Author:  Lori Alden

Audience:  High school and college economics students

Time required:  About 30 minutes

NCEE Standards:  12, 15

Summary:  This exercise demonstrates that ten payments of $100,000 over a ten year period does not equal $1,000,000.  A simple net present value equation is used.

Student handout:

Joe just won $1,000,000 in a lottery.  He plans to build a house, travel and buy lots of CDs.  But when he goes to collect his prize he's told that he can't have it all at once.  Instead, the lottery officials say they'll pay him $100,000 today, plus $100,000 a year for the next 9 years.  That's okay, Joe thinks, $100,000 times 10 payments is still $1,000,000.  Or is it?

Not even close.  Since dollars received in the future aren't worth as much as dollars received today, Joe's prize is worth much less than $1,000,000.  To see how much Joe really won, you need to ask this question:  How much money would Joe need to put in the bank today to be able to collect $100,000 a year over a 10-year period? 

The answer depends on the rate of interest Joe can get on his savings.  If the interest rate is 7%, then Joe could withdraw $100,000 from his account one year from now by putting only $93,458 in the bank today.   We call this amount the present value of $100,000 received next year, assuming the interest rate is 7%.  

Here's a simple formula for calculating the present value (PV) of any future value (FV) received t years from now, assuming that the interest rate is r.

PV = FV/(1 + r)^t

For example, the present value of a $100,000 payment that would be received two years from now equals:

PV = $100,000/(1.07)²

= $87,344

To find out to find out the present value of Joe's lottery winnings before taxes, have your students calculate the rest of the values in the first column, then sum the total.  

 

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