Question

Lottery Prize (millions)	$                           14.00		millions
Annuity (millions)	$                             1.00		per year
APR ( R )	7.00%		annual
N (begin now) in years	25.00		years
Benefit of lumpsum option (Excel)	Gain/Loss of	????	millions
Benefit of lumpsum option (VBA)	Gain/Loss of	????	millions
Benefit of lumpsum (Math, Extra Credit)	Gain/Loss of	????	millions

Juan has just won a lottery. He can get $14 million now (after-tax, lumpsum or one-time option), or he can get $1 million annually for 25 years starting today (after-tax, 25 payments of $1 million each). Whichever option he chooses, he can save his money at a local bank, which is offering a 7% per year return on deposits.
Juan is not sure if he should pick a lumpsum option or 25-payments option. He comes to you for help. What is the benefit (or loss) of choosing the lumpsum option in today’s dollars?

Answer 1

Present value of lump-sum option = $14 million

Present value of annuity = 1+1.07^-1+1.07^-2+1.07^-3+.........+1.07^-24= (1 - 1.07^-25) / (1 - 1.07^-1) =$12.469334 million

As the PV of lump- sum option is higher, Juan should opt for the lump-sum option with a benefit of

$(14 - 12.469334) million=$1530666 in today's dollars.