Present Value and Future Value of Money

Value of Money Depends Upon Time

In the previous article we learned about the concept of nominal and real values of money. We realized that money today is more valuable than the same sum received at a future date because there is no risk involved in obtaining it and also the real value of money is not expected to decrease by the time we receive it.

The simple implication of this is that we cannot compare the dollars we have on hand today to the dollars that we have been promised at a future date. In corporate finance, we call the value of money that we have on hand today the present value and the value of amount of money that we will receive at a future date the future value of money.

In corporate finance, we may often come across complex schedules of payments and receipts. Sometimes cash may have to be paid today while sometimes we may have to pay it at a later date. Similarly the receipts may be today or at a later date. Hence, to calculate, we must first convert all the values to present values. This article will explain how to do so with the help of an example:

Calculating Future Values

Let’s understand the future values calculation with the help of an example. Let’s say that we have $1000 today and we have calculated that our cost of capital is 10%. This 10% reflects both the expectation of inflation i.e. fall in the real value of money as well as the risk involved in this investment. Let’s consider that we have to invest this money for a period of 3 years.

The formula for calculating the future values is as follows:

Future Value = Present Value (1 + (cost of capital / 100)^{number of years}

i.e. Future Value = $ 1000(1.10)³

i.e. Future Value = $ 1331

This means that the equivalent sum of money that we should expect in 3 years, given our cost of capital is $1331. This means that we should accept proposals where future value is more than $1331, reject proposals where future value is less than $1331 and be indifferent towards proposals where future value is equal to $1331.

From henceforth, we will refer to this by stating that the future value of $1000, at our given cost of capital, for a period of 3 years is $1331. Also, it must be noted that future values are nominal in nature.

Present Values

Present values are the exact opposite of future values. During future values we were compounding a present value at a given rate to reach a future value. But in present value calculations, we will discount the future values, which are nominal in nature, at the given cost of capital for the given period to reach the present value. Let’s look at it with the help of an example.

Now, we have a proposal that offers to pay us $1000, 3 years from hence. Our given cost of capital is 10%.

The formula for calculating the present values is as follows:

Present Value = Future Value / (1 + (cost of capital / 100)^{number of years}

i.e. Present Value = $1000 / (1.10)³

i.e. Present Value = $ 751.31

This means that the equivalent sum of money that we should expect today, given our cost of capital is $751.31. This means that we should accept proposals where present value is more than $751.31, reject proposals where present value is less than $751.31 and be indifferent towards proposals where future value is equal to $751.31.

When the term present value is used, finance professionals are referring to the discounted present day values which are equivalent to nominal future values.

The concept of present values and future values form the basis of corporate finance. Hence, it is essential that any student be well versed with these concepts. Variations of these concepts will be regularly used throughout the corporate finance course and hence due attention must be paid to mastering this concept before moving forward.