Question

Kristina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $61 million, to receive 10 end-of-year payments of $9.4 million, or to receive 30 end-of-year payments of $5.4 million.

If she thinks she can earn 7% percent annually, which should she choose?

If she expects to earn 8% annually, which is the best choice?

If she expects to earn 9% annually, which option would you recommend?

Explain how interest rates influence her choice.

Answer 1

7%:
Present value of lumpsum=61 million

Present value of 10 year payments=9.4/7%*(1-1/1.07^10)=66.02 million

Present value of 30 year payments=5.4/7%*(1-1/1.07^30)=67.01 million

Choose 30 year payments

8%:
Present value of lumpsum=61 million

Present value of 10 year payments=9.4/8%*(1-1/1.08^10)=63.07 million

Present value of 30 year payments=5.4/8%*(1-1/1.08^30)=60.79 million

Choose 10 year payments

9%:
Present value of lumpsum=61 million

Present value of 10 year payments=9.4/9%*(1-1/1.09^10)=60.33 million

Present value of 30 year payments=5.4/9%*(1-1/1.09^30)=55.48 million

Choose lumpsum

Higher the interest rate, the choice shifts to lesser year payments and finally lumpsum today