Note: This is the latest entry in the Acton blog series, “What Christians Should Know About Economics.” For other entries in the series see this post.
The Term: Time Value of Money
What It Means: The time value of money (TVM) is the concept that because of potential earning capacity, money available at the present time is worth more than the same amount at a future time.
Why It Matters: Would you rather receive $100 today or $100 one year in the future? You probably don’t have to consider the question too long before deciding the obvious answer is that you’d prefer the money today. But why is that the case? Because even if you’re unfamiliar with the concept, you likely have an intuitive understanding of the time value of money.
Money is more valuable today than tomorrow for two reasons: inflation and interest.
Inflation is the general increase in prices. If prices rise 5 percent a year, then a dollar you earn today will only be able to purchase 95 cents worth of the same goods and services a year from now. So when the inflation rate is high and rising you are usually better off not only having the dollar today but also spending that dollar as soon as possible.
But what if there is nothing you want to spend it on this year? That’s where the second factor — interest — comes in. Some people are willing to pay you in the future for the dollar you loan them today. They either believe they can use the money to earn more money (e.g., buying a car so they can become an Uber driver) or they are willing to sacrifice future money to purchase something they want today (i.e., a mortgage on a home).
Here’s why interest makes money in the present time even more valuable than in the future. Let’s say the simple interest rate is 10 percent a year, which means someone is willing to pay 10 cents a year for every dollar you loan them. If I borrow $100 from you at 10 percent a year, then next year you’ll have $110. (If the inflation rate is 5 percent, then your purchasing power is reduced to $105, which is still $5 more than it would have been.) So if someone gives you $100 today you can loan that money out and earn $110 — $10 more than if you had waited to accept the gift next year.
In Matthew 25, Jesus tells the Parable of the Bags of Gold which relies on an understanding of the time value of money:
To one [servant he] gave five bags of gold, to another two bags, and to another one bag, each according to his ability. Then he went on his journey. The man who had received five bags of gold went at once and put his money to work and gained five bags more. So also, the one with two bags of gold gained two more. But the man who had received one bag went off, dug a hole in the ground and hid his master’s money.
“After a long time the master of those servants returned and settled accounts with them. The man who had received five bags of gold brought the other five. ‘Master,’ he said, ‘you entrusted me with five bags of gold. See, I have gained five more.’
“His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’
“The man with two bags of gold also came. ‘Master,’ he said, ‘you entrusted me with two bags of gold; see, I have gained two more.’
“His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’
“Then the man who had received one bag of gold came. ‘Master,’ he said, ‘I knew that you are a hard man, harvesting where you have not sown and gathering where you have not scattered seed. So I was afraid and went out and hid your gold in the ground. See, here is what belongs to you.’
“His master replied, ‘You wicked, lazy servant! So you knew that I harvest where I have not sown and gather where I have not scattered seed? Well then, you should have put my money on deposit with the bankers, so that when I returned I would have received it back with interest. [Emphasis added]
While this parable is about the Kingdom of God and not about investing, the story does provide us useful framework for financial stewardship. If we are responsible stewards of the disposable income we have today, we will consider whether it is better to save and invest our extra resources to create more wealth that can be used for God’s purposes in the future.
Other Stuff You Might Want to Know:
• We gain a better understanding of the time value of money — and can make more prudent decisions about the future value of money — when we understand the inflation rate. But many of us who lived through periods of high inflation tend to overestimate the year-to-year rates of inflation. For example, many people would estimate the current annual inflation rate to be 4 percent or higher. But in reality it hasn’t been that high since 2007, when it was 4.1 percent. Since 2012 the rate has been under 2 percent, and was only 0.7 percent last year. By overestimating the inflation rate we my underestimate how much we can benefit from investments at even modest interest rates.
• There is a basic formula that can help you calculate the time value of money. The variables you need for the calculation are:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Based on these variables, the formula for TVM is:
FV = PV x (1 + (i / n)) ^ (n x t)
For example, if we invest $10,000 for one year at 10 percent interest the future value of that money is:
FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000
We can also use these variable to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7 percent interest:
PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673
Note: You can use an online financial calculator to make the calculation easier.
• The time value of money depends not only on interest rate, inflation rate, and time horizon, but how many times the compounding calculations are computed each year. For example, using the $10,000 example above, if the number of compounding periods is increased to quarterly, monthly or daily, the ending future value calculations are:
Quarterly Compounding: FV = $10,000 x (1 + (10% / 4) ^ (4 x 1) = $11,038
Monthly Compounding: FV = $10,000 x (1 + (10% / 12) ^ (12 x 1) = $11,047
Daily Compounding: FV = $10,000 x (1 + (10% / 365) ^ (365 x 1) = $11,052
Over time, this change in compounding rates can have an significant impact on savings and investment.
• Earlier we noted that people tend to prefer money today to money in the future. There is one especially noteworthy exception: tax refunds.
Let’s say you get a tax refund of $1,200. That would mean you paid about $100 more in taxes every month than you needed to cover your tax payment. Instead of getting that $100 every month and saving it (thereby earning interest), you are loaning the federal government that money at a zero percent rate, and asking them to return it to you after April 15 the following year.
It is rational or prudent for people to give interest-free loans to the government every month? Probably not. But some people do it as a type of forced savings plan. Because they do not believe they are disciplined enough to save small amounts every month (and earn the interest), they give it to the government to hold for them.
