Present Value of Money Explained – MBA Monday

by Darwin on January 17, 2011

The present value of money is explained with real-life examples in this week’s session of Darwin’s MBA Mondays (click for all topics).  If you don’t routinely perform present value versus future value comparisons, the relevance and importance may not be at the top of your list of things to focus on when making decisions.  However, as noted below, everyday we’re confronted with circumstances where people or companies will seek to exploit the present value of money – and consumers’ lack of knowledge on the topic, to boost their bottom line. A personal favorite trick I’ve encountered personally on numerous occasions is when someone pushing a mortgage acceleration MLM scheme or someone in the mortgage industry says,But you’ll save $50,000 in interest payments ….”.  This “savings” is complete nonsense – don’t be fooled.  I’ll show you why – by understanding the present value of money in the right context.

Present Value of Money Explained

First, let’s understand the concept of present value at its most basic level, then we’ll get into more detail.  Since we tend to live in inflationary environments at all times (even though the government claims to be fearing deflation at the moment), financial models always assume something will cost more in the future than it does now.  For this reason, people and businesses make calculations about whether they should defer a payment into the future or spend the money now.  When possible, financial outlays are deferred when possible.  $100 today is worth more than $100 in a year.  If I need something a year from now, I’d sooner keep the $100 and invest it, with $104 to show for it in a year and just pay the $100 then.

You should always be thinking of money in terms of today’s value vs. future value – and not confusing the two.

Taking this a bit further with some real math and assumptions involved, one key consideration is what is your interest rate assumption is.  I like to consider what is my “assumed rate of return/risk-free interest rate” or “inflation” or some other measure when considering what my money would be worth TODAY if converting from future dollars or vice versa.  For simplicity, let’s assume we’re talking in terms of assumed inflation of 3%.

PV = Present Value

FV = Future Value

i = interest rate (percentage, or 0.03 in our example)

n = number of periods (let’s use years for simplicity – and note: interest rate must be an annual rate too then).

  PV \ = \ \frac{FV}{(1+i)^n}

So for example, if someone’s talking about paying you a lump-sum payment of $100,000 in 30 years, it may sound like…about a hundred grand!  But that money’s only really equivalent to about $41,000 in today’s dollars using a very conservative inflation interest rate.  If you’re more aggressive with your assumptions and use say, the 8% you think you could make in stocks long term, then you’re talking just $10K!  That’s right – if you can reasonably make 8% over a long period of time, that $100K in the future isn’t really that impressive.  In excel, here’s what that equation looked like:

=100000/(1.08)^30

In essence, under this 8% and 30 year example above, if I were confronted with the option of either taking $15,000 today or $100,000 in 30 years, I’d take the money now!

This emphasizes just how important it is to consider what your interest rate is and the decay effect time has on money when discounted back to present dollars.

Present Value of Money Examples in Real Life

  • Mortgage Acceleration Programs – I was approached once by a co-worker pushing a scammy “money merge account” which was some useless software that basically told you to pay your mortgage early.  I could do that without software, but for this privilege which would give me the “discipline” to do so and use some hocus-pocus with a desperate account, I’d pay like $3000 up front and then make pre-payments to my mortgage.  The guy touted how given my mortgage, I’d save something like $50,000 in interest payments off my mortgage!  Sounds great right?  No, it’s silly.  My mortgage rate is already 4.625% and with the mortgage interest deduction, it’s probably an effective rate of about 4%.  I could reasonably earn more than that with even a moderate mix of stocks and bonds over 30 years.  Additionally, when I joked with him about what the Future Value of that $3,000 was, he looked bewildered.  The answer?  It’s well into the 5 figures for a reasonable interest rate.  So, if he wants to talk Future Value by touting 50K over 30 years he should also talk Future Value for the fee for this dumb system.  Or vice versa.  I’d argue that the benefit from this system is present dollars is ZERO minus the $3K.  At its simplest level, it only makes sense to pre-pay your mortgage if you don’t think you can earn more than the effective interest rate you’re paying on it.  To sell such a move with “interest payment savings” spread across an obnoxious 30 years is disingenuous.  It’s ignoring the present value of that $50K value, it’s ignoring tax deductions and it’s ignoring what the same money would have earned invested in another vehicle.
  • Retirement Planning Estimates – I ran a pension analysis tool at work a while back.  I don’t recall the exact number, but let’s say the projected lump sum at retirement was $1 Million.  That sounds like a lot of money, right?  Well, the first thing I did was to discount that number back to present dollars.  $1 Million is completely arbitrary if you’re not talking in terms of present dollars.  So, if I’m 25 years from retirement and my interest rate is say, 6%, that $1Million is really only worth $232K – certainly not enough to retire on!  Assuming a 4% drawdown of principal of your nest egg in retirement, you’d have to plan on living off $40K per year.  Since that’s well below our current annual income, that would be problematic.  Of course, there’s Social Security (or what’s left of it) and other investments – but someone in my shoes might be lulled into complacency thinking about how they’re going to retire a “Millionaire”, when really, it’s only a Quarter-Millionaire in today’s dollars.

These are just a few examples of routine situations we encounter if life that require some critical thinking and assumptions to figure out what the true present value of money is, as opposed to quoted future dollars or cash flows.  Without discounting future dollars back to present day dollars, you may be lulled into a foolish investment or purchase.

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