## 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 earning potential in the interim. Because money can grow when it is invested, a delayed payment is a lost opportunity for growth. The time value of money is a core principle of finance. It is also referred to as the present discounted value.

### Key Takeaways

- The time value of money means that a sum of money is worth more now than the same sum of money in the future.
- The principle of the time value of money recognizes that money can grow in value by investing it, and a delayed investment is a lost opportunity.
- 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 and similar accounts, the number of compounding periods is an important determinant as well.
- Inflation has a negative impact on the time value of money because your purchasing power decreases as prices rise.

## Understanding the Time Value of Money (TVM)

Most investors would rather receive money today than wait to receive the same amount in the future. That's because a sum of money, once invested, can grow over time. For example, money deposited into a high-yield savings account will earn interest. Over the ensuing months and years, that interest will be added to the principal, earning even more interest. That's what's known as the power of compound interest.

In addition, if money is not invested, its value can erode over time. If you hide $1,000 in a mattress for three years, you will not only lose out on any additional money you could have earned by investing it, but it will have even less buying power than it once did because inflation will have reduced its value.

The concept of the time value of money is often attributed to Martin de Azpilcueta, a Spanish theologian and economist of the 16th century.

## Time Value of Money Formula

The basic time value of money formula doesn't calculate "TVM" itself. Instead, it shows the change in the value of money over a period of time. It calculates the future value of a sum of money based on:

- Its present value
- Interest rate
- Number of compounding periods per year
- Number of years

Based on these variables, the TVM formula is:

$\begin{aligned}&FV = PV \Big ( 1 + \frac {i}{n} \Big ) ^ {n \times t} \\&\textbf{where:} \\&FV = \text{Future value of money} \\&PV = \text{Present value of money} \\&i = \text{Interest rate} \\&n = \text{Number of compounding periods per year} \\&t = \text{Number of years}\end{aligned}$FV=PV(1+ni)n×twhere:FV=FuturevalueofmoneyPV=Presentvalueofmoneyi=Interestraten=Numberofcompoundingperiodsperyeart=Numberofyears

This allows you to see the difference between the future value and the present value. In most cases, the future value will be higher, which is why it is better to receive that money now rather than at a later date.

The TVM formula may change slightly depending on the situation. For example, in the case of annuity or perpetuity payments, the generalized formula will have additional or fewer factors.

The time value of money doesn't take into account any capital losses that you may incur or any negative interest rates that may apply. In these cases, you may be able to use negative growth ratesto calculate the time value of money

## Examples of Time Value of Money

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

$\begin{aligned}FV &= \$10,000 \times \Big ( 1 + \frac{10\%}{1} \Big ) ^ {1 \times 1} \\ &= \$11,000 \\\end{aligned}$FV=$10,000×(1+110%)1×1=$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:

$\begin{aligned}PV &= \Big [ \frac{ \$5,000 }{ \big (1 + \frac {7\%}{1} \big ) } \Big ] ^ {1 \times 1} \\&= \$4,673 \\\end{aligned}$PV=[(1+17%)$5,000]1×1=$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: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 4 } \Big ) ^ {4 \times 1} = \$11,038$FV=$10,000×(1+410%)4×1=$11,038
- Monthly Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 12 } \Big ) ^ {12 \times 1} = \$11,047$FV=$10,000×(1+1210%)12×1=$11,047
- Daily Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 365 } \Big ) ^ {365 \times 1} = \$11,052$FV=$10,000×(1+36510%)365×1=$11,052

This shows that the TVM depends not only on the interest rate and time horizon but also onhow 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 to inflation. Therefore, a sum of money that is expected to be paid in the future, no matter how confidently its payment is expected, is losing value in the meantime. There is an opportunity cost (the opportunity to invest and earn) to being paid in the future rather than in the present.

## Why Is the Time Value of Money Important?

The concept of the time value of money can help guide investment decisions. For instance, suppose a business can choose between 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 cash flow (DCF) analysis, 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.

## How Does Inflation Relate to the Time Value of Money?

The value of money changes over time and several factors can affect it. Inflation, which is the general rise in prices of goods and services, has a negative impact on the future value of money. That's because when prices rise, your money doesn't go as far. Even a slight increase in prices means that your purchasing power drops. So that dollar you earned in 2019 and kept in your piggy bank buys less today than it would have back then.

## The Bottom Line

The future value of money isn't the same as present-day dollars. And the same is true about money from the past. This phenomenon is known as the time value of money (TVM). Both businesses and individuals can use the concept to make smart investment decisions.