# Method of discounting cash flows - Securities market. Theory and practice

## Cash flow discounting method

If the yield of a deposit in a bank is chosen as an alternative when comparing yields as an alternative, the general method of alternative yield set forth coincides with the cash flow discounting method, which is widely used in financial calculations. If you use the discounted cash flow method, you need to know the following information:

• the value of the deposit rate of a commercial bank, accepted as a base,

• The scheme for calculating money in the bank (in the form of a simple or compound interest).

The answer to the first question is usually formulated as follows: "As the base, choose the rate of a reliable, stable bank". However, this statement is valid for United States conditions with a certain degree of approximation. Everyone knows examples of "reliable, stable banks" that failed to withstand the crisis and went bankrupt. Sometimes considered as a base level is the refinancing rate of the US Central Bank. However, this choice also raises objections due to the fact that the value of this indicator is not formed by the market, but is used by the US Central Bank to influence the market. However, the fact that, when solving many problems, the value of the bank rate, which should be taken as the base, is one of the conditions of the problem comes to the aid.

The second question is easier to answer: consider both cases, i.e. accrual of interest income on a simple and at a difficult interest rate. However, as a rule, preference is given to the scheme for calculating interest income on a compound interest rate. Recall that in the case of accrual of funds under the simple interest income scheme, it is accrued on the principal amount of money deposited on the deposit account with the bank. When calculating cash according to the scheme of a compound interest, the income is calculated both for the initial amount and for the accrued interest income. In the second case, it is assumed that the investor does not withdraw the principal deposit amount and interest thereon from the bank account. As a result, this operation is more risky. However, it also brings in more income, which is an additional payment for greater risk.

For a method of numerical estimation of the parameters of operations with securities based on the discounting of cash flows, we introduce our own conceptual apparatus and our own terminology, which are described below.

Increment and discounting. Different options for investment attachments have different payment schedules, which makes it difficult to directly compare them. Therefore, it is necessary to bring cash receipts to one point in time. If this moment is in the future, then this procedure is called increment, if in the past - by discounting.

The future value of money. The money that the investor currently has at the moment gives him the opportunity to increase his capital by placing it on a deposit with the bank. As a result, in the future, the investor will have a large amount of money, which is called the future value of money. In the case of accrual of bank interest income under the simple interest scheme, the future value of money is equal to

For a compound interest scheme, this expression takes the form

where P F is the future value of money;

P C - the initial amount of money (the current value of money);

β - bank deposit rate;

n - the number of periods of accrual of cash income.

The coefficients (1+ β) n for a compound interest rate and (1 + n β) for a simple interest rate are called build factors.

The original value of money. In case of discounting, the reverse task is worthwhile. We know the amount of money that we expect to receive in the future, and we need to determine how much money we need to invest at present to have a given amount in the future, that is, in other words, we need to calculate

where the factor is called the discount factor. Obviously, this expression is valid for the case of deposit accrual according to the scheme of a compound interest income.

Internal rate of return. This rate is the result of solving a problem in which the present value of investments and their future value are known, and the unknown value is the deposit interest rate of bank interest income, at which certain investments in the present will provide a given value in the future. The internal rate of return is calculated using the formula

Discounting of cash flows. Cash flows are the incomes received at different times by investors from investments in the monetary form. Discounting, which is a reduction of the future value of investments to their current value, allows you to compare the different types of investments made at different times and on different conditions.

Consider the case when a financial instrument brings an income equal to C0 at the initial moment of time, for the period of the first interest payments - C1, the second - C 2, ..., for the period n - x interest payments - C n. Total revenue from this operation will be

Discounting this scheme of cash receipts to the initial point in time will give the following expression for calculating the value of the current market value of a financial instrument:

(15)

Annuities. In the case when all payments are equal to each other, the above formula is simplified and takes the form

If these regular payments are received annually, they are called annuities. The value of the annuity is calculated as

At present, this term is often applied to all the same regular payments regardless of their periodicity.

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