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Macroeconomics deals with aggregate economic quantities, such as national output and national income.

In a general sense, economics is the study of production, distribution, and consumption and can be divided into two broad areas of study: macroeconomics and microeconomics. Macroeconomics deals with aggregate economic quantities, such as national output and national income. Macroeconomics has its roots in microeconomics , which deals with markets and decision making of individual economic units, including consumers and businesses. Microeconomics is a logi

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. Demand , in economics, is the willingness and ability of consumers to purchase a given amount of a good or service at a given price.

In this reading, we will explore a model of household behavior that yields the consumer demand curve. Demand , in economics, is the willingness and ability of consumers to purchase a given amount of a good or service at a given price. Supply is the willingness of sellers to offer a given quantity of a good or service for a given price. Later, study on the theory of the firm will yield the supply curve.

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The basic model of markets is the demand and supply model. The demand function represents buyers’ behavior and can be depicted (in its inverse demand form) as a negatively sloped demand curve. The supply function represents sellers’ behavior and can be depicted (in its inverse supply form) as a positively sloped supply curve. The interaction of buyers and sellers in a market

ay’s global economy, an understanding of the demand and supply model is essential for any analyst who hopes to grasp the implications of economic developments on investment values. Among the points made are the following: <span>The basic model of markets is the demand and supply model. The demand function represents buyers’ behavior and can be depicted (in its inverse demand form) as a negatively sloped demand curve. The supply function represents sellers’ behavior and can be depicted (in its inverse supply form) as a positively sloped supply curve. The interaction of buyers and sellers in a market results in equilibrium. Equilibrium exists when the highest price willingly paid by buyers is just equal to the lowest price willingly accepted by sellers. Goods markets are the interactions of consumers as buyers and firms as sellers of goods and services produced by firms and bought by households. Factor markets are the i

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s buyers and firms as sellers of goods and services produced by firms and bought by households. Factor markets are the interactions of firms as buyers and households as sellers of land, labor, capital, and entrepreneurial risk-taking ability. <span>Capital markets are used by firms to sell debt or equity to raise long-term capital to finance the production of goods and services. <span><body><html>

sloped supply curve. The interaction of buyers and sellers in a market results in equilibrium. Equilibrium exists when the highest price willingly paid by buyers is just equal to the lowest price willingly accepted by sellers. <span>Goods markets are the interactions of consumers as buyers and firms as sellers of goods and services produced by firms and bought by households. Factor markets are the interactions of firms as buyers and households as sellers of land, labor, capital, and entrepreneurial risk-taking ability. Capital markets are used by firms to sell debt or equity to raise long-term capital to finance the production of goods and services. Demand and supply curves are drawn on the assumption that everything except the price of the good itself is held constant (an assumption known as ceteris paribus or “hol

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Valor absoluto de una cantidad es el número que representa la can tidad prescindiendo del signo o sentido de la cantidad, y valor relativo es el sentido de la cantidad, representado por el signo. Así, el valor absoluto de + $8 es $8, y el valor relativo haber, expre sado por e

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ous characteristics and manifestations. In this reading, we address the foundations of demand and supply analysis and seek to understand the sources of consumer demand through the theory of the consumer, also known as consumer choice theory. <span>Consumer choice theory can be defined as the branch of microeconomics that relates consumer demand curves to consumer preferences. Consumer choice theory begins with a fundamental model of how consumer prefe

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In effect, consumer choice theory first models what the consumer would like to consume, and then it examines what the consumer can consume with limited income.

o goods (or two baskets of goods), both of which the consumer finds beneficial. Consumer choice theory then recognizes that to consume a set of goods and services, consumers must purchase them at given market prices and with a limited income. <span>In effect, consumer choice theory first models what the consumer would like to consume, and then it examines what the consumer can consume with limited income. Finally, by superimposing what the consumer would like to do onto what the consumer can do, we arrive at a model of what the consumer would do under various circumstances. Then by chang

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In general, we can represent the utility function as Equation (1) U=f(Qx1,Qx2,...,Qxn) where the Qs are the quantities of each of the respective goods and services in the bundles. In the case of two goods—say, ounces of wine (W) and slices of bread (B)—a utility function might be simply Equation (2) U = f(W,B) = WB or the

ferences. The number itself is referred to as the utility of that basket and is measured in utils , which are just quantities of happiness, or well-being, or whatever comes to mind such that more of it is better than less of it. <span>In general, we can represent the utility function as Equation (1) U=f(Qx1,Qx2,...,Qxn) where the Qs are the quantities of each of the respective goods and services in the bundles. In the case of two goods—say, ounces of wine (W) and slices of bread (B)—a utility function might be simply Equation (2) U = f(W,B) = WB or the product of the number of ounces of wine and the number of slices of bread. The utility of a bundle containing 4 ounces of wine along with 2 slices of bread would equal 8 utils, and it would rank lower than a bundle containing 3 ounces of wine along with 3 slices of bread, which would yield 9 utils. The important point to note is that the utility function is just a ranking of bundles of goods. If someone were to replace all those pieces of paper with new numbers that m

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Here is the big shocker about the hippocampus: It can only hold so much information before it must be processed and pushed into short-term memory. Studies show that the maximum amount is about 20 minutes of information.

r learning products. The brain structures that are involved in learning include the hippocampus, the amygdala, and the basal ganglia. To design the best learning experiences, we need to understand and respect the neuroscience of learning. <span>Tip #2: Focus is the starting point of learning The hippocampus is the part of the brain that takes in information and moves it to our memory. When it's damaged, people lose access to past memories and no longer can make new ones. The hippocampus acts like a recorder or data drive; like those devices, it has an "on" button. Physiologically, it's when our eyes and ears attune to something that causes the hippocampus to begin recording. Richard Davidson, from the University of Wisconsin, calls this "phase locking" and it's the starting point of all learning. As a result, we must design our learning environments to help people focus and we must bust the myth that you can multitask while learning. Research has proved that when we divide our attention, our focus switches back and forth between the two activities, also known as switch tasking. The hippocampus loses vital pieces of information for both of the things we were trying to attend to. I call this "Swiss tasking" because we end up with holes in the data the hippocampus was capturing and, therefore, holes in our learning that cannot be recovered. Here is the big shocker about the hippocampus: It can only hold so much information before it must be processed and pushed into short-term memory. Studies show that the maximum amount is about 20 minutes of information. Lecture-style sessions never have demonstrated good results for retention, and now we know why—it works against the brain's natural functioning. The good news is that many other learning activities can help. All the hippocampus needs is a few minutes of processing to push that data into short-term memory and it's ready again for more. I now build all my learning events in chunks of 15 min

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From an analytical perspective, one can obtain industry supply data to calculate the elasticity of supply , which measures the sensitivity of quantity supplied to a change in price.

er competing firms to compete away any economic profit over the long run. Economic profit that exists over the long run is usually found where competitive conditions persistently are less than perfect in the market. <span>2.1.3. Economic Rent The surplus value known as economic rent results when a particular resource or good is fixed in supply (with a vertical supply curve) and market price is higher than what is required to bring the resource or good onto the market and sustain its use. Essentially, demand determines the price level and the magnitude of economic rent that is forthcoming from the market. Exhibit 1 illustrates this concept, where P 1 is the price level that yields a normal profit return to the business that supplies the item. When demand increases from Demand 1 to Demand 2 , price rises to P 2 , where at this higher price level economic rent is created. The amount of this economic rent is calculated as (P 2 – P 1 ) × Q 1 . The firm has not done anything internally to merit this special reward: It benefits from an increase in demand in conjunction with a supply curve that does not fully adjust with an increase in quantity when price rises. Exhibit 1. Economic Rent Because of their limited availability in nature, certain resources—such as land and specialty commodities—possess highly inelastic supply curves in both the short run and long run (shown in Exhibit 1 as a vertical supply curve). When supply is relatively inelastic, a high degree of market demand can result in pricing that creates economic rent. This economic rent results from the fact that when price increases, the quantity supplied does not change or, at the most, increases only slightly. This is because of the fixation of supply by nature or by such artificial constraints as government policy. How is the concept of economic rent useful in financial analysis? Commodities or resources that command economic rent have the potential to reward equity investors more than what is required to attract their capital to that activity, resulting in greater shareholders’ wealth. Evidence of economic rent attracts additional capital funds to the economic endeavor. This new investment capital increases shareholders’ value as investors bid up share prices of existing firms. Any commodity, resource, or good that is fixed or nearly fixed in supply has the potential to yield economic rent. From an analytical perspective, one can obtain industry supply data to calculate the elasticity of supply , which measures the sensitivity of quantity supplied to a change in price. If quantity supplied is relatively unresponsive ( inelastic ) to price changes, then a potential condition exists in the market for economic rent. A reliable forecast of changes in demand can indicate the degree of any economic rent that is forthcoming from the market in the future. When one is analyzing fixed or nearly fixed supply markets (e.g., gold), a fundamental comprehension of demand determinants is necessary to make rational financial decisions based on potential economic rent. EXAMPLE 1 Economic Rent and Investment Decision Making The following market data show the global demand, global supply, and price on an annual basis for gold over the period 2006–2008. Based on the data, what observation can be made about market demand, supply, and economic rent? Year 2006 2007 2008 Percent Change 2006–2008 Supply (in metric tons) 3,569 3,475 3,508 –1.7 Demand (in metric tons) 3,423 3,552 3,805 +11.2 Average spot price (in US$) 603.92 695.39 871.65 +44.3 Source: GFMS and World Gold Council. Solution: The amount of total gold supplied to the world market over this period has actually declined slightly by 1.7 percent during a period when there was a double-digit increase of 11.2 percent in demand. As a consequence, the spot price has dramatically increased by 44.3 percent. Economic rent has resulted from this market relationship of a relatively fixed supply of gold and a rising demand for it. 2.2. Comparison of Profit Measures All three types of profit are interconnected because, according to Equation 4, acco

