount rate r(i) – is the rate of return (in Year i) for investment media/portfolios of presumed (most likely) buyers and sellers of the subject asset, if they operate in the same environment and are able to transact on the same markets accessible to both parties
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