Time Warping Money (or present valuing it)

When this blockbuster got dropped on me my sophomore year in college I was floored.  I highly doubt it will have the same effect on you but hopefully it will add something to your arsenal.  After I learned it happily pounded away on my HP-10C for hours figuring out how much money that was saved at different rates was worth at different times.  I also enjoy casually reading annual reports.....sorry.  Anyways...."Time Warping Money" is a concept called "Present Value" but that does not accurately portray it's level of coolness.

The concept of "Present Value and Future Value" or "PV and FV" as any financial calculator would say is very simple.  They are pretty much one concept that once understood really opens your horizons for valuing any cash flows.  The idea is to be able to compare a dollar today to a dollar in the future or vice-versa, which come to think of it would be the same thing.  This is important because dollars at different points in time are worth different amounts - our economist out there will know that the opportunity cost of a dollar is of course the forgone interest you could have earned. 

Suppose we have a dollar today and someone offers to pay us five dollars in eight years if he can borrow our one dollar.  Also suppose that if we invest that dollar today we can get a 12% return.  Should we keep the dollar or lend it out for five future or eight year dollars.  Present value concepts allow to see how much that five dollar bill received eight years from now is worth today with some quick math as shown below.

$5.00/(1+.12)^8=$2.02 - this is our equation used to turn that future five dollars into today's money

or

FV/(1+r)^t=PV (explained below)

So what are we doing, we are taking our interest rate, known as "i," and raising it to our time factor of eight or "n."  We then take our future amount of cash and divide it by that number and have the value of that five dollars but in today's money.  We can now compare that to our dollar today.  It turns out we should loan out our dollar because $2.02 (our five dollars in today's money) is more than we can get investing our $1.00 at 12% for five years....but how to we know that.  Above we just future valued, now lets present value. You heard me right, get excited.

$1.00*(1.12)^8=$2.48

or

PV*(1+r)^t=FV

So if we move around our equation a little we can find out what one dollar invested at 12% for eight years will grow to $2.48, which is far less than our five dollars.  So again, this means that we should lend out our dollar for five future dollars because it is going to earn us more money than simply investing our dollar at 12% rates for eight years. 

And that little equation is how we compare money in different time frames.  Later I will teach you all how to derive that (among other things such as annuities).  In the real world there are other factors, the main one being risk but for now this should be a good starting point and check for different investments you are considering.  Think on this as you finish this article - we could make keeping the dollar a better deal than lending it out for five future dollars, but only if we increased our interest rate past 12% or increased our time frame.