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costs arise based on what has actually been purchased as opposed to implicit costs that arise based on what has actually been given up other than money. Explicit costs have a paper trail and provide audit documentation. Implicit costs are not <span>traceable in a financial system. While management will utilize explicit costs when viewing business operations, implicit costs are only utilized in decision-making or choosing between multiple alternatives. </sp

hased are examples of explicit costs. Although the depreciation of an asset is not an activity that can be tangibly traced, depreciation expense is an explicit cost because it relates to the cost of the underlying asset that the company owns. <span>Explicit Costs vs. Implicit Costs Explicit costs arise based on what has actually been purchased as opposed to implicit costs that arise based on what has actually been given up other than money. Explicit costs have a paper trail and provide audit documentation. Implicit costs are not traceable in a financial system. While management will utilize explicit costs when viewing business operations, implicit costs are only utilized in decision-making or choosing between multiple alternatives. Opportunity Costs Explicit costs are used in the computation of opportunity costs. An opportunity cost is the total value of an item forgone. It is calculated by adding the explicit and

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he cash flows from the old asset must be considered in replacement decisions. Specifically, in a replacement project, the cash flows from selling old assets should be used to offset the initial investment outlay. Analysts also need to compare <span>revenue/cost/depreciation before and after the replacement to identify changes in these elements. Expansion projects. Projects concerning expansion into new products, services, or markets i

ood capital budgeting decisions can be made). Otherwise, you will have the GIGO (garbage in, garbage out) problem. Improve operations, thus making capital decisions well-implemented. <span>Project classifications: Replacement projects. There are two types of replacement decisions: Replacement decisions to maintain a business. The issue is twofold: should the existing operations be continued? If yes, should the same processes continue to be used? Maintenance decisions are usually made without detailed analysis. Replacement decisions to reduce costs. Cost reduction projects determine whether to replace serviceable but obsolete equipment. These decisions are discretionary and a detailed analysis is usually required. The cash flows from the old asset must be considered in replacement decisions. Specifically, in a replacement project, the cash flows from selling old assets should be used to offset the initial investment outlay. Analysts also need to compare revenue/cost/depreciation before and after the replacement to identify changes in these elements. Expansion projects. Projects concerning expansion into new products, services, or markets involve strategic decisions and explicit forecasts of future demand, and thus require detailed analysis. These projects are more complex than replacement projects. Regulatory, safety and environmental projects. These projects are mandatory investments, and are often non-revenue-producing. Others. Some projects need special considerations beyond traditional capital budgeting analysis (for example, a very risky research project in which cash flows cannot be reliably forecast). LOS a. describe the capital budgeting process and distinguish among the various categories of capital projects; <span><body><html>

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Accounting profits only measure the return on the invested capital. Accounting income calculations reflect non-cash items and ignore the time value of money. They are important for some purposes, but for capital budgeting, cash flows are what are relevant. Economic income is an investme

Capital budgeting decisions are based on incremental after-tax cash flows discounted at the opportunity cost of capital. Assumptions of capital budgeting are: Capital budgeting decisions must be based on cash flows, not accounting income. Accounting profits only measure the return on the invested capital. Accounting income calculations reflect non-cash items and ignore the time value of money. They are important for some purposes, but for capital budgeting, cash flows are what are relevant. Economic income is an investment's after-tax cash flow plus the change in the market value. Financing costs are ignored in computing economic income. Cash flow timing is critical because money is worth more the sooner you get it. Also, firms must have adequate cash flow to meet maturing obligations. The opportunity cost should be charged against a project. Remember that just because something is on hand does not mean it's free. See below for the definition of opportunity cost. Expected future cash flows must be measured on an after-tax basis. The firm's wealth depends on its usable after-tax funds. Ignore how the project is financed. Interest payments should not be included in the estimated cash flows since the effects of debt financing are reflected in the cost of capital used to discount the cash flows. The existence of a project depends on business factors, not financing. Important capital budgeting concepts: A sunk cost is a cash outlay that has already been incurred and which

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stment's after-tax cash flow plus the change in the market value. Financing costs are ignored in computing economic income. Cash flow timing is critical because money is worth more the sooner you get it. Also, firms must <span>have adequate cash flow to meet maturing obligations. The opportunity cost should be charged against a project. Remember that just because something is on hand does not mean it's free. See below for the definition of opport

Capital budgeting decisions are based on incremental after-tax cash flows discounted at the opportunity cost of capital. Assumptions of capital budgeting are: Capital budgeting decisions must be based on cash flows, not accounting income. Accounting profits only measure the return on the invested capital. Accounting income calculations reflect non-cash items and ignore the time value of money. They are important for some purposes, but for capital budgeting, cash flows are what are relevant. Economic income is an investment's after-tax cash flow plus the change in the market value. Financing costs are ignored in computing economic income. Cash flow timing is critical because money is worth more the sooner you get it. Also, firms must have adequate cash flow to meet maturing obligations. The opportunity cost should be charged against a project. Remember that just because something is on hand does not mean it's free. See below for the definition of opportunity cost. Expected future cash flows must be measured on an after-tax basis. The firm's wealth depends on its usable after-tax funds. Ignore how the project is financed. Interest payments should not be included in the estimated cash flows since the effects of debt financing are reflected in the cost of capital used to discount the cash flows. The existence of a project depends on business factors, not financing. Important capital budgeting concepts: A sunk cost is a cash outlay that has already been incurred and which

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hen management places a constraint on the size of the firm's capital budget during a particular period. In such situations, capital is scarce and should be allocated to the projects most likely to maximize the firm's aggregate NPV. The firm's <span>capital budget and cost of capital must be determined simultaneously to best allocate the firm's capital. On the other hand, a firm can raise the funds it wants for all profitable projects simply by p

In a non-conventional cash flow pattern, the initial outflow can be followed by inflows and/or outflows. <span>Some project interactions: Independent versus mutually exclusive projects. Mutually exclusive projects are investments that compete in some way for a company's resources - a firm can select one or another but not both. Independent projects, on the other hand, do not compete for the firm's resources. A company can select one or the other or both, so long as minimum profitability thresholds are met. Project sequencing. How does one sequence multiple projects over time, since investing in project B may depend on the result of investing in project A? Unlimited funds versus capital rationing. Capital rationing occurs when management places a constraint on the size of the firm's capital budget during a particular period. In such situations, capital is scarce and should be allocated to the projects most likely to maximize the firm's aggregate NPV. The firm's capital budget and cost of capital must be determined simultaneously to best allocate the firm's capital. On the other hand, a firm can raise the funds it wants for all profitable projects simply by paying the required rate of return. Learning Outcome Statements b. describe the basic principles of capital budgeting; c. explain how the evaluat

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ccounting income calculations reflect non-cash items and ignore the time value of money. They are important for some purposes, but for capital budgeting, cash flows are what are relevant. Economic income is an investment's <span>after-tax cash flow plus the change in the market value. Financing costs are ignored in computing economic income. <span><body><html>

Capital budgeting decisions are based on incremental after-tax cash flows discounted at the opportunity cost of capital. Assumptions of capital budgeting are: Capital budgeting decisions must be based on cash flows, not accounting income. Accounting profits only measure the return on the invested capital. Accounting income calculations reflect non-cash items and ignore the time value of money. They are important for some purposes, but for capital budgeting, cash flows are what are relevant. Economic income is an investment's after-tax cash flow plus the change in the market value. Financing costs are ignored in computing economic income. Cash flow timing is critical because money is worth more the sooner you get it. Also, firms must have adequate cash flow to meet maturing obligations. The opportunity cost should be charged against a project. Remember that just because something is on hand does not mean it's free. See below for the definition of opportunity cost. Expected future cash flows must be measured on an after-tax basis. The firm's wealth depends on its usable after-tax funds. Ignore how the project is financed. Interest payments should not be included in the estimated cash flows since the effects of debt financing are reflected in the cost of capital used to discount the cash flows. The existence of a project depends on business factors, not financing. Important capital budgeting concepts: A sunk cost is a cash outlay that has already been incurred and which

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hamberlin (US) and Joan Robinson (UK), identified this hybrid market and came up with the term because there are strong elements of competition in this market structure and also some monopoly-like conditions. The competitive characteristic is <span>a notably large number of firms, while the monopoly aspect is the result of product differentiation. That is, if the seller can convince consumers that its product is uniquely different from other, similar products, t

apital). This does not mean that all perfectly competitive industries are doomed to extinction by a lack of profits. On the contrary, millions of businesses that do very well are living under the pressures of perfect competition. <span>Monopolistic competition is also highly competitive; however, it is considered a form of imperfect competition. Two economists, Edward H. Chamberlin (US) and Joan Robinson (UK), identified this hybrid market and came up with the term because there are strong elements of competition in this market structure and also some monopoly-like conditions. The competitive characteristic is a notably large number of firms, while the monopoly aspect is the result of product differentiation. That is, if the seller can convince consumers that its product is uniquely different from other, similar products, then the seller can exercise some degree of pricing power over the market. A good example is the brand loyalty associated with soft drinks such as Coca-Cola. Many of Coca-Cola’s customers believe that their beverages are truly different from and better than all other soft drinks. The same is true for fashion creations and cosmetics. The oligopoly market structure is based on a relatively small number of firms supplying the market. The small number of firms in the market means that each firm must cons

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The brain structures that are involved in learning include the hippocampus, the amygdala, and the basal ganglia. To design the best learning experiences, we need to understand and respect the neuroscience of learning.

what I learned really changed how I approach training design and delivery. Some of the studies confirmed things I had learned through trial and error long ago, and others completely shifted how I approached my craft. Here are six takeaways. <span>Tip #1: Work with the brain Different parts of the brain play core roles in how a person first learns information, then stores that information into memory, and finally uses that learning to create real and lasting behavior change. If we don't work with the brain and its natural processes, even the most popular or highly rated programs won't deliver in the long run. It is imperative that talent development professionals keep their finger on the pulse of brain science. As researchers learn more about how the brain and nervous system work, it will only enhance the quality of our learning products. The brain structures that are involved in learning include the hippocampus, the amygdala, and the basal ganglia. To design the best learning experiences, we need to understand and respect the neuroscience of learning. Tip #2: Focus is the starting point of learning The hippocampus is the part of the brain that takes in information and moves it to our memory. When it's damaged, people lose access

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Economic profit is the total return a company receives based on all costs incurred to attain that revenue. These costs include all explicit and implicit costs.

actually purchased. An implicit cost is the greatest benefit that could have resulted from the use of the funds. This cost could reflect a different vehicle that could have been purchased or the benefit gained from using the funds elsewhere. <span>Economic Profit Explicit costs are also utilized in the calculation of economic profit. Economic profit is the total return a company receives based on all costs incurred to attain that revenue. These costs include all explicit and implicit costs. Economic profit is utilized for long-term decision-making. Economic profit is used extensively to determine whether a business should enter or exit a market or industry.

