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Does there exist a Taylor series in powers of z - 1 - i

Advanced Engineering Mathematics | 9th Edition | ISBN: 9780471488859 | Authors: Erwin Kreyszig ISBN: 9780471488859 172

Solution for problem 32 Chapter Chapter 15

Advanced Engineering Mathematics | 9th Edition

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Advanced Engineering Mathematics | 9th Edition | ISBN: 9780471488859 | Authors: Erwin Kreyszig

Advanced Engineering Mathematics | 9th Edition

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Problem 32

Does there exist a Taylor series in powers of z - 1 - i that diverges at 5 + 5i but converges at 4 + 6i?

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Chapter 12 : Cost of Capital Explaining Important More Important 1) Cost of Capital Basics : The cost of various capital sources varies from company to company, and depends on factors such as its operating history, profitability, credit worthiness, etc. In general, newer enterprises with limited operating histories will have higher costs of capital than established companies with a solid track record, since lenders and investors will demand a higher risk premium for the former. Cost of capital is the required return necessary to make a capital budgeting project, such as building a new factory, worthwhile. Cost of capital includes the cost of debt and the cost of equity. A company uses debt, common equity and preferred equity to fund new projects, typically in large sums. In the long run, companies typically adhere to target weights for each of the sources of funding. When a capital budgeting decision is being made, it is important to keep in mind how the capital structure may be affected. 2) Cost of equity : Cost of equity refers to a shareholder's required rate of return on an equity investment. It is the rate of return that could have been earned by putting the same money into a different investment with equal risk. The cost of equity is the rate of return required to persuade an investor to make a given equity investment. In general, there are two ways to determine cost of equity. First is the dividend growth model: Cost of Equity = (Next Year's Annual Dividend / Current Stock Price) + Dividend Growth Rate Second is the Capital Asset Pricing Model (CAPM): r a r + Bf(r -r )a m f where: rf= the rate of return on risk-free securities (typically Treasuries) Ba= the beta of the investment in question rm= the market's overall expected rate of return 3) Dividend Growth Models : Equity valuation is a subject of great depth and complexity. Valuation entails understanding a business; forecasting its performance, selecting the appropriate valuation model; converting such forecasting to a valuation and making a recommendation whether or not to purchase. Valuation models are as nuanced as the companies to which their application would appear to be best suited. For the purpose of the CFP® examination, candidates are expected to demonstrate proficiency in the basic mechanics and application of the dividend discount model which utilizes a firm's cost of capital to discount dividends to arrive at an approximate intrinsic value of the company. a. Constant (Gordon) Dividend Growth Model: P=D/k-g Where: P=security\'s price; D=dividend payout ratio; k=required rate of return (derived from the capital asset pricing model; g=dividends\' expected growth rate. b. The model's assumptions are that: (i) the dividend growth rate is constant; the growth rate cannot equal or exceed the required rate of return; the investor's required rate of return is both known and constant. In practice, a company's earnings and growth rates are not known and not constant. 4) SML approach : Advantages and Disadvantages of SML • Advantages 1 Explicitly adjusts for systematic risk 2 Applicable to all companies, as long as we can compute beta • Disadvantages 1 Have to estimate the expected market risk premium, which does vary over time 2 Have to estimate beta, which also varies over time 3 We are relying on the past to predict the future, which is not always reliable 5) Cost of Debt : The effective rate that a company pays on its current debt. This can be measured in either before- or after-tax returns; however, because interest expense is deductible, the after-tax cost is seen most often. This is one part of the company's capital structure, which also includes thecost of equity. A company will use various bonds, loans and other forms of debt, so this measure is useful for giving an idea as to the overall rate being paid by the company to use debt financing. The measure can also give investors an idea as to the riskiness of the company compared to others, because riskier companies generally have a higher cost of debt. To get the after-tax rate, you simply multiply the before-tax rate by one minus the marginal tax rate (before-tax rate x (1-marginal tax)). If a company's only debt were a single bond in which it paid 5%, the before-tax cost of debt would simply be 5%. If, however, the company's marginal tax rate were 40%, the company's after-tax cost of debt would be only 3% (5% x (1-40%)).

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Chapter Chapter 15, Problem 32 is Solved
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Textbook: Advanced Engineering Mathematics
Edition: 9
Author: Erwin Kreyszig
ISBN: 9780471488859

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Does there exist a Taylor series in powers of z - 1 - i