## Blog entry by Karim Mansour

Anyone in the world

Relevant to the following CISI qualifications: ICWIM, ICAWM, Securities, Risk in Financial Services

### DEFINITION

The time value of money is based on the premise that most people would choose to receive, say, $10,000 now, rather than the same sum in five years’ time. Why? Firstly, because any rational person knows that the$10,000 will almost certainly buy you less in five years’ time than it will today. Secondly, there is no certainty that you will actually receive the money five years from now. As the proverb says, a bird in the hand is worth two in the bush.

Businesses use time-value-of-money formulae to make rational decisions on future expectations.

Discounting allows us to understand what we would need to invest today if we wanted to receive a certain amount in the future. Compounding helps us to calculate the sum that we will receive in the future if we invest a certain amount today.

Several other equations can be used to calculate loans, mortgages, the future values of annuities, etc. These equations are frequently combined for particular uses. For example, bonds can be readily priced using these equations. A typical coupon bond is composed of two types of payment: a stream of coupon payments similar to an annuity, and a lump-sum return of capital when the bond matures—that is, a future payment. The two  formulae can be combined to determine the present value of the bond.

For an annuity that makes one payment per year, there is an annual interest rate. However, the time frame in years must be converted into the number of periods consistent with the compounding frequency of the rate. For an income or payment stream with a different payment schedule, the interest rate must be converted into the relevant periodic interest rate. For example, if a mortgage requires monthly payments, the interest rate has to be divided by twelve.

The rate of return in these calculations can be either the variable solved or a predefined variable that measures a discount rate, interest, inflation, rate of return, cost of equity, cost of debt, or any number of similar concepts. The choice of the suitable rate is vital to the exercise, and the use of an incorrect discount rate will make the results worthless.

For calculations involving annuities, you must decide whether the payments are made at the end of each period (i.e. ordinary annuity) or at the beginning of each period (i.e. annuity due).

Most formulae are available on financial calculators or can be set up on a spreadsheet.

Time-value-of-money formulae are generally easy to understand and are widely used.

• The data used by the formulae are readily available.

• Discounting tells us what we would need to invest today if we wanted to receive a certain amount in the future.

• Compounding helps us to calculate the sum that we will receive in the future if we invest a certain amount today.

• It can often be difficult to identify the appropriate formula without expert help.

• The data on which the initial investment was made often change over the lifetime of the investment.

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