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The four principal financial statements are: Income statement (statement of earnings) Balance sheet (statement of financial position) Cash flow statement Statement of changes in owners' or stockholders' equity

ad>Financial statements are the most important outcome of the accounting system. They communicate financial information gathered and processed in the company's accounting system to parties outside the business. The four principal financial statements are: Income statement (statement of earnings) Balance sheet (statement of financial position) Cash flow statement Statement of changes in owners' or stockholders' equity These four financial statements, augmented by footnotes and supplementary data, are interrelated. In addition, there are other sources of financial i

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Making someone feel validated and heard is the carpool lane to deeper friendships, especially when you combine it with humor.

st a bit of awareness and effort. Next, I needed to befriend him and become more than an acquaintance. If I could get into his inner circle, I could get that same type of snarky argumentation on my side, and that could be valuable. <span>Making someone feel validated and heard is the carpool lane to deeper friendships, especially when you combine it with humor. Finally, I learned to defend myself from the extraneous and often off-base accusations and arguments he was making. Along with making sure that I was heard and people didn’t

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ing it. In other words, you’ll be a Negative Nancy (or Depressing Dan) and like attracts like. So assuming that you have internalized the possibility of positivity coming into your life, how do you graciously accept the compliment? <span>You compliment it!<span><body><html>

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The first step is to observe the vocabulary and vernacular someone uses.

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when it comes to getting along with people, it doesn’t really matter if you think someone hasn’t earned your respect or doesn’t deserve respect any at all. You have to project the illusion of respect regardless of how you feel internally sometimes

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So when people have the spotlight, their goal is usually to feel heard and gain validation from others.

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phere of conversation advice, it’s commonly held that people like to talk about themselves. This is undeniably true. But I’ll add an addendum in the context of this chapter – people aren’t so much interested in talking about themselves as <span>feeling heard and like they matter.<span><body><html>

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What is 'Free Cash Flow - FCF' Free cash flow (FCF) is a measure of a company's financial performance, calculated as operating cash flow minus capital expenditures. FCF represents the cash that a company is able to generate after spending the money required to maintain or expand its ass

<span>What is 'Free Cash Flow - FCF' Free cash flow (FCF) is a measure of a company's financial performance, calculated as operating cash flow minus capital expenditures. FCF represents the cash that a company is able to generate after spending the money required to maintain or expand its asset base. FCF is important because it allows a company to pursue opportunities that enhance shareholder value. BREAKING DOWN 'Free Cash Flow - FCF' FCF is an assessment of the amount of cash a company generates after accounting for all capital expenditures, su

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pany’s marginal cost of capital (MCC) may increase as additional capital is raised, whereas returns to a company’s investment opportunities are generally believed to decrease as the company makes additional investments, as represented by the <span>investment opportunity schedule (IOS).2 We show this relation in Figure 1, graphing the upward-sloping marginal cost of capital schedule against the downward-sloping investment opportunity schedule. In the context of a comp

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The additional information provided may include: A letter from the chairman of the company, A report from management discussing the results (typically called management discussion and analysis or management commentary), An external auditor’s report providing assurances, A governance report describing the structure of the company’s board of directors, and a corporate responsibility

with the required financial statements, a company typically provides additional information in its financial reports. In many jurisdictions, some or all of this additional information is mandated by regulators or accounting standards boards. <span>The additional information provided may include a letter from the chairman of the company, a report from management discussing the results (typically called management discussion and analysis [MD&A] or management commentary), an external auditor’s report providing assurances, a governance report describing the structure of the company’s board of directors, and a corporate responsibility report. As part of his or her analysis, the financial analyst should read and assess this additional information along with the financial statements. The following sections describe and illustr

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tatements are prepared in accordance with IFRS as adopted by the European Union, that the statements are prepared in compliance with German law, that the statements are denominated in millions of euros unless otherwise specified, and that the <span>figures have been rounded, which might give rise to minor discrepancies when figures are added.<span><body><html>

erstanding the information provided in the primary statements. Volkswagen’s 2009 financial statements, for example, include 91 pages of notes. The notes disclose the basis of preparation for the financial statements. For example, <span>Volkswagen discloses in its first note that its fiscal year corresponds to the calendar year, that its financial statements are prepared in accordance with IFRS as adopted by the European Union, that the statements are prepared in compliance with German law, that the statements are denominated in millions of euros unless otherwise specified, and that the figures have been rounded, which might give rise to minor discrepancies when figures are added. Volkswagen also discloses that its financial statements are on a consolidated basis—that is, including Volkswagen AG and all of the subsidiary companies it controls. The no

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The exposure draft identifies five content elements of a “decision-useful management commentary.” Those content elements include 1) the nature of the business; 2) management’s objectives and strategies; 3) the company’s significant resources, risks, and relationships; 4) results of operations; and 5)

ASB) issued an exposure draft in June 2009 that proposed a framework for the preparation and presentation of management commentary. Per the exposure draft, that framework will provide guidance rather than set forth requirements in a standard. <span>The exposure draft identifies five content elements of a “decision-useful management commentary.” Those content elements include 1) the nature of the business; 2) management’s objectives and strategies; 3) the company’s significant resources, risks, and relationships; 4) results of operations; and 5) critical performance measures. In the United States, the SEC requires listed companies to provide an MD&A and specifies the content.7 Management must highlight any favorable or unfavorable trends and

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Investing activities are those activities associated with acquisition and disposal of long-term assets. Examples include the purchase of equipment or sale of surplus equipment (such as an oven) by a restaur

g of an entity. Examples include the sale of meals by a restaurant, the sale of services by a consulting firm, the manufacture and sale of ovens by an oven-manufacturing company, and taking deposits and making loans by a bank. <span>Investing activities are those activities associated with acquisition and disposal of long-term assets. Examples include the purchase of equipment or sale of surplus equipment (such as an oven) by a restaurant (contrast this to the sale of an oven by an oven manufacturer, which would be an operating activity), and the purchase or sale of an office building, a retail store, or a factory. Financing activities are those activities related to obtaining or repaying capital. The two primary sources for such funds are owners (shareholders) or creditors. Examp

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Financing activities are those activities related to obtaining or repaying capital. The two primary sources for such funds are owners (shareholders) or creditors. Examples include issuing common shares, tak

us equipment (such as an oven) by a restaurant (contrast this to the sale of an oven by an oven manufacturer, which would be an operating activity), and the purchase or sale of an office building, a retail store, or a factory. <span>Financing activities are those activities related to obtaining or repaying capital. The two primary sources for such funds are owners (shareholders) or creditors. Examples include issuing common shares, taking out a bank loan, and issuing bonds. Understanding the nature of activities helps the analyst understand where the company is doing well and where it is not doing so well. Ideally, an analyst would pre

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Ideally, an analyst would prefer that most of a company’s profits (and cash flow) come from its operating activities.

rs. Examples include issuing common shares, taking out a bank loan, and issuing bonds. Understanding the nature of activities helps the analyst understand where the company is doing well and where it is not doing so well. <span>Ideally, an analyst would prefer that most of a company’s profits (and cash flow) come from its operating activities. Exhibit 1 provides examples of typical business activities and how these activities relate to the elements of financial statements described in the following section.

