Discounted cash flowThe discounted cash flow (DCF) analysis, in finance, is a method used to value a security, project, company, or asset, that incorporates the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate development, corporate financial management, and patent valuation. Used in industry as early as the 1700s or 1800s, it was widely discussed in financial economics in the 1960s, and U.S. courts began employing the concept in the 1980s and 1990s.
Free cash flowIn financial accounting, free cash flow (FCF) or free cash flow to firm (FCFF) is the amount by which a business's operating cash flow exceeds its working capital needs and expenditures on fixed assets (known as capital expenditures). It is that portion of cash flow that can be extracted from a company and distributed to creditors and securities holders without causing issues in its operations. As such, it is an indicator of a company's financial flexibility and is of interest to holders of the company's equity, debt, preferred stock and convertible securities, as well as potential lenders and investors.
Valuation using discounted cash flowsValuation using discounted cash flows (DCF valuation) is a method of estimating the current value of a company based on projected future cash flows adjusted for the time value of money. The cash flows are made up of those within the “explicit” forecast period, together with a continuing or terminal value that represents the cash flow stream after the forecast period. In several contexts, DCF valuation is referred to as the "income approach".
Corporate financeCorporate finance is the area of finance that deals with the sources of funding, and the capital structure of corporations, the actions that managers take to increase the value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to maximize or increase shareholder value. Correspondingly, corporate finance comprises two main sub-disciplines.
Consumer debtIn economics, consumer debt is the amount owed by consumers (as opposed to amounts owed by businesses or governments). It includes debts incurred on purchase of goods that are consumable and/or do not appreciate. In macroeconomic terms, it is debt which is used to fund consumption rather than investment. The most common forms of consumer debt are credit card debt, payday loans, student loans and other consumer finance, which are often at higher interest rates than long-term secured loans, such as mortgages.
Cash flow forecastingCash flow forecasting is the process of obtaining an estimate of a company's future financial position; the cash flow forecast is typically based on anticipated payments and receivables. There are two types of cash flow forecasting methodologies in general: Direct cash forecasting Indirect cash forecasting. Financial forecastCash management and Treasury management#Cash and Liquidity Management Cash flow forecasting is an element of financial management.
DebtDebt is an obligation that requires one party, the debtor, to pay money borrowed or otherwise withheld from another party, the creditor. Debt may be owed by sovereign state or country, local government, company, or an individual. Commercial debt is generally subject to contractual terms regarding the amount and timing of repayments of principal and interest. Loans, bonds, notes, and mortgages are all types of debt. In financial accounting, debt is a type of financial transaction, as distinct from equity.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Risk premiumA risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky return less the risk-free return, as demonstrated by the formula below. Where is the risky expected rate of return and is the risk-free return. The inputs for each of these variables and the ultimate interpretation of the risk premium value differs depending on the application as explained in the following sections.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Free cash flow to equityIn corporate finance, free cash flow to equity (FCFE) is a metric of how much cash can be distributed to the equity shareholders of the company as dividends or stock buybacks—after all expenses, reinvestments, and debt repayments are taken care of. It is also referred to as the levered free cash flow or the flow to equity (FTE). Whereas dividends are the cash flows actually paid to shareholders, the FCFE is the cash flow simply available to shareholders. The FCFE is usually calculated as a part of DCF or LBO modelling and valuation.
Yield curveIn finance, the yield curve is a graph which depicts how the yields on debt instruments – such as bonds – vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or years remaining to maturity, with the shortest maturity on the left and progressively longer time periods on the right. The vertical or y-axis depicts the annualized yield to maturity. Those who issue and trade in forms of debt, such as loans and bonds, use yield curves to determine their value.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Cost of capitalIn economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet. For an investment to be worthwhile, the expected return on capital has to be higher than the cost of capital.
Forecast period (finance)In corporate finance, in the context of discounted cash flow valuation, the forecast period is the time period during which explicitly forecast, individual yearly cash flows are input to the valuation-formula. Cash flows after the forecast period are represented by a fixed number - the "terminal value" - determined using assumptions relating to the sustainable compound annual growth rate or exit multiple. There are no fixed rules for determining the duration of the forecast period.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
Long-Term Capital ManagementLong-Term Capital Management L.P. (LTCM) was a highly leveraged hedge fund. In 1998, it received a $3.6 billion bailout from a group of 14 banks, in a deal brokered and put together by the Federal Reserve Bank of New York. LTCM was founded in 1994 by John Meriwether, the former vice-chairman and head of bond trading at Salomon Brothers. Members of LTCM's board of directors included Myron Scholes and Robert C. Merton, who three years later in 1997 shared the Nobel Prize in Economics for having developed the Black–Scholes model of financial dynamics.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Payment systemA payment system is any system used to settle financial transactions through the transfer of monetary value. This includes the institutions, payment instruments such as payment cards, people, rules, procedures, standards, and technologies that make its exchange possible. A common type of payment system, called an operational network, links bank accounts and provides for monetary exchange using bank deposits. Some payment systems also include credit mechanisms, which are essentially a different aspect of payment.
Event horizonIn astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact objects that even light cannot escape. At that time, the Newtonian theory of gravitation and the so-called corpuscular theory of light were dominant. In these theories, if the escape velocity of the gravitational influence of a massive object exceeds the speed of light, then light originating inside or from it can escape temporarily but will return.
