Understand Finance - Finance Tutorials and Finance How To's

Before reading this tutorial, be sure you have a good grasp on moving cash flows
around on a timeline. You will really need this foundation to be able to undersand
uneven cash flows. In the world of finance, we will often deal with different
cash flows occurring at very different times. To illustrate this point, take a look at
the following timeline:

You should notice right away that we aren’t dealing with an annuity. These are cash
flows of different amounts and they do not occur at the end of every year. If our
appropriate discount rate to use is 12%, what is this cash flow stream worth to us
today?

To find the answer to this problem, we’re going to need to discount each of these cash
flows, one by one, back to time zero. This is extremely simple. First, set your
future value equal to $200. N is 3, Interest is 12, and solve for present value. On your
calculator, you will press (for the first cash flow in year 3):

Texas Instruments BAII Plus

Step 1. Clear the calculator: Step 2. Annual compounding: Step 3. Set N = 3 Step 4. Set I/Y = 12% Step 5. Set FV = 200 Step 6. Compute PV

Hewlett-Packard 10BII

Step 1. Clear the calculator: Step 2. Annual compounding: Step 3. Set N = 3 Step 4. Set I/YR = 12% Step 5. Set FV = 200 Step 6. Compute PV

We found out that the $200 cash flow in year 3 is worth $142.36 to us
today. We’re not done yet! Now find what the other two cash flows are worth at time zero.
Remember, you just set them as the future values and change your N. Everything else
should stay the same. Here is the finished timeline:

When you’ve found the present values of each cash flow, you can add them up to find
out the total value today of $659.14. Try the next problem on your own
to make sure you understand this concept.

Practice Problem
ABC Company has the opportunity to receive $50,000 at the end of year 6, $65,000 at the
end of year 7, and $25,000 at the end of year 10. If their opportunity cost of funds is
8%, how much is this worth to them today?

Solution:
Not too bad, right? Just discout these three cash flows back in the same way we did
above, add the time 0 values up, and you will get an answer of
$81,015.20.

I think you’ve got it! If you have a question on this tutorial, please leave us a note in the comment section. I love hearing from the readers!