Mega Millions Winner!

Quantitative Finance Level 3

If you win a Mega Millions Jackpot of $500 million, you can either take a lump-sum payment of $360 million, or take an annual payout of $19 million a year over 26 years. In both cases, you will receive a payment today.

What discount rate (in %) would make you indifferent between these two payment options?

Ignore taxation rates.

Image credit: Flickr msspider66

The answer is 2.73.

1 solution

Chew-Seong Cheong
Feb 25, 2015

This is a case of equating the present values of two methods of payment. The present value of 26 annual payouts of $19 million with discount rate $r$ is given by:

$V_0 = 19 + \dfrac {19}{1+r}+ \dfrac {19}{(1+r)^2} +...+ \dfrac {19}{(1+r)^{25}}$

$\displaystyle \quad \space = 19 \sum _{n=0} ^{25} {\frac {1}{(1+r)^n} } = \frac {19 \left( 1- \left( \frac{1}{1+r} \right) ^{26} \right) }{1-\frac{1}{1+r}} = 360$

Using numerical method, we find $r = \boxed{2.73} \%$

I used Newton's method with a spreadsheet (see below):

We can also use the Internal Rate of Return (IRR) function in a spreadsheet (see below). Please note that the year-1 net cash flow is $-360+19=-341$ . How IRR function is keyed in is also shown (=IRR(B2:AA2,0). The $0$ entered is the guessed value for the rate.

The interest rate being so low makes it almost obvious that one should accept the lump sum payment, as opposed to waiting it out. E.g. It would be beneficial to use it to pay off credit card debt, mortgage loans, car loans, student loans, etc.

Given that, I wonder why it's so low. I guess it's tied to the low interest rate environment that we're currently in. They could also be lump-sum tax concerns.

Calvin Lin Staff - 6 years, 3 months ago

Mega Millions Winner!

Image credit: Flickr msspider66

The answer is 2.73.

1 solution

0 pending reports