Determinants Of Firm Terminal Value: The Perspective Of North American And European Financial Analysts

Company valuation models attempt to estimate the value of a company in two stages: (1) comprising of a period of explicit analysis and (2) based on unlimited production period of cash flows obtained through a mathematical approach of perpetuity, which is the terminal value. In general, these models, whether they belong to the Dividend Discount Model (DDM), the Discount Cash Flow (DCF), or RIM (Residual Income Models) group, discount one attribute (dividends, free cash flow, or results) to a given discount rate. This discount rate, obtained in most cases by the CAPM (Capital asset pricing model) or APT (Arbitrage pricing theory) allows including in the analysis the cost of invested capital based on the risk taking of the attributes. However, one cannot ignore that the second stage of valuation that is usually 53-80% of the company value (Berkman et al., 1998) and is loaded with uncertainties. In this context, particular attention is needed to estimate the value of this portion of the company, under penalty of the assessment producing a high level of error. Mindful of this concern, this study sought to collect the perception of European and North American financial analysts on the key features of the company that they believe contribute most to its value. For this feat, we used a survey with closed answers. From the analysis of 123 valid responses using factor analysis, the authors conclude that there is great importance attached (1) to the life expectancy of the company, (2) to liquidity and operating performance, (3) to innovation and ability to allocate resources to R&D, and (4) to management capacity and capital structure, in determining the value of a company or business in long term. These results contribute to our belief that we can formulate a model for valuating companies and businesses where the results to be obtained in the evaluations are as close as possible to those found in the stock market

Determinants of Terminal Value in the Evaluation of Companies: A Panel Data Approach to the Context of European Companies.

The uncertainty of the future of a firm has to be modelled and incorporated into the evaluation of companies outside their explicit period of analysis, i.e., in the continuing or terminal value considered within valuation models. However, there is a multiplicity of factors that influence the continuing value of businesses which are not currently being considered within valuation models. In fact, ignoring these factors may cause significant errors of judgment, which can lead models to values of goodwill or badwill, far from the substantial value of the inherent assets. Consequently, these results provided will be markedly different from market values. So, why not consider alternative models incorporating life expectancy of companies, as well as the influence of other attributes of the company in order to get a smoother adjustment between market price and valuation methods? This study aims to provide a contribution towards this area, having as its main objective the analysis of potential determinants of firm value in the long term. Using a sample of 714 listed companies, belonging to 15 European countries, and a panel data for the period between 1992 and 2011, our results show that continuing value cannot be regarded as the current value of a constant or growth perpetuity of a particular attribute of the company, but instead be according to a set of attributes such as free cash flow, net income, the average life expectancy of the company, investment in R&D, capabilities and quality of management, liquidity and financing structure.

The Terminal Value (TV) Performing in Firm Valuation: The Gap of Literature and Research Agenda

The uncertainty about the future of firms must be modeled and incorporated in the valuation of enterprises outside the explicit period of analysis, i.e., in the continuing or terminal value (TV). There is a multiplicity of factors that influence the TV of firms which are not being considered within current evaluation models. This aspect leads to the incurring of unrecoverable errors, thus leading to values of goodwill or bad will far away from the substantial value of intrinsic assets. As a consequence, the evaluation results will be presented markedly different from market values. There is no consensus in the scientific community about the method of computation of the TV as a forecast in an infinite horizon. The size of the terminal, or non-explicit period, assumed as infinite, is never called into question by scientific literature, or the probability of business bankruptcy. This paper aims to promote a study of the existing literature on the TV, to highlight the fragility of the evaluation models of companies that have been used by the academic community and by financial analysts, and to point out lines for future research to minimize these errors.

A marketingeszközök és –tevékenységek részvényesi értékre gyakorolt hatása (The effect of marketing assets and activities on shareholder value)

