You are currently browsing the archives for the Finance 400 category.

Archive for the ‘Finance 400’ Category

My AHAAA! Moment, Or How to Use a Financial Calculator

 :: Posted by ifm89408 on 06-06-2011

I can trace my financial beginnings back to several epochal moments in my life.  One of the most meaningful came when I was working on my MBA back …..  well, back a long time ago.  We were working on present value, discounted value, sinking funds and other problems that required complex cash flows and compound interest calculations.  Back in those days (OK, now I’m dating myself) financial calculators were not that readily available (OK, you can laugh now – I was an engineer at the time and I actually had a slide rule…).  Instead we used a book of tables that you would look up the appropriate multiplier from a table and use it to calculate your result.

What happened was almost divine guidance.  I was working on my problems and learning how to use that book of interest rate tables and I got curious.  Instead of my problems for school I started to wander through the tables and just started to look at each type of table and the “pattern” that they ascribed.  I zeroed in on the “sinking fund” table.  This is a table specifically for when you put away the same amount of money at given intervals for a certain period of time (IRA and 401(K) accounts were just starting to gain popularity at the time and they are sinking funds).  Simple problem:  You deposit $4,000 a year for 40 years and get an 8% return.  You would go to the table of sinking funds, go down to the row for 40 years, and then over to the column for 8%.  There you would find a number (259.78) to multiply your deposit by to calculate the total value in 40 years.  I started looking at the tables and saw how they “Hockey Sticked” as the years went on (The longer you stayed at it, the multiplier described by the table grew really fast).

This taught me two things:

  1. That if I had time (which I did at age 22) I could easily accumulate tremendous amounts of money making regular deposits.  If I wasted my time, I was screwed!
  2. You have to keep going to get to those later years where things really accelerate.  For instance:
    1. The multiplier for year 5 is 5.87 and for year 10 is 14.49.  A difference of 8.62 times your annual deposit.  Of course 5 of that 8.62 was the annual deposits you made.
    2. The multiplier for year 35 is 172.32 and for year 40 is 259.78.  A difference of 87.46.  Again, 5 of it was from your annual deposits but a full 82.46 was due to “THE MIRACLE OF COMPOUND INTEREST”.  As you can see you MUST get to those later years – you CANNOT RAID YOUR LONG TERM SAVINGS.

Not long after that financial calculators started showing up.  My first a HP-12C was a bit arcane but I learned to use it and it replaced my book of tables (which I kept by my bedside for several years).  You had to know a bit about “cash flows” and their directions to properly use that calculator.  Today, there are a myriad of calculators available to you.  Handhelds, Internet, Specific Programs (Like TValue), even using a spreadsheet (one of my favorites).

 

These allow you to do what I did – play, plug in numbers and dream, start to make plans, understand the impact of decisions you make (like robbing your 401(k) to buy a car).  So let’s learn some basics:

Most calculators will have a TVM group of buttons (Time Value of Money).  Usually consists of the following:

PV (Present Value) – The current Value of the account.

FV(Future Value)- Account value at the end of the time period.

PMT (Payment) – The amount paid each period.

N (Number) – Number of periods (you decide what a period is, month year or whatever).

I (Interest rate) – The Interest Rate you will get.  Make sure it is for the period specified (12% annually is just 1% monthly).

Now things are pretty simple.  Fill out any four of the variables and the computer will calculate the fifth unknown variable.  One thing to Know for many calculators is that they are DIRECTIONAL.  That refers to the numbers used for the PV, FV and PMT.  It is important to identify which are POSITIVE and which are negative (this related only to PV, FV and PMT).  I like to think that “money in” is positive and “money out” is negative.  So if I am starting with a positive PV and adding money to it the PMT is positive, and the FV will then be negative (as though it is a final withdrawal).  This is standard CONVENTION for financial calculators and is necessary for more complex calculations of cash flow.  Simple calculators like what is  available on the internet just show everything as positive but it is good to be aware of the sign convention if it is a more sophisticated calculator (Positive means money added, Negative means money withdrawn).

