### The Ching Paradox: The Forward-Looking Solution of Value Replacing the Backward-Looking Peer Review Process Demonstrated by Fuzzy Logic with Finite Range of Tolerance Replacing Exact Logic with Zero Range of Tolerance in the Fuzzy Infinite Spreadsheet

Hugh Ching (USA), Chien Yi Lee (China), Benjamin Li (Canada)

#### Abstract

The P/E Ratio (Price/Earning) is one of the most popular concepts in stock analysis, yet its exact interpretation is lacking. Most stock investors know the P/E Ratio as a financial indicator with the useful characteristics of being relatively time-invariant. In this paper, a rigorous mathematical derivation of the P/E Ratio is presented. The derivation shows that, in addition to its assumptions, the P/E Ratio can be considered the zeroth order solution to the rate of return on investment. The commonly used concept of the Capitalization Rate (Cap Rate = Net Income / Price) in real estate investment analysis can also be similarly derived as the zeroth order solution of the rate of return on real estate investment. This paper also derives the first order solution to the rate of return (Return = Dividend/Price + Growth) with its assumptions. Both the zeroth and the first order solutions are derived from the exact future accounting equation (Cash Return = Sum of Cash Flow + Cash from Resale). The exact equation has been used in the derivation of the exact solution of the rate of return. Empirically, as an illustration of an actual case, the rates of return are 3%, 73%, and 115% for a stock with 70% growth rate for, respectively, the zeroth order, the first order, and the exact solution to the rate of return; the stock doubled its price in 2004. This paper concludes that the zero-th, the first order, and the exact solution of the rate of return all can be derived mathematically from the same exact equation, which, thus, forms a rigorous mathematical foundation for investment analysis, and that the low order solutions have the very practical use in providing the analytically calculated initial conditions for the iterative numerical calculation for the exact solution. The solution of value belongs to recently classified Culture Level Quotient CLQ = 10 and is in the process of being updated by fuzzy logic with its range of tolerance for predicting market crashes to advance to CLQ = 2.

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DOI: https://doi.org/10.22158/jrph.v5n1p7

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