# Time Value of Money (TVM)

Understand the Time Value of Money Concept

• What is the meaning of the time value of money?
• Why is a dollar worth more today than in the future?
• How is the discount rate related to the time value of money?
• How can you determine the appropriate discount rate?

## How to Calculate the Time Value of Money

In short, receiving money today is preferable (i.e. more valuable) than receiving the same amount of money on a later date.

Under the time value of money concept, a dollar received today is worth more than a dollar received at a later date — which is one of the most fundamental concepts in corporate finance.

Why is that the case?

There are two main reasons backing this theory:

1. Opportunity Cost: If you have capital on hand currently, the funds could be used to invest into other projects to achieve a higher return — i.e. the “opportunity cost” of the money.
2. Inflation: There are risks to consider such as inflation or the probability that the company in question might go bankrupt in the future — i.e. future uncertainty should be costlier than the lower risks identified on the present date.

Since money tends to decline in value across time due to factors such as inflation, the purchasing power of money also decreases.

With that said, cash flows received in the future (and with increased uncertainty) are worth less than the present value (PV) of the cash flows.

If you risk one dollar in an investment, you should reasonably expect gains of more than solely your initial one-dollar contribution as a return.

For each incremental unit of risk you take on, you should expect a proportionally higher return in exchange.

## Present Value (PV) and the Time Value of Money Example

The time value of money is the basis of the net present value (NPV) calculation.

As a brief example, let’s say that there are two investment options, as outlined below:

• In the first option, you can receive \$10,000 right now.
• In the second option, you can receive \$11,000 — but it’ll take one year in the future before the funds are received.

To pick the “right” option rationally, you must consider the time value of money, which is essentially the required rate of return (i.e. cost of capital).

In this example, \$11,000 is 10% greater than \$10,000 — this serves as the minimum required rate of return if you would be indifferent between these investment options.

For the second option to make sense from a monetary perspective, the returns should exceed that of the 1st option, i.e. if you receive the \$10,000 on the present date and receive a return >10%, you should pick the first option, as it is more profitable.

## Time Value of Money Formula

### Present Value (PV) Formula

The formula for the time value of money, from the perspective of the current date, is as follows:

PV = FV / [1 +( i / n) ^(n * t)

• PV = Present Value
• FV = Future Value
• i = Annual Rate of Return (Interest Rate)
• n = Number of Compounding Periods Each Year
• t = Number of Years

### Future Value (FV) Formula

Alternatively, to calculate the future value given the present value, the formula used is:

FV = PV * [ 1 + (i / n) ] ^ (n * t)

In both formulas, “i” represents the rate of interest on comparable investments.

## Present Value & Future Value Calculation Example

For instance, if the present value (PV) of an investment is \$10 million, and the amount is invested at a rate of return of 10% for one year, the future value (FV) is equal to:

• FV = \$10 million * [1 + (10% / 1] ^ (1 * 1) = \$11 million

Moreover, using the same formula as above, we can calculate the future value (FV) assuming quarterly compound interest — i.e. 4.0x times a year:

Thus, the calculation for our example is as follows:

• FV = \$10 million * [1 + (10% / 4)] ^(4 x 1) = \$11.04 million
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