Congratulations: you have just won the PowerBall lottery.  You have
four choices about how to take the prize; two choices come from the
state and two from a private firm.  For each choice, the first payment
comes today.

State choices:
a.	$105 million now (it was a big PowerBall prize)
b.	$195 million paid out as $7.8 million per year for 25 years

Private firm choices:
c.	$120 million paid out as $40 million per year for 3 years
d.	$9 million a year forever (after you die, the payout will go to
your beneficiaries, their beneficiaries, etc.)

A.	If your opportunity cost of funds is 9% per year, which of the four
choices would you prefer?
B.	What discount rate would make you indifferent between a) and b)?  
C.	What discount rate would make you indifferent between c) and d)?

Missmallprincess --

Ah, what a pleasant problem to start a Tuesday morning!  First, I'd
buy the sailboat . . . whoops, I'm off-topic!

Microsoft Excel is a wonderful tool to run these calculations,
particularly for questions B and C.  The NPV function calculates the
present value of future income streams; I've also used the Present
Value (or PV) function to calculate an annuity.  What you'll find with
an annuity is that after about 200 years, the present value of an
income stream approaches a limit -- though the example that I've used
below has 500 years in it.  This spreadsheet should be viewable in
your browser, even if you don't have Excel:
http://www.mooneyevents.com/Powerball.xls

You can see the present values in the first 4 rows of column B.  Note
that each has an immediate payment (year 0), plus 24 additional -- to
total 25 years of payments.  And the same was done for the two private
firm choices.

Note that in a Present Value calculation, the number is negative
because you're RECEIVING rather than making the payment.

---

To answer B and C, I've taken the same calculations and altered
interest rates until we get something close enough for "indifference"
in the NPV of payments.  For A/B it turns out to be a discount rate of
6.077% (download this Excel file to your own system and you can
manipulate the percentages in the NPV formula).

Indifference between C/D happens at a discount rate of about 8.88%.

Best regards,

Omnivorous-GA

Thank you very much for your speedy responce.  You answers were
wonderful.  I loved that you made a spreadsheet rather than just gave
me numbers.  I hope that you will answer more of my questions in the
future.  I will post more on Thursday!

In real life, it is not just a matter of math.

You must also consider your age & all other circumstances.

Different people could quite sensibly choose different options.