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.
Thomas SmithAssistant Professor in the Practice of Finance
