Summary in haiku form
Today versus tomorrow.
Use present value.
Summary in one paragraph
Optimizing individuals often have to make choices over time, e.g., between money today and money tomorrow. These cannot be directly compared because of inflation and also because most individuals have a preference for sooner rather than later. In order to compare money today and money tomorrow we can use the interest rate at the bank to convert everything into a common unit: present value, the amount of money you’d need to put in the bank today in order to finance one or more payments in the future. We can use the concept of present value to find a “money today” equivalent for future payments received as lump sums, annuities, or perpetuities, with the surprising conclusion that a perpetuity—a perpetual stream of annual payments, e.g., $100 a year forever—is not worth an infinite amount of money.
Notes on specific pages
Page 32: “Present value is the value today of one or more future payments.”
Fine examples of present value can be found in the 2009 Social Security Trustees Report or the 2009 Medicare Trustees Report. These are giant documents, so just search for the phrase “present value” until you find the sections about how the present value of the 75-year deficits (i.e., the amount required to keep these programs solvent for the next 75 year) are $5.3 trillion for Social Security, $13.4 trillion for Medicare HI (hospital care), $23.2 trillion for Medicare Part B (out-patient) and $9.4 trillion for Medicare Part D (prescriptions drugs). (If you think these are big numbers, consider the “infinite-horizon” deficits, which are $15.1 trillion for Social Security, $36.4 trillion for Medicare HI, $50.1 trillion for Medicare Part B, and $20.3 trillion for Medicare Part D.) For a summary of the status of Social Security and Medicare, scroll down to Charts B and C in this summary from the Social Security and Medicare Boards of Trustees.
You can also look in the glossary at the end of these reports to get their definition: “Present value. The present value of a future stream of payments is the lump-sum amount that, if invested today, together with interest earnings would be just enough to meet each of the payments as it fell due. At the time of the last payment, the invested fund would be exactly zero.” Note that they’re assuming investments in U.S. government bonds, which as the safest investment in the world also have the lowest interest rate.
Page 30: “Inflation, a general increase in prices over time.”
The U.S. Bureau of Labor Statistics has an inflation calculator that you can use to look at the Consumer Price Index (one measure of inflation), and there’s an optional chapter in the textbook on inflation, but remember that even without inflation there is still a positive interest rate because people have a preference for sooner rather than later!
Page 35: “You can still blow it all today even if you take the annuity!”
Google “sell annuity” and you’ll find dozens of firms eager to pay cash upfront in exchange for annuities or other “structured payments”.
