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Understanding the Time Value of Money

Time is money! We all know it. Well, some of us heard this at some point after capitalism became a thing in my country, but that’s a different story. Today, about the time value of money. Which is a slightly different approach to the money and time correlation.

Time is money, but what’s the time value of money?

When I’m in a hurry I might use the “time is money” expression meaning that there is a cost of opportunity of me not doing what I was supposed to do. Which is often true and it happens to all of us to accept some opportunity costs or not. But, the time value of money is something else, and we should make this clear.

Say, you win the lottery? Say, that you have a winning of $370 million. Would you accept the offer of receiving $20 million/year for 30 years, or just ask for the lump sum. When you do the math, you’ll find out that the first option means $590 million. But, you are over eighty years old. What would you choose?

$1 today is worth more than $1 tomorrow

The case is real, it happened in 2013, and the winner asked for the lump sum, accepting a loss of over 220 million, a very significant sum, and the age must have been a huge argument in favor of this choice. But, this choice is more common that you might think and whenever there is an investment to be made for example.

This is a concept that has applications across an array of financial decisions that everyone makes: individuals, corporations and even governments. Decisions involving what investments we should consider, how much a stock or bond or piece of real estate might be worth, when we should retire or whether a municipality should offer tax incentives to businesses to relocate their involve this type of considerations.

The basic ideas behind the time value of money

In fact not a single financial or investment decision does not involve the basic ideas behind the time value of money, and – as a starting point – I imagine that we all have an intuitive sense that a dollar in our pockets today is worth more than that same dollar in our pockets tomorrow. But why?

There are four reasons why a dollar today is worth more than a dollar tomorrow. The primary reason is that we are able to invest money we have today and earn some return on whether that return might be. Secondly we all prefer current consumption over future consumption and so we must be compensated in some way to give up our current consumption for something in the future.

The third reason a dollar today is worth more than a dollar tomorrow is inflation. Rising prices allow us to purchase less in the future with the same money we have today. Most of us can intuitively understand that in the event we have higher inflation the value of money in our pocket goes down. And finally there is risk, an extraordinarily important concept in finance and investing. Future cash flows involve risk.

Discounting and discounting rates

The question we must try to answer is how much more is my money worth today versus tomorrow or next year or 10 years from now And, to o figure that out we need to introduce two related terms: discounting and the discount rate.

Discounting is the process by which future cash flows are adjusted to some equivalent amount today, and the discount rate is the interest rate we use to capture inflation risk and our preference for current consumption over future consumption. This is the rate we actually use in the discounting process.

Compounding, a powerful force of economy

Compounding is the idea that you earn returns not just on your original investment, but on any return that investment has previously generated. It may not seem like much but over a longer term investment horizon it can really add up.

To demonstrate the point if you save $15,000 each year for 30 years earning 7% a year after taxes, you will have over $1,5 million dollars on the $450,000 you actually invested. Which is something that matters, and also helps you imagine the flip-side of keeping money under mattress if yo factor in the cost of opportunity and the inflation.

Present value and future value

Present value represents the value of a future cash flow that we expect to receive in today’s dollars. That is if I expect to receive $100 in three years how much is that money worth today? And it’s true that, in real life scenario we use figures that make mental calculations difficult, but there are now a myriad of websites providing tools for making this calculations.

Future value represents the value in the future a sum amount we invest today. So, if we stick to the $100 example, we would say that the future value of $100, invested for two years, earning 4% compounded annually is $108.16. Conversely we would say that the present value of $108.16 to be received in two years, at a discount rate of 4%, is $100.

Not complicated, but extremely powerful when applied to different types of cash flow.