The time value of money is a simple concept. A dollar today is worth more than a dollar tomorrow. A dollar today is worth more than a dollar in a year. But this plain and simple concept is the foundation of all finance. It doesn’t matter if you’re taking out a loan for a car, deciding on whether to spend $1 million for a project at your company, government selling bonds, and of course Wall Street herself.
If you want to borrow a dollar from me and pay me back in one year, I’ll likely ask for more than a dollar. Instead of loaning that dollar to you, I could invest it, loan it to someone else, or save it. In any of these circumstances I would expect to get more than a dollar in a year. If I invested it with the government, I would expect 3% back if that was the going rate. Since the government has the least risk in defaulting on this loan, anyone else I would loan my money to would have to pay me more. We often call this the interest rate, but it has many other names depending on the application in finance.
So if a dollar is worth more to me today than tomorrow, how much is a dollar tomorrow worth to me today? Was that a bit confusing? Let’s try again. Let’s say I won $1 million in the lottery and I would be paid in exactly one year’s time that amount. The lottery company offers to give me $950k today. Should I take the deal? In order to figure this out I need to know how much $1 million is worth to me today. To figure this out I need to decide how I would invest/save the money if I got it today. If I would invest it with the government I’d evaluate this offer using 3%. This is called the “discount rate,” it’s the rate we are discounting the $1 million. Discounting $1 million at 3% is roughly $971k. 971 is more than 950 so I’d rather have the million in a year than 950k today.
There is another way we could have figured that out. We could have just taken $950k and multiplied it times 1.03 to figure out the 3% return on investing the cash today. If that amount is less than $1 million then again we’d take the $1 million in a year.
So why do the discounting at all? Well what if you were getting $100k a year, each year, for 10 years or $950k now. The way that was the easy way now becomes much harder. So much harder that I’m not even going to explain it. But if we take the present value of those $100k cash flows using the 3% discount rate, it becomes much easier. The present value (PV) of those 10 years of cash flows is $853k. So given the choice between $853k in today’s money, or $950k in today’s money, is easy.
The examples above allow you to compare dollar amounts from different time periods. The discount rate you use is entirely up to you. It all depends on what you would do with the money today. If you would invest it in the stock market and expect 10% back each year, the PV of those $100k cash flows becomes $614k. As you can see, determining the appropriate discount rate is half the battle.
One of the best applications for time value of money calculations is with annuities. Is an annuity a good deal for you? Or maybe if you wanted the cash up-front from a settlement. You’ve seen the JG Wentworth commercials. You probably asked yourself how those companies make money if they give you money now. Well they are calculating the PV of your cash flows, and offering you something less than that. In the example above, you could assume you won a $1 million settlement paid out in $100k payments. JG Wentworth might offer you $800k today (remembering the PV of those cash flows is $853k).
If your mind is blown then don’t worry about it too much. Even if you learned the term then you learned something. If you’re up for learning more about the time value of money, there may be a more advanced course in the future. In the mean time, you can learn how to calculate the time value of money manually or in excel by just doing a couple of Google searches.
 By The Weakonomist |
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Said,
I keep trying to find a way to make present value calculations accessible. It’s not a hard concept, but it’s a subtle one. Any talk of it is all too prone to make people’s eyes glaze over.
But nothing else is as important to sound decision making–for individuals, for groups, and for public policy.
If you don’t understand present value you’re not going to be able to make the best choices about anything having to do with money or resources.
Glad to have your contribution to the effort.
Philip Brewer´s last blog ..Guest Post: Living off Capital