A vállalati marketing pénzügyi teljesítményre, különösen részvényesi értékre gyakorolt hatásának kimutatása mind fontosabbá válik a marketingráfordítások nagyságának növekedésével, valamint annak felismerésével, hogy a részvényesek számára vevői érték nélkül nem lehet hosszú távon értéket biztosítani, azonban kedvező piaci eredményekkel sem feltétlenül valósul meg a pénzügyi teljesítmény növekedése. A szerzők tanulmányukban a marketingeszközök és -tevékenységek részvényesi értékre gyakorolt hatását vizsgálják, rámutatnak arra, hogy milyen módon befolyásolhatják a részvényeseket megillető szabad pénzáramot, a tulajdonosi megtérülést, a stratégiai tervezési időhorizontot és a végértéket. A marketing néhány lehetséges negatív hatását is kiemelik. Ezt követően felvázolják a marketingjellegű beruházások reálopciós karakterisztikáit, valamint játékelméleti összefüggéseit dinamikusan változó környezetben. ________ Proving the effect of corporate marketing on financial performance, especially on shareholder value, becomes more and more important as marketing expenditures increase. Furthermore by the recognition that for shareholders without customer value it is not possible to provide value in the long run, however, neither good market results can assure the growth of financial performance. In this paper the authors examine the effect of marketing assets and activities on shareholder value, they point out how these can influence free cash flow to equity, shareholder return, strategic planning time period and terminal value. They emphasize also some possible negative effects of marketing. The authors outline the real optional characteristics of marketing investments and their game theoretical relations in dynamic environment.

Asuntosijoittamisen kilpailukykyisyys eläkesäästämismuotona

Tutkielman tarkoituksena on selvittää asuntosijoittamisen kilpailukykyisyyttä eläkesäästämismuotona. Vertailu tehdään kvantitatiivisena ja vertailukohtana ovat ns. perinteiset eläkesäästämismuodot, kuten rahastosijoitus, osakesijoitus, eläkevakuutus ja pankkitilisijoitus. Vertailu on tehty neljällä eri sijoittajaprofiililla. Profiilit eroavat toisistaan säästöajan ja säästösumman suhteen. Kaikissa tapauksissa kokonaissäästösumma on 36 000 euroa. Asuntosijoituksen lähtökohtana on osakehuoneisto, joka vuokrataan eteenpäin asumiskäyttöön. Asunnon ostoon otetaan pankkilaina, jota maksetaan pois vuokratuloilla sekä omalla osuudella niin, että kuukausittainen omaosuus lainan lyhennyksestä olisi vastaavan suuruinen kuin vaihtoehtoissijoituksen ns. perinteiseen eläkesäästämistuotteeseen. Tutkielmassa esiintyvät laskelmat on tehty Excel-taulukkolaskentaohjelmalla. Analyysissä keskitytään ensisijaisesti analysoimaan verojen ja kaikkien kulujen jälkeistä sijoitusten loppuarvoa, todellista vuosittaista tuottoprosenttia sekä koko sijoitetun pääoman tuottoprosenttia koko sijoitusajalta.

What Is a Firm’s Life Expectancy? Empirical Evidence in the Context of Portuguese Companies

It is a fact that the uncertainty about a firm’s future has to be measured and incorporated into a company’s valuation throughout the explicit analysis period – in the continuing or terminal value within valuation models. One of the concerns that can influence the continuing value of enterprises, which is not explicitly considered in traditional valuation models, is a firm’s average life expectancy. Although the literature has studied the life cycle of a firm, there is still a considerable lack of references on this topic. If we ignore the period during which a company has the ability to produce future cash flows, the valuations can fall into irreversible errors, leading to results markedly different from market values. This paper aims to provide a contribution in this area. Its main objective is to construct a mortality table for non-listed Portuguese enterprises, showing that the use of a terminal value through a mathematical expression of perpetuity of free cash flows is not adequate. We provide the use of an appropriate coefficient to perceive the number of years in which the company will continue to operate until its theoretical extinction. If well addressed regarding valuation models, this issue can be used to reduce or even to eliminate one of the main problems that cause distortions in contemporary enterprise valuation models: the premise of an enterprise’s unlimited existence in time. Besides studying the companies involved in it, from their existence to their demise, our study intends to push knowledge forward by providing a consistent life and mortality expectancy table for each age of the company, presenting models with an explicitly and different survival rate for each year. Moreover, we show that, after reaching a certain age, firms can reinvent their business, acquiring maturity and consequently postponing their mortality through an additional life period.

