Welcome to Alanis Business Academy.
In this lesson you're going to learn how to solve for the present value.
First of all, the present value reflects the current worth of a future sum of money given
a specified rate of return.
Translated into plain English, we're expecting some money to be paid at a later date and
we want to know what its worth today.
Due to the time value of money, we know that the money that we have today is worth more
than that same amount of money in the future.
This is due to a number of different reasons, including inflation and opportunity costs.
So in order to make an accurate assessment, we engage in this process of discounting,
which means we reduce the value of a future sum of money to account for the time value
of money and determine it's equivalent worth today.
Say a friend of ours was offering to pay us $500 two years from now if we were to lend
him $450 today.
Because of the time value of money, we immediately know that this $500 doesn't hold the value
of $500 today.
But how much is it actually worth today?
To see if we're getting a fair deal, we need to solve for the present value.
Just so you have a visual of what we're doing here, I'm going to draw a timeline showing
the process of discounting.
When I was learning this concept myself, I found it was helpful to have a visual representation
of the process.
So hopefully this helps you as well.
Here we have the $500 that we expect to receive two years from now, and we need to discount
it to today to see how much it's really worth.
On the left side in parenthesis, which denotes a negative value, we have the $450 that we
may loan our friend.
The next thing we need to know is the interest rate that we'll be using to discount our future
monies.
If you're solving for the present value as part of a class exercise or exam than the
interest rate is usually provided.
Unfortunately, real life doesn't work this way.
We need to actually determine a reasonable interest rate.
A good way to think about this, is by asking yourself what interest rate could we earn
on those monies if we had them in our possession?
Lets say that we figure this to be 5 percent annually.
We now have everything needed to solve for the present value, except the equation of
course.
To solve for the present value, we need to divide our future value by the result of one
plus i to the nth power.
Now let me briefly explain each of these variables that we have here.
Our future value, which is represented by the letters FV, is the sum or money or cash
flows that we expect to receive in the future.
For us, this is the $500 that our friend is promising to pay.
The little i represents the interest rate that we'll use to discount our monies.
One note of importance is that we need to convert all percentages into decimal form
to perform the calculations accurately.
So instead of using 5 percent, we'll actually be using .05.
Lastly, you'll notice we have a lower case n, which represents the number of periods
that we'll discount our future value.
The reason that I say periods, and not years, is that we can choose to discount a value
by years, quarters, months, weeks, or really any duration of our choosing.
However, if you're going to do that you must also change the interest rate for the increased
number of periods.
We'll talk more about this in future lessons.
Now that we understand the equation and have each of the required variables, we're ready
to solve for the present value.
First, lets plug our values into their respective variables.
Directing our attention first to the denominator of our equation, we add one to .05 to get
1.05, and 1.05 squared equals 1.1025.
Lastly, we divide our future value of 500 by 1.1025 to get $453.52 after rounding to
the nearest hundredth.
Congratulations, you've just solved for the present value.
But what exactly does this value mean to us?
What this means is that the $500 that we expect to receive two years from now discounted by
5 percent compounded annually is the equivalent of $453.52 today.
So technically, this deal makes financial sense.
For one, we're earning slightly over 5 percent annually on our original $450.
And to make it even better, we get to help our friend.
Lets just hope he actually pays us back.
Thanks for watching this lesson on the present value.
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