Time Value of Money

Time value of money A time value of money calculation is one which solves for one of several variables in a financial problem. In a typical case, the variables might be: a balance (the real or nominal value of a debt or a financial asset in terms of monetary units); a periodic rate of interest; the number of periods; and a series of cash flows (in the case of a debt, these are payments against principal and interest; in the case of a financial asset, these are contributions to or withdrawals from the balance). More generally, the cash flows may not be periodic but may be specified individually. Any of the variables may be the independent variable (the sought-for answer) in a given problem. For example, one may know that: the interest is 0.5% per period (per month, say); the number of periods is 60 (months); the initial balance (of the debt, in this case) is 25,000 units; and the final balance is 0 units. The unknown variable may be the monthly payment that the borrower will need to pay. For example, £100 invested for one year, earning 5% interest, will be worth £105 after one year; therefore, £100 paid now and £105 paid exactly one year later both have the same value to a recipient who expects 5% interest. That is, £100 invested for one year at 5% interest has a future value of £105.[1] This notion dates back at least to Martín de Azpilcueta (1491–1586) of the School of Salamanca. This principle allows for the valuation of a likely stream of income in the future, in such a way that annual incomes are discounted and then added together, thus providing a lump-sum "present value" of the entire income stream; all of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, "discounted" to the present by an amount equal to the time value of money. For example, the future value sum FV to be received in one year is discounted at the rate of interest r to give the present value sum PV: PV = \frac{FV}{(1+r)} Some standard calculations based on the time value of money are: Present value: The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Future cash flows are "discounted" at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to valuing future cash flows properly, whether they be earnings or obligations.[2] Present value of an annuity: An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.[3] Present value of a perpetuity is an infinite and constant stream of identical cash flows.[4] Future value: The value of an asset or cash at a specified date in the future, based on the value of that asset in the present.[5] Future value of an annuity (FVA): The future value of a stream of payments (annuity), assuming the payments are invested at a given rate of interest. From Wikipedia, the free encyclopedia