Monte Carlo Simulations: Advanced Techniques - A BVR Special Report

Appraisal Experts Untangle the Issues addresses the unique concerns and challenges of valuing a company with real estate. With perspective from both real estate and business appraisers, this report will help steer the profession toward a more sensible consensus. It sparks thought and provides insight for those valuation professionals who are interested in providing fair value services related to business combinations. This must-have reference, which includes a case study, navigates readers through performing fair value engagements, reviewing client reports, and how to maintain quality in reporting.

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Essential for practitioners who wish to elevate their valuation analyses for complex assignments, Monte Carlo Simulations: Advanced Techniques is a report that takes simulations out of the laboratory and into practical application. Experts explain Monte Carlo simulations and how they can be applied to real-life valuation problems, and readers will learn how and when to use Monte Carlo simulations, as well as be able to identify pitfalls and prepare for potential problems. The Comprehensive Guide to the Use and Application of Transaction Databases is the go-to resource for anyone who relies on the market approach.

Highlights of this guide include: Clear explanations of the differences between the most commonly used transaction databases and how to avoid common traps Key concepts in applying valuation multiples Thorough analysis of the most popular and well-regarded transaction databases Taxes and Value The On-Going Research and Analysis Relating to the S Corporation Valuation Puzzle Taxes and Value: Fannon Taxes and Value: The Ongoing Research and Analysis Relating to the S Corporation Valuation Keith Sellers Puzzle provides a substantive contribution to the controversial issue of how to value pass-through entities.

Authors Nancy Fannon and Keith Sellers present the findings of decades of academic research on the impact of taxes on firm value and demonstrate that historical market returns impound the effects of shareholder taxes. This research is used to demonstrate how these returns can be adjusted to estimate a cost of capital appropriate for the valuation of a pass-through entity. A few comments from the technical review panel Great job marshalling the arguments and presenting them in a logical way. Now in its second edition, Benchmarking Identifiable Intangibles and Their Useful Lives in Business Combinations delivers a compilation of reported, vetted, and carefully analyzed data, particularly focused on useful lives of intangible assets as reflected in over 6, purchase price allocations.

Who uses this publication? With so much opportunity at stake, striking the right balance between IP exploitation and protection is an increasingly key business objective for many organizations. With data analyzed and presented from the ktmine database, you can now have a comprehensive report on global licensing royalty rates and an analysis of value within specific industries, which will help you benchmark IP transactions over a year period.

This valuable, two-volume resource offers practical guidance for determining John Stockdale Sr. BVR the DLOM and includes a compendium with analysis of more than of the most important cases that have made it into the courts. Case reviews shed light on how judges have viewed experts use of the relevant facts and economic principles to determine a DLOM. Insight into the IRS view on DLOM Expanded discussion of pre-ipo studies and minority public stock evidence Studies on the matched pairs approach and discounts in private companies Expanded coverage of benefit of the bargain damages Computational methods and models including the revised Finnerty and the Ghaidarov average strike put option Comprehensive and easy-to-read court case summary table BVR s Guide to Personal v.

Enterprise Goodwill delivers first-hand knowledge and the most current issues in goodwill with expertise from Mark O. Save valuable research time with the one resource that business valuation professionals need to have in their business valuation library. The most current thought leadership with articles on personal and enterprise goodwill The most important court cases regarding goodwill, including digests of critical decisions Easy-to-use summary data including a newly updated article with aggregate summary data from the Goodwill Registry on medical and dental practices published by The Health Care Group.

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This guide helps practitioners whenever employee-owner compensation is subject to review and adjustment and is an invaluable resource when valuing noncompete agreements or calculating personal versus enterprise goodwill. Seigneur and Yeanoplos provide a point checklist Court case digests of key compensation cases. In this edition, expert Michael Pellegrino delivers real-world case studies of IP valuation analyses from start to finish in each of the primary IP categories. This practical, hands-on guide presents an objective framework for conducting due diligence of IP rights, performing the legal analysis, and correlating the impacts of IP rights on value.