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Unlike the financial statement elements, there is no standard set of accounts applicable to all companies.

ded in every individual account are summarized and grouped appropriately within a financial statement element. Exhibit 2 provides a listing of common accounts. These accounts will be described throughout this reading or in following readings. <span>Unlike the financial statement elements, there is no standard set of accounts applicable to all companies. Although almost every company has certain accounts, such as cash, each company specifies the accounts in its accounting system based on its particular needs and circumstances. For examp

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A company’s challenge is to establish accounts and account groupings that provide meaningful summarization of voluminous data but retain enough detail to facilitate decision making and preparation of the financial statements. The actual accounts used in a company’s accounting system will be set forth in a char

ount for each of its ovens, with the accounts named “Oven-1” and “Oven-2.” In its financial statements, these accounts would likely be grouped within long-term assets as a single line item called “Property, plant, and equipment.” <span>A company’s challenge is to establish accounts and account groupings that provide meaningful summarization of voluminous data but retain enough detail to facilitate decision making and preparation of the financial statements. The actual accounts used in a company’s accounting system will be set forth in a chart of accounts . Generally, the chart of accounts is far more detailed than the information presented in financial statements. Certain accounts are used to offset other accounts. For example, a common asset account is accounts receivable, also known as “trade accounts receivable” or “trade receivab

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A statement of retained earnings can be viewed as a component of the statement of stockholders’ equity, which shows all changes to owners’ equity, both changes resulting from retained earnings and changes resulting fro

ements noted previously serve as the inputs for equations that underlie the financial statements. This section describes the equations for three of the financial statements: balance sheet, income statement, and statement of retained earnings. <span>A statement of retained earnings can be viewed as a component of the statement of stockholders’ equity, which shows all changes to owners’ equity, both changes resulting from retained earnings and changes resulting from share issuance or repurchase. The fourth basic financial statement, the statement of cash flows, will be discussed in a later section. The balance sheet presents a company’s financial position at a pa

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entity, but the equation remains the same. Owners’ equity at a given date can be further classified by its origin: capital contributed by owners, and earnings retained in the business up to that date:4 Equation (2) <span>Owners’ equity = Contributed capital + Retained earnings The income statement presents the performance of a business for a specific period of time. The equation reflected in the income statement is the following: E

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on of the income statement. To provide a combined representation of the balance sheet and income statement, we can substitute Equation 2 into Equation 1a. This becomes the expanded accounting equation: Equation (5a) <span>Assets = Liabilities + Contributed capital + Ending retained earnings Or equivalently, substituting Equation 4b into Equation 5a, we can write: Equation (5b) Assets=Liabilities+Contributedcapital+Beginningretainedea

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Assets=Liabilities+Contributedcapital+Beginningretainedearnings+Revenue−Expenses−DividendsAssets=Liabilities+Contributedcapital+Beginningretainedearnings+ Revenue−Expenses−Dividends

on: Equation (5a) Assets = Liabilities + Contributed capital + Ending retained earnings Or equivalently, substituting Equation 4b into Equation 5a, we can write: Equation (5b) <span>Assets=Liabilities+Contributedcapital+Beginningretainedearnings+Revenue−Expenses−DividendsAssets=Liabilities+Contributedcapital+Beginningretainedearnings+ Revenue−Expenses−Dividends The last five items, beginning with contributed capital, are components of owners’ equity. The statement of retained earnings shows the linkage between the b

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A decrease to an asset is recorded on the right side of a T-account.

e sheet (and accounting equation) and hence are on the left side of the T-account. Assets are, therefore, recorded with a debit balance. In other words, to record an increase in an asset, an entry is made to the left-hand side of a T-account. <span>A decrease to an asset is recorded on the right side of a T-account. Liabilities and owners’ equity are referred to as the right side of the balance sheet (and accounting equation). Increases to liabilities and owners’ equity are recorded on the right si

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This principle also comes across in the weight we give the advice of other people around us – even people unqualified to give a good opinion.

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Those who received an email from someone who had a similar sounding name returned the forms more that those who didnt.

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we also like people who we find to be attractive. There is a theory, which states that, people who are attractive are also going to possess other qualities such as being loyal and committed and thus, people are more likely to listen t

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People do not necessarily know where their emotions are coming from. You can lead their emotions, in many man ways.

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A positive aspect of unearned revenue is that increases in unearned revenue are an indicator of future revenues. For example, a large liability on the balance sheet of an airline relates to cash received for future airline

ved and the corresponding liability to deliver newsletters) and, subsequently, 12 future adjusting entries, the first one of which was illustrated as Transaction 12. Each adjusting entry reduces the liability and records revenue. <span>In practice, a large amount of unearned revenue may cause some concern about a company’s ability to deliver on this future commitment. Conversely, a positive aspect is that increases in unearned revenue are an indicator of future revenues. For example, a large liability on the balance sheet of an airline relates to cash received for future airline travel. Revenue will be recognized as the travel occurs, so an increase in this liability is an indicator of future increases in revenue. <span><body><html>

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A positive aspect of unearned revenue is that increases in unearned revenue are an indicator of future revenues. For example, a large liability on the balance sheet of an airline relates to cash received for future airline travel. Revenue will be recognized as the travel occurs, so an increase in this liability is an indicator of future increases in revenue.

ved and the corresponding liability to deliver newsletters) and, subsequently, 12 future adjusting entries, the first one of which was illustrated as Transaction 12. Each adjusting entry reduces the liability and records revenue. <span>In practice, a large amount of unearned revenue may cause some concern about a company’s ability to deliver on this future commitment. Conversely, a positive aspect is that increases in unearned revenue are an indicator of future revenues. For example, a large liability on the balance sheet of an airline relates to cash received for future airline travel. Revenue will be recognized as the travel occurs, so an increase in this liability is an indicator of future increases in revenue. <span><body><html>

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A journal is a document or computer file in which business transactions are recorded in the order in which they occur (chronological order). The general journal is the collection of all business transactions in an accounting system sorted by date. All accounting systems have a general journal to record all transactions. So

ved and the corresponding liability to deliver newsletters) and, subsequently, 12 future adjusting entries, the first one of which was illustrated as Transaction 12. Each adjusting entry reduces the liability and records revenue. <span>In practice, a large amount of unearned revenue may cause some concern about a company’s ability to deliver on this future commitment. Conversely, a positive aspect is that increases in unearned revenue are an indicator of future revenues. For example, a large liability on the balance sheet of an airline relates to cash received for future airline travel. Revenue will be recognized as the travel occurs, so an increase in this liability is an indicator of future increases in revenue. <span><body><html>

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A journal is a document or computer file in which business transactions are recorded in the order in which they occur (chronological order). The general journal is the collection of all business transactions in an accounting system sorted by date. All accounting systems have a general journal to record all transactions. Some accounting systems

ved and the corresponding liability to deliver newsletters) and, subsequently, 12 future adjusting entries, the first one of which was illustrated as Transaction 12. Each adjusting entry reduces the liability and records revenue. <span>In practice, a large amount of unearned revenue may cause some concern about a company’s ability to deliver on this future commitment. Conversely, a positive aspect is that increases in unearned revenue are an indicator of future revenues. For example, a large liability on the balance sheet of an airline relates to cash received for future airline travel. Revenue will be recognized as the travel occurs, so an increase in this liability is an indicator of future increases in revenue. <span><body><html>

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On the top line of the income statement, companies typically report revenue. Revenue generally refers to amounts charged (and expected to be received) for the delivery of goods or services in the ordinary activities of a business. The term <span>net revenue means that the revenue number is reported after adjustments (e.g., for cash or volume discounts, or for estimated returns). Revenue may be called sales or turnover.4 Exhibits 1 and 2 sh

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Certain items, such as revenue, finance costs, and tax expense, are required to be presented separately on the face of the income statement.

3; In addition to presenting the net income, income statements also present items, including subtotals, which are significant to users of financial statements. Some of the items are specified by IFRS but other items are not specified.7 <span>Certain items, such as revenue, finance costs, and tax expense, are required to be presented separately on the face of the income statement. IFRS additionally require that line items, headings, and subtotals relevant to understanding the entity’s financial performance should be presented even if not specified. Expenses may b

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The specific calculations of gross profit and operating profit may vary by company, and a reader of financial statements can consult the notes to the statements to identify significant variations across companies.

ss segments, operating profit can be useful in evaluating the performance of the individual business segments, because interest and tax expenses may be more relevant at the level of the overall company rather than an individual segment level. <span>The specific calculations of gross profit and operating profit may vary by company, and a reader of financial statements can consult the notes to the statements to identify significant variations across companies. Operating profit is sometimes referred to as EBIT (earnings before interest and taxes). However, operating profit and EBIT are not necessarily the same. Note that in both E

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y, and a reader of financial statements can consult the notes to the statements to identify significant variations across companies. Operating profit is sometimes referred to as EBIT (earnings before interest and taxes). However, <span>operating profit and EBIT are not necessarily the same. Note that in both Exhibits 1 and 2, interest and taxes do not represent the only differences between earnings (net income, net earnings) and operating income. For example, both companie

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With a letter of credit what happens In the event that the buyer is unable to make payment on the purchase? the bank will be required to cover the full or remaining amount of the purchase.

What is a 'Letter Of Credit' <span>A letter of credit is a letter from a bank guaranteeing that a buyer's payment to a seller will be received on time and for the correct amount. In the event that the buyer is unable to make payment on the purchase, the bank will be required to cover the full or remaining amount of the purchase. Due to the nature of international dealings, including factors such as distance, differing laws in each country, and difficulty in knowing each party personally, the use of letters of credit has become a very important aspect of international trade. BREAKING DOWN 'Letter Of Credit' Because a letter of credit is typically a negotiable instrument, the issuing bank pays the beneficiary or any bank

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Through this programme, the overseas buyer can open a "letter of credit" in favour of the Indian exporter and can import goods and services from India on deferred payment terms.

Inspiration to expand possibilities Buyer's Credit is our unique credit facility programme that motivates Indian exporters to explore new geographies. <span>Through this programme, the overseas buyer can open a "letter of credit" in favour of the Indian exporter and can import goods and services from India on deferred payment terms. While on the one hand, the exporter enjoys reduced transaction costs and complexities of international trade transactions, on the other hand, the Indian exporter gets to compete in the

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What is 'Depletion' Depletion is an accrual accounting technique used to allocate the cost of extracting natural resources such as timber, minerals and oil from the earth. Unlike depreciation and amortization, which

<span>What is 'Depletion' Depletion is an accrual accounting technique used to allocate the cost of extracting natural resources such as timber, minerals and oil from the earth. Unlike depreciation and amortization, which mainly describe the deduction of expenses due to the aging of equipment and property, depletion is the actual physical depletion of natural resources by companies. !--break--For accounting and financial reporting purposes, depletion is meant to assist in accurately identifying the value of the assets on the balance sheet and recording expenses in

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It is with the heart that one sees rightly; what is essential is invisible to the eye. ANTOINE DE SAINT-EXUPÉRY

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The neocortex is the seat of thought; it contains the centers that put together and comprehend what the senses perceive.