So let’s take some examples:  You want to see what you need to deposit today to have $1,000,000 in 30 years if you can get an 8% return.  FV=-1,000,000 (negative because that is what you will withdraw at the end), N=30, I=.08 (8%), PMT=0.  Now just press the PV key and you will get something like $99,377.33, the amount you need to put away today.

Example #2:  You have a 401(k) with $68,500 in it and you are putting $6,000 in it each year and that is matched 25% by your company and you have been getting a 6% return on that account – what should you have in 15 years when you want to retire?.  PV=$68,500, PMT=$7,500 (your $6,000 and the employers 25% match of $1,500), N=15, I=.06 (6%).  Enter these and press the FV and you should get something like -$349,208.20.  Notice the amount is negative, this is the amount that would be withdrawn since we used positive to represent amounts deposited (both the present value and the annual payments).

Here is a great website with a bunch of calculators.  I suggest playing with these and looking at things such as”

  • How you can build a large amount of money over a long period of time.
  • How much interest gets paid on a mortgage of 30 years length vs a 15 year mortgage.
  • What happens if you build an account for 10 years then spend that money, vs keep on saving.
  • Note how most of these calculators are just variations on a them of the basic Time Value of Money (TVM) calculator.

http://www.financialcalculator.org/calculators

 

THIS IS ALL INFORMATION THAT IS INTENDED TO EMPOWER YOU – THE INDIVIDUAL.  The more you play with these numbers and calculators the more familiar you will be with them and how cash flow works.  This will give you ammunition when getting a loan, buying a home and getting a mortgage, making long term savings decisions, choosing retirement savings vehicles,  saving for a child’s education, anything that uses compound interest calculations – which freak most people out.  Knowledge is power and these calculators provide unimaginable power when not long ago we need a book of tables!

 

Here is where it gets complicated

 

Cash Flows – not all problems are simple put money down and see what it is worth some years later.  When I would talk to my Dad in his later years I would ask him what his investment return was for the past year.  I knew he did not “really” know because he did not have a calculator to compute all the money he moved in and out of his investment accounts, but he could give me a “wag”, which is an educated estimate and it was a good topic to discuss.  I want you to be able to tell what your returns really are instead of wagging them, but it takes some work.

Let’s look at a sample problem.  You have an investment account that you have had for 15 years.  You started by putting in $1,000 and it is now worth $175,000.  You could just put this into the TVM calculator and come up with a return of 41.10%.  That’s probably not real because you forgot to add the $25,000 you deposited in year 3, the $40,000 you got from a home sale in year 6, the $31,000 you deposited from a bonus you got in year 7, and the $11,000 you took out last year for Junior’s education.  Whoa, now how the heck do we do this?

You need something more sophisticated and there are options:

  1. You can track your investment accounts using a program like Quicken.  If you properly enter your transactions, your dividends, interest, purchases, sales, deposits and withdrawals then you can just ask Quicken to do the calculation for you and VIOLA it is done!
  2. You can use a program I use called TValue.  In this you would enter each cash flow on a separate line in a table and ask TValue to perform the calculation.
  3. You can enter each cash flow with the date in a two column excel spreadsheet and then use the “XIRR” formula.

Lets look at how this would look in TValue or Excel (assuming “Today” is 1/1/2011):

1/1/1996          $1,000

1/1/1999        $26,000

1/1/2002        $40,000

1/1/2003        $31,000

1/1/2010      -$11,000

1/1/2011     -$175,000

 

I enter these into an excel spreadsheet and then use the function “XIRR” which returns an “Internal Rate of Return” for a series like this.  This is the same as saying, “If I put these same deposits and withdrawals in a bank what would the actual return be that I received.  In this case “XIRR” returns .069157 or 6.9157%.  That is a long way from 41%.

The Key here is we need to be able to distinguish actual cash flows but it is much more simple than you might think.  It is just simply money into and out of the account.  “Money in” is POSITIVE, and “money out” is NEGATIVE.  You have to keep track of those flows but you can just create a spreadsheet and each year add the dates and individual cash flows and extend the spreadsheet.

If you are able to calculate basic loans, sinking funds, estimate future value of an amount and especially tell what your rate of return has been on a complex set of cash flows you are light years ahead of the average person and that is very powerful.