Decision Factor #4: The Time Value of Money
A bird in the hand is worth two in the bush–Miguel de Cervantes
The time value of money is fundamental to money management. It is the key to understanding stocks, bonds, financing your loans, and making good business investments. It’s the reason why lottery winners often take lump-sum payments at a 40-50% discount of the jackpot value. And, as I explain below, it’s the reason why some checking accounts aren’t really free.
We all know the time value of money intuitively: $100 now is better than $100 one year from now. One reason we prefer money today is because then we have the option to immediately spend it on some thing we want (rather than wait one year). Your preferences indicate how important this factor is to you. Another reason we want money now instead of later is so that we have the opportunity to invest the money and gain interest. In other words, we can measure the opportunity cost of getting the money later.
Future Values and Present Values
Here is an example that illustrates the opportunity cost of getting money later. If you have $100 now, you could invest it in an online savings account and get about a 5% interest rate. At the year’s end, the money would be worth $100 x 1.05 = $105 (called the future value in one year). And in two years, the money would be worth $105 x 1.05 = $110.25 (called the future value in two years). And each following year, the interest is compounded on top of what’s already accumulated.
Just like we can calculate the future value of money we already have, it is easy and more common to calculate the present value of an expected stream of payments. Let’s say a business associate offers you an investment that will pay you $105 one year from now, and that you are guaranteed payment. What is the most you are willing to pay for the investment today? The investment is definitely not worth more than the present value of $105, which is found by “dividing out” one year’s interest: $105 / 1.05 = $100. If the $105 was promised two years from now, you would need to “divide out” two years of interest, so you would not pay more than $105 / 1.05^2 = $95.24.
Example: Minimum Balance Checking Accounts
The future value of money is one reason why banks can offer you checking with “no monthly fee” if you maintain a balance of at least $10,000. The bank is glad to hold your money and pay you no interest while they rake in at least a risk free 5% annual interest rate. If you would normally have held much less in the checking account, say $4,000, then the extra $6,000 you’ve deposited is worth $6,000 x 5% = $300 in lost annual interest. This means you are basically paying them the equivalent of a $25 “monthly fee!” Now, those no minimum checking accounts with even a $20 monthly fee sound good in comparison (of course don’t do this as there are even better banks with no minimums and no monthly fee).
Further applications
The time value of money is extremely important in finance. Bonds, stocks, loans, and business investments are many times valued by determining the present value of an expected cash flow (also called “discounting” the cash flow). When the good in question is something other than money, its value is quantified in money terms first. For instance, a business may estimate the value of a product by discounting its expected future revenues. Interested in learning more? Be sure check to my blog in the upcoming weeks as I’ll be giving more details on these financial techniques, including basic bond and stock valuation.