Risk stratification in neonates and infants submitted to cardiac surgery with cardiopulmonary bypass: A multimarker approach combining inflammatory mediators, N-terminal pro-B-type natriuretic peptide and troponin I

Low cardiac output syndrome (LCOS) is a common problem following cardiac surgery with cardiopulmonary bypass (CPB) in neonates and infants, and its early recognition remains a challenging task. We aimed to test whether a multimarker approach combining inflammatory and cardiac markers provides complementary information for prediction of LCOS and death in children submitted to cardiac surgery with CPB. Forty-six children younger than 18 months with congenital heart defects were prospectively enrolled. No intervention was made. Blood samples were collected pre-operatively, during CPB and post-operatively (PO) for measurement of interleukin (IL)-6, IL-8, IL-10, tumor necrosis factor (TNF)-alpha, cardiac troponin I (cTnI) and N-terminal pro-B-type natriuretic peptide (NT-proBNP). Clinical data and outcome variables were recorded. Logistic regression was used to identify predictors of LCOS and death. Multivariate logistic regression identified pre-operative NT-proBNP and IL-8 4 h PO as independent predictors of LCOS, while cTnI 4 h PO and CPB length were independent predictors of death. The use of inflammatory and cardiac markers in combination improved sensitivity, negative predictive value and accuracy of the models. In conclusion, the combined assessment of inflammatory and cardiac biochemical markers can be useful for identifying young children at increased risk for LCOS and death after heart surgery with CPB. (C) 2008 Elsevier Ltd. All rights reserved.

Neuroprotection in cerebral ischemia : an effect of c-Jun N-terminal kinase inhibition on the inflammatory response

RESUMESuite à un accident vasculaire cérébral (AVC) ischémique, les cellules gliales ducerveau deviennent activées, de nombreuses cellules inflammatoires pénètrent dans letissu lésé et sécrètent une grande variété de cytokines et chémokines. Aujourd'hui, ilexiste des interrogations sur les effets bénéfiques ou délétères de cette inflammation surla taille de la lésion et le pronostic neurologique.Ce projet vise à évaluer l'effet d'un peptide neuroprotecteur, D-JNKI1, inhibiteur de lavoie pro-apoptotique de signalisation intracellulaire c-Jun N-terminal kinase (JNK), surl'inflammation post-ischémique.Nous montrons d'abord que la microglie est largement activée dans toute la région lésée48 h après l'induction d'une ischémie chez la souris. Cependant, malgré l'inhibition dela mort neuronale par D-JNKI1 évaluée à 48 h, nous n'observons de modification ni del'activation de la microglie, ni de son nombre. Ensuite, nous montrons que le cerveaupeut être protégé même s'il y a une augmentation massive de la sécrétion de médiateursinflammatoires dans la circulation systémique très tôt après induction d'un AVCischémique. De plus, nous notons que la sécrétion de molécules inflammatoires dans lecerveau n'est pas différente entre les animaux traités par D-JNKI1 ou une solutionsaline, bien que nous ayons obtenu une neuroprotection significative chez les animauxtraités.En conclusion, nous montrons que l'inhibition de la voie de JNK par D-JNKI1n'influence pas directement l'inflammation post-ischémique. Ceci suggère quel'inhibition de l'inflammation n'est pas forcément nécessaire pour obtenir en hautdegré de neuroprotection du parenchyme lésé après ischémie cérébrale, et que lesmécanismes inflammatoires déclenchés lors d'une ischémie cérébrale ne sont pasforcément délétères pour la récupération du tissu endommagé.SUMMARYAfter cerebral ischemia, glial cells become activated and numerous inflammatory cellsinfiltrate the site of the lesion, secreting a large variety of cytokines and chemokines. Itis controversial whether this brain inflammation is detrimental or beneficial and how itinfluences lesion size and neurological outcome.This project was aimed at critically evaluating whether the neuroprotective peptide DJNKI,an inhibitor of the pro-apopotic c-Jun N-terminal kinase (JNK) pathway,modulates post-ischemic inflammation in animal models of stroke. Specifically, it wasasked whether JNK inhibition prevents microglial activation and the release ofinflammatory mediators.In the first part of this study, we showed that microglia was activated throughout thelesion 48 h after experimental stroke. However, the activation and accumulation ofmicroglia was not reduced by D-JNKI1, despite a significant reduction of the lesionsize. In the second part of this project, we demonstrated that neuroprotection measuredat 48 h occurs even though inflammatory mediators are released in the plasma veryearly after the onset of cerebral ischemia. Furthermore, we found that secretion ofinflammatory mediators in the brain was not different in groups treated with D-JNKI1or not, despite a significant reduction of the lesion size in the treated group.Altogether, we show that inhibition of the JNK pathway using D-JNKI1 does notinfluence directly post-stroke inflammation. Inhibition of inflammation is therefore notnecessarily required for neuroprotection after cerebral ischemia. Thus, post-strokeinflammation might not be detrimental for the tissue recovery.