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Under the percentage-of-completion method, revenue is recognized based on the stage of completion of a transaction or contract and is, thus, recognized when the services are rendered.

a licensing arrangement, the company may recognize the revenue on a prorated basis over the period of time of the contract rather than at the end of the contract term. Under IFRS, this may be done using the percentage-of-completion method.16 <span>Under the percentage-of-completion method, revenue is recognized based on the stage of completion of a transaction or contract and is, thus, recognized when the services are rendered. Construction contracts are examples of contracts that may span a number of accounting periods and that may use the percentage-of-completion method.17 IFRS provide that when the outcome

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Under the completed contract method, the company does not report any income until the contract is substantially finished (the remaining costs and potential risks are insignificant in amount), although provision sho

d incurred. Under this method, no profit is recognized until all the costs had been recovered. Under US GAAP, but not under IFRS, a revenue recognition method used when the outcome cannot be measured reliably is the completed contract method. <span>Under the completed contract method, the company does not report any income until the contract is substantially finished (the remaining costs and potential risks are insignificant in amount), although provision should be made for expected losses. Billings and costs are accumulated on the balance sheet rather than flowing through the income statement. Under US GAAP, the completed contract method is also acceptable when the entity

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an advantage of the percentage-of-completion method is that it results in better matching of revenue recognition with the accounting period in which it was earned.

han the completed contract method and thus may be considered a less conservative approach. In addition, the percentage-of-completion method relies on management estimates and is thus not as objective as the completed contract method. However, <span>an advantage of the percentage-of-completion method is that it results in better matching of revenue recognition with the accounting period in which it was earned. Because of better matching with the periods in which work is performed, the percentage-of-completion method is the preferred method of revenue recognition for long-term contracts and is

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thod and the cost recovery method . Under the installment method, the portion of the total profit of the sale that is recognized in each period is determined by the percentage of the total sales price for which the seller has received cash. <span>Under the cost recovery method, the seller does not report any profit until the cash amounts paid by the buyer—including principal and interest on any financing from the seller—are greater than all the seller’s costs of the property. Note that the cost recovery method is similar to the revenue recognition method under international standards, described above, when the outcome of a contract cannot be measured reliabl

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Revenue recognition issues related to barter transactions became particularly important as e-commerce developed.

Revenue recognition issues related to barter transactions became particularly important as e-commerce developed. As an example, if Company A exchanges advertising space for computer equipment from Company B but no cash changes hands, can Company A and B both report revenue? Such an exchange is ref

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rrent period will remain unsold at the end of the current period and so will be sold in a following period. Matching requires that a company recognizes cost of goods sold in the same period as revenues from the sale of the goods. <span>Period costs , expenditures that less directly match revenues, are reflected in the period when a company makes the expenditure or incurs the liability to pay. Administrative expenses are an example of period costs. Other expenditures that also less directly match revenues relate more directly to future expected benefits; in this case, the exp

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Common acceleration factors are 150 percent and 200 percent. The latter is known as double declining balance depreciation because it depreciates the asset at double the straight-line rate.

the amount of future expenses resulting from its warranties, to recognize an estimated warranty expense in the period of the sale, and to update the expense as indicated by experience over the life of the warranty. <span>4.2.3. Depreciation and Amortisation Companies commonly incur costs to obtain long-lived assets. Long-lived assets are assets expected to provide economic benefits over a future period of time greater than one year. Examples are land (property), plant, equipment, and intangible assets (assets lacking physical substance) such as trademarks. The costs of most long-lived assets are allocated over the period of time during which they provide economic benefits. The two main types of long-lived assets whose costs are not allocated over time are land and those intangible assets with indefinite useful lives. Depreciation is the process of systematically allocating costs of long-lived assets over the period during which the assets are expected to provide economic benefits. “Depreciation” is the term commonly applied to this process for physical long-lived assets such as plant and equipment (land is not depreciated), and amortisation is the term commonly applied to this process for intangible long-lived assets with a finite useful life.32 Examples of intangible long-lived assets with a finite useful life include an acquired mailing list, an acquired patent with a set expiration date, and an acquired copyright with a set legal life. The term “amortisation” is also commonly applied to the systematic allocation of a premium or discount relative to the face value of a fixed-income security over the life of the security. IFRS allow two alternative models for valuing property, plant, and equipment: the cost model and the revaluation model.33 Under the cost model, the depreciable amount of that asset (cost less residual value) is allocated on a systematic basis over the remaining useful life of the asset. Under the cost model, the asset is reported at its cost less any accumulated depreciation. Under the revaluation model, the asset is reported at its fair value. The revaluation model is not permitted under US GAAP. Here, we will focus only on the cost model. There are two other differences between IFRS and US GAAP to note: IFRS require each component of an asset to be depreciated separately and US GAAP do not require component depreciation; and IFRS require an annual review of residual value and useful life, and US GAAP do not explicitly require such a review. The method used to compute depreciation should reflect the pattern over which the economic benefits of the asset are expected to be consumed. IFRS do not prescribe a particular method for computing depreciation but note that several methods are commonly used, such as the straight-line method, diminishing balance method (accelerated depreciation), and the units of production method (depreciation varies depending upon production or usage). The straight-line method allocates evenly the cost of long-lived assets less estimated residual value over the estimated useful life of an asset. (The term “straight line” derives from the fact that the annual depreciation expense, if represented as a line graph over time, would be a straight line. In addition, a plot of the cost of the asset minus the cumulative amount of annual depreciation expense, if represented as a line graph over time, would be a straight line with a negative downward slope.) Calculating depreciation and amortisation requires two significant estimates: the estimated useful life of an asset and the estimated residual value (also known as “salvage value”) of an asset. Under IFRS, the residual value is the amount that the company expects to receive upon sale of the asset at the end of its useful life. Example 9 assumes that an item of equipment is depreciated using the straight-line method and illustrates how the annual depreciation expense varies under different estimates of the useful life and estimated residual value of an asset. As shown, annual depreciation expense is sensitive to both the estimated useful life and to the estimated residual value. <span><body><html>

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me. These are only a few of the choices and estimates that affect a company’s reported net income. As with revenue recognition policies, a company’s choice of expense recognition can be characterized by its relative conservatism. <span>A policy that results in recognition of expenses later rather than sooner is considered less conservative. In addition, many items of expense require the company to make estimates that can significantly affect net income. Analysis of a company’s financial statements, and particularly compari

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analysts should exclude items that are non-recurring in nature when predicting a company's future earnings and cash flows

sustainable income and therefore should be the primary focus of analysis. Segregating the results of recurring operations from those of non-recurring items facilitates the forecasting of future earnings and cash flows. Generally, <span>analysts should exclude items that are non-recurring in nature when predicting a company's future earnings and cash flows. However, this does not mean that every non-recurring item in the income statement should be ignored. Management tends to label many items in the income statement as "non-recurring

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Management tends to label many items in the income statement as "non-recurring," especially those that reduce reported income.

flows. Generally, analysts should exclude items that are non-recurring in nature when predicting a company's future earnings and cash flows. However, this does not mean that every non-recurring item in the income statement should be ignored. <span>Management tends to label many items in the income statement as "non-recurring," especially those that reduce reported income. For the purpose of analysis, an important issue is to assess whether non-recurring items are really "non-recurring," regardless of their accounting labels. There

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Extraordinary items are BOTH unusual in nature AND infrequent in occurrence, and material in amount. They must be reported separately (below the line) net of income tax.

. Subsidiaries and investees also qualify as separate components. Disposal of a portion of a business component does not qualify as discontinued operations. Instead, this is recorded as an unusual or infrequent item. <span>2. Extraordinary items Extraordinary items are BOTH unusual in nature AND infrequent in occurrence, and material in amount. They must be reported separately (below the line) net of income tax. Common examples are: Expropriations by foreign governments. Uninsured losses from earthquakes, eruptions, and tornadoes. Note that gains and losses from the early retirement of debt used to be treated as extraordinary items; SFAS No. 145 now requires them to be treated as part of continuing operations. 3. Unusual or infrequent items These are either unusual in nature OR infrequent in occurrence but not both. They may be disclosed separately (as a single-line

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Simply by reminding someone that they have acted a certain way in the past, will start to cement their minds onto that track of thought and action.

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The starting place for analyzing a company is typically the balance sheet. Think of the balance sheet as a photo of the business at a specific point in time. It presents the assets, liabilities, and equity ownership of a company as of a specific date. A

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in light of accounting policies applied in order to answer the question of how the values relate to economic reality and to each other. Current Assets Current assets are presented in the balance sheet in order of liquidity. <span>The five major items found in the current assets section are: Cash. Valued at its stated value. Cash restricted for purpose other than payment of current obligations or for use in current operations should be excluded from the current asset section. Marketable securities. Valued at cost or lower of cost and market value. Accounts receivables. Amounts owed to the company by its customers for goods and services delivered. Valued at the estimated amount collectible. Inventories. Products that will be sold in the normal course of business. They should be measured at the lower of cost or net realizable value. Refer to Reading 28 [Inventories] for details. Pre-paid expenses. These are expenditures already made for benefits (usually services) to be received within one year or the operating cycle, whichever is longer. Typical examples are pre-paid rent, advertising, taxes, insurance policies, and office or operating supplies. They are reported at the amount of un-expired or unconsumed cost. Current Liabilities Current liabilities are typically paid from current assets or by incurring new short-term liabilities. They are not reported in any consist

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(bonds). Loans and receivables. Financial liabilities: All other liabilities (such as bonds payable or notes payable). Accounting for Gains and Losses on Marketable Securities <span>Held-to-maturity securities. Debt securities that management intends to hold to their maturity dates. At year-end, they are reported at cost adjusted for the effect of interest (debit the securities account and credit the interest income account) and unrealized holding gains and losses are not recognized. Trading securities. Debt and equity securities bought and held mainly for sale in the short term to generate income on price changes. At year-end, they are report

