True cost of a new toy

File this one under finances-- might not be too interesting to some of you, but I thought I'd share.

 

I've just been considering buying a new toy.  It's $160, and there's no way I could say it's a necessity.  My thinking got to be, what's this money worth to me?  What would I be doing with it if not spending it?

Obviously, there are tradeoffs-- it could be a nice dinner or a couple nights out drinking.  It could also be something useful or practical, but I tend to budget for those things appropriately.  If I don't spend this money, it will end up in savings.  Or put another way, if I buy this toy, the money's coming out of my savings.

I really have nothing specific set up for my savings.  It will probably go toward a house at some point, depending on the mortgage market, but I'm cautiously believing that will be an asset that appreciates at least as well as my portfolio, so it's really just another vehicle for savings.  In the end, it's going to be my retirement or my offsprings' inheritance.

So how much will it actually cost?  The following are some quick estimations.  I realize I round a few corners here-- it's for simplicity's sake, and anywhere you predict 40 years' worth of market returns and the year of your own death, you've got to admit to some level of inaccuracy.

 

Let's start with some round numbers.  Adjust to your own as you see fit:

Let's say I've got 40 years between now and retirement.  And I plan on dying 30 years after that.  We'll also assume inflation averages to 3.5% and my investment will return 8.5%, giving me an appreciation of 5% a year in today's dollars (go with me...)

If I forgo this toy and don't use the money, my kids will have 160*1.05^70 = $4800 extra in their inheritance, minus taxes.  Not too bad...

If I end up needing this money in my 30 long years of retirement, it nets an extra $70 a year (again, minus taxes) for each of those 30 years.  I essentially pay myself back in the first two years, then it's a free $70 annual income for the last 28. The math for this one is a bit longer, so I'll put it at the end.

All that for skipping out on this one thing.  Of course, I think I'm still going to get it, but at least I know what I'm really spending now.

 

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Math for estimating the annual payout of an amount saved now:

 

C = item cost

W = working years (years until retirement)

Y = retirement years (years from retirement until death)

R = net rate of return (appreciation - inflation)

 

P = savings at retirement = C*(1+R)^W

F = rate of appreciation during retirement = (1+R)^Y

Annual payout = R*P*F/(F-1)