You just won the 800 million dollar lottery.
You have the option of taking 500 million as one lump sum or 25.8 million TODAY (year 0) then 25.8 million for the next 30 years.
a) What is the discount rate that makes taking either option equivalent (hint rember you get 25.8 million year zero then 25.8 million for 30 years)? In other words, what return do you need on the payments to make the lump sum equivalent? Think of it as a NPV with CF year 0: -500 and +25.8
b) We need to pay taxes. Assume the tax rate is 40 percent for all payments. How does this change the above? Apply the tax rate to both the lump sum and the yearly payments.
c) Now, on top of the taxes above, consider the fact that any money you make on your investments every year will also be taxed at 40 percent. What rate of return will you need after taxes to make both options equivalent? What is the discount rate pre tax you will need?