## Time value of money

[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 (NEq.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

1. A.A. Groppelli and Ehsan Nikbakht. Barron’s FinanceFifth Edition.  2006, Barron’s Educational Series, New York.