# Time Value of Money (TVM)

Time value of money is the concept that the value of a dollar to be received in future is less than the value of a dollar on hand today. One reason is that money received today can be invested thus generating more money. Another reason is that when a person opts to receive a sum of money in future rather than today, he is effectively lending the money and there are risks involved in lending such as default risk and inflation. Default risk arises when the borrower does not pay the money back to the lender. Inflation is the decrease in purchasing power of money due to a general increase level of overall price level.

## Present value

When a future payment or series of payments are discounted at the given interest rate to the present date to reflect the time value of money, the resulting value is called present value.

For example, if you have to pay \$1,000 in one year and the bank offers an annual percentage rate of 10% on any money that you deposit, you must deposit at least \$909.1 (=\$1,000/(1+10%)) today. This is the present value of \$1,000 payment to be made in one year.

Present value of an annuity finds out the present value of a series of equal cash flows that occur after equal period of time. The present value of annuity further depends on whether it is an (ordinary) annuity or an annuity due.

## Future value

Future value is amount that is obtained by enhancing the value of a present payment or a series of payments at the given interest rate to reflect the time value of money.

Let us that you deposit \$909.1 in a bank today which pays 10% annual percentage rate. Your account would grow to \$1,000 (=\$909.1 × (1 + 10%)) by the end of first year. This is the future value.

Future value of an annuity equals the accumulated value at a future date of a series of equal equidistant payments/receipts.

## Interest

Interest is charge against use of money paid by the borrower to the lender in addition to the actual money lent. The amount of interest depends on whether there is simple interest or compound interest. In simple interest, there is no interest on interest but in compound interest, interest is calculated on both principal and interest already earned. It also depends on whether we are working with an interest rate or a discount rate.

## Time value of money relationships

In any time value of money relationship, there are following components:

• A value today called present value (PV),
• A value at some future date called future value (FV),
• Number of time periods between the PV and FV, referred to as n,
• Annual percentage interest rate labeled as r,
• Number of compounding periods per year, m,
• An annuity payment (only case of annuities), PMT.

If the interest rate is high, time duration is longer and compounding periods are more frequent, the present value is lower and vice versa.

 PV↑ if FV↑ n↓ m↓ r↓

Similarly, future value of a single sum or an annuity is high when the interest rate is high, time duration is longer, compounding is more frequent, and vice versa.

 FV↑ if PV↑ n↑ m↑ r↑

## Application of time value of money principle

Time value of money is one of the most fundamental phenomenon in finance. It is underlying theme embodies in financial concepts such as:

It is the basis used to work out the intrinsic value of a firm, a share of common stock, a bond or any other financial instrument.

by Irfanullah Jan, ACCA and last modified on

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