Question

Congratulations! You have just won the State Lottery. The lottery prize was advertised as an annualized $105 million paid out in 30 equal annual payments beginning immediately. The annual payment is determined by dividing the advertised prize by the number of payments. Instead you could take a one lump cash prize of the present value of all the annuity payments using a 4.5% discount rate. You now have up to 60 days to determine whether to take the cash prize or the annuity. Which option is better and why. Be sure to cite sources and provide any calculations that can help in determining the best outcome.

Answer 1

The Lottery amount =105
The Number of Periods =30
Equal Lottery amount =105/30 =3.5 per year
Rate =4.5%
PV of annuity due payments =(1+4.5%)*3.5*((1-(1+4.5%)^-30)/4.5%)=59.58

Since discount rate is on the lower side . It is better to take the Lump sum amount as compared to the annuity because discount rate could be higher than 4.5% leading to lowering value of the Present value. Discount rate has to be higher than risk free rate . Current 30 year bonds have nearly 3% the premium of discount rates has to be greater than 4.5% considering the maturity, default and inflation premium .. This lump sum amount better than the annuities.