Question

Congratulations! You have just won the Lottery. The Lottery Commission informs you that you can choose between three different pay out options: (1) $500,000 cash payment today, (2) $50,000 cash payments at the end of each year for twenty years, or (3) $1,000,000 in cash in one payment after 20 years. Current CD’s are paying 3.50% annual interest. Which do you choose and why?

Answer 1

1.Present value of inflows=$500,000

2.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=$50,000[1-(1.035)^-20]/0.035

=$50,000*14.2124033

=710620.17(Approx).

3.Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

=$1,000,000/1.035^20

=$1,000,000*0.502565884

=502565.88(Approx).

Hence option 2 must be chosen having highest present value.