Introduction and Review of Simple Concepts

One of the most basic concepts of finance is “time value of money”. Dollars, like quantities in physics, also have a measure of units other than the magnitude measure. This unit measure is the time at which the magnitude of money is available to you to be used. Financial markets offer investors the opportunity to invest their money rather than “keeping it idle”. If you have a certain amount of money, for example $1000, that you do not need now but only in a year, this money can be invested for a year. In most of this book we are concerned with risk-less investments, which means that there are no uncertainties about the return of the investment. It is fixed at the time the investment is made, and the likelihood that it will not be realized as promised is zero. While we shall touch on the meaning of “risk-free” investment in the next section, for now let us just take it for granted. The existence of such risk-free investment possibilities introduces the second dimension (unit) of monies, which is time. Assume that one can get r for each dollar invested for a year. If r for example is 10%, then $1000 today will grow to be 1000(1.10) or in general to 1000+1000r. Therefore $1000 today is not equivalent to $1000 a year from today. If one needs $1000 in a year, one only needs to have 1000(1+r)−1. Given 1000(1+r)−1 today and investing it for a year generates [1000(1+r)−1](1+r) = 1000 which is the required amount. We see therefore that $X in a year is equivalent to today. is termed the present value of X. Similarly Y dollars today is equivalent to Y(1+r) in a year and the latter is termed the future value of Y. The conversion of dollars of a year from now to dollars of today is done by multiplying by (1+r)−1, which is termed a discount factor. It is usually denoted by d with a sub index of the time. It is a discount factor for a year from now and will be denoted by d1. The future value of a dollar in a year can thus be written also as .