Table of contents:
- Simple and compound interest
- Development of the concept of compound interest
- The future value of the annuity
- Present value of mixed income stream
2023 Author: Henry Conors | [email protected]. Last modified: 2023-11-26 12:05
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. That's right, but only when it's not about time.
The time value of money is related to the fact that as long as there are alternative and diverse income opportunities, the value of money will always depend on the point in time when it is supposed to be received. Since there is a possibility of earning interest on the funds available, the sooner the income from the financial instrument or business is received, the better. Here, “rather” also means more often, that is, the sooner and / or with greater frequency the income is received, the better. Therefore, when making any investment decision, the concept of the change in the value of money over time, or the future value of money, should always be taken into account. In fact, this concept involves bringing to a "common denominator" money, spread over time.
Any economy in the world is subject to inflationary processes, which consist in a constant increase in prices for goods and services. Inflation rates can be catastrophic, as, for example, in Venezuela or Somalia, and in Russia in the early 1990s, but also moderate and quite comfortable for the national economy. That is, prices are constantly and steadily growing, so one ruble today can buy, albeit a little, but more than the same ruble tomorrow.
Thus, the concept of the change in the value of money over time can be approached from two different angles. 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, money lying without movement is constantly losing its value, expressed in the amount of goods and services that can be purchased with this money. In both cases, the key issue is to determine the future value of the money currently available. This is true for both businesses and individuals.
Simple and compound interest
Money is invested in various financial instruments at interest, and the profitability of any business is also measured by interest. There are two generally accepted ways to calculate interest on an invested amount. Simple interest, as their name suggests, is very easy to calculate. Usually it is an annual percentage. The amount of return for the year can be determined by taking the declared percentage of return for the year on the amount invested. Simple interestare charged 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 and the constant change in the amount on which this interest is charged. If to determine the income from simple interest it is enough to know the value of the annual interest and the period of investment, then for compound interest, the frequency of payments is added to this, as well as the fact of capitalization, that is, the addition of interest received to the principal amount of investments. Compound interest is calculated according to a formula that involves raising the interest rate to a power by the number of accruals for the entire investment period. It is for compound interest that the main calculations are carried out to assess the effectiveness of one or another investment of money.
Development of the concept of compound interest
The future value of money is nothing more than the amount to which current investments will increase over the period from their investment with compound interest to the end of the investment period. This is sometimes referred to as "accumulated value". The formula for the future value of money is completely identical to the formula for calculating compound interest:
FV (future value) – future value of money;
PV (present value) - the present value of money;
E - interest rate for one accrual period;
N - number of accrual periods.
Because this is not about a deposit in a particular bank, where the interest rate is rigidly definedthis bank, and on determining the future value of available funds, the issue of determining the interest rate is extremely important. There are many approaches to solving this issue. The main ones include:
- the average bank interest rate for a certain region, prevailing in the market at the time of investment;
- discount rate of the Central Bank of the country;
- fixed inflation rate, either for consumer goods or 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 doing an economic calculation of the future value of money, it often takes much longer to choose a rate than to discuss the forecast cash flow.
The process of determining the future value of money is connected with the inverse problem - determining the present value of money, that is, the process of discounting. It is quite obvious that in this case, the specified formula is simply converted according to mathematical rules, namely:
PV=FV / (1+ E)ⁿ
The problem of discounting arises when you need to estimate the future cash flow at the current moment, which is almost always necessary when preparing business plans and other economic calculations.
Despite sciencethe name, the concept of an annuity is just a designation for the flow of equal amounts of money that arise at regular intervals. This phenomenon is very common. Well-known examples can be cited. Receipt of wages, periodic payments for utilities, payment for a mobile phone at an unlimited rate, periodic contributions to a savings account, and so on. Cash flows can be income inflows from investments or outflows of funds invested to generate future income. In the feasibility studies of almost any project, annuity is always found.
The future value of the annuity
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 installment is also added, and interest is already charged on this amount for the next period. There is a formula for calculating, it looks a bit complicated:
FV=PV ((1+ E)ⁿ-1) / E
In practice, this formula is inconvenient, usually they use either tables with accrual factors for an annuity of one monetary unit, or, more often, built-in formulas in the EXCEL application.
An example of such a table is shown below:
The data in the above table are multipliers for determining the future value of money in an annuity. Accordingly, when it is necessary to determine the true value of money, that is, to discount the annuity, thesethe multipliers become the denominators of the respective cash flow amounts.
Present value of mixed income stream
Mixed income stream, in reality, is much more common than the classic annuity. The value of money in this flow is determined by what is called "manually". To do this, the present values of all incomes must be found and then summarized. The main practical benefit of all these calculations is to be able to compare different investment options. At the same time, a necessary condition for any investment of money is the excess of all discounted income over all discounted costs to extract these incomes.
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