A Question of Value

Damn, I wish I have enough luck to get winnings like these!

$365m, shared by 8 people!

Bit O Math

After tax, these guys will be getting $15.5m each. This struck me as strangely low, and procrastinating from studies (yes, it's exam season for me again), I decided to dig into this a bit more. 8 people won the lottery, so the total winnings sum to $124m. In the UK, lottery winnings are not taxed, but apparently the US federal tax on winnings is a shocking 38%! So, this brings the total pre-tax winnings to $200m (124/0.62). Where'd the other $165m go??

Bit More Math

At first glance, it looks like our winners have let go of $165m in order to satisfy their immediate hunger for riches. So what would the amount have been if the winners decided to take the winnings in instalments? It turns out that the discrepancy is only due to annuities. The $200m they have now, is worth about $365m in 30 years time, if inflation stays at about 2% per year (worked out by: 200 x 1.02^30). So there's absolutely no financial advantage to getting the money paid through instalments.

But wait! How much would they have received each year, if they decided to get paid by instalments?

Well, the annuity would have a present value of $200m. So, over 30 years, discounting at the standard UK inflation rate of 2% (hmm, is that a valid indicator? It'll have to be for now), we'll arrive at a discount factor of about 22.396 (1/0.02)*(1-(1/1.02^30)). This means that the annual payments should be about $9m (200/22.396).

So each winner would be able to live on a "salary" of about $1m, in current terms, for the next 30 years of their lives! Not a shabby deal eh? Still, I'd prolly take the cash now, given the choice...

Conclusion?

Now i know why everyone chooses to take up the cash winnings instantly. Great. Back to my books. Sigh.