It is easy to fantasize about making a lot of money.
It is much more depressing to actually calculate how much money you or I would need to stop working, because it means that we'd need to calculate our expenses on a yearly/monthly basis until our terminal point, our deaths. And we can do the math, with a few assumptions.
I'm 30 years old. I'll most likely live to about 80. That's 50 years.
Current monthly expenses: approximately 2000-2500, so about $30,000 after taxes to live at current levels without any bumps in the road, or new purchases (like a car).
But let's build in an extra $10,000 a year for those interruptions. Now I need $40,000.
And then we'd need to take into account some inflation. Okay, let's assume an even 5% Now I must open excel. Perhaps though I can get an average rate of return from investments equal to about 5%.
And let's say tax is approximately 30%.
So, an income of $60,000 yields $42,000 after taxes. That's enough given the above assumptions. Now, 60k * 50 years = $3.0 million.
There you have it folks. Simple, assumption loaded. Anyone have 3 million around so I can retire early?
Edit: It is more than likely that if I actually had that money I wouldn't be capable of budgeting it appropriately, and that I'd value the present higher and spend accordingly--30k when you have 3,000,000 looks a lot different than when you have 42,000.
Another pedantic nitpick: your assumptions are actually stronger than what you say about them. For example, you say (or imply) that, over the course of those 50 years, you're assuming an average inflation rate equal to average rate of return on investment. But you are actually assuming something much stronger, namely a constant (and equal to zero) difference between inflation and ROI rate for each of those 50 years. Why? Because if you only assume that average inflation rate and average ROI rate are equal, it may very well be the case that 50 payments of $60,000 are not will not sum up to $3,000,000. The reason is that assuming average rates are equal, they may (and most likely will be) different in any given particular year, and then your annual income for that year will be less or more than $60,000; but how much less or more will depend on the stock of money you will have invested that year. IOW, for any year t, your income in that year is a function of the stock of your investment in year t, and the difference between inflation rate and ROI rate which, under your assumption, need not be zero.
ReplyDeleteYou're right, that is a nitpick. Only because the feasibility of me gaining that amount of money is so small as to be ridiculous to talk about, not because t is inaccurate. However, should I receive a large sum, I'll make sure to allow a buffer between ROI and inflation that is greater than zero.
ReplyDeleteWhat you're saying is mathematically inaccurate. A stream of 50 annual payments of $60,000 assuming average annual rate of inflation equal to average annual rate of return on investment does not equal $3 million. To make the equality true mathematically you need different assumptions than the ones you stated.
ReplyDeleteI'll have a refined version of this post with some different assumptions soon.
ReplyDeleteHere's a numerical example to show what I mean. Suppose that each of the next four years you'll be getting a payment of $100 (in nominal terms). The original version of your post seems to be saying that if you assume that average annual inflation rate and average annual ROI are equal (say, both are 5%), then after four years you'll have $400. This claim is wrong, and here's a counter-example. Suppose that, in year 1, ROI was 20% while inflation rate was 0%, in year 2 and year 3 both rates were 0%, and in year 4 ROI was 0% while inflation rate was 20%. The average annual ROI is 5%. The average annual inflation rate is also 5%. Yet after four years you end up with $336.
ReplyDeleteIn year 1, you get 100 with an ROI of 20% and inflation stays flat, so you have $120. In years 2 and 3, you get 100 each, so you now have $320. In year four you get $100, but it is only worth $80 because inflation hit you in the gut at 20%. $320 and $80 is $400.
ReplyDeletenote, i'm not doing any compounding or anything fancy, obviously.
ReplyDeleteI didn't mean anything fancy.
ReplyDeleteCompounding can make a big difference, however, if you're not careful about your assumptions. For example, suppose that in each of the first 25 years of your retirement your money will grow 5% annually, and in each of the next 25 years it will shrink by 5% annually. In this admittedly ridiculously unrealistic (but nonetheless consistent with your original assumptions) scenario, in order to ensure an annual income of $60,000 for those 50 years, you don't need to save $3 million. Slightly less than $1.8 million will suffice.
It's an interesting question though--how big of a stock of money do you need to have saved in order to ensure t annual payments of x dollars, assuming you spend the whole amount x each year, and that each year your stock will grow or shrink with some (not too large) interest rate r(t) such that the mean of all t of those rates is zero (or very close to it)? I am sure this question has an analytic answer. I'm not good enough at calculus to try to re-create it though. But, it's a fun project for some simulations. For example, you could simply assume that the annual net interest rates you'll encounter is simply a vector of t random draws from a standard normal. This'll mean that your annual rates will be between -3% and 3% like 99% of the time. For t=50, the mean annual net interest rate will be less than 0.015 away from 0 95% of the time. It seems realistic enough to start with. I think I'll go do this now.
Correction: for t = 50, 95% of the time the mean annual net interest rate will be somewhere between -0.28% and 0.28%, since 1.9*(1/sqrt(50)) = 0.28.
ReplyDelete