# The Time Value of Money and Why People Aren’t Rationale

I’m amazed sometimes at just how irrational people can be, especially when it comes to a subject like the time value of money.

I have been fascinated by this topic ever since I first started learning about it in my financial management class in college. Back then, we didn’t have fancy online calculators and excel was barely even a thing. If you wanted to figure out how much a dollar would be worth in 20 years at 10% interest, you had to use a table of multipliers to figure it out.

Related: How to get started investing

What I’m saying is, back then we used a pen and paper to figure out the answers to most complicated financial calculations that we now can use a computer to do. And by finding the answers this way, I developed a sincere and curious fascination into what the numbers meant and how they worked.

Last week I was brought back to those days while mediating a case for a client that was looking at a financial choice. He could either pay his wife \$3,000 per month in alimony for the next 8 years or pay her \$100,000 now. (I’m changing the numbers slightly, to protect the facts of my case, but you get the idea).

Many people might be tempted to say that they would gladly pay \$3,000 per month for 8 years to avoid paying a \$100,000 lump sum today, and they would be dead wrong.

## The Power of The Time Value of Money

I evaluated this with my client a number of different ways. First, I ran a present value calculation on the \$1,500 per month series of cash flows. If we assumed a conservative, 5% internal rate of return, those payments were worth \$236,968 today. If we jacked the interest rate a bit, to a more historical 8%, that number drops to a still whopping \$212,213.

So either way, my client would be making a bad deal by agreeing to 8 years of alimony payments.

Now here is the thing, alimony will terminate when one of 4 things happen. If my client dies, his wife dies, his wife remarries, or if his wife cohabitates with someone in a marriage type relationship, then alimony will terminate.

So if my client were to agree to the monthly payment, he must believe that one of those 4 things is going to happen in the very near future.

But how soon would it have to happen? What is the breakeven point?

## The Breakeven Point of This Analysis

So I ran some numbers in excel. My client rejected my present value calculation because he said that he would never have to pay alimony for the full 8 years.

Turns out, assuming a modest 5% rate of return, my client breaks even in 36 months – that’s just 3 years. Every payment he makes after 36 months is a windfall to his Wife, essentially.

So unless she has a boyfriend waiting in the wings, chances are not good that my client will win this bet with the assumption that alimony will terminate within the next 3 years.

Fair question. The alimony payments my client makes are tax deductible to him, and he is in the 28% marginal tax bracket.

So every payment of \$3,000 he makes is really only \$2,160 because of the amount of money he will save on taxes. (This is only federal taxes, he will also have state income taxes to pay). So let’s round down to \$2,000 per month, assuming the additional \$160 per month will be saved on state taxes.

At 5% internal rate of return, that series of cash flows over 8 years is worth \$157,979. At 8%, it is worth \$141,475. But, the break-even point now jumps to 4 years and 9 months at 5%.

So what would you do? My client still wasn’t convinced that the lump-sum payment was the right way to go. So I changed tactics…

## What Would Things Look Like in 8 Years?

My client was concerned that he would lose his entire nest-egg and be left destitute. So I reminded him that he could simply invest that \$3,000 per month instead of paying it to his wife. How long would it take him to save \$100,000? What would this look like in 8 years?

In 8 years, he could have saved just over \$400,000 by investing that \$3,000 per month instead of paying his wife. Or, if he only wanted to invest \$2,000 (his after-tax negative cash flow), he would have saved \$267,737 in 8 years.

But what if he decided on the alternative? Let’s say he just invested the \$100,000 while paying his wife \$3,000 per month? His \$100,000 “nest egg” would grow to \$189,245 over the course of 8 years. And in the meantime, he would have paid out \$192,000 after-tax dollars to his Wife during that same time. So in 8 years, he would basically be at zero.

Let’s say he just invested the \$100,000 while paying his wife \$3,000 per month? His \$100,000 “nest egg” would grow to \$189,245 over the course of 8 years. But in the meantime, he would have paid out \$192,000 in after-tax dollars to his Wife during that same time.

## The Irrational Client

My recommendation was clearly for my client to pay the lump sum. It was too good of a deal to pass up.

But neither I nor the mediator who took my side could convince my client that this was the right decision. At the end of the day, he decided to take the payments and save his cash.

I just hope he doesn’t wake up today to realize what a mistake he made.