Present and Future Value of Money

Inflation is defined as the overall rise in the price of goods and services in an economy. To avoid losing value to inflation, businesses have two options:

·         Capitalize – Businesses can spend their cash on purchasing additional assets such as machinery, supplies, personnel, etc.

·         Invest – Businesses can invest their cash. This gives businesses the opportunity to make their money worth more, tomorrow, by allowing it to earn interest. The time value of money concept means the money that your organization has in hand today can be put to work earning interest, once invested.

If you have a present value (PV) of money invested, you can calculate its accumulated interest to determine its future value at some later date. To make this calculation, however, you must provide two pieces of information in addition to the investment's present value:

·         The interest rate (i) per compounding period. The interest rate, a percentage, is sometimes called the rate of return (r).

·         The number of compounding periods (N) over the life of the investment.

There are presently two types of interest:

·         simple interest

·         compound interest

Simple interest

This is where the bank or lending institution, in exchange for the use of your money, periodically pays you a percentage of the initial investment amount.

For example, assume you deposit $100 in the bank and earn 5% interest each year. Assume too that the bank pays only simple interest, or interest on the $100 principal only. At the end of year 1 you would have $100 plus $5 = $105. At the end of year 2 you would have $110, and so on.

Compound interest

This is interest added to the account at the end of each compounding period. Then, at the end of the next compounding period, the bank pays interest both on the original deposit (the principal) and on the interest accumulated from the prior period. For example, assume you deposit $100 in a bank that pays 5% interest and compounds it annually. At the end of year 1, you would have the same $105 as in the previous example. However, at the end of year 2, you would have $105 plus $5.25 = $110.25.

Calculating future value

In order to effectively implement the time value of money concept, managers must be able to recognize the variables used to calculate the relationship between the present value (PV) and the future value (FV) of money.

The formula for calculating the future value (FV) of money reads as follows: FV=PV(1+i)^N

The variables expressed in this equation are:

·         PV = present value of money at hand currently

·         i = interest rate per compounding period, otherwise known as the rate of return

·         N = number of compounding periods over the life of the investment

For example, assume you are team leader of one of your company's key support services. As a result of effective budget planning, you have invested a $10,000 surplus into an account that will earn 4% interest, compounded twice a year for the period of 3 years total. To calculate by how much the investment would grow by the end of the third year, you need to follow several steps.

·         (1+i) – The interest rate (i) per compounding period is usually expressed as an annual percentage. If your 4% interest is compounded annually, i=.04. If your 4% interest is compounded twice a year, as is the case here, the interest rate per period is 4%/2 or .04/2. In other words, i=.02.

·         (1+i)^N – To find N, you multiply the number of years of the investment by the number of times per year that interest is compounded. If interest is compounded annually, N is simply the number of years of the investment. If interest is compounded twice a year, N is the number of years (3) times 2 (N=6).

·         PV(1+i)^N – Applying the formula, FV=PV(1+i)^N, where we've determined that PV=10,000, i=.02, and N=6, we get, FV=10,000 (1+.02)^6. Simplified (and rounded out to the nearest one hundredth), FV=10,000 (1.13) or $11,300.

This example demonstrates that the key to solving for the future value of money, FV, is to perform the calculation in three progressive steps: (1+i)?(1+i)^N?PV(1+i)^N

If you know the present value of money, the number of compounding periods, and the interest rate, you can calculate the future value of money using the formula FV=PV(1+i)^N.