LogFAQs > #927697025

This ended up eating at me as I was deliberating over which option to go for.

I did some back of the envelope calculations, assuming 100 years (50 for me + a further 50 for my child since you essentially are trying to calculate how many more years after you die since the time you're both alive is served concurrently). For anyone wanting to reperform my calcs, 100 years = 36525 days.

Basically using the annuity formula for 100 years, Excel's goal seek has told me that 5.6025% is the breakeven point where a discount rate of LESS than 5.6025% will mean the present value of the daily annuity is worth more. A discount rate MORE than 5.6025% would mean taking the lump sum is the better option.

Then in debating over what discount rate to use, I have oversimplified this a bit but to cater for the inflation adjustment to the payments, you would deduct that growth rate from the discount rate used - or if we're working backwards, add it back on to the 5.6025%. Assuming the inflation rate is 1%, then it would be 6.6025%.

Based on this, if you're able to beat 6.6025% consistently in your investment returns, go for the lump sum. Otherwise take the daily payment.

Most savvy investors would scoff at 6.6% as an easy target but remember this is consistent and a risk-free return more akin to a US Treasury bond status or (pre-GFC) Fed guaranteed bank deposit.

If you play the flipside and work on an assumed discount rate, say 1.5% to reflect time value of money and build in the inflation adjustment feature, that would have a NPV of $56.529 million (i.e. above the $20m lump sum option).

Hopefully my sleep deprived brain at 11pm hasn't mixed this up though.

Excel formula
=C20*(1-(1/((1+D19)^C18)))/D19

C18 is number of periods (or days in this case)
C20 is payment per day
D19 is the discount rate adjusted from annual to daily

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If you can understand this, I'm 2/cosC for you.