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d mainly for sale in the short term to generate income on price changes. At year-end, they are reported at their fair market value. Any unrealized holding gains or losses are recognized on the company's income statement as part of net income. <span>When they are sold, the realized gains or losses will also appear on the income statement. Realized gains and losses are not affected by any unrealized gains or losses recognized before. Available-for-sale securities. Debt and equity securities not classified

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ncome statement as part of net income. When they are sold, the realized gains or losses will also appear on the income statement. Realized gains and losses are not affected by any unrealized gains or losses recognized before. <span>Available-for-sale securities. Debt and equity securities not classified as held-to-maturity or trading securities. Unrealized gains and losses are reported as part of other comprehensive income (in contrast, the unrealized gains or losses of trading securities are reported in the income statement as

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ompany since its inception less all dividends paid out. Treasury stock. This is a company's own stock that has Already been fully issued and was outstanding; Been reacquired by the company; and Not been retired. <span>It decreases stockholder's equity and total shares outstanding. Accumulated comprehensive income. This includes items such as the minimum liability recognized for under-funded pension plans, market value changes in non-current

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hanges. Refer to Reading 24 [Understanding the Income Statement] for details. Statement of Changes in Shareholders' Equity This statement reflects information about increases or decreases to a company's net assets or wealth. <span>It reveals much more about the year's stockholders' equity transactions than the statement of retained earnings. The statement of shareholders' equity is a financial statement that summarizes changes that occurred during the accounting period in components of the stockholders' equity

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of dollars of current assets available to meet current obligations. It is the best-known liquidity measure. A current ratio of less than 1 indicates the company has negative working capital. <span>Quick Ratio (Acid-Test Ratio) eliminates less liquid assets, such as inventory and pre-paid expenses, from the current ratio. If inventory is not moving, the quick ratio is a better indicator of cash and near-cash items that will be available to meet current obligations. &

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ory in the quick ratio, there is no guarantee that the receivables will be collected. Solvency ratios measure a company's ability to meet long-term and other obligations. <span>Long-Term Debt-Equity Ratio is an indicator of the degree of protection available to the creditors in the event of insolvency of a company. Higher debt-equity ratio indicates higher financial risk. Debt-Equity Ratio includes short-term debt in the numerator.

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cash and cash flow are also vital to a company's long-term success. Information on the sources and uses of cash helps creditors, investors, and other statement users evaluate the company's liquidity, solvency, and financial flexibility. <span>Cash receipts and cash payments during a period are classified in the statement of cash flows into three different activities: Operating Activities These involve the cash effects of transactions that enter into the determination of net income and changes in the working capital accounts

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Operating Activities These involve the cash effects of transactions that enter into the determination of net income and changes in the working capital accounts (accounts receivable, inventory, and accounts payable). <span>Cash flows from operating activities (CFOs) reflect the company's ability to generate sufficient cash from its continuing operations. CFOs are derived by converting the income statement from an accrual basis to a cash basis. For

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est paid, and (5) income taxes paid. Special items to note: Interest and dividend revenue, and interest expenses, are considered operating activities, but dividends paid are considered financing activities. Note that <span>interest expense is reported on the income statement while dividends flow through the retained earnings statement. Remember that an interest/dividend item is an operating activity if it appears on the income statement. For example,

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affiliates and long-term investments in securities. Loans to other entities or collection of loans from other entities. Financing Activities These involve liability and owner's equity items, and include: <span>Obtaining capital from owners and providing them with a return on (and a return of) their investments. Borrowing money from creditors and repaying the amounts borrowed. In general, the items in this section relate to the debt and the equity items on the balance sheet. Financ

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ough a capital lease. Obtaining long-term assets by issuing notes payable to the seller. Exchanging one non-cash asset for another non-cash asset. The purchase of non-cash assets by issuing equity or debt securities. For example, <span>if a company purchases $200,000 of land by issuing a long-term bond, this transaction is a non-cash one, as it does not involve direct outlays of cash. Therefore, it is excluded from the statement of cash flows. These types of transactions should be disclosed in a separate schedule as part of the statement of cash flows or in the footn

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reconciles net income to net cash flow from operating activities by adjusting net income for all non-cash items and the net changes in the operating working capital accounts. It shows why net income and operating cash flows differ. It <span>is used by most companies. The direct and indirect methods are alternative formats for reporting net cash flows from operating activities. Both methods produce the same net figure (dollar

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Exhibit 2. Common Accounts Assets Cash and cash equivalents Accounts receivable, trade receivables Prepaid expenses Inventory Property, plant, and equipment Investment propert

ounting periods), and sales returns and allowances (an offset to revenue reflecting any cash refunds, credits on account, and discounts from sales prices given to customers who purchased defective or unsatisfactory items). <span>Exhibit 2. Common Accounts Assets Cash and cash equivalents Accounts receivable, trade receivables Prepaid expenses Inventory Property, plant, and equipment Investment property Intangible assets (patents, trademarks, licenses, copyright, goodwill) Financial assets, trading securities, investment securities Investments accounted for by the equity method Current and deferred tax assets [for banks, Loans (receivable)] Liabilities Accounts payable, trade payables Provisions or accrued liabilities Financial liabilities Current and deferred tax liabilities Reserves Unearned revenue Debt payable Bonds (payable) [for banks, Deposits] Owners’ Equity Capital, such as common stock par value Additional paid-in capital Retained earnings Other comprehensive income Minority interest Revenue Revenue, sales Gains Investment income (e.g., interest and dividends) Expense Cost of goods sold Selling, general, and administrative expenses “SG&A” (e.g., rent, utilities, salaries, advertising) Depreciation and amortization Interest expense Tax expense Losses For presentation purposes, assets are sometimes categorized as “current” or “non-current.” For example, Tesco (a large European retailer) prese

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Exhibit 2. Common Accounts Assets Cash and cash equivalents Accounts receivable, trade receivables Prepaid expenses Inventory Property, plant, and equipment Investment propert

ounting periods), and sales returns and allowances (an offset to revenue reflecting any cash refunds, credits on account, and discounts from sales prices given to customers who purchased defective or unsatisfactory items). <span>Exhibit 2. Common Accounts Assets Cash and cash equivalents Accounts receivable, trade receivables Prepaid expenses Inventory Property, plant, and equipment Investment property Intangible assets (patents, trademarks, licenses, copyright, goodwill) Financial assets, trading securities, investment securities Investments accounted for by the equity method Current and deferred tax assets [for banks, Loans (receivable)] Liabilities Accounts payable, trade payables Provisions or accrued liabilities Financial liabilities Current and deferred tax liabilities Reserves Unearned revenue Debt payable Bonds (payable) [for banks, Deposits] Owners’ Equity Capital, such as common stock par value Additional paid-in capital Retained earnings Other comprehensive income Minority interest Revenue Revenue, sales Gains Investment income (e.g., interest and dividends) Expense Cost of goods sold Selling, general, and administrative expenses “SG&A” (e.g., rent, utilities, salaries, advertising) Depreciation and amortization Interest expense Tax expense Losses For presentation purposes, assets are sometimes categorized as “current” or “non-current.” For example, Tesco (a large European retailer) prese

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measure the cash available to a company for discretionary uses after making all required cash outlays. It accounts for capital expenditures and dividend payments, which are essential to the ongoing nature of the business. <span>The basic definition is cash from operations less the amount of capital expenditures required to maintain the company's present productive capacity. Free cash flow = CFO - capital expenditure Free Cash Flow to the Firm (FCFF): Cash available to shareholders and bondholders after taxes,

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urrent to future consumption, the risk-free interest rate is the rate of compensation required to postpone current consumption. For example, the interest rate paid by T-bills is a risk-free rate of interest. In an uncertain world, <span>there are two factors that complicate interest rates: Inflation: When prices are expected to increase, lenders charge not only an opportunity cost for postponing consumption but also an inflation premium that takes into accoun

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heir ability to repay lenders. Lenders therefore charge interest rates that incorporate default risk. The return that borrowers pay thus comprises the nominal risk-free rate (real rate + an inflation premium) and a default risk premium. <span>Compounding is the process of accumulating interest over a period of time. A compounding period is the number of times per year that interest is paid. Continuous compounding occurs when the number of compounding periods becomes infinite; interest is added cont

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In practice with investments, analysts frequently need to find present values indexed at times other than t = 0. Subscripting the present value and evaluating a perpetuity beginning with $100 payments in Year 2, we find PV 1 = $100/0.05 = $2,000 at a 5 percent discount rate. Further, we can calcu

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To quickly approximate the number of periods, practitioners sometimes use an ad hoc rule called the Rule of 72 : Divide 72 by the stated interest rate to get the approximate number of years it would take to double an investment at the interest rate. Here, the approximation gives 72/7 = 10.3 years. The Rule of 72 is loosely based on the observation that it takes 12 years to double an amount at a 6 percent interest rate, giving 6 × 1

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eceding time period t P t - P t-1 = price appreciation of the investment D t = cash distributions received during time period t: for common stock, cash distribution is the dividend; for bonds, cash distribution is the coupon payment. <span>It has two important characteristics: It has an element of time attached to it: monthly, quarterly or annual returns. HPR can be computed for any time period. It has no currency unit attached to it; the result holds regardless of the currency in which prices are denominated. Example A stock is currently worth $60. If you purchased the stock exactly one year ago for $50 and received a $2 dividend over the course of the year, what is your ho

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d). Note that for common stocks the distribution is the dividend; for bonds, the distribution is the coupon payment. The holding period return for any asset can be calculated for any time period (day, week, month, or year) simply <span>by changing the interpretation of the time interval. Return can be expressed in decimals (0.05), fractions (5/100), or as a percent (5%). These are all equivalent. <span><body><html>

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the portfolio is performing well (poorly), the dollar-weighted rate of return will be inflated (depressed). The time-weighted rate of return measures the compound growth rate of $1 initial investment over the measurement period. <span>Time-weightedmeans that returns are averaged over time. This approach is not affected by the timing of cash flows; therefore, it is the preferred method of performance measurement. Example Jayson bought a share of I

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eighted rate of return will be inflated (depressed). The time-weighted rate of return measures the compound growth rate of $1 initial investment over the measurement period. Time-weightedmeans that returns are averaged over time. <span>This approach is not affected by the timing of cash flows; therefore, it is the preferred method of performance measurement. Example Jayson bought a share of IBM stock for $100 on December 31, 2000. On December 31, 2001, he bought another share for $150. On December 31, 2002, he sold

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Money market instruments are low-risk, highly liquid debt instruments with a maturity of one year or less. There are two types of money market instruments: interest-bearing instruments (e.g., bank certificates of deposit), and pure discount instruments (e.g., U.S. Treasury bills). Pure discount instruments such as T-bills are quoted differently than U.S. government bonds. They are quoted on a bank discount basis rather than on a price basis: &#

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ument at its maturity (that is, interest). Since a pure discount instrument (e.g., a T-bill) makes no interest payment, its HPY is (P 1 - P 0 )/P 0 . Note that HPY is computed on the basis of purchase price, not face value. <span>It is not an annualized yield. The effective annual yield is the annualized HPY on the basis of a 365-day year. It incorporates the effect of compounding interest.