Highlights of this edition include: Practical guidance on valuing IP includes boilerplate report requirements, royalty rate analysis, demand analysis, and guidance on presenting the most reliable statistics Thorough discussion of valuation approaches and due diligence Analysis of patent, copyright, and trademark-specific issues and considerations Royalty Rates in Biotech A BVR Guide to Full-Text Licensing Agreements Royalty Rates in Biotech: These hard-to-find agreements provide valuable guidance in setting royalty rates and addressing complex issues in a license agreement.

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By reviewing the actual agreements, readers will learn how companies characterize and monetize their trade secrets with specific attention paid to the language used, the enhancements to the economic value of the license the trade secrets add, the industries where this is a common practice, and the actual royalty rates. Discussion of what a trade secret is Trade secret misappropriation Keeping trade secrets secret Trade secret value and licensing Trade secret analysis and agreement terms Trade secret value sources Example agreements: Through the transfer of copyright intellectual property rights, creators monetize their works.

It illustrates how others have realized value from their copyrights through licensing and readers can gain empirical insight into relative values of these intellectual properties. This guide includes agreements on: Music composition and recording Famous personages: Edited by healthcare valuation thought leader Mark Dietrich, the guide provides Third Edition current and comprehensive how-to guidance on valuation approaches. While estate and gift tax issues are one of the top revenue Edited by Linda Trugman producers for business appraisers, this area of the valuation profession continues to face new challenges.

BVR It is crucial for appraisers to stay current with the legal arguments, regulations, and technical theory that apply to estate and gift issues relating to the business valuation profession. Adam Manson Appraisal actions under both dissent and oppression statutes are on the increase, and it is a fertile field BVR for business appraisers.

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BVR s Business Valuation and Healthcare Case Law Compendium features the most discussed and the most recent court cases involving business valuation disputes in the healthcare industry. Our legal analysts have crafted this one-of-a-kind resource, which breaks down the cases and the decisions to save you hours of research.

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Most of the light propagating into the mucosa penetrates into the submucosa. The submucosa comprises larger blood vessels compared to mucosa. As a result, the light incident on the mucosa is more heavily absorbed in the submucosa, especially in the green part of the spectrum, where the hemoglobin features the highest absorption. Hence, only a small fraction of the incident light can penetrate into the deeper layers [ 24 , 26 , 29 ].

Typically the thicknesses of the mucosa and submucosa are comparable. Moreover, as the muscularis mucosa is very thin and probably features a scattering behavior quite similar to that of the submucosa, in the model it will be lumped together with the submucosa into a single layer, referred to as the submucosa throughout the rest of this paper. To model the propagation of polarized light in ex-vivo colon samples we have represented such samples as multi-layered scattering structures. In a first step we assumed that the mucosa and the submucosa layers consist of a surrounding medium with mono-dispersed scattering spheres.

Due to very small thickness of the muscularis mucosa and the similarity between the muscularis mucosa and submucosa optical properties, the muscularis mucosa will be included in the submucosa layer in our model. All underlying layers were lumped into a totally depolarizing Lambertian substrate. In a second step, we considered the layers with bimodal populations representing both the collagen spheres and the sub-cellular organelles - the most important scatterers - within each layer.

We used the description of normal colon tissue proposed in [ 26 ] to specify the characteristics of each scattering layer. The scattering spheres with radius r , and optical index n s were embedded in an extra cellular matrix with optical index n m. The number density N was calculated from the volume fraction F of the scatterers i.

All layers of the virtual sample were placed within a cylinder diameter 1 cm, variable depth h , see Fig. The lateral walls of cylinder were assumed to be totally absorbing. The bottom of cylinder was either absorbing or Lambertian substrate. For the layer with bimodal population, the radii, number density and optical index contrast of the two types of scatterers are different; r 1 , r 2 , MFP 1 , MFP 2 , m 1 and m 2.

This is a first approximation of the response of the underlying layers, based on the assumption of a complete randomization of the polarization and emerging direction of the backscattered photons due to a large number of scattering events. Finally, as shown in Fig. In particular, in cancerous regions the surface may remain flat or may develop an exophytic growth adenomatous polyps. The possible changes in sample morphology have also been considered in our model by deforming the multilayer structure in two different ways, as shown below.

