Professor Rosilyn Overton | Time Value Of Money
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# Time Value Of Money

Being able to compute the Time Value of Money is an important personal skill, not just something you need for this class. If you understand the Time Value of Money instinctively, you will do everything in your power to pay off your mortgage in 15 years instead of 30, will think twice before buying on credit, and will be able to make better financial decisions overall.

The text has an excellent discussion on the theory of the time value of money. If you are finding the text difficult, there is an extremely basic slide show about the Time Value of Money (TVM) at http://cw.prenhall.com/divisions/bp/app/wachowicz/ppt/ch03.ppt. that you can read, then read your text. He refers to a TVM table at the end of the slide show. That is how we computed TVM before financial calculators became so cheap. The table simply shows what one dollar invested would be worth at that interest rate over that number of periods, so all you have to do is multiply by the dollars invested.

Once you understand TVM conceptually, this page is designed to make it easy for you to compute it using your financial calculator. The directions are not specific to any calculator. You should consult your calculator’s instruction book to see the procedures for the Present Value of a Future Sum, Future Value, Present Value of an Annuity Due,(PVAD) Present Value of an Ordinary Annuity (PVOA), etc.

To solve any Time Value of Money problem with even payments, you need to know all but one of the following variables. If you get in the habit of writing down the five variables’ abbreviations in a column before you read the problem, you can fill them in as you go, and will be able to solve the problem easily.

PV (Present Value) =
FV (Future Value) =
PMT (Payment) =
N (Number of periods) =
I (interest rate) =

In addition, you will need to know whether the payment is at the Beginning or the End of the period, and how many times per year payments are made.

When computing simple Present Values of a Future Sum, or Future Value of a Single Sum, the payment variable is always zero, and Begin or End is irrelevant. HOWEVER, we recommend that you always enter the 0 payment in your calculator. That way, if a previous calculation that had a payment is still in the calculator, the payment amount will be corrected. You may think that you would never forget to clear your calculator, but everyone sometimes makes mistakes.

So, write down the 5 variables, write B/E, and Numof payments per period.
Then, as you read the problem, fill in the numerical values. If there are a number of periods per year, on some calculators you must multiply the number of years by the payments per year to get N, and divide the annual interest rate by the number of payments per year to get I. On other calculators, you simply put in the number of periods per year, and it does the calculation for you. Know which kind of calculator yours is. We will practice this in class so that you internalize the methodology and become facile at it.

You should also go onto your computer and open Excel. Set up a spread sheet with the same five variables and your begin/end question listed, then click on Fx to use a function.
Choose Financial, then PV. This will compute the Present Value for you just as you could with a regular calculator or with your financial calculator.

If you are good with Excel, you can set yourself up with a general worksheet that will solve your TVM homework for you. See if you can do it!

## How To vs. Theory

The instructions at right are an example of How to do something with no explanation of the theory. At this stage of the game, you should understand the theory behind what you do.

The textbook has a good explanation of the theory, but if you find it a bit difficult to understand at first, think about this:

If you put a deposit in the bank, and were to get interest paid once a year, and you wanted to know what it would be worth at the end of the fifth year, what would you do? Assuming that all you had was a paper and pencil, or a simple calculator, you would take the Present Value (PV) and multiply it by the interest rate (I) to get the interest earned by the end of the first year, and add that to PV. Or, you could just multiply by 1 + the interest rate to get the ending value (1+i).

So, the FV after 1 year ( we write this as FV (1)) would be
FV(1) = PV (1+i)

To get the value at the end of the second year, we would multiply the FV(1) by 1+i

So, FV(2) = FV(1) (1+i)

or FV(2) = PV (1+i) (1+i)
Which is the same as…

FV (2) = PV (1 + i)2

To get FV(3), we would just multiply FV(2) by (1 + i) again, so
FV(3) = PV(1+i)3

If we keep repeating, we get a general equation:

FV(n) = PV (1+i)n

The other equations are derived similarly. Hopefully, this will make the book clearer for you.