Understanding the time value of money

What is the time value of money for?

The time value of money is an important concept that will make it possible to calculate the future value of an investment or to determine the value today (the present value) of future flows. It is therefore imperative to discount future flows. Investors and financial analysts often use tools such as net present value (NPV) and the internal rate of return (IRR) to take the time value of money into account in their analysis.

For example, if you expect to receive 1,000 € in a year, this sum is not worth as much as 1,000 € today because I could invest the latter. As the value of receiving 1 euro in the future is lower than receiving 1 euro today, the 1,000 € to be received in the future must be discounted in order to take account of interest rates and therefore of 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 € today in a bank account and the bank promises me an interest rate of 5%, I will have, after 1 year, 1,000 euros in my account.

How to calculate the time value of money?

Calculating the time value of money is a key concept in finance that makes it possible 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, also called an opportunity cost of capital. An opportunity cost of capital is defined as the expected return for another investment of the same risk over a comparable horizon. If I invest my money in one project, I cannot invest it in another project. I therefore forgo receiving the return expected from that other project. Forgoing this return is therefore a cost called an opportunity cost of capital.

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

PV = [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, and the discount rate is 5%, the PV will be calculated as follows:

PV = [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 flow.

In summary, the time value of money is a key concept in finance that makes it possible to determine the present value of a future amount. This concept is the basis of the valuation of projects, shares, bonds or companies in general.

What are the risks if the time value of money is wrongly assessed?

-> An incorrect estimate of the present value of future cash flows: when assessing an investment project, it is essential to take into account all future cash flows, whether positive or negative. If the time value of money is not taken into account, the present value of future cash flows will be wrongly estimated, which can lead to inappropriate investment decisions.

-> An overestimation of the project's profitability: if the time value of money is not taken into account, it is possible to overestimate the profitability of a project. Indeed, not taking the time value of money into account implies that a euro in the future is also worth a euro today. There will therefore be an overestimation of the present value of future cash flows and therefore of the project's profitability.

These fundamental points will be addressed in particular in our training on investment criteria and decisions.