Question

Lisa just won $2.5 million in the state lottery. She is given the option of receiving a lump sum $1.3 million now, or she can elect to recieve $100,000 at the end of each of the next 25 years. If Gabrielle can earn 5% annually on her investments, which option should she take? Please provide formula used to solve answer.

Answer 1

We will calculate the PV of annual payments of $100,000 for 25 years @5% and then we will compare this
PV with lump sum payment today i.e. $ 1,300,000.
PV of annuity
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be calculated
PMT = the dollar amount of each annuity payment	$          100,000
r = the effective interest rate (also known as the discount rate)	5%
n = the number of periods in which payments will be made	25
PV of annuity	= PMT x (((1-(1 + r) ^- n)) / r)
PV of annuity	= 100000*(((1-(1 + 5%) ^- 25)) / 5%)
PV of annuity	$ 1,409,394.46
Options	Present value
1	$ 1,300,000.00
2	$ 1,409,394.46
As we can see that the PV of 2nd options i.e. annual payment for 25 years is higher than lump sum payment so option 2 should be selected.