Microscopic structure of a healthy colon sample, with its different layers: The stochastic paths of the incident photons were simulated numerically by means of Monte Carlo algorithm. The diffuse light illumination of the sample was modeled with the photons impinging the sample surface at a random location. At each scattering event the changes of photon polarization and direction of propagation were calculated making use of the exact Mie solution for the scattering of plane wave on spherical particle.

The implementation of the rejection method and flux-at-point estimation technique allowed us to accelerate the convergence of the statistical algorithm [ 27 ]. We first performed the simulation with the single layer model varying the values of model parameters in order to identify the impact of each individual parameter on the ratio of linear to circular polarization of the backscattering light. Then we performed the simulation with the double layer model to find out if the single layer model can be considered as an approximation of the complex multi-layered structure of the colon tissue.

For the principal model parameters we retained the average values given in [ 26 ]. No absorption either from the medium or from the spheres was taken into account so far. The value of the Lambertian albedo a was chosen in order to account for the absorption by the mucosa and submucosa layers and the global contribution from the deeper layers. We considered reasonable to vary albedo a values between 0 and 0.

In a first instance, we considered the mucosa alone, on top of a Lambertian representing the submucosa and all underlying layers see Fig. This is typical of Mie scattering regime [ 14 ]. The albedo a had to be increased to 0. As a result, the single layer model with the nominal values of the parameters for the mucosa is certainly not adequate. Seeking for the characteristics of the phantom tissue that could reverse the regime of scattering from Mie to Rayleigh-like we tuned the model parameters one by one while keeping others constant.

The results are summarized in Fig. We first decreased the radius of the scattering spheres from nm to 50 nm to determine the typical size of organelles which may reverse the scattering regime from Mie to Rayleigh. It turned out that this regime reversal occurred already at nm radius Fig. Increasing the MFP is equivalent to shortening the thickness of the scattering medium, thus reducing: We also explored the influence of the sample thickness h , between 0.

Moreover, the Lambertian albedo a was set equal to 0. It is therefore natural to explore the polarimetric response of more complex structures, which might provide better models of the complex colon tissue structure. We performed simulations with two superimposed layers, representing the mucosa and submucosa, instead of a single one, on top of the Lambertian substrate. We set the parameters of the mucosa and submucosa layers at the nominal values defined at the beginning of this section.

The results of these simulations are shown in Fig. In contrast, the histograms 2 and 3 of the diagonal Mueller matrix elements, calculated with Lambertian albedos equal to 0. The fact that the relation between the diagonal elements of the simulated backscattering Mueller matrix image of the multi-layered model remains unchanged compared to that of the single-mucosa-layered model confirms that the single-layered model is a quite good approximation of colon tissue.

This observation supports the idea that only a small fraction of the incident light reaches the submucosa layer and an even smaller fraction is backscattered from the submucosa, without any major effect on the total polarimetric response. As a result, in the following we will consider only models with a single layer above the Lambertian. Normally the initial stage of colon cancer development is linked to the growth of a polyp exophytic growth.

So the question arises: To answer this question we modified the model geometry see Fig. We performed the simulations for different heights h s of the bump 0. As shown on the right panel of Fig. However the Rayleigh-like relation between the diagonal elements of the Mueller matrix does not hold anymore when the morphological changes are combined with an increase of the mucosa layer thickness. Figures 6 a, c represent two different modeled non-uniform deformations of colon tissue originating in the mucosa layer.

The results shown in Figs.

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This trend is consistent with that seen on flat surfaces and shown in Fig. However we never experimentally observed any inversion for the diagonal coefficients of the measured Mueller matrix images of the light backscattered from healthy or cancerous colon tissue. The essential conclusion that can be drawn from the results presented in this subsection is thus that the models involving only monodisperse populations of scatterers are prone to switches between the two scattering regimes, for reasonable values of the various parameters, in contradiction with the experimental data.

We now consider bimodal populations in each layer, an approach which seems reasonable to better reproduce the variety of scatterers actually found in real tissues. Moreover, due to their isotropic scattering, small scatterers may significantly impact the polarimetric response in the backscattering geometry, even at relatively low concentrations, with a strong Rayleigh type contribution, thus improving the qualitative agreement with experimental data.

