Question

You are the lucky winner of the Megazillions lottery. Your prize is $600 million . The Lottery Commission has given you a choice: equal annual payments for the next 30 years, or an immediate check for $250 million. Using a 6.5% discount rate, which is the optimal decision from a financial standpoint? (Please show the correct formula)

Answer 1

	The option that has the higher PV is to be selected.
1]	PV of equal annual payments:
	These receipts constitute an annuity.
	The PV of an annuity is got by using the formula:
	PV of annuity = A*[(1+r)^n-1)]/[r*(1+r)^n]
	Where,
	A = The annual payments
	r = Rate of interest
	n = number of years
	Substituting values, we have
	PV = (600/30)*(1.065^30-1)/(0.065*1.065^30) =	$          261.17	million
2]	PV of immediate check	$          250.00	million
	[This amount does not require discounting as it is to
	be paid now itself]
	OPTIMAL DECISION:
	As the annual payment option gives higher PV, it should be preferred.