Let's look at an example where present value and future value in the calculations can help good decision making and understand the decisions that people are making. Probably just like you, I have envisioned what it would be like to win the lottery. David Sneath of Michigan actually won the lottery and perhaps he, just like you thought, before he won, whether he would take it in a lump sum or the payments, or the truth is that he didn't really win $136 million. Instead, he took a single cash buyout for only 84,367,246. I don't exactly feel bad for the guy, but why did he choose to take the lump sum payment rather than the $136 million? Well the truth is that what's going to happen in Michigan anyway is that $136 million is actually paid out in 26 equal installments starting on the day that he actually wins the lottery. So he would get 26 equal payments of $5,230,769.23 and if you sum up each of those 5 million and change payments, it would equal $136 million. But he identified that the future flow of those $5 million when you sum them up isn't really worth $136 million, not in its present value. What's the calculation? Well suppose, for example that David's discount rate is 10%, his interest rate is 10%. He might get that interest rate by asking what other investments he could use for that money. What is his opportunity cost? And so, let's suppose the S&P, the Standard and Poor's 500 returns 10% year over year. So he says, hey if you gave me some money right now, I could put it in the stock market and it would grow at 10%. Then 10% is the presiding interest rate, as far as he's concerned. But at this interest rate, at this discount rate, the value of 26 equal payments of $5 million in change is really only equal to $47,918,719. He doesn't like that. So if his interest rate is 10%, he is much better off by taking a single lump sum of $84 million rather than accumulating for what is all intents and purposes only $47 million, right? So he's getting a great deal if 10% is his real discount rate. Of course, Michigan doesn't know what David's discount rate it. And so it must be a good deal for Michigan to give him $87 million, otherwise they wouldn't offer him this lump sum. We can calculate what Michigan's internal rate of return is, so here is, we know that Michigan was planning to give David 26 equal payments of 5 million and change. And there must be an interest rate such that, all of those payments, when you add them up and take the present value of them, is exactly equal to the 80 some odd million that Michigan is planning to give him. Well the truth is that when you do the calculation. It turns out that Michigan's interest rates is about 4%. So if they can get their money at a little bit less than 4%, then they're doing good mathematics. David's discount rate is 10%. He's doing good mathematics. Everybody here is actually making out pretty well. Michigan is paying David a little bit less than they would have otherwise, David is taking a little bit more than what he feels the value of his income streams are. So using the calculations, everybody, all the parties involved, are able to make sound decisions based on quantitative analysis.