In our refined model we represented the scatterers in epithelial cells in the mucosa layer - by their nuclei, the scatterers in connective tissue - by collagen in the extra-cellular matrix, the scatterers in cytoplasm and the extracellular matrix - by sub-organelles in physiological liquid. We kept the totally depolarizing Lambertian substrate with typical albedo value of 0.

The Monte Carlo algorithm was modified in order to take into account the bimodal population of scatterers and a possible absorption by the surrounding medium. The scatterers themselves were still considered as non-absorbing this limitation will be removed in future work. The overall mean free path of the medium is thus. The average Mueller matrix of the sample was defined as weighted average of Mueller matrices of the monodisperse media [ 27 ].

To investigate the effect of the sub-organelles we excluded the nuclei from the phantom tissue. The insertion of the sub-organelles modified the scattering regime of the phantom tissue already at 0. This trend is certainly due to a rapid increase of the Rayleigh type contribution due to the small spheres to the backscattered light. Increasing the concentration of the small spheres enhances the Rayleigh type contribution over the Mie type contribution due to the large spheres and strengthens the Rayleigh-like nature of the backscattering from the phantom tissue with bimodal population.

Figure 8 shows the diagonal element values versus layer thickness ranging from 0. The images were calculated at different volume fraction of the r 2 -sphere a: We point out that M 44 coefficient takes negative values as the concentration of the small spheres overpass 0. In contrast with the monodisperse models investigated in the previous section, the bimodal population model does not change its scattering regime with the layer thickness increase. Moreover, at all concentration of the small scatterers, the diagonal coefficients of the Mueller matrix obey the experimental criterion Eq.

To take into account the wavelength dependence of the simulated results the values of optical index contrast, scattering and absorption coefficients have been calculated as a function of the wavelength from the optical dispersion laws defined in the appendix Eqs. The results are reported in Table 1. The absorption from the medium was included in the model by modifying the extinction coefficient:. The data shown in Table 1 suggest that introducing the absorption should hardly change the polarimetric response.

The results presented on Fig. Wavelength dependent ex-vivo measurements of colon tissue show that this tissue behaves as a pure depolarizer throughout the visible spectrum. The relation between the diagonal elements of the experimental backscattering Mueller matrices provides the criterion to discard wrong models of colon tissue. Colon tissue was described using multi-layered model with monodisperse or bimodal populations of scatterers. Simulated backscattering Mueller matrix images of the double layer mucosa and submucosa model with monodisperse radius nm mucosa and monodisperse radius 1.

As a result, the single layer mucosa model constitutes a valid simplification of colon tissue. The possible effects of the budding shape of tumors at early stages were also investigated by describing the tumor as a monodisperse scattering layer over a Lambertian, assuming that the budding was due to either the mucosa or the Lambertian. In both cases unrealistic Mie scattering regimes were observed for reasonable parameter values. We therefore concluded that the monodisperse model of the mucosa had to be rejected.

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Conversely, the simulations of the backscattering Mueller matrix images of the bimodal population model showed that the mixture comprising small and medium compared to wavelength scatterers was in the Rayleigh regime of scattering already at small volume concentration of the small scatterers. Moreover the ratio of linear to circular polarization of the backscattering Mueller matrix of the phantom tissue always obeyed the experimental criterion see Eq.

This means that the presence of the small scatterers stabilizes the optical response of the phantom tissue in the Rayleigh regime of scattering, ensuring for qualitative agreement between experimental and simulations. The simulations of the backscattering Mueller matrix images of the phantom tissue mixing large representing the nuclei , medium and small representing the cell organelles and sub-organelles respectively scatterers need to be performed to attain quantitative agreement between experiment and modeling.

Including the absorption by the medium in our model did not modify the relation between the diagonal elements of the Mueller matrix and their absolute values at all studied wavelengths. However, the absorption cannot be neglected in the realistic model of colon tissue. The next step will be to introduce the absorbing scatterers to the model in order to reproduce the experimentally observed spectral dependence of diagonal elements of the Mueller matrix. The identification of the key model parameters providing quantitative agreement between experimental and modeling at various stages of cancer evolution can help in the interpretation of the experimental data and consequently, in proper cancer staging and early cancer detection.

The dispersion law for collagen was defined as [ 38 , 39 ]:.