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(The combination formula, or the binomial formula): For example, if you select two of the ten stocks you are analyzing, how many ways can you select the stocks? 10! / [(10 - 2)! x 2!] = 45. <span>An ordered listing is known as a permutation, and the formula that counts the number of permutations is known as the permutation formula. The number of ways that we can choose r objects from a total of n objects, where the order in which the r objects is listed does matter, is: For example, if you select two of the ten stocks you are analyzing and invest $10,000 in one stock and $20,000 in another stock, how many ways ca

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unt basis D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, P t = the number of days remaining to maturity 360 = the bank convention of the number of days in a year. <span>Bank discount yield is not a meaningful measure of the return on investment because: It is based on the face value, not on the purchase price. Instead, return on investment should be measured based on cost of investment. It is annualized using a 360-day year, not a 365-day year. It annualizes with simple interest and ignores the effect of interest on interest (compound interest). Holding period yield (HPY) is the return earned by an investor if the money market instrument is held until maturity: P 0 =

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The role of financial reporting is to provide information about a company's financial position and performance for use by parties both internal and external to the company.

The role of financial reporting is to provide information about a company's financial position and performance for use by parties both internal and external to the company. Financial statements are issued by management, who is responsible for their form and content. The role of financial statement analysis, on the other hand, is to take these

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Unblock @BorgesJorgeL Report Tweet Add to other Moment Add to new Moment <span>Lo que yo encuentro sobre todo malo en los deportes es la idea de que alguien gane y de que alguien pierda, y de que este hecho suscite rivalidades. Translate from Spanish Translated from Spanish by Bing What I find especially bad at sports is the idea that someone wins an

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A trend stationary process is not strictly stationary, but can easily be transformed into a stationary process by removing the underlying trend, which is solely a function of time.

rting. In the latter case of a deterministic trend, the process is called a trend stationary process, and stochastic shocks have only transitory effects after which the variable tends toward a deterministically evolving (non-constant) mean. <span>A trend stationary process is not strictly stationary, but can easily be transformed into a stationary process by removing the underlying trend, which is solely a function of time. Similarly, processes with one or more unit roots can be made stationary through differencing. An important type of non-stationary process that does not include a trend-like behavior is

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erences 8 External links History[edit source] The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. [2] [3] [4] Strategy[edit source] <span>Since the objective function is unknown, the Bayesian strategy is to treat it as a random function and place a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be. Examples[edit source] Examples of acquisition functions include probability of improvement, expected improvement, Bayesian expected losses, upper confidence bounds (UCB), Thompson s

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s 7 Generalization 8 Implementations in programming languages 9 See also 10 Notes 11 References 12 External links 12.1 History of science 12.2 Information 12.3 Computer code 12.4 Use of the matrix in simulation 12.5 Online calculators <span>Statement[edit source] The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form A = L L ∗ , {\displaystyle \mathbf {A} =\mathbf {LL} ^{*},} where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L. Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. [2] If the matrix A is Hermitian and positive semi-definite, then it still has a decomposition of the form A = LL* if the diagonal entries of L are allowed to be zero. [3] When A has real entries, L has real entries as well, and the factorization may be written A = LL T . [4] The Cholesky decomposition is unique when A is positive definite; there is only one lower triangular matrix L with strictly positive diagonal entries such that A = LL*. However, the decomposition need not be unique when A is positive semidefinite. The converse holds trivially: if A can be written as LL* for some invertible L, lower triangular or otherwise, then A is Hermitian and positive definite. LDL decomposition[edit source] A closely related variant of the classical Cholesky decomposition is the LDL decomposition, A =

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8 down vote accepted It depends a lot on the details of the problem being solved. You can find a tabular comparison between them here, which links to more information. You are right about <span>VB generally requiring more iterations, however sometimes each iteration is much cheaper than an EP iteration. Your third bullet is worded like a disadvantage of EP but it's more like an advantage---you can use the same approximating family as VB if you want, but you don't have to.

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3 天前 • Karthik Ganeshan <span>in LBM, one solves the boltzmann equation depending on the various parameters and use a relaxation time to reach equilibrium. NSE are a special case derived from boltzmann equation mostly using Chapman enskog expansion. So basically you are solving a flow problem starting from transient state itself rather than solving on equilibrium state only. While in FVM, FEM, FDM, SPECTRAL methods or other traditional methods which focus to solve NSE. What actually is being solved is approximate algebraic equation derived from PDE(NSE). Essentially algebraic equations are being solved. Conclusively, what actually you are solving is far different than what actual NSE represents leave aside Boltzmann's equation. I hope you can understand what advantages or efficient, accurate solution will be. 收起 展开 回复 0

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are wave [imagelink] Fourier transforms Continuous Fourier transform Fourier series Discrete-time Fourier transform Discrete Fourier transform Discrete Fourier transform over a ring Fourier analysis Related transforms <span>In mathematics, a Fourier series ( English: /ˈfʊəriˌeɪ/) [1] is a way to represent a function as the sum of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or, equivalently, complex exponentials). The discrete-time Fourier transform is a periodic function, often defined in terms of a Fourier series. The Z-transform, another example of application, reduces to a Fourier series for

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Variational Bayes can be seen as an extension of the EM (expectation-maximization) algorithm from maximum a posteriori estimation (MAP estimation) of the single most probable value of each parameter to f

om. In particular, whereas Monte Carlo techniques provide a numerical approximation to the exact posterior using a set of samples, Variational Bayes provides a locally-optimal, exact analytical solution to an approximation of the posterior. <span>Variational Bayes can be seen as an extension of the EM (expectation-maximization) algorithm from maximum a posteriori estimation (MAP estimation) of the single most probable value of each parameter to fully Bayesian estimation which computes (an approximation to) the entire posterior distribution of the parameters and latent variables. As in EM, it finds a set of optimal parameter values, and it has the same alternating structure as does EM, based on a set of interlocked (mutually dependent) equations that cannot be s

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VB generally requiring more iterations, however sometimes each iteration is much cheaper than an EP iteration.

8 down vote accepted It depends a lot on the details of the problem being solved. You can find a tabular comparison between them here, which links to more information. You are right about <span>VB generally requiring more iterations, however sometimes each iteration is much cheaper than an EP iteration. Your third bullet is worded like a disadvantage of EP but it's more like an advantage---you can use the same approximating family as VB if you want, but you don't have to.

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EP finds approximations to a probability distribution. It uses an iterative approach that leverages the factorization structure of the target distribution.

Expectation propagation From Wikipedia, the free encyclopedia Jump to: navigation, search Expectation propagation (EP) is a technique in Bayesian machine learning. <span>EP finds approximations to a probability distribution. It uses an iterative approach that leverages the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as Variational Bayesian methods. References[edit source] Thomas Minka (August 2–5, 2001). "Expectation Propagation

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Computers usually solve square systems of linear equations using the LU decomposition, and it is also a key step when inverting a matrix, or computing the determinant of a matrix.

rization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. The LU decomposition can be viewed as the matrix form of Gaussian elimination. <span>Computers usually solve square systems of linear equations using the LU decomposition, and it is also a key step when inverting a matrix, or computing the determinant of a matrix. The LU decomposition was introduced by mathematician Tadeusz Banachiewicz in 1938. [1] Contents [hide] 1 Definitions 1.1 LU factorization with Partial Pivoting 1.2 LU facto

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In numerical analysis and linear algebra, LU decomposition (where 'LU' stands for 'lower upper', and also called LU factorization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix.

on - Wikipedia ocultar siempre | ocultar ahora LU decomposition From Wikipedia, the free encyclopedia Jump to: navigation, search <span>In numerical analysis and linear algebra, LU decomposition (where 'LU' stands for 'lower upper', and also called LU factorization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. The LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of lin

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The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L. Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. [2] If the matrix A is Her

s 7 Generalization 8 Implementations in programming languages 9 See also 10 Notes 11 References 12 External links 12.1 History of science 12.2 Information 12.3 Computer code 12.4 Use of the matrix in simulation 12.5 Online calculators <span>Statement[edit source] The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form A = L L ∗ , {\displaystyle \mathbf {A} =\mathbf {LL} ^{*},} where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L. Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. [2] If the matrix A is Hermitian and positive semi-definite, then it still has a decomposition of the form A = LL* if the diagonal entries of L are allowed to be zero. [3] When A has real entries, L has real entries as well, and the factorization may be written A = LL T . [4] The Cholesky decomposition is unique when A is positive definite; there is only one lower triangular matrix L with strictly positive diagonal entries such that A = LL*. However, the decomposition need not be unique when A is positive semidefinite. The converse holds trivially: if A can be written as LL* for some invertible L, lower triangular or otherwise, then A is Hermitian and positive definite. LDL decomposition[edit source] A closely related variant of the classical Cholesky decomposition is the LDL decomposition, A =

