John Fortuna won the state lottery, which provides him with $50,000 in
payments on September 1 of each year for 20 years. After a few years,
John needed cash and decided to sell the next two lottery payments.

If you require a 12% annual yield, what is the maximum price you should
offer John on April 1 preceding the next payment?

It would appear that this is a simple problem of discounting two payments of $50,000 @ 12% to find the Present Value – which would be the maximum price to be paid for these payments.

But this is an oversimplification, since you would have to wait 5 months from settlement to receive the first $50,000 payment and another year to receive the second.

Therefore this is an uneven cashflow problem in which the first cashflows (measured from April 1 to Sept. 1) consist of 4 monthly returns of zero cashflows (May 1, June 1, July 1, Aug.1), one payment of $50,000 on Sept. 1, then 11 more months of zero payments, and a final cashflow of $50,000.

The discount rate must be expressed on a monthly basis ( 12%/12) since the payments are expressed monthly.

HP-12C calculator entries would be:

0 CFo
0 CFj
4 Nj
50,000 CFj
0 CFj
11 Nj
50,000 CFj
12/12 i
f  NPV