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How Big Is That Jackpot, Anyway?
For a clear example of present value at work, lending the money to the federal government).
consider the case of lottery jackpots. The money would have been invested in such a
On March 6, 2007, Mega Millions set the way that the investments would pay just enough
record for the largest jackpot ever in North to cover the annuity. This worked, of course, be-
America, with a payout of $390 million. Well, sort cause at the interest rates prevailing at the
of. That $390 million was available only if you time, the present value of a $390 million annuity
chose to take your winnings in the form of an spread over 26 years was just about $233 mil-
“annuity,” consisting of an annual payment for lion. To put it another way, the opportunity cost
the next 26 years. If you wanted cash up front, to the lottery of that annuity in present value David Gould/Photographers Choice RF/Getty Images
the jackpot was only $233 million and change. terms was $233 million.
Why was Mega Millions so stingy about quick So why didn’t they just call it a $233 million
payoffs? It was all a matter of present value. If jackpot? Well, $390 million sounds more im-
the winner had been willing to take the annuity, pressive! But receiving $390 million over 26
the lottery would have invested the jackpot years is essentially the same as receiving $233
money, buying U.S. government bonds (in effect million today.

they are realized; costs are indicated by a minus sign. The fourth column shows
the equations used to convert the flows of dollars into their present value, and the
fifth column shows the actual amounts of the total net present value for each of the
three projects.
For instance, to calculate the net present value of project B, we need to calculate
the present value of $115 received in one year. The present value of $1 received in
one year would be $1/(1 + r). So the present value of $115 is equal to 115 × $1/(1 + r);
that is, $115/(1 + r). The net present value of project B is the present value
of today’s and future benefits minus the present value of today’s and future costs:
−$10 + $115/(1 + r).
From the fifth column, we can immediately see which is the preferred project—it is
project C. That’s because it has the highest net present value, $100.82, which is higher
than the net present value of project A ($100) and much higher than the net present
value of project B ($94.55).
This example shows how important the concept of present value is. If we had failed
to use the present value calculations and instead simply added up the dollars generated
by each of the three projects, we could have easily been misled into believing that proj-
ect B was the best project and project C was the worst.

Module 24 AP Review

Solutions appear at the back of the book.
Check Your Understanding

1. Consider the three hypothetical projects shown in Table 24.1. b. Explain why the preferred choice is different with a 2%
This time, however, suppose that the interest rate is only 2%. interest rate from with a 10% interest rate.
a. Calculate the net present values of the three projects. Which
one is now preferred?

module 24 The Time Value of Money 241