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JoshuaFox comments on Open Thread, September 30 - October 6, 2013 - Less Wrong Discussion
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Here's a twist on prospect theory.
I installed solar panels, which were pretty expensive, but pay back as they generate electricity.
The common question was "How long will it take to earn your investment back?" I understand why they're asking. The investment is illiquid, even more than a long-term bank deposit. But if wanted to get my money "back," I'd keep it in my checking account. The question comes from a tendency to privilege a bird in the hand over those that are still in the bush.
The important point they should ask about is my probability-adjusted return on investment.
If the panels have a total breakdown before I get my investment back, that's bad, but it's just a negative RoI, no worse than losing money to inflation or to a down stock market.
If I get my money back, and then the panels break down right away, I won't say "at least I got my money back," I'll say "I wish my RoI had been greater." If I get my investment back, but it takes far longer than I expected, I won't say "at least I got it back." I'd say "too bad that my annualized RoI is near zero; at least it's not negative."
And if my RoI is super-duper, and I get my money back quick, I won't say "hurrah, I got my money back," I'll say "hurrah, I'm getting better RoI than any other investment I can make today," which is actually what I'll say even before I get my investment back. And then I'll keep smiling so long as the panels keep laying the golden eggs.
Correct.
If you want to be even more correct :-) you should estimate your IRR (internal rate of return) and compare it with your opportunity costs for the money invested.
Yes, good point. It took me a while to figure out by myself the best way I should be calculating my rate of return on my variable-return investments, before discovering this in Excel.
But in this case, the panels produce (hopefully) a pretty constant annual amount of electricity, and the price I get is a fixed amount, so it seems that calculating IRR is easy.
As long as we are the topic, maybe the smart folks here can explain, mathematically, why the summation formula for IRR does not admit a closed-form solution? I asked on Quant StackExchange and didn't get much of an answer.
Your calculation is presumably for a fairly long term. In the long term prices don't remain fixed, things break down, need maintenance, etc. For example, hail might damage some of your panels. Or your roof might start to leak and the presence of the panels will substantially add to the cost of repairing it.
Excellent. I had an overly-simplistic mental model in which the panels would last until they fail.
But yes, unexpected costs that are nonetheless below full price of the panels are a real possibility.