When approaching money, a simple arithmetic and seemingly logical approach does not always work. It would seem that if one is equal to one, then one ruble is equal to one ruble always and everywhere. This is correct, but only when it is not about time.
Concept
The value of money in time is due to the fact that as long as there are alternative and diverse ways to generate income, the value of money will always depend on the point in time when it is supposed to be received. Since it is possible to obtain interest on available funds, the sooner the income from a financial instrument or business arrives, the better. Here, “sooner” also means more often, that is, the sooner and / or with greater frequency the income arrives, the better. Therefore, when making any investment decisions, the concept of the change in the value of money over time, or the future value of money, should be constantly taken into account. In fact, this concept involves bringing to a “common denominator” of money spaced in time.
Inflation
Any economy in the world is subject to inflationary processes, which consist in a constant increase in prices for goods and services. Inflation can be catastrophic, as, for example, in Venezuela or Somalia, and in Russia in the early 90s, but also moderate and quite comfortable for the national economy. That is, prices are constantly and steadily rising, so for one ruble today you can buy, albeit a little, but more than for the same ruble tomorrow.
Thus, the concept of changing the value of money over time can be approached from two different sides. On the one hand, today's money can be invested at interest and generate income. That is, there is an increase in lost profits. On the other hand, non-moving funds constantly lose their value, expressed in the amount of goods and services that can be purchased with this money. In both cases, the key issue is determining the future value of the money currently available. This is true for both business and individuals.
Simple and compound interest
Investing in various financial instruments is carried out at interest, while interest also measures the profitability of any business. There are two generally accepted methods for calculating interest on an invested amount. Simple percentages, as their name implies, are calculated very simply. Usually we are talking about annual interest. The amount of income for the year can be determined by taking the announced percentage of return for the year from the invested amount. Simple interest is accrued on savings certificates, coupon income of bonds, on certain types of bank deposits and in a number of other cases. The difference between compound interest and simple interest lies in the frequency of interest accrual and the constant change in the amount at which these interest accrues. If in order to determine income from simple interest it is enough to know the value of the annual interest and the investment period, then for compound interest, the periodicity of payments, as well as the fact of capitalization, that is, the addition of the received interest to the main amount of investments is added to this. Compound interest is calculated according to a formula providing for raising the interest rate to the amount of charges for the entire investment period. It is for compound interest that basic calculations are made to evaluate the effectiveness of one or another investment of money.
The development of the concept of compound interest
The future value of money is nothing but the amount to which current investments will increase over the period from their investment with the accrual of compound interest until the end of the investment term. This is sometimes called “value added.” The formula for the future value of money is completely identical to the formula for calculating compound interest:
FV = PV * (1+ E) ⁿ
FV (future value) - the future value of money;
PV (present value) - the true value of money;
E - interest rate for one accrual period;
N is the number of accrual periods.
Since this is not about a contribution to a particular bank, where the interest rate is strictly determined by that bank, but about determining the future value of available cash, it is extremely important to determine the interest rate. There are many approaches to solving this issue. The main ones include:
- the average bank interest rate for a particular region, prevailing in the market at the time of investment;
- the discount rate of the Central Bank of the country;
- a fixed inflation rate, either for consumer goods or for industrial prices, depending on the object;
- forecast inflation rates approved by the Ministry of Economic Development;
- LIBOR rates increased by country risk when settlements are made for foreign partners.
When conducting an economic calculation of the future value of money, often, choosing a rate takes much longer than discussing the forecast cash flow.
Discounting
The process of determining the future value of money is associated with the inverse problem of determining the true value of money, that is, the discounting process. It is completely obvious that in this case the indicated formula is simply converted according to mathematical rules, namely:
PV = FV / (1+ E) ⁿ
The discount task arises when it is necessary to evaluate the future cash flow at the current moment, which is almost always necessary when preparing business plans and other economic calculations.
Annuity
Despite the sci-fi name, the concept of annuity is just a designation of the flow of equal amounts of cash arising at regular intervals. This phenomenon is very common. Well-known examples may be given. Salary, periodic payments for utilities, payment of a mobile phone at an unlimited rate, periodic contributions to a savings account and so on. Cash flows can be cash inflows received from investing, or cash outflows invested in order to obtain future income. In feasibility studies of almost any project, annuity is always found.
The future value of an annuity
The calculation of the future or present value of money in an annuity differs little from the calculation of compound interest already described. Just for each interim period, in addition to interest, a periodic contribution is also added, and interest on the next period is already calculated on this amount. There is a formula for calculating, it looks a little complicated:
FV = PV * ((1+ E) ⁿ-1) / E
In practice, this formula is inconvenient, usually they use either tables with accumulation factors for an annuity of one monetary unit, or, what is more common, built-in formulas in the EXCEL application.
An example of such a table is given below:
The data in the table are factors for determining the future value of money in an annuity. Accordingly, when it is necessary to determine the real value of money, that is, to discount the annuity, these factors become the denominators of the corresponding amounts of cash flow.
