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Time Value of Money

Time value of money is the economic concept that money (or capital) received today has a different value than money that will be received in the future. Understanding and applying the concept of the time value of money is important in deciding which alternative to pursue when the alternatives will generate revenue or incur costs at different times in the future.

This page reviews the concept of time value of money. discusses the analytical process of discounting future payments to present value, and presents several applications of the concept of time value of money (including capitalizing the present value of future payments to determine the value of an asset). Embedded in this explanation is a discussion of how to determine a discount rate .

Time Value of Money — The concept

Time value of money is an economic concept that money (or capital) received today has less value than money that will be received in the future. Several reasons account for this difference in value, for example,

• Money received today is a certainty — you have the cash — whereas money that is to be received in the future may never be received. Risk and uncertainty is one reason why money received today is more valuable than money that may be received in the future.
• Money received today can be invested and generating income, that is, not receiving the payment until a later time has an opportunity cost .
• Inflation between now and when the money is received in the future decreases the purchasing power of the future cash; we know that $4 today will allow me to buy at least one gallon of gas; but will $4 five years from now still buy a gallon of gas at that time. Expected inflation explains why money received today has a greater value than an equal amount of money that will be received in the future.
• Money received today can be spent today and the benefit (utility) of having that item today is greater than being able to purchase that item sometime in the future after the future payment is received. The basic principle is that people prefer to consume (place more value on having) something today rather than receiving and consuming it in the future.

Except in extraordinary circumstances, the value of money received today will have greater value than an equal amount of money that will be received in the future. For example, $10 today is has more value than receiving $10 in the future due to the four factors listed above.

Present value is todays value of a payment that will be received in the future.

The corollary is that the present value of a future payment is less than the amount of the future payment. For example, a $10 payment that will be received in the future has a present value of less than $10.

Example. Due to the four reasons listed above, I may be willing to accept $9.50 today rather than wait to receive $10 a year from now.

Because a payment received in the future has less value than an equal payment today, we often refer to this thought process or analytical process as discounting the future payment to its present value .

Time also is a consideration. A higher present value will be placed on a future payment that will be received sooner than the present value that will be placed on a payment that will be received later.

Example. A $10 payment that will be received 6 months from now has a higher present value than a $10 payment that will be received one year from now. The further into the future a payment will be received, the less the value that will be placed on it today. With the passage of time, the present value of a future payment increases because the length of time until the payment is growing shorter.

Individuals will Place Different Present Values on the Same Future Payment

Everyone will not place the same value on a future payment. Consider the following example.

• If I had a choice between receiving $10 one year from now and receiving $9.50 today, and I was indifferent between the two options, we know that I consider a $10 payment one year from now to have a present value of $9.50. Restated, I consider the present value of $10 that I will receive one year from now to be $9.50.
• If a second person readily chooses to receive the $10 payment one year from now (rather than the $9.50 today), we know that this person feels the present value of the $10 one year from now is more than $9.50.
• If a third person prefers to receive the $9.50 today, we know that the third person feels the present value of $10 one year from now is less than $9.50.

Because each of us thinks differently about the four factors listed above, we will not place the same value on a future payment

Can this Difference be explained?

The extent to which a person discounts future payments depends on his or her discount rate ; that is, each individual can have a different discount rate because we have different perceptions of risk, opportunity cost, inflation, and preference to consumer now.

For example, a person concerned about risk, or who has a strong preference to consume now would likely have a high discount rate and place a relatively lower value on future payments. Likewise, someone who is concerned that future inflation will be relatively high or who has a good investment opportunity also would have a high discount rate.

Introduction to Discount Rate

A discount rate is generally stated as an annual percentage rate. For example, someone may reduce the value of a future payment by 7% for each year until the payment is received. The 7% accounts for this person’s concern about risk and inflation, the income that could be earned if the cash was available now, and the preference to consume now rather than in the future.

Even though each of us uses a different discount rate in assessing our opportunities or alternatives, we begin to demonstrate our collective assessment of the discount rate in the market place, more specifically, in the financial markets. For example, the interest rate a bank must pay to motivate you to deposit your cash in a savings account (rather than spend the cash today) is an indication of the value you place on consuming today versus consuming in the future.

research.stlouisfed.org/fred2/data/WGS10YR.txt .

Despite individuals different assessments of the future, there are some basic concepts about present value that all business persons need to understand. The process of calculating present value is such a concept.

Calculating Present Value of a Future Payment

In order to compare the value of several payments, each payment or series of payments need to be discounted to present value.

Discounting is the analytical process by which the present value of a future payment is calculated. For example, discounting allows us to calculate that $10 we are promised to receive a year from now is worth $9.50 today.

Example of Calculating Present Value of a Future Payment

The present value of a future payment can be calculated if the amount of the future payment, the time of the future payment, and the discount rate are specified. For example, an individual who expects to receive $50 twenty-one (21) months from now and who discounts future payments by 6% for each year until the payment is received can calculate the present value of that payment.

• The formula for computing the present value of a future payment is PV = FV/(1+d)^n. where:

• PV is present value,
• FV is amount of the future payment,
• d is the discount rate (expressed as a decimal), and
• n is the number of time periods until the future payment is received (although it may not be obvious on this web page, n is treated as an exponent to the factor in parenthesis)

Example. An individual will be paid $50 twenty-one (21) months from now. The individual has an annual discount rate of 6%; that is, the individual feels a payment received one year from now is only worth about 94% of what it would be worth if the payment was received today. Twenty-one months is 1.75 years; since the discount rate is expressed as an annual rate, the time period has to be measured in terms of years. Using the present value formula,