Application of the Modigliani–Miller Theory, Modified for the Case of Advance Payments of Tax on Profit, in Rating Methodologies

During a couple years we have suggested a new approach to rating methodology of non–financial issuers, as well for project rating. The key factors of a new approach are: 1) The adequate use of discounting of financial flows virtually not used in existing rating methodologies, 2) The incorporation of rating parameters (financial "ratios") into the modern theory of capital structure (Brusov–Filatova–Orekhova (BFO) theory) and into its perpetuity limit. Recently we have generalized the Modigliani and Miller theory for a more realistic method of payments of tax on profit: for the case of advance payments of tax on profit, which is widely used in practice. Modigliani – Miller theory accounts these tax payments as annuity–immediate, while in practice these payments are making in advance and thus should be accounting as annuity–due. We have shown that this generalization leads to some important consequences, which change seriously all the main statements by Modigliani and Miller. In current paper we use the modified Modigliani – Miller theory (MMM theory) and apply it for rating methodologies needs. A serious modification of MMM theory in order to use it in rating procedure has been required. The financial "ratios" were incorporated into MMM theory. The dependence of the weighted average cost of capital (WACC), which plays the role of discount rate, on coverage and leverage ratios is analyzed.  Obtained results make possible to use the power of this theory in the rating and create a new base for rating methodologies

Modification of the Modigliani–Miller Theory for the Case of Advance Payments of Tax on Profit

The first serious study (and first quantitative study) of influence of capital structure of the company on its indicators of activities was the work by Nobel Prize Winners Modigliani and Miller. Their theory has a lot of limitations. One of the most important and seriouse assumptions of the Modigliani – Miller theory is that all financial flows as well as all companies are perpetuity. This limitation was lift out by Brusov–Filatova–Orekhova in 2008 (Filatova et al. 2008), who have created BFO theory – modern theory of capital cost and capital structure for companies of arbitrary age.  Despite the fact that the Modigliani–Miller theory is currently a particular case of the general theory of capital cost and capital structure – Brusov–Filatova–Orekhova (BFO) theory – it is still widely used at the West. In current paper we discuss one more limitation of Modigliani – Miller theory: a method of tax on profit payments. Modigliani – Miller theory accounts these payments as annuity–immediate while in practice these payments are making in advance and thus should be accounted as annuity–due. We generalize the Modigliani–Miller theory for the case of advance payments of tax on profit, which is widely used in practice, and show that this leads to some important consequencies, which change seriously all the main statements by Modigliani and Miller. These consequencies are as following: WACC starts to depend on debt cost kd, WACC turns out to be lower than in case of classical Modigliani–Miller theory and thus company capitalization becomes higher than in ordinary Modigliani–Miller theory.We show that dependence of equity cost on leverage level L is still linear, but the tilt angle with respect to L–axis turns out to be smaller: this could lead to modification of the divident policy of the company. Correct account of a method of tax on profit payments demonstrates that shortcomings of Modigliani – Miller theory are dipper, than everybody suggested: the underestimation of WACC really turns out to be bigger, as well as overestimation of the capitalization of the company. This means that systematic risks arising from the use of modified Modigliani – Miller theory (MMM theory) (which is more correct than "classical' one) in practice are higher than it was suggested by the "classical" version of this theory

Statistics of Coulomb blockade peak spacings for a partially open dot

We show that randomness of the electron wave functions in a quantum dot contributes to the fluctuations of the positions of the conductance peaks. This contribution grows with the conductance of the junctions connecting the dot to the leads. It becomes comparable with the fluctuations coming from the randomness of the single particle spectrum in the dot while the Coulomb blockade peaks are still well-defined. In addition, the fluctuations of the peak spacings are correlated with the fluctuations of the conductance peak heights.Comment: 13 pages, 1 figur

Finite temperature effects in Coulomb blockade quantum dots and signatures of spectral scrambling

The conductance in Coulomb blockade quantum dots exhibits sharp peaks whose spacings fluctuate with the number of electrons. We derive the temperature-dependence of these fluctuations in the statistical regime and compare with recent experimental results. The scrambling due to Coulomb interactions of the single-particle spectrum with the addition of an electron to the dot is shown to affect the temperature-dependence of the peak spacing fluctuations. Spectral scrambling also leads to saturation in the temperature dependence of the peak-to-peak correlator, in agreement with recent experimental results. The signatures of scrambling are derived using discrete Gaussian processes, which generalize the Gaussian ensembles of random matrices to systems that depend on a discrete parameter -- in this case, the number of electrons in the dot.Comment: 14 pages, 4 eps figures included, RevTe

Direct evidence of soft mode behavior near the Burns' temperature in PbMg1/3_{1 / 3}Nb2/3_{2 / 3}O3_{3} (PMN) relaxor ferroectric

Inelastic neutron scattering measurements of the relaxor ferroelectric PbMg$_{1 / 3}$Nb$_{2 / 3}$O$_{3}$ (PMN) in the temperature range 490~K$<$T$<$880~K directly observe the soft mode (SM) associated with the Curie-Weiss behavior of the dielectric constant $\varepsilon$(T). The results are treated within the framework of the coupled SM and transverse optic (TO1) mode and the temperature dependence of the SM frequency at q=0.075 a* is determined. The parameters of the SM are consistent with the earlier estimates and the frequency exhibits a minimum near the Burns temperature ($\approx$ 650K)Comment: 6 figure

A framework for digital sunken relief generation based on 3D geometric models

Sunken relief is a special art form of sculpture whereby the depicted shapes are sunk into a given surface. This is traditionally created by laboriously carving materials such as stone. Sunken reliefs often utilize the engraved lines or strokes to strengthen the impressions of a 3D presence and to highlight the features which otherwise are unrevealed. In other types of reliefs, smooth surfaces and their shadows convey such information in a coherent manner. Existing methods for relief generation are focused on forming a smooth surface with a shallow depth which provides the presence of 3D figures. Such methods unfortunately do not help the art form of sunken reliefs as they omit the presence of feature lines. We propose a framework to produce sunken reliefs from a known 3D geometry, which transforms the 3D objects into three layers of input to incorporate the contour lines seamlessly with the smooth surfaces. The three input layers take the advantages of the geometric information and the visual cues to assist the relief generation. This framework alters existing techniques in line drawings and relief generation, and then combines them organically for this particular purpose

Adjustment of the electric current in pulsar magnetospheres and origin of subpulse modulation

The subpulse modulation of pulsar radio emission goes to prove that the plasma flow in the open field line tube breaks into isolated narrow streams. I propose a model which attributes formation of streams to the process of the electric current adjustment in the magnetosphere. A mismatch between the magnetospheric current distribution and the current injected by the polar cap accelerator gives rise to reverse plasma flows in the magnetosphere. The reverse flow shields the electric field in the polar gap and thus shuts up the plasma production process. I assume that a circulating system of streams is formed such that the upward streams are produced in narrow gaps separated by downward streams. The electric drift is small in this model because the potential drop in narrow gaps is small. The gaps have to drift because by the time a downward stream reaches the star surface and shields the electric field, the corresponding gap has to shift. The transverse size of the streams is determined by the condition that the potential drop in the gaps is sufficient for the pair production. This yields the radius of the stream roughly 10% of the polar cap radius, which makes it possible to fit in the observed morphological features such as the "carousel" with 10-20 subbeams and the system of the core - two nested cone beams.Comment: 8 pages, 1 figur

Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model

We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change