The lucky winner of a lottery was given an option. She could either receive $1 million a year for 20 years, for a total of $20 million, or simply receive $10 million today. Why would anyone take the $10 million today?
To answer this question, we need to use the concept of present value. A dollar paid today is not the same as a dollar paid next year. Depending on the interest rate, the $10 million today might be more valuable than the $20 million paid over 20 years. Indeed, if interest rates were 10 percent, you could take the $10 million today, put it in the bank, and earn $1 million in interest (10 percent of $10 million) forever not just for 20 years! To determine which payment option is best, our lottery winner would first need to calculate the present value of $1 million for each of the 20 years, add up the results, and compare the sum to the $10 million being offered to her today. With an 8 percent interest rate, the present value of an annual payment of $1 million every year for 20 years is $9.8 million. So if interest rates exceed 8 percent, it is better to take the $10 million dollars. (The actual calculation adding up the present value at an 8 percent interest rate for all 20 years is a bit tedious. In the problems at the end of the chapter, we show you how to make this calculation using an Excel spreadsheet.)