Modulation of the c-Jun N-terminal kinase activity in the embryonic heart in response to anoxia-reoxygenation: involvement of the Ca2+ and mitoKATP channels.

Whether the response of the fetal heart to ischemia-reperfusion is associated with activation of the c-Jun N-terminal kinase (JNK) pathway is not known. In contrast, involvement of the sarcolemmal L-type Ca2+ channel (LCC) and the mitochondrial KATP (mitoKATP) channel has been established. This work aimed at investigating the profile of JNK activity during anoxia-reoxygenation and its modulation by LCC and mitoK(ATP) channel. Hearts isolated from 4-day-old chick embryos were submitted to anoxia (30 min) and reoxygenation (60 min). Using the kinase assay method, the profile of JNK activity in the ventricle was determined every 10 min throughout anoxia-reoxygenation. Effects on JNK activity of the LCC blocker verapamil (10 nM), the mitoK(ATP) channel opener diazoxide (50 microM) and the blocker 5-hydroxydecanoate (5-HD, 500 microM), the mitochondrial Ca2+ uniporter (MCU) inhibitor Ru360 (10 microM), and the antioxidant N-(2-mercaptopropionyl) glycine (MPG, 1 mM) were determined. In untreated hearts, JNK activity was increased by 40% during anoxia and peaked fivefold relative to basal level after 30-40 min reoxygenation. This peak value was reduced by half by diazoxide and was tripled by 5-HD. Furthermore, the 5-HD-mediated stimulation of JNK activity during reoxygenation was abolished by diazoxide, verapamil or Ru360. MPG had no effect on JNK activity, whatever the conditions. None of the tested pharmacological agents altered JNK activity under basal normoxic conditions. Thus, in the embryonic heart, JNK activity exhibits a characteristic pattern during anoxia and reoxygenation and the respective open-state of LCC, MCU and mitoKATP channel can be a major determinant of JNK activity in a ROS-independent manner.

A peptide inhibitor of c-Jun N-terminal kinase protects against both aminoglycoside and acoustic trauma-induced auditory hair cell death and hearing loss.

Hearing loss can be caused by a variety of insults, including acoustic trauma and exposure to ototoxins, that principally effect the viability of sensory hair cells via the MAP kinase (MAPK) cell death signaling pathway that incorporates c-Jun N-terminal kinase (JNK). We evaluated the otoprotective efficacy of D-JNKI-1, a cell permeable peptide that blocks the MAPK-JNK signal pathway. The experimental studies included organ cultures of neonatal mouse cochlea exposed to an ototoxic drug and cochleae of adult guinea pigs that were exposed to either an ototoxic drug or acoustic trauma. Results obtained from the organ of Corti explants demonstrated that the MAPK-JNK signal pathway is associated with injury and that blocking of this signal pathway prevented apoptosis in areas of aminoglycoside damage. Treatment of the neomycin-exposed organ of Corti explants with D-JNKI-1 completely prevented hair cell death initiated by this ototoxin. Results from in vivo studies showed that direct application of D-JNKI-1 into the scala tympani of the guinea pig cochlea prevented nearly all hair cell death and permanent hearing loss induced by neomycin ototoxicity. Local delivery of D-JNKI-1 also prevented acoustic trauma-induced permanent hearing loss in a dose-dependent manner. These results indicate that the MAPK-JNK signal pathway is involved in both ototoxicity and acoustic trauma-induced hair cell loss and permanent hearing loss. Blocking this signal pathway with D-JNKI-1 is of potential therapeutic value for long-term protection of both the morphological integrity and physiological function of the organ of Corti during times of oxidative stress.

