# Finding Present Value in Your Finances

Let me ask you a simple question. What would you prefer— $10 today or $10 in five years?

The answer is pretty simple for most. Cash today is better for a lot of reasons. For one, the United States has inflation pretty much every year. That means $10 in five years is worth less than $10 today.

But let’s say there was no inflation, and no option to earn interest on money either. Would your answer change? Again, for most people, the $10 today is still better. By immediately taking possession of the $10, you can buy something you want *today* rather than waiting five years to buy it. People tend to prefer things sooner rather than later, everything else held constant. Economists call this *time preference*.

Additionally, even if you didn’t want to spend the $10 right away, you’d probably still prefer to have it today. After all, choosing the option of keeping it *today* gives you the option to spend it any time between today and five years from now. Accepting it five years from now simply limits options.

This underlying truth—that people prefer money today over the same amount of money tomorrow—gives rise to the market for lending and borrowing as well as one of the most important concepts to learn in personal finance: present value.

## Buying Money

To illustrate this, consider the common mortgage loan. The standard mortgage loan is 30 years. Assuming someone can pay back their loan, this implies that over 30 years they would be able to build up enough money to buy a house. So why take out a loan at all? Why not save for 30 years and just buy the house at the end of 30 years?

The answer probably seems obvious. People don’t want to wait 30 years to have a house. Receiving the house today is preferable to receiving it in 30 years. In fact, people prefer a house today so much that they are willing to pay *more than the price* in order to get a loan. We call this additional amount interest.

If you take out a $300,000 loan to buy a house, you aren’t just on the hook for $300,000. You have to pay back the loan plus interest. The fact that people are willing to pay interest on loans reveals to us that present money is more valuable than the same amount of money in the future.

This leads to another problem, though. If money today is more valuable than money tomorrow, then how do we make decisions that involve different amounts of money over time?

Let’s consider an example of this problem, and discuss how we can solve it.

## Making the Tradeoff Across Time

Imagine you get a degree in computer science. You have two different job opportunities contracting you to build a website. For the sake of simplicity, assume both jobs are meant to only last three years.

Job 1: You are paid $20,000 at the beginning of each year for three years.

Job 2: You are paid $55,000 once at the beginning of the three-year contract.

Which one should you take? It isn’t obvious based on the information given. Job 1 gives you more money in total, but Job 2 gives you money sooner.

To figure out which is better, we need one more piece of information—the interest rate. The interest rate tells you how much it costs to borrow, or how much money you could earn by lending.

In the real world, there are several interest rates depending on factors like the risk of the loan. But all else constant there would only be one interest rate, much like there is one price for gasoline. We’ll specify that in our example the interest rate is 10% and interest accrues annually.

By using the interest rate, we can figure out what both offers will be worth at the end of three years starting with Job 2.

In Job 2 you get all the money up front, and you can earn interest right away for three years. In the first year, to find out how much you make on interest you simply multiply the total by 10% or 0.10. Then you add that to the total. The formula that represents this is:

FV=PV*(1+i)

Where FV is the future value, PV is the present value of the money and “i” is the interest rate. Plugging in the values for Job 2 we get:

FV=$55,000*(1+0.10)=$60,500

This means after 1 year of interest the $55,000 becomes $60,500. In the second year, interest accrues on this new amount of $60,500. So we have to do this again with $60,500 instead of $55,000. This would get us $66,550. Then, the third year we would have to add interest to $66,550.

Rather than doing this step by step we can recognize we are just multiplying by 1.1 three times (once for each year that passes). We can now adjust our formula to account for having to do this for multiple years. It would now be:

FV=PV*(1+i)^{T}

In this case T just means the number of years since interest accrues annually in our example. So for Job 2 we have:

FV=$55,000*(1+0.10)^{3}

=$55,000*1.1*1.1*1.1

=$60,500*1.1*1.1

=$66,550*1.1

FV=$73,205

So we have the value of Job 2 today ($55,000) and at the end of three years ($73,205).

Now let’s move on to Job 1. This time, instead of finding the future value of Job 2, we’re going to find the present value. Using some basic algebra, we can rearrange our formula for future value to solve for present value.

PV=FV/(1+i)^{T}

In Job 1, we receive three separate streams of income. The first $20,000 is received right away, so its present value is easy. The present value of $20,000 received in the present is just $20,000.

The second $20,000 is received at the beginning of the second year or after one full year. So we can use our formula here.

PV=$20,000/(1+0.10)^{1}

=$20,000/1.1

=$18,181

The second payment is worth $18,181 in present value terms.

Lastly, the third payment occurs at the beginning of the third year or after two full years. So for the third payment the present value is:

PV=$20,000/(1+0.10)^{2}

=$20,000/1.21

=$16,529

So the total present value of Job 1 is $20,000+$18,181+$16,529 for a total of $54,710. Thus, even though the total dollars associated with Job 1 is greater, the fact that some of the payments are in the future devalues it to the point of being a worse deal than getting $55,000 up front.

## Applying Present Value

There are many instances in life where you may need to compare present and future costs and benefits.

For example, should you skip college and get a job right away to earn more money up front, or should you take a long time to pursue a degree that will likely mean a higher yearly pay in the end? It depends how much you think you’ll be paid in each case and the interest rate! Should you lease a car, finance it, or buy it up front? Again, you need to be able to compare either the present value of each option or the future value. Let’s say you can buy membership at a grocery store which offers monthly savings to members. Is the future savings worth the upfront cost? Again, this is a present value calculation question.

A few months back, I had to decide if buying a $20 reusable coffee mug at my local coffee shop was worth the 20% savings on drinks, and I really used the concept of present value to help in the decision!

In the real world and business, these questions get a bit more complicated. Sometimes interest accrues monthly, daily, or even continuously. Some decisions have both future benefits and future costs, both of which must be put in present value terms and deducted from one another to find the *net present value*.

Regardless of these complications, the logic remains the same. Money received in the future is worth less than money received today. Understanding this is an important tool in decision-making with your own finances.

*Content syndicated from Fee.org (FEE) under Creative Commons license.*