Understanding the Time Value of Money

The time value of money is an important concept in finance that describes how money increases in value over time as a result of interest rates. If I receive one euro today, I can put it in the bank and it will earn me more than one euro in the future. The difference between the amount in my bank account in the future and the value invested today, plus interest, is called the time value of money. In other words, a euro today is worth more than a euro in the future, because money can be invested and earn interest over time. Obviously, a bank account is just one example of an investment but it can easily be generalised to other situations.

What is the time value of money?

The time value of money is an important concept that can be used to calculate the future value of an investment or to determine the present value of future cash flows. It is therefore essential to discount future cash flows. Investors and financial analysts often use tools such as net present value (NPV) and internal rate of return (IRR) to factor the time value of money into their analysis.

For example, if you expect to receive €1,000 in a year's time, this sum is not worth as much as €1,000 today because I could invest the latter. As the value of receiving €1 in the future is less than receiving €1 today, we need to discount the €1,000 to be received in the future to take account of interest rates and therefore the time value of money. Using an interest rate of 5%, the present value of this sum will be €952.38 today. In other words, if I invest €952.38 in a bank account today and the bank promises me an interest rate of 5%, after 1 year I will have €1,000 in my account.

How do you calculate the time value of money?

Calculating the time value of money is a key concept in finance. It is used to determine the present value of an amount of money that will be received or paid at a future date. The present value that incorporates the time value of money depends, among other things, on inflation, interest rates and other economic factors.

Mathematically, in order to discount, we need a discount rate. An interest rate is an example of a discount rate or an opportunity cost of capital. An opportunity cost of capital is defined as the expected return on another investment with the same risk over a comparable time horizon. If I invest my money in one project, I cannot invest it in another. I therefore forego the expected return on that other project. Giving up this return is therefore a cost called the opportunity cost of capital.

The formula for the present value of a future cash flow based on a discount rate is as follows:

VA = [F / (1 + r)^n]

where :

• PV: present value of a future cash flow
• F: future cash flow
• r: discount rate or opportunity cost of capital
• n: number of years before the future cash flow is received or paid

For example, if you have a future cash flow of €1,000 that will be received in three years' time, and the discount rate is 5%, the PV will be calculated as follows:

VA = [1,000 / (1 + 0.05)^3] = €863.8

The present value of this future cash flow is €863.8, taking into account the time value of money. This present value is much smaller than the value of the future cash flow.

In a nutshell, the time value of money is a key concept in finance that enables the present value of a future amount to be determined. This concept is the basis for valuing projects, shares, bonds and companies in general.

These fundamental points will be covered in our training course in investment criteria and decisions.