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The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L.

s 7 Generalization 8 Implementations in programming languages 9 See also 10 Notes 11 References 12 External links 12.1 History of science 12.2 Information 12.3 Computer code 12.4 Use of the matrix in simulation 12.5 Online calculators <span>Statement[edit source] The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form A = L L ∗ , {\displaystyle \mathbf {A} =\mathbf {LL} ^{*},} where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L. Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. [2] If the matrix A is Hermitian and positive semi-definite, then it still has a decomposition of the form A = LL* if the diagonal entries of L are allowed to be zero. [3] When A has real entries, L has real entries as well, and the factorization may be written A = LL T . [4] The Cholesky decomposition is unique when A is positive definite; there is only one lower triangular matrix L with strictly positive diagonal entries such that A = LL*. However, the decomposition need not be unique when A is positive semidefinite. The converse holds trivially: if A can be written as LL* for some invertible L, lower triangular or otherwise, then A is Hermitian and positive definite. LDL decomposition[edit source] A closely related variant of the classical Cholesky decomposition is the LDL decomposition, A =

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The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L.

s 7 Generalization 8 Implementations in programming languages 9 See also 10 Notes 11 References 12 External links 12.1 History of science 12.2 Information 12.3 Computer code 12.4 Use of the matrix in simulation 12.5 Online calculators <span>Statement[edit source] The Cholesky decomposition of a Hermitian positive-definite matrix A is a decomposition of the form A = L L ∗ , {\displaystyle \mathbf {A} =\mathbf {LL} ^{*},} where L is a lower triangular matrix with real and positive diagonal entries, and L* denotes the conjugate transpose of L. Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. [2] If the matrix A is Hermitian and positive semi-definite, then it still has a decomposition of the form A = LL* if the diagonal entries of L are allowed to be zero. [3] When A has real entries, L has real entries as well, and the factorization may be written A = LL T . [4] The Cholesky decomposition is unique when A is positive definite; there is only one lower triangular matrix L with strictly positive diagonal entries such that A = LL*. However, the decomposition need not be unique when A is positive semidefinite. The converse holds trivially: if A can be written as LL* for some invertible L, lower triangular or otherwise, then A is Hermitian and positive definite. LDL decomposition[edit source] A closely related variant of the classical Cholesky decomposition is the LDL decomposition, A =

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Since the objective function is unknown, the Bayesian strategy (of optimisation) is to treat it as a random function and place a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distr

erences 8 External links History[edit source] The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. [2] [3] [4] Strategy[edit source] <span>Since the objective function is unknown, the Bayesian strategy is to treat it as a random function and place a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be. Examples[edit source] Examples of acquisition functions include probability of improvement, expected improvement, Bayesian expected losses, upper confidence bounds (UCB), Thompson s

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Since the objective function is unknown, the Bayesian strategy (of optimisation) is to treat it as a random function and place a prior over it.

erences 8 External links History[edit source] The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. [2] [3] [4] Strategy[edit source] <span>Since the objective function is unknown, the Bayesian strategy is to treat it as a random function and place a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be. Examples[edit source] Examples of acquisition functions include probability of improvement, expected improvement, Bayesian expected losses, upper confidence bounds (UCB), Thompson s

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ace a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. <span>The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be. <span><body><html>

erences 8 External links History[edit source] The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. [2] [3] [4] Strategy[edit source] <span>Since the objective function is unknown, the Bayesian strategy is to treat it as a random function and place a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be. Examples[edit source] Examples of acquisition functions include probability of improvement, expected improvement, Bayesian expected losses, upper confidence bounds (UCB), Thompson s

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The posterior distribution (of the objective function), in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be.

erences 8 External links History[edit source] The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. [2] [3] [4] Strategy[edit source] <span>Since the objective function is unknown, the Bayesian strategy is to treat it as a random function and place a prior over it. The prior captures our beliefs about the behaviour of the function. After gathering the function evaluations, which are treated as data, the prior is updated to form the posterior distribution over the objective function. The posterior distribution, in turn, is used to construct an acquisition function (often also referred to as infill sampling criteria) that determines what the next query point should be. Examples[edit source] Examples of acquisition functions include probability of improvement, expected improvement, Bayesian expected losses, upper confidence bounds (UCB), Thompson s

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Hermitian matrices can be understood as the complex extension of real symmetric matrices.

A = A T ¯ {\displaystyle A={\overline {A^{\text{T}}}}} , in matrix form. <span>Hermitian matrices can be understood as the complex extension of real symmetric matrices. If the conjugate transpose of a matrix A {\displaystyle A} is denoted by A H

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Hermitian matrices can be understood as the complex extension of real symmetric matrices.

A = A T ¯ {\displaystyle A={\overline {A^{\text{T}}}}} , in matrix form. <span>Hermitian matrices can be understood as the complex extension of real symmetric matrices. If the conjugate transpose of a matrix A {\displaystyle A} is denoted by A H

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In linear algebra, the Cholesky decomposition or Cholesky factorization is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful e.g. for efficient numerical solutions and Monte Carlo simulations.

ikipedia ocultar siempre | ocultar ahora Cholesky decomposition From Wikipedia, the free encyclopedia Jump to: navigation, search <span>In linear algebra, the Cholesky decomposition or Cholesky factorization is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful e.g. for efficient numerical solutions and Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems

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OOP is about producing well organized code — an important determinant of productivity

ramming, and nicely supported in Python OOP has become an important concept in modern software engineering because It can help facilitate clean, efficient code (if used well) The OOP design pattern fits well with many computing problems <span>OOP is about producing well organized code — an important determinant of productivity Moreover, OOP is a part of Python, and to progress further it’s necessary to understand the basics About OOP¶ OOP is supported in many languages: JAVA and Ruby are relativel

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he frequency domain representation of the function, f̂, is the collection of these peaks at the frequencies that appear in this resolution of the function. One motivation for the Fourier transform comes from the study of Fourier series. <span>In the study of Fourier series, complicated but periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. The Fourier transform is an extension of the Fourier series that results when the period of the represented function is lengthened and allowed to approach infinity. [10] Due to the pr

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One motivation for the Fourier transform comes from the study of Fourier series. In the study of Fourier series, complicated but periodic functions are written as the sum of simple waves mathematically represented by sines and cosines. <span>The Fourier transform is an extension of the Fourier series that results when the period of the represented function is lengthened and allowed to approach infinity. [10] Due to the properties of sine and cosine, it is possible to recover the amplitude of each wave in a Fourier series using an integral. In many cases it is desirable to use Euler's

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write Fourier series in terms of the basic waves e 2πiθ . This has the advantage of simplifying many of the formulas involved, and provides a formulation for Fourier series that more closely resembles the definition followed in this article. <span>Re-writing sines and cosines as complex exponentials makes it necessary for the Fourier coefficients to be complex valued. The usual interpretation of this complex number is that it gives both the amplitude (or size) of the wave present in the function and the phase (or the initial angle) of the wave. These complex exponentials sometimes contain negative "frequencies". If θ is measured in seconds, then the waves e 2πiθ and e −2πiθ both complete one cycle per second, but t

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s formula half-lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann–Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel's conjecture v t e <span>Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos x + i sin x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more

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f references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (September 2010) (Learn how and when to remove this template message) <span>Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used in complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various

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s sorts of relationships among the three types of random variables, as might be described by a graphical model. As is typical in Bayesian inference, the parameters and latent variables are grouped together as "unobserved variables". <span>Variational Bayesian methods are primarily used for two purposes: To provide an analytical approximation to the posterior probability of the unobserved variables, in order to do statistical inference over these variables. To derive a lower bound for the marginal likelihood (sometimes called the "evidence") of the observed data (i.e. the marginal probability of the data given the model, with marginalization performed over unobserved variables). This is typically used for performing model selection, the general idea being that a higher marginal likelihood for a given model indicates a better fit of the data by that model and hence a greater probability that the model in question was the one that generated the data. (See also the Bayes factor article.) In the former purpose (that of approximating a posterior probability), variational Bayes is an alternative to Monte Carlo sampling methods — particularly, Markov chain Monte Carlo met

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ceedings of Machine Learning Research Volume 5 All Volumes JMLR MLOSS FAQ Submission Format [imagelink] <span>Variational Learning of Inducing Variables in Sparse Gaussian Processes [edit] Michalis Titsias ; Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, PMLR 5:567-574, 2009. Abstract Sparse Gaussian process methods that use inducing variables require the selection of the inducing inputs and the kernel hyperparameters. We introduce a variational formulation for sparse approximations that jointly infers the inducing inputs and the kernel hyperparameters by maximizing a lower bound of the true log marginal likelihood. The key property of this formulation is that the inducing inputs are defined to be variational parameters which are selected by minimizing the Kullback-Leibler divergence between the variational distribution and the exact posterior distribution over the latent function values. We apply this technique to regression and we compare it with other approaches in the literature. Related Material Download PDF @InProceedings{pmlr-v5-titsias09a, title = {Variational Learning of Inducing Variables in Sparse Gaussian Proc

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he parameters and latent variables. As in EM, it finds a set of optimal parameter values, and it has the same alternating structure as does EM, based on a set of interlocked (mutually dependent) equations that cannot be solved analytically. <span>For many applications, variational Bayes produces solutions of comparable accuracy to Gibbs sampling at greater speed. However, deriving the set of equations used to iteratively update the parameters often requires a large amount of work compared with deriving the comparable Gibbs sampling equations. Th