# 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.

# Time is Money The Time Value of Money

The Fundamental Principle of Finance

Time is money, literally. If there is a prospect of receiving a certain sum, then the sooner you receive it, the more it is worth. There is risk in waiting. A bird in the hand is worth two in the bush. Interest rates describe this function between present value and future value. This is the fundamental concept of finance. We will explore this relationship between present and future value from different angles and I will phrase it in different ways in order to let it sink in, but this in a nutshell is the fundamental  concept underlying all of finance.

This is the underlying principle of how banks function, how stocks and bonds are priced, how assets and companies are valued, how projects are analyzed, and how you should think about money. A bird in the hand is worth two in the bush. Receiving money today is worth more than getting the same amount in the future; and the value of the prospect of receiving money diminishes the further into the future the promise to deliver money. The rate at which a dollar in the future decreases relative to a dollar today is inversely proportional to the rate at which a dollar invested today will increase in the future. The future and the present value are two sides of the same coin (pun intended) and they are related by the interest rate.

The concept of the time value of money explains why interest is paid or earned. Interest, whether it is on a bank deposit or debt, compensates the depositor or lender for the time value of money. Risk has to do with the uncertainty of being repaid and interest rates reflect the level of this uncertainty or risk.

It also underlies investment in stocks or company assets. An investor is willing to forego spending their money now if they expect a favorable return on their investment in the future. The return required is related to the perceived risk of getting one’s money back in the future; the higher the perceived risk, the higher the required rate of return. An investor is willing to part with their precious capital when greed overcomes fear.

The interest rate on an investment is often referred to as the yield and often is calculated as return on investment or ROI.

History Lesson The concept of the time value of money dates back at least to Martín de Azpilcueta of the School of Salamanca. Martín de Azpilcueta (Azpilikueta in Basque) (December 13, 1491 – June 1, 1586), also known as Doctor Navarrus, was an important Basque theologian, and an early economist and the first person to develop monetarist theory. He invented the mathematical concept of the time value of money. It’s an idea that is about 500 years old. This blog post is distilled from our book MBA ASAP Understanding Corporate Finance.  It is available from Amazon as an eBook for Kindle, paperback or audiobook.  The audiobook is also available from Audible.  Check it out!

Here is a cool summary of the Time Value of Money ideas in an Infographic 