Diferencias en costo efectividad del cuidado paliativo domiciliario frente a la atención convencional hospitalaria para el manejo de enfermedades crónicas en fase terminal

En Colombia la dinámica poblacional ha experimentado cambios a través de los años; lo cual modifica las características epidemiológicas y los perfiles de morbimortalidad de la población, aumentando la incidencia y prevalencia de enfermedades crónicas de difícil pronóstico dentro de la población; siendo estos grupos etarios hacía quienes deben destinarse nuevas modalidades de atención y soporte paliativo. Se realizó una revisión sistemática de diversos artículos, clasificados con niveles de evidencia I y II; cuyas variables de análisis fueron: El lugar de fallecimiento del paciente, alivio de la sintomatología, nivel de satisfacción del paciente y sus cuidadores con los servicios recibidos, número de ingresos hospitalarios independientemente de la causa y días promedio de estancia hospitalaria. El 88% de los pacientes que fueron vinculados a la atención domiciliaria falleció en su hogar; el 68% refirió haber experimentado disminución en la intensidad de al menos 2 síntomas como resultado de la atención en casa. El nivel de satisfacción para el cuidado en casa puntuó 19 puntos porcentuales por encima de la calificación que obtuvo el manejo hospitalario. El 23% de los pacientes tratados en su hogar, requirió al menos una hospitalización durante el manejo; mostrando una disminución en el tiempo de estancia hospitalaria de 3.4 días promedio. El manejo paliativo domiciliario de pacientes crónicos en fase terminal, no sólo es una alternativa en la reducción de costos para el sistema de salud, sino que es un factor protector de tipo emocional que refleja también una importante disminución de los riesgos de la hospitalización.

Avaliação da biologia reprodutiva de Plagioscion squamosissimus (HECKEL, 1840) e Plagioscion surinamensis (BLEEKER, 1873) no terminal de Vila do Conde e área adjacente (Barcarena - PA)

O Porto de Vila do Conde, situado no município de Barcarena/PA, vêm sofrendo diversos desastres ambientais nos últimos anos o que pode eventualmente acarretar no desequilíbrio do uso que os recursos aquáticos fazem do ambiente e no ecossistema como um todo. A pesca artesanal nesta região é bastante relevante, destacando Plagioscion squamosissimus e P. surinamensis que são importantes como fontes de renda e de alimento para a população. O objetivo deste estudo foi descrever as áreas de concentração e a biologia reprodutiva de P. squamosissimus e P. surinamensis na área adjacente ao Porto de Vila do Conde, destacando a importância da utilização destes ambientes para reprodução. Para identificar a época e os pesqueiros de maior abundância foram realizados cálculos de CPUE (Kg/viagem) por meio de dados obtidos no período de junho de 2007 a maio de 2008. A determinação do uso da área para reprodução e a descrição da biologia reprodutiva foi efetuada através da coleta de 40 a 53 indivíduos de cada espécie por bimestre, obtidos pela pesca comercial. Em laboratório, foram obtidos valores de peso e comprimento e as gônadas foram retiradas para a determinação do estágio de maturidade. A abundância de P. squamosissimus é máxima entre setembro a fevereiro e P. surinamensis ocorreu principalmente entre março a maio. A relação peso-comprimento mostrou isometria para as fêmeas de P. squamosissimus e ambos os sexos de P. surinamensis. Apenas os machos da espécie P. squamosissimus apresentaram alometria positiva. A proporção sexual foi favorável aos machos de P. surinamensis (1,05macho: 1fêmea) e favorável às fêmeas (1,11fêmea: 1macho) para P. squamosissimus. O valor de L50 (Tamanho de primeira maturidade) para P. squamosissimus foi 16,14 cm para fêmeas e 21,43 cm para machos. P. surinamensis apresentou valor de L50 de 27,65 cm para fêmeas e 27,13 cm para os machos. O percentual de indivíduos em reprodução da P. squamisissimus é relevante. O pico da reprodução desta espécie (outubro/novembro e fevereiro/março) coincide com o pico de abundância, indicando que esta espécie está na área para reprodução. P. surinamensis apresentou maior porcentagem de indivíduos nos estádios imaturo e em maturação, indicando que a mesma utiliza esta área principalmente como área de criadouro. Os indivíduos que estavam reproduzindo foram mais numerosos entre agosto/setembro e outubro/novembro.

Von Willebrand Factor Improves Risk Prediction in Addition to N-Terminal Pro-B-type Natriuretic Peptide in Patients Referred to Coronary Angiography and Signs and Symptoms of Heart Failure and Preserved Ejection Fraction.

