# Time value of money

## 12. what is the temporary value of money?

The term «interest» is used to designate the rental cost for the use of money. It can also be used to represent the percentage earned on an investment in a productive operation. From the lender’s point of view, the interest rate is the ratio between the profit received and the investment over a period of time, which is a contribution to the risk of loss, administrative expenses and pure gain or profit. From the borrower’s point of view, the interest rate can be expressed as the ratio between the amount paid for the use of funds and the amount of funds requested. In this case, the interest to be paid must be less than the expected profit.

Since money can yield a profit at a certain rate of interest through its investment over a period of time, it is important to recognize that a unit of money received at some future date does not yield as much profit as that unit of money does in the present. It is this relationship between interest and time that leads to the concept of the «time value of money».

## Introduction to the time value of money

Understanding the relationship between the time value of money and time is fundamental when it comes to investing. Most of our financial decisions are strongly influenced by this relationship and we must avoid confusion and misunderstandings. Below we analyze the concept of the time value of money, understanding the ideas underlying the calculations to clarify concepts.

With these two ideas clear we will look at the two basic techniques used in any financial calculation involving a time horizon: compound interest, also called compound annual growth, and the process for calculating present value.

Compound interest involves thinking about the value of money in the future. It consists of determining the future value of an investment made in the present, taking into account a series of possible periodic contributions.

Calculating present value involves thinking about the value of money back in time. It consists of determining the present value of an amount of money that will be received in the future, taking into account a series of possible periodic contributions. The present value is determined by applying a discount rate (opportunity cost) to the money that will be received in the future.

### The power of compound interest and the key to generating wealth

There are numerous concepts that revolve around the time value of money, including present value, future value, amortization and opportunity costs. These concepts are extremely important in analyzing and managing investment opportunities. By using various time value of money concepts, a person can effectively compare various investment opportunities. The premise of these concepts is to determine whether a series of payments over an extended period of time in the future is more valuable than a lump sum today.

Present value is one of the most popular time value of money concepts. When analyzing an income stream, calculating present value allows a person to determine how much a future payment would be worth today. Many factors must be considered when calculating present value, including the interest rate and the length of time before the future payment is completed.

Calculating the internal rate of return (IRR) on an investment is another formula that is based on the concepts of the time value of money. This calculation is performed to determine the compound average annual rate of return on a particular investment. Analyzing internal rates of return can help investors determine whether certain investments will produce returns that are greater than the cost of capital used to make the investments.

### The disappearance of the time value of money (e1415)

We begin this chapter by analyzing, basically, the two dynamic methods most commonly used for the selection of investment projects: the net present value (NPV) and the internal rate of return (IRR). There are, however, others of a static nature, i.e., which do not take into account the time factor when valuing the cash flows that could derive from the investment (both collections and payments), such as net cash flows (without updating them in the time in which they occur) and the so-called pay back or investment recovery period. We do not consider these static methods here, both because of their simplicity with respect to the necessary mathematical calculations (additions and subtractions of collections and payments), and because of their limitations, since they do not incorporate the time value of money, a fundamental pillar of any valuation concerning both investment projects and financial operations in general.

The present value of an amount receivable or payable in the future is the conversion to today’s euros of these amounts in future euros. Therefore, what is involved is to transfer, at the present time (t0), a certain amount in monetary units of the future time (t1, t2,…, tn).