Question

Which option would you select if you had the chose of receiving $1 million dollars in lottery or $100,00 a year over the next 10 years. Current 10 year interest rates are at 5% and the current tax on lottery winnings is 40%. Explain!

Answer 1

We have to calculate the present value of both the alternatives and check which alternative has higher present value.

First we will take the present value of $100000 a year over the next 10 years as per below:

After tax cash flows of $100000 a year over the next 10 years will be :

$100000 * (100% - 40%) = $100000 * 60% = $60000

So, there will be $60000 net cash flows per year for next 10 years.

Since, $60000 payment is equal / uniform every year, so it is a case of annuity. We will use the present value of annuity of $1 table to find the required present value.

Present value = $60000 * PVA (5%, 10 Years)

The value of PVA (5%, 10 years) from the present value of annuity of $1 table is 7.7217. Putting this value in the above equation, we get,

Present value = $60000 * 7.7217 = $463302

Now, the present value of $1 million now is $1 million minus the applicable tax rate, which comes,

Present value = $1000000 * (100% - 40%) = $1000000 * 60% = $600000

As we can see that that the present value of receiving $1 million is more than the present value of receiving $100000 in the next 10 years, so we should accept the option of receiving $1 million today.