BACKGROUND Heart failure with preserved ejection fraction (HFpEF) represents a growing health burden associated with substantial mortality and morbidity. Consequently, risk prediction is of highest importance. Endothelial dysfunction has been recently shown to play an important role in the complex pathophysiology of HFpEF. We therefore aimed to assess von Willebrand factor (vWF), a marker of endothelial damage, as potential biomarker for risk assessment in patients with HFpEF. METHODS AND RESULTS Concentrations of vWF were assessed in 457 patients with HFpEF enrolled as part of the LUdwigshafen Risk and Cardiovascular Health (LURIC) study. All-cause mortality was observed in 40% of patients during a median follow-up time of 9.7 years. vWF significantly predicted mortality with a hazard ratio (HR) per increase of 1 SD of 1.45 (95% confidence interval, 1.26-1.68; P<0.001) and remained a significant predictor after adjustment for age, sex, body mass index, N-terminal pro-B-type natriuretic peptide (NT-proBNP), renal function, and frequent HFpEF-related comorbidities (adjusted HR per 1 SD, 1.22; 95% confidence interval, 1.05-1.42; P=0.001). Most notably, vWF showed additional prognostic value beyond that achievable with NT-proBNP indicated by improvements in C-Statistic (vWF×NT-proBNP: 0.65 versus NT-proBNP: 0.63; P for comparison, 0.004) and category-free net reclassification index (37.6%; P<0.001). CONCLUSIONS vWF is an independent predictor of long-term outcome in patients with HFpEF, which is in line with endothelial dysfunction as potential mediator in the pathophysiology of HFpEF. In particular, combined assessment of vWF and NT-proBNP improved risk prediction in this vulnerable group of patients.

Detection of muscle wasting in patients with chronic heart failure using C-terminal agrin fragment: results from the Studies Investigating Co-morbidities Aggravating Heart Failure (SICA-HF).

AIMS Skeletal muscle wasting affects 20% of patients with chronic heart failure and has serious implications for their activities of daily living. Assessment of muscle wasting is technically challenging. C-terminal agrin-fragment (CAF), a breakdown product of the synaptically located protein agrin, has shown early promise as biomarker of muscle wasting. We sought to investigate the diagnostic properties of CAF in muscle wasting among patients with heart failure. METHODS AND RESULTS We assessed serum CAF levels in 196 patients who participated in the Studies Investigating Co-morbidities Aggravating Heart Failure (SICA-HF). Muscle wasting was identified using dual-energy X-ray absorptiometry (DEXA) in 38 patients (19.4%). Patients with muscle wasting demonstrated higher CAF values than those without (125.1 ± 59.5 pmol/L vs. 103.8 ± 42.9 pmol/L, P = 0.01). Using receiver operating characteristics (ROC), we calculated the optimal CAF value to identify patients with muscle wasting as >87.5 pmol/L, which had a sensitivity of 78.9% and a specificity of 43.7%. The area under the ROC curve was 0.63 (95% confidence interval 0.56-0.70). Using simple regression, we found that serum CAF was associated with handgrip (R = - 0.17, P = 0.03) and quadriceps strength (R = - 0.31, P < 0.0001), peak oxygen consumption (R = - 0.5, P < 0.0001), 6-min walk distance (R = - 0.32, P < 0.0001), and gait speed (R = - 0.2, P = 0.001), as well as with parameters of kidney and liver function, iron metabolism and storage. CONCLUSION CAF shows good sensitivity for the detection of skeletal muscle wasting in patients with heart failure. Its assessment may be useful to identify patients who should undergo additional testing, such as detailed body composition analysis. As no other biomarker is currently available, further investigation is warranted.

On the Absence of Carrier Drift in Two-Terminal Devices and the Origin of Their Lowest Resistance per Carrier RK= h/q^2

After a criticism on today’s model for electrical noise in resistors, we pass to use a Quantum-compliant model based on the discreteness of electrical charge in a complex Admittance. From this new model we show that carrier drift viewed as charged particle motion in response to an electric field is unlike to occur in bulk regions of Solid-State devices where carriers react as dipoles against this field. The absence of the shot noise that charges drifting in resistors should produce and the evolution of the Phase Noise with the active power existing in the resonators of L-C oscillators, are two effects added in proof for this conduction model without carrier drift where the resistance of any two-terminal device becomes discrete and has a minimum value per carrier that is the Quantum resistance RK/(2pi)