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Doctor of Philosophy / Department of Mathematics / Ivan Blank / In the Fermi Lectures on the obstacle problem in 1998, Caffarelli gave a proof of the mean value theorem which extends to general divergence form uniformly elliptic operators. In the general setting, the result shows that for any such operator L and at any point [chi]₀ in the domain, there exists a nested family of sets { D[subscript]r([chi]₀) } where the average over any of those sets is related to the value of the function at [chi]₀. Although it is known that the { D[subscript]r([chi]₀) } are nested and are comparable to balls in the sense that there exists c, C depending only on L such that B[subscript]cr([chi]₀) ⊂ D[subscript]r([chi]₀) ⊂ B[subscript]Cr([chi]₀) for all r > 0 and [chi]₀ in the domain, otherwise their geometric and topological properties are largely unknown. In this work we begin the study of these topics and we prove a few results about the geometry of these sets and give a couple of applications of the theorems.

M.Com. (Economics) / The objective of the thesis is to examine the fiscal importance' of indirect taxation with specific reference to value added taxation. The investigation takes cognisance of the unique characteristics of the South African economy, especially its strong dualistic characteristics, very unequal distributlon of income and extensive backlogs in the areas of social services and infrastructure. The South African tax system has undergone a rather fundamental shift in the early 1970s when the sales duty was replaced by a general sales tax. This tax, implemented in July 1978 at the rate of 4 per cent provided for the exemption of basic foodstuffs and the issuing of exemption certificates mandating the non-taxation of certain goods. These certificates led to abuse and fraud. The tax was a cascading tax and double taxation was an inherent characteristic of it. Within 13 years of its existence the rate of the tax soured to 13 per cent. An European-styled value added tax, engineered on the New Zealand model, was implemented in September 1991. Value added tax has in the past been criticised on account of its regressive properties. Unions have depicted value added tax as an unfair tax because of its skewed income and wealth effects. Providing relief for the perceived regressivity of valued added tax is not an easy decision. The regressivity of value added tax can be reduced by zero ratings, differential rates and exemptions, but it was found that there are convincing reasons why the value added tax base should be kept as broad as possible. Internationally it is accepted that economic distortions are kept to a minimum when value added tax is levied on a broad base with a minimum number of zero ratings and differential rates. A broadly based tax effects current and future consumption to the same degree and is therefore neutral as to consumption and saving. Irrespective of this best-policy-advice, various countries still make considerable use of zero ratings and differential rates to lessen the regressivity of the tax system. Theoretically value added tax does not add to inflationary pressures. Notwithstanding this theoretical view there is some evidence that value added tax could sometimes lead to cost push inflation should compensating salary increases follow after a broadening of the base. The dissertation agrees with South African studies indicating that the cascading effects of value added tax is negligible. Although the rate of inflation increased during the twelve month period following the introduction of the tax in South Africa, it had an once-off impact on the general level of prices and could thus not be typified as inflation. Financial services are by and large exempted from value added tax due to its many definitional problems. In this connection, the Poddar-English model is regarded by some observers as a means of addressing this problem. The model does not provide solutions for all the problems and remains to a large extent impractical. Notwithstanding this, the extension of the tax base to include financial services will enhance the efficiency of the tax.

Global supply and demand for platinum benefited from favourable local and global economic environments over the past decade, and presented unique growth opportunities for platinum mining companies. Companies operating in a growing industry, such as platinum during the past decade, are expected to deliver superior returns, and to create economic value for shareholders. With markets becoming more globalized, deregulated, and liquid, investors move their capital to where they believe it will be most productively employed, and companies therefore need to demonstrate their ability to meet increasing shareholder demands for growth and economic value added. Economic Value Added (EVA®), as a measure of company performance, has been widely adopted by companies and securities analysts globally but its use in South African platinum mining companies has been limited to date. In order to address this gap through this research, EVA® was calculated for the three primary South African platinum mining companies, Anglo Platinum, Implats, and Lonmin. EVA® for the respective companies was then compared to company growth rates, share price performance, and alternative, conventional performance metrics. Through analysis it was found that, although the respective platinum mining companies experienced similar production and turnover growth rates during the review period, 2000 to 2006, Anglo Platinum was able to generate higher EVA® than Implats and Lonmin respectively. Share price has been found to correlate well with EVA® for both Anglo Platinum and Implats respectively, but this relationship was not statistically significant for Lonmin, and EPS was the only metric among the alternative performance metrics, EPS, P/E, ROA, and EBITDA, found to have a correlation with EVA® for Anglo Platinum and Implats respectively. The correlation between the other metrics and EVA® was found not to be statistically significant. / Dissertation (MBA)--University of Pretoria, 2010. / Gordon Institute of Business Science (GIBS) / unrestricted

