# Present Value and Future Value

Money invested in income producing assets can grow exponentially over time. The time value of money is the relationship between the present value of a dollar and its future value. This relationship is represented as an interest rate.

Related Post: Time Value of Money

Here is an example to explore the concept.

$100 invested for one year, earning 5% interest, will be worth $105 after one year; therefore, $100 paid now and $105 paid exactly one year later both have the same value to a recipient who expects 5% return. That is, $100 invested for one year at 5% interest has a future value of $105. This assumes that inflation is zero percent.

The equation in this case would look like this:

$105 = $100 * (1+.05)

The general formula for solving for future value is

FV = PV * (1+r)

Where

FV is future value

PV is present value, and

r is the interest rate

The reciprocal formula to solve for present value juggles the terms using basic algebra and restates the relationship as:

PV = FV/(1+r)

It simply puts the (1+r) term on the other side of the equation to solve for PV by dividing both sides by (1+r). If this is confusing just replace (1+r) by the term X for the moment.

FV = PV * X

If you divide both sides by X you get:

FV/X = PV * X/X

Since the term X/X is equal to one, the term goes away on that side of the equation. So we are left with

FV/X = PV

Now replace the X with (1+r) and you see the derivation of our equation.

Take a moment to make sure you really understand this because it is the basis of project finance and asset valuation. This is the formula we use to calculate future cash flows as a present value.

This concept is used to calculate the value today of a projected stream of income in the future. In this case, annual cash flows are discounted and then added together and the sum is the present value of the entire income stream.

This blog post is excerpted and revised from my book MBA ASAP 10 Minutes to Understanding Corporate Finance. It is a available from Amazon as an eBook for Kindle, paperback, and audiobook. The audiobook is also available from Audible.

Check it out and level up your financial literacy and skills!

Here is a link to the beginning of a series in Khan Academy on the time value of money and present value calculations http://bit.ly/1Ul43VT Sal Khan is great at explaining concepts and these videos will be very helpful in solidifying your understanding of this concept.