The Lottery and Net Present Value
Is it Better to Take Cash or Payments?
An examination on whether it is better to take a lump sum on lottery winnings based on the calculation of Net Present Value.
When a person buys a lottery ticket for a large drawing, such as the MegaMillions or PowerBall, they have the option of taking the winnings in a lump sum or in payments over many years.
The amount of jackpot is stated in the sum of the total payments, but the lump sum amount is considerably lower. The lump sum amount is known as the Net Present Value (NPV) in financial terms.
How Net Present Value Works
Intuitively, most people know that they would rather have $10 million today than the same amount spread over 20 years.
Money a person has today is considered to be worth more than the same amount of money later. This is known as the time value of money. As an example, if a person has $1 today, they can invest it at 5% and have $1.05 in a year.
Net Present Value is used in many instances in everyday life. The cost of a home or car that is purchased with a loan is the Net Present Value of all the payments over the course of the loan.
In order to see this, add the total amount of the payments made on a loan and compare it to the purchase price. The total payments are likely to be considerably more than what was borrowed.
This is the big reason that borrowing on credit cards can be so difficult to pay off. Adding to the problem is that many people continue to add new charges to credit cards.
Computing Net Present Value
NPV can be calculated fairly easily in Excel or other software programs. The items needed are:
- The interest rate
- Number of payments
- Payment amount
Use the NPV function in Excel to compute the Net Present Value.
Understanding Lottery Payouts
Consider a typical large lottery jackpot of $162 million from 2004. A winner would receive the $162 million over 26 years, unless they chose a lump sum payout (prior to the drawing), in which case they would receive an immediate payment of $95,000,000, before taxes.
This amount, the NPV, is computed by the lottery based on the interest rate. Using Excel, we can calculate that the interest rate used is 4.5%. In effect, taking the payments results in the state paying the winnings plus 4.5% interest per year.
Is it Better to Take Cash or Payments?
The rate of 4.5% is more than historical inflation, but less than the average return from the stock market. Each person should decide whether they could reasonably expect to earn more than 4.5% per year.
It would appear that it is more advantageous to take the lump sum payout and invest the money, but there are other factors to consider. The investment with the state would be fairly secure, and other investments may end up losing money, and if the winner has the money, there will be the temptation to spend it unwisely.
