Suppose you win a 100 million lottery and you can choose the following two payment options:
1) receive 25 equal payments of $4,000,000- one payment today and one payment at the end of each of next 24 years.
2) one time lump sum payment of $59 million.
Question 1: If you can invest your proceeds and earn 6 percent, which payment option you will choose?
Questions 2: At what rate of return, would you be indifferent between the lump sum and annual payment options?
Answer 1:
Option 1: Equal annual payments of $4,000,000 for 25 years starting today
Rate of return = 6%
Option 2: One time lump sum payment = $59 million = $59,000,000
PV of option 2 = $59,000,000
To get PV of option 1, we will use PV function of excel:
PV (rate, nper, pmt, fv, type)
PV (6%, 25, 4000000, 0, 1)
= $54,201,430.11
Since $59,000,000 > $54,201,430.11, we will choose option 2 (One time lump sum payment of $59 million)
We will choose option 2
Answer 2:
The rate of return will be rate at which PV of option 1 = PV of option 2
PV = $59,000,000
Annual payments each year at the start of year = $4,000,000
Period = 25 years
RATE (nper, pmt, pv, fv, type)
RATE (25, 4000000, -59000000, 0, 1)
= 5.03634%
= 5.04%
The rate of return, at which you would be indifferent between the lump sum and annual payment options = 5.03634%
or 5.04%
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