Present and Future Value of a Cash Flow
Present and Future Value of a Cash Flow
Embedded Files
In the last section, we mentioned that cash flows which comes at different points in time can't be added without being adjusted, because, as you know, $100 today is different from $100 in a year.
Now that we know time value of money, the interest. One thing we can finally do now is to figure out the precise value of a cash flow given different times. And then we can add cash flows from these different times together.
But for beginners, let's first learn how to adjust the value of a cash flow given a specific point in time. We will start with the present value and future value of a cash flow.
Learning by Examples: Present Value (PV) and Future Value (FV)
Learning by Examples: Present Value (PV) and Future Value (FV)
You have $100 today and you are going to put it into a saving account that offers you an annual interest rate of 10%. Your banker proudly tells you that it will be worth $121 in two sharp years. In the timeline, they look like this:
Whether your cash is $100 today or it is worth $121 in two years, we are referring to the same cash flow. We call the $100 today the present value (PV) of the cash flow, and $121 the future value (FV) of the cash flow.
The most important takeaway of this example that is $100 today and $121 in two years are equivalent. Keep this in mind, because it is all what Time Value of Money is about — the correct exchange rate of money between now and any point on the timeline!
Finally, let's get back to the example. How do we know that $121 is the correct future value? There is actually a formula which tells you how to calculate the future value given the present value, among with other two important inputs: time periods (t) and interest rate (r).
The formula is listed as below.
In this formula, FV is the unknown future value, PV is 100, r is 0.1 (10%), and t is 2 (years). So we plug all three inputs into the formula, and the FV is indeed $121.
On last thing to note: the unit of the interest rate, r, and the unit of the time period, t, should be consistent.
Here in the above example, the unit for both interest rate (10% per year) and the time period (2 years) are the same: YEAR. If you run into inconsistent units of these two, you HAVE TO convert them first. We will talk more about it in the future.
Page updated
Google Sites
Report abuse