## What Is the Time Value of Money (TVM)?

The time value of money (TVM) is the concept that a sum of money is worth more now than the same sum will be at a future date due to its earnings potential in the interim.

This is a core principle of finance. A sum of money in the hand has greater value than the same sum to be paid in the future.

Time value of money is also referred to as present discounted value.

• Time value of money means that a sum of money is worth more now than the same sum of money in the future.
• This is because money can grow only through investing. An investment delayed is an opportunity lost.
• The formula for computing the time value of money considers the amount of money, its future value, the amount it can earn, and the time frame.
• For savings accounts, the number of compounding periods is an important determinant as well.

## Understanding the Time Value of Money (TVM)

Investors prefer to receive money today rather than the same amount of money in the future because a sum of money, once invested, grows over time. For example, money deposited into a savings account earns interest. Over time, the interest is added to the principal, earning more interest. Thats the power of compounding interest.

If it is not invested, the value of the money erodes over time. If you hide \$1,000 in a mattress for three years, you will lose the additional money it could have earned over that time if invested. It will have even less buying power when you retrieve it because inflation has reduced its value.

As another example, say you have the option of receiving \$10,000 now or \$10,000 two years from now. Despite the equal face value, \$10,000 today has more value and utility than it will two years from now due to the opportunity costs associated with the delay.

In other words, a payment delayed is an opportunity missed.

## Formula for Time Value of Money

Depending on the exact situation, the formula for the time value of money may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or fewer factors. But in general, the most fundamental TVM formula takes into account the following variables:

• FV = Future value of money
• PV = Present value of money
• i = interest rate
• n = number of compounding periods per year
• t = number of years

Based on these variables, the formula for TVM is:

FV = PV x [ 1 + (i / n) ] (n x t)

## Time Value of Money Examples

Assume a sum of \$10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:

FV = \$10,000 x [1 + (10% / 1)] ^ (1 x 1) = \$11,000

The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the present day dollar amount compounded annually at 7% interest that would be worth \$5,000 one year from today is:

PV = \$5,000 / [1 + (7% / 1)] ^ (1 x 1) = \$4,673

### Effect of Compounding Periods on Future Value

The number of compounding periods has a dramatic effect on the TVM calculations. Taking the \$10,000 example above, if the number of compounding periods is increased to quarterly, monthly, or daily, the ending future value calculations are:

• Quarterly Compounding: FV = \$10,000 x [1 + (10% / 4)] ^ (4 x 1) = \$11,038
• Monthly Compounding: FV = \$10,000 x [1 + (10% / 12)] ^ (12 x 1) = \$11,047
• Daily Compounding: FV = \$10,000 x [1 + (10% / 365)] ^ (365 x 1) = \$11,052

This shows TVM depends not only on interest rate and time horizon, but also on how many times the compounding calculations are computed each year.

## How Does the Time Value of Money Relate to Opportunity Cost?

Opportunity cost is key to the concept of the time value of money. Money can grow only if it is invested over time and earns a positive return.

Money that is not invested loses value over time. Therefore, a sum of money that is expected to be paid in the future, no matter how confidently it is expected, is losing value in the meantime.

## Why Is the Time Value of Money Important?

The concept of the time value of money can help guide investment decisions.

For instance, suppose an investor can choose between two projects: Project A and Project B. They are identical except that Project A promises a \$1 million cash payout in year one, whereas Project B offers a \$1 million cash payout in year five.

The payouts are not equal. The \$1 million payout received after one year has a higher present value than the \$1 million payout after five years.

## How Is the Time Value of Money Used in Finance?

it would be hard to find a single area of finance where the time value of money does not influence the decision-making process.

The time value of money is the central concept in discounted cashflow analysis (DCF), which is one of the most popular and influential methods for valuing investment opportunities.

It is also an integral part of financial planning and risk management activities. Pension fund managers, for instance, consider the time value of money to ensure that their account holders will receive adequate funds in retirement.

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