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Many academic studies in the past have focussed on how to create value for businesses in terms of adding profit to the bottom line through performance, and many argue that adding value for the client is also viewed as a profitable business strategy. This strategy translates as a win-win business relationship since long-term relationships ensure customer loyalty, customer retention and repeat business. In the services sector, it is difficult to quantify the worth or value that a particular service has since services are intangible products. The perception of value of such a service is known as “perceived value” since value recognition rests with the consumer who attempts to quantify the worth of that service. It is generally accepted in the services sector that establishing long-term, mutually beneficial, meaningful business relationships add value for the client and helps them to attach a value to the services that company provides. A company cannot establish such relationships without the help of its employees who represents the face of the organisation and implements the value adding strategy on the organisation’s behalf. Recent studies have begun to address this, examining value creation in business relationships in the context of the sale of tangible goods. The process of value creation for customers in services relationships remains underresearched. Perceived value explains why customers choose one particular service over another, why service companies gain competitive advantage by maintaining genuine longterm customer relationships, and why “the personal touch”, created through emotional attributes such as trust, caring and empathy, adds value from customers’ perspective. This dissertation presents a study of perceived value from the perspective of the customer within the context of the delivery of a credence product in a services relationship model. Using grounded theory methodology; following in-depth interviews with consumers of general insurance, a number of customer-value creation dimensions for businesses have been identified. Parallel interviews with members of staff from the supplier company add a further perspective. This research demonstrates how organisations or suppliers in the services industry can add value when delivering a credence product in a services relationship context. It is believed that an understanding of the value-adding dimensions can be implemented to create opportunities to build value for customers, with commensurate benefits for suppliers. Following analysis of the interviews held with each buyer, a total of six value dimensions are identified in the findings chapter. Each dimension is individually described, discussed, and illustrated with quotations from customers and supplier’s staff. Other issues relating to value arising from the interviews are examined in the discussion chapter. Three areas for further research are proposed in the conclusion.

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This study evaluates a number of different approaches which have been used to estimate the value of goods and activities which are not traded in conventional private markets. Experimental evidence is obtained from surveys of individuals' expressed preferences for a number of different goods and services, with emphasis placed on values associated with the natural environment. Both contingent and real questions are used, with subjects' responses to hypothetical situations shown to correspond closely to the behavior which is observed when real transactions are employed. A central concern of this thesis is the comparison of measures of economic value based on an individual's willingness to pay to obtain or retain a good and the amount of compensation which is demanded if it is relinquished. In contrast to prevailing economic theory, these two approaches are shown to yield estimates of value which in many cases are systematically and significantly different. Four principal reasons for this disparity are advanced and each is discussed in the light of evidence developed as part of this as well as previous studies. These are the size of the good or payment level under consideration, the availability of substitutes, the perceived legitimacy of the transaction and the influence of responsibility costs, regret or other process considerations. Empirical evidence is also developed on several other concerns which arise when hypothetical questions are used to value non-market goods. These include the selection of a preferred payment measure, the significance of motivational or cognitive biases, and the potential influence of both framing effects and a number of behavioral considerations. In each case the analysis of individuals' responses leads to an improved understanding of key methodological considerations and suggests additional research opportunities. / Graduate and Postdoctoral Studies / Graduate

Pension funds have been part of the private sector since the 1850’s. Defined Benefit pension plans [DB], where a company promises to make regular contributions to investment accounts held for participating employees in order to pay a promised lifelong annuity, are significant capital markets participants, amounting to 2.3 trillion dollars in 2010 (Federal Reserve Board, 2013). In 2006, Statement of Financial Accounting Standards No.158 (SFAS 158), Employers’ Accounting for Defined Benefit Pension and Other Postemployment Plans, shifted information concerning funding status and pension asset/liability composition from disclosure in the footnotes to recognition in the financial statements. I add to the literature by being the first to examine the effect of recent pension reform during the financial crisis of 2008-09. This dissertation is comprised of three related essays. In my first essay, I investigate whether investors assign different pricing multiples to the various classes of pension assets when valuing firms. The pricing multiples on all classes of assets are significantly different from each other, but only investments in bonds and equities were value-relevant during the recent financial crisis. Consistent with investors viewing pension liabilities as liabilities of the firm, the pricing multiples on pension liabilities are significantly larger than those on non-pension liabilities. The only pension costs significantly associated with firm value are actual rate of return and interest expense. In my second essay, I investigate the role of accruals in predicting future cash flows, extending the Barth et al. (2001a) model of the accrual process. Using market value of equity as a proxy for cash flows, the results of this study suggest that aggregate accounting amounts mask how the components of earnings affect investors’ ability to predict future cash flows. Disaggregating pension earnings components and accruals results in an increase in predictive power. During the 2008-2009 financial crisis, however, investors placed a greater (and negative) weight on the incremental information contained in the individual components of accruals. The inferences are robust to alternative specifications of accruals. Finally, in my third essay I investigate how investors view under-funded plans. On average, investors: view deficits arising from under-funded plans as belonging to the firm; reward firms with fully or over-funded pension plans; and encourage those funds with unfunded pension plans to become funded. Investors also encourage conservative pension asset allocations to mitigate firm risk, and smaller firms are perceived as being better able to handle the risk associated with underfunded plans. During the financial crisis of 2008-2009 underfunded status had a lower negative association with market value. In all three models, there are significant differences in pre- and post- SFAS 158 periods. These results are robust to various scenarios of the timing of the financial crisis and an alternative measure of funding.

"There is no more fundamental theorem in calculus than the mean-value theorem. Much of the theory of calculus depends, either directly or indirectly, on this theorem. As a consequence of its importance, the theorem has been investigated by a number of mathematicians with the result that various modifications and extensions of the basic theorem have been made"--Introduction. / "May 1956." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Includes bibliographical references (leaf 17).