Principles of Finance/Section 1/Chapter 2/Time Value of Money/Introduction

Introduction
The time value of money is the premise that a fixed amount of money available today is more valuable/desired than the same amount of money available in the future. This premise can be generalized for economic resources (of which money is an embodiment by social contract). We can state two reasons to justify the premise for all resources: 1) We prefer to have in our control a resource today rather than in the future, because of the inherent uncertainty that characterizes any future event. We cannot be certain that we will acquire the resource in the future. 2) We prefer to have in our control a resource today rather than in the future, because we could use to our favor this resource in the meantime (this is a temporal version of the notion of "opportunity cost").

Especially for money, there is a third reason, namely the existence of inflation: given inflation, the same amount of money will buy tomorrow fewer goods than today. It must be noted however that while Uncertainty of the Future and Opportunity Cost, are rooted in the very foundations of human existence, inflation is a historical event that may change direction. In the case of "negative inflation", ie where money increases rather than loses its value as time passes, then "money tomorrow" tends to be more valuable than "money today" (or at least, it partially offsets the pull of the other two fundamental reasons given above towards the opposite direction). Nevertheless, in modern market economies, a consistent trend of negative inflation is absent for almost a century.

A fourth reason is the belief that maybe the money might not be around in the future. The borrower might not be around or the repayment contract could be lost. The currency could be abolished or a catastrophy could occur rendering money valueless.

The Discount Rate
The time value of money can be easily quantified at a personal level. A person can ask herself, "What do I prefer, 100 euros today or XXX euros in a year from now?" When she finds the amount that makes her "indifferent", then she can calculate easily her Personal Discount Rate. Assume that given the question, "100 euros now or 120 euros in one year from now," a person replies, "it's all the same to me". Then this person's Yearly Personal Discount Rate (YPDR) is calculated as

$$ YPDR = (120/100)-1 = 1,2 - 1 = 0,2 = 20%$$

and in general terms

YPDR = (Equally preferred value in a year / Value today)-1

Note that YPDR quantifies together the effects of all the reasons given above that lead to "money tomorrow" being worth less than "money today".

If a person has calculated his own YPDR honestly, carefully, and rationally, and has tested it over a period of time for stability of preferences, he can then use it as a tool to assist him in taking economic decisions that involve different amounts and timings of money (to be given or to be received). Essentially, by using the discount rate, we can calculate what amount of money received or given today is -for us- equivalent with an amount of money to be received (or to be given) in the future.