John has just won the state lottery and has three award options from which to choose. He can elect to receive a lump sum payment today of $46 million, 10 annual end-of-year payments of $7 million, or 30 annual end-of-year payments of $4 million. If he expects to earn a 7% annual return on his investments, which option should he choose and why?

John should opt for the 30 annual end-of-the-year payments of $4 million as that gives the highest present of value of $49,636,164.73 as shown below.

Explanation:

The options are evaluated as follows:

Option 1 $46,000,0000 today

Option 2

The present of value of this option is calculated using the below formula:

Present value of annuity = ((1 - (1 / ((1+i) ^n)) / i) X PMT

where i=rate=7%

n=10years

PMT=$7m

PV = ((1 - (1 / ((1+0.07) ^10)) / 0.07) X 7000000

PV=$ 43,834,929.21

Option 3

The present value of this option using the formula in option 2 is:

PV = ((1 - (1 / ((1+0.07) ^30)) / 0.07) X 4000000

PV=$49,636,164.73

Hence, the last option is preferable.