An Explanation
Simply put, time value of money is the value of money figuring in a given amount of interest for a given amount of time. For example 100 pounds of today's money held for a year at 5 percent interest is worth 105 pounds, therefore 100 pounds paid now or 105 pounds paid exactly one year from now is the same amount of payment of money with that given interest at that given amount of time. This notion dates at least to Martín de Azpilcueta of the School of Salamanca .
The method also allows the valuation of a likely stream of income in the future, in such a way that the 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 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, a sum of FV to be received in one year is discounted (at the rate of interest r) to give a sum of PV at present: PV = FV — r·PV = FV/(1+r).
Some standard calculations based on the time value of money are:
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Present Value
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- 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, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations .
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Present Value of an Annuity
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- 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 .
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Present Value of a Perpetuity
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- This is a constant stream of identical cash flows with no end.
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Future Value
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- This is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today .
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Future Value of an Annuity (FVA)
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- Described as the future value of a stream of payments (annuity), assuming the payments are invested at a given rate of interest.
Discounts
Discounting is a financial 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. The discount, or charge, is simply 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 discount is usually associated with a discount rate, which is also called the discount yield. The discount yield is simply the proportional share of the initial amount owed (initial liability) that must be paid to delay payment for 1 year.
It is also the rate at which the amount owed must rise to delay payment for 1 year.
Since a person can earn a return on money invested over some period of time, most economic and financial models assume the "Discount Yield" is the same as the Rate of Return the person could receive by investing this money elsewhere (in assets of similar risk) over the given period of time covered by the delay in payment. The Concept is associated with the Opportunity Cost of not having use of the money for the period of time covered by the delay in payment. The relationship between the "Discount Yield" and the Rate of Return on other financial assets is usually discussed in such economic and financial theories involving the inter-relation between various Market Prices, and the achievement of Pareto Optimality through the operations in the Capitalistic Price Mechanism, as well as in the discussion of the "Efficient (Financial) Market Hypothesis". The person delaying the payment of the current Liability is essentially compensating the person to whom he/she owes money for the lost revenue that could be earned from an investment during the time period covered by the delay in payment. Accordingly, it is the relevant "Discount Yield" that determines the "Discount", and not the other way around.