Things are starting to heat up again, and I’m not referring to the scorching pre-summer heat! The Powerball Lottery, played in 43 states, is approaching all-time highs. Saturday’s drawing is estimated at $600 million and gearing up to be the second-largest jackpot in US history. According to the Powerball Lottery, the odds of winning this prize are just less than 1 in 175 million. The ultimate prize to those able to match all five of the regular numbers and the Powerball is a guaranteed stream of 30 annual payments, with the first one taking place immediately.
In financial terms, this is similar to an annuity due. An annuity due is a stream of equivalent payments occurring at the beginning of a predefined number of periods. In the case of the Powerball lottery, there are 30 annual payments, with the first occurring immediately; however, the payments aren’t equivalent in dollar amount – they increase gradually to account for inflation, which the Powerball folks estimate at 4%. Rather than collecting equivalent dollar amounts each year, the winner(s) collect(s) equivalent “real” amounts. Additionally, the payments are enhanced with an investment return arising from the lottery’s investment activities with the “seed” or cash value set aside for the winner. This means that instead of collecting 30 equal amounts (the “plant”) of $20 million [$660 million / 30 payments], the winner collects an amount lower than the $20 million today and waits to collect higher dollar amounts in the subsequent years. In place of this payment stream, the lottery offers a lump sum cash option, roughly equivalent to the present value of the stream of expected cash flows (in this case equal to approximately $376.9 million).
Why the drastic drop from $600 million to $376.9 million?
To those not familiar with the concept of time value of money, this may be confusing at first. Time value of money is the premise that a dollar today (otherwise known as the “present value”) is worth more than a dollar in the future (otherwise known as the “future value”). One reason this is true is because it is possible to invest the dollar today, earn interest, and have more than one dollar in the future. The opportunity to loan the dollar and collect interest makes the present dollar more valuable than the future dollar.
Another reason for why the present value of 1 dollar is more valuable than the future value of an identical amount is due to inflation, or the rising of general price levels. Simply put, as time passes, inflation eats away at money. In other words, it lessens the value of an equivalent number of dollars with the more time that passes. The one dollar example faces an identical fate. The purchasing power of the one dollar in the future will be less than the purchasing power of the same dollar today.
So, what’s $100 worth today? Today’s $100 bill is worth exactly its face value – $100. What will $100 be worth in the future? If one can invest the money over the next 2 years and earn 4% simple interest, the investment would be worth $108 [$100 Principal + $4 first year simple interest + $4 second year simple interest]. Compound interest provides a greater return because it provides for interest to be earned on top of previously earned interest. Continuing our example with $100, one would have the same $104 at the end of the first year as in the case of simple interest; however, by the end of the second year, one would earn 4% interest on the $104 base [$100 principal + $4 interest earned during year 1], resulting in $4.16 in interest. The total value at the end of year 2 would be $108.16. The formula for calculating the future value of any amount over n periods is:
Future Value = Present Value X (1 + interest rate) n periods
The application of compound interest resulted in an investment worth $0.16 more than the simple interest approach. As Albert Einstein said, “Compound interest is the eighth wonder of the world. He who understands it, earns it… he who doesn’t … pays it.”
Recall that in the above example of compound interest, we started with a present value of $100 and computed a future value after two periods of compounding (for our purposes, two years) to calculate the equivalent future value of $108.16. Suppose we were offered an investment that yields exactly $108.16 (the future value) at the end of two years and asked how much we would be willing to invest for it today (the present value)? In other words, how much would a reasonable investor exchange today for the right to receive $108.16 in the future? Assuming the same 4% return, the answer is $100. We simply reverse the steps outlined in the compound interest example. Instead of “growing” our investment of $100 by the rate of return, we “discount” the $108.16 by same rate of return, 4%. Algebraically, we divide both sides of the future value formula by “(1 + compound interest rate) n periods ” to calculate the present value:
Present Value = Future Value / (1 + interest rate) n periods
With an understanding of the basics of the time value of money, we can now return to our initial subject, the Powerball Lottery. If the winner chooses the stream of cash flows, the winner will collect 1 immediate payment and 29 future gradually increasing (inflation-adjusted) guaranteed payments which will total approximately $600 million. However, if the winner opts for cash value upfront, approximately $223.1 [$600 m – $376.9 m] in nominal dollars won’t be paid because of the time value of money. This doesn’t mean the winner is “poorer” by $223.1 m. The winner can take the $376.9 m and invest it to reach an equivalent or potentially greater wealth depending on his investing choices. If the investor believes he can earn a higher rate of return than the discount rate being used by the lottery, then it’s wise to take the cash value. If not, the investor should take the stream of payments.