[updated on 12/20/2014]

The changing value of money affects everyone. Unfortunately, the prices of most things eventually increase by a process called inflation. Because of inflation –and other economic risks– investors should assume that money has a greater purchasing power ‘today’ than ‘tomorrow’. That change in purchasing power is called the* time value* of money. In other words, the difference between the future value and present value of money is its *time value*, or *total discount *

^{Ref 1}.

Financial planners use the following nomenclature to describe the time value of money:

## Future value

Today’s money can be used to buy things now, save for an emergency, or invest in the *future value *of money. The *future value* is predictable with assumptions about the expected *rate of return* (*R*) and time (*N*) ^{Eq.1, Ref 1}.

#### future value = present value * (1+R)^{N} , Eq. 1

Eq. 1 is useful for predicting an investment’s return. The expected rate of return, *R, * is either published for the type of project, estimated from historical changes in market value, or arbitrarily chosen for an assumed level of risk. *N *is the number of time periods reserved for growth.

## Present value

The *present value* is today’s cash value of an investment’s future return ^{Ref 1}. Eq. 2 is used to discount (i.e., reduce) the future value.

#### present value = future value / (1+R)^{N} , Eq. 2

The *discount rate*, *R*, adjusts the future value for the risk of investment and the uncertainty of time (e.g., high R for high risk and high N for more uncertainty).

Applications: The present value enables the comparison of profitability among different projects of a give time period. Other applications include the design of an annuity contract and analysis of variable cash flows ^{Ref 1}.

## Discount rate

The *discount rate* is a factor that discounts the future value of an investment. It often serves as an interest rate applied to a series of future payments to adjust for risk and the uncertainty of time ^{Ref 1}. In other applications, it is the required rate of return that a firm must achieve to justify an investment.

## Reference

- A.A. Groppelli and Ehsan Nikbakht. Barron’s Finance. Fifth Edition. 2006, Barron’s Educational Series, New York.