In economics and finance, an intertemporal budget constraint is a constraint faced by a decision maker who is making choices for both the present and the future. The term intertemporal is used to describe any relationship between past, present and future events or conditions. In its general form, the intertemporal budget constraint says that the present value of current and future cash outflows cannot exceed the present value of currently available funds and future cash inflows. Typically this is expressed as
where is expenditure at time t, is the cash that becomes available at time t, T is the most distant relevant time period, 0 is the current time period, and is the discount factor computed from the interest rate r.
Complications are possible in various circumstances. For example, the interest rate for discounting cash receipts might be greater than the interest rate for discounting expenditures, because future inflows may be borrowed against while currently available funds may be invested temporarily pending use for future expenditures, and borrowing rates may exceed investment returns.
Applications
In most applications, the entire budget would be used up, because any unspent funds would represent unobtained potential utility. In these situations, the intertemporal budget constraint is effectively an equality constraint.
In an intertemporal consumption model, the sum of utilities from expenditures made at various times in the future, these utilities discounted back to the present at the consumer's rate of time preference, would be maximized with respect to the amounts xt consumed in each period, subject to an intertemporal budget constraint.
In a model of intertemporal portfolio choice, the objective would be to maximize the expected value or expected utility of final period wealth. Since investment returns in each period generally would not be known in advance, the constraint effectively imposes a limit on the amount that can be invested in the final period—namely, whatever the wealth accumulated as of the end of the next-to-last period is.
The discounted cash flow (DCF) analysis, in financial analysis, 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.
In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.
The net present value (NPV) or net present worth (NPW) is a way of measuring the value of an asset that has cashflow by adding up the present value of all the future cash flows that asset will generate. The present value of a cash flow depends on the interval of time between now and the cash flow because of the Time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.
Internal rate of return (IRR) is a method of calculating an investment's rate of return. The term internal refers to the fact that the calculation excludes external factors, such as the risk-free rate, inflation, the cost of capital, or financial risk.
In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of borrowed funds is less than the total amount of money paid to the lender.
The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference.
Intertemporal choice is the study of the relative value people assign to two or more payoffs at different points in time. This relationship is usually simplified to today and some future date. Intertemporal choice was introduced by John Rae in 1834 in the "Sociological Theory of Capital". Later, Eugen von Böhm-Bawerk in 1889 and Irving Fisher in 1930 elaborated on the model.
In economics, a budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within their given income. Consumer theory uses the concepts of a budget constraint and a preference map as tools to examine the parameters of consumer choices. Both concepts have a ready graphical representation in the two-good case. The consumer can only purchase as much as their income will allow, hence they are constrained by their budget. The equation of a budget constraint is where is the price of good X, and is the price of good Y, and m is income.
In marketing, customer lifetime value, lifetime customer value (LCV), or life-time value (LTV) is a prognostication of the net profit contributed to the whole future relationship with a customer. The prediction model can have varying levels of sophistication and accuracy, ranging from a crude heuristic to the use of complex predictive analytics techniques.
Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.
In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis is actively being studied by neuroeconomics researchers.
Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preferences.
A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman's “principle of optimality" prescribes. The equation applies to algebraic structures with a total ordering; for algebraic structures with a partial ordering, the generic Bellman's equation can be used.
In economics, discounted utility is the utility (desirability) of some future event, such as consuming a certain amount of a good, as perceived at the present time as opposed to at the time of its occurrence. It is calculated as the present discounted value of future utility, and for people with time preference for sooner rather than later gratification, it is less than the future utility. The utility of an event x occurring at future time t under utility function u, discounted back to the present using discount factor Is
Capital budgeting in corporate finance, corporate planning and accounting is an area of capital management that concerns the planning process used to determine whether an organization's long term capital investments such as new machinery, replacement of machinery, new plants, new products, and research development projects are worth the funding of cash through the firm's capitalization structures. It is the process of allocating resources for major capital, or investment, expenditures. An underlying goal, consistent with the overall approach in corporate finance, is to increase the value of the firm to the shareholders.
In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms or as a percentage of the amount invested. The latter is also called the holding period return.
The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.
Consumption smoothing is an economic concept for the practice of optimizing a person's standard of living through an appropriate balance between savings and consumption over time. An optimal consumption rate should be relatively similar at each stage of a person's life rather than fluctuate wildly. Luxurious consumption at an old age does not compensate for an impoverished existence at other stages in one's life.
In financial economics, the dividend discount model (DDM) is a method of valuing the price of a company's capital stock or business value based on the assertion that intrinsic value is determined by the sum of future cash flows from dividend payments to shareholders, discounted back to their present value. The constant-growth form of the DDM is sometimes referred to as the Gordon growth model (GGM), after Myron J. Gordon of the Massachusetts Institute of Technology, the University of Rochester, and the University of Toronto, who published it along with Eli Shapiro in 1956 and made reference to it in 1959. Their work borrowed heavily from the theoretical and mathematical ideas found in John Burr Williams 1938 book "The Theory of Investment Value," which put forth the dividend discount model 18 years before Gordon and Shapiro.
Intertemporal portfolio choice is the process of allocating one's investable wealth to various assets, especially financial assets, repeatedly over time, in such a way as to optimize some criterion. The set of asset proportions at any time defines a portfolio. Since the returns on almost all assets are not fully predictable, the criterion has to take financial risk into account. Typically the criterion is the expected value of some concave function of the value of the portfolio after a certain number of time periods—that is, the expected utility of final wealth. Alternatively, it may be a function of the various levels of goods and services consumption that are attained by withdrawing some funds from the portfolio after each time period.
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