Acc 306- Mathematics for Accounting

Chapter 1 Accumulation and Discounting 1.1. Time Factor in Quantitative Analysis of Financial Transactions The basic elements of financial models is time and money. In essence, financial models reflect one extent or another the quantitative relations between sums of money referring to various time points. The fact that with time the cost or, better to say, the value of money changes now due to constant inflation, is obvious to everyone. The ruble today and the ruble tomorrow, in a week, month or year – are different things. Perhaps, it is less obvious, at least not for an economist, that even without inflation, the time factor nevertheless influences the value of money. Let us assume that possessing a ―free‖ sum you decide to place it for a time deposit in a bank at a certain interest. In time, the sum on your bank account increases, and at the term-end, under favourable conditions, you will get a higher amount of money than you placed initially. Instead of the deposit, you could buy shares or bonds of a company that can also bring you a certain profit after some time. Thus, also, in this case, the sum invested initially turns into a larger amount after some time period. Of course, you may choose to not undertake anything and simply keep the money at home or at a bank safe. In this case, their sum will not change. The real cost will not change either unless there is inflation. In another case, it will certainly decrease. However, having at least and in principle an opportunity to invest and not doing it is, from the economist’s point of view, irrational and you have quite a real loss in the economic sense. This loss bears the title of implicit cost or loss of profit. Therefore, the naïve point of view differs from the economic one. When counting (in absence of inflation) the amount of money that is kept in the safe and does not lose its cost, you, from the economist’s point of view, are mistaken. In this case, the value of money will also change over time. By all means, the ―economic‖ approach implies the presence of some mechanisms for ―managing the cost‖ of money. In the present society, it is realized through the presence of investment, in particular, the financial, markets. Banks, insurance companies, investment funds, and broker’s companies make a wide spectrum of assets whose purchase leads (often but not always) to an increase in the value of the invested capital. Accumulation of the invested capital value starts a ―process of transformation‖ of the value of money in time. Hence, the ruble invested today turns into two rubles in a few years; on the other hand, the future amounts have a lower cost from the point of view of the current (today’s) moment at least because, in order to acquire them in the future, it is sufficient to invest a smaller amount today