scholarly journals From P/E Ratio to Fuzzy Infinite Spreadsheet—Mathematically Rigorous Derivations of the Zeroth and the First Order Solutions of Rate of Return

2022 ◽  
Vol 5 (1) ◽  
pp. p7
Author(s):  
Hugh Ching (USA) ◽  
Chien Yi Lee (China) ◽  
Benjamin Li (Canada)
Keyword(s):  
Exact Solution ◽  
Real Estate ◽  
Initial Conditions ◽  
Investment Analysis ◽  
Rate Of Return ◽  
Exact Equation ◽  
Zeroth Order ◽  
Real Estate Investment ◽  
First Order ◽  
Order Solution

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.

Bubble Dynamics and Cavitation Inception Theory

1988 ◽  
Vol 32 (03) ◽  
pp. 155-167
Author(s):  
Blaine R. Parkin ◽  
Brian B. Baker
Keyword(s):  
Initial Conditions ◽  
Second Order ◽  
Order System ◽  
Refined Theory ◽  
Zeroth Order ◽  
Order Problem ◽  
Cavitation Inception ◽  
First Order ◽  
Order Solution ◽  
Forcing Function

In order to provide some theoretical background and to motivate the more refined theory introduced herein, some encouraging known theoretical results on bubble-ring cavitation inception are reviewed. This review is followed by the development of the theory of bubble-ring cavitation cutoff. Its outcome, when compared with experiment, shows the need for a more refined inception theory. The above comparison and the basic ideas behind the cutoff theory's formulation suggest a possible approach for a refinement based on a multiple scales expansion. This seems reasonable because the forcing function pulse in "laboratory time" f, varies slowly compared with the characteristic "bubble time,", which characterizes the response time of a typical microscopic cavitation nucleus. The ratio of these two times gives a small parameter, , appearing in the forcing function, with the result that this problem involves only a soft excitation. Expanding the forced Rayleigh-Plesset equation and its initial conditions to the second order in c, the zeroth-order problem is found to be the well-known autonomous nonlinear equation with nonhomogeneous initial conditions, giving free oscillations of a typical nucleus. The first-order system is a nonautonomous linear system with homogeneous initial conditions which governs the forced bubble growth. The second-order system consists of a linear autonomous differential equation and homogeneous initial conditions. It is needed to establish integrability conditions for the first-order solution. The first-order solution is left for future research and the zeroth-order problem is analyzed in the phase plane. Then a novel approximate integration, = t(u), is given in terms of elliptic integrals and functions. It was not possible to invert this solution and so the inverse u = u() is found numerically. These data are then used to find an analytical approximation for use in future first-order calculations.

Real Estate Investment Analysis and Taxation.

1970 ◽  
Vol 25 (1) ◽  
pp. 200
Author(s):  
Halbert C. Smith ◽  
Paul F. Wendt ◽  
Alan R. Cerf
Keyword(s):  
Real Estate ◽  
Investment Analysis ◽  
Real Estate Investment

A Theoretical Analysis of Laminar Forced Flow and Heat Transfer About a Rotating Cone

1965 ◽  
Vol 87 (2) ◽  
pp. 184-190 ◽  
Author(s):  
C. L. Tien ◽  
I. J. Tsuji
Keyword(s):  
Heat Transfer ◽  
Cone Angle ◽  
Forced Flow ◽  
Zeroth Order ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Flow And Heat Transfer ◽  
Rotating Cone ◽  
Fast Rotating

The present paper presents analytically a method of attack on the problem of laminar forced flow and heat transfer about a rotating cone. The nonsimilar nature of the general problem requires that separate consideration be given to a slow rotating cone and a fast rotating cone, depending on the relative magnitude of the rotating speed with respect to the free-stream velocity. The Mangler transformation first reduces the problem of a slow rotating cone to one of wedge flow with a transverse velocity component. The problem is then solved by a perturbation scheme which uses the solution of wedge flow as the zeroth-order solution. The case of a fast rotating cone is solved by a series-expansion scheme which gives successive corrections to the zeroth-order solution, i.e. the solution of a rotating disk in a quiescent fluid. The zeroth-order and first-order equations for both cases are given in the present work, together with the numerical results for the special case of a cone of about 107-deg cone angle. The first-order results in both cases are shown for the drag and torque coefficients, and the local Nusselt number. Higher-order results can be obtained according to the present analysis. The effect of cone angle on the flow and heat-transfer characteristics is indicated by the comparison between the results of the 107-deg cone and those of the disk, i.e., the 180-deg cone.

FMRR and Duration: Implications for Real Estate Investment Analysis

1976 ◽  
Vol 4 (3) ◽  
pp. 49-67 ◽  
Author(s):  
Guilford C. Babcock ◽  
M. Chapman Findlay ◽  
Stephen D. Messner
Keyword(s):  
Real Estate ◽  
Investment Analysis ◽  
Real Estate Investment

REAL ESTATE INVESTMENT ANALYSIS

1984 ◽  
Vol 2 (4) ◽  
pp. 356-365 ◽  
Author(s):  
JOHN BAILEY
Keyword(s):  
Real Estate ◽  
Investment Analysis ◽  
Real Estate Investment
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