Yer a bright boy
Do a search
People buy these & install them because they work & save $$
I've been searching and analyzing the issue for quite some time, which is why I've concluded that it's not a slam-dunk for cost-effectivness in many (or even most) situations. You're the one making the assertion that this isn't correct, so I need to see your analysis to figure out where I've gone rong, eh?
The simple math on a $5K solution that delivers an 80% solar fraction with electric element backup @ 12 cents/kwh (considerably less than I pay) for the remainder, compared to a 0.58EF gas fired tank at $1/therm (what I paid, full-retail, on my last gas bill) goes something like this:
Tank capiliziation: $500 up front, $500/decade for replacement & maintenance.
Tank fuel use: 250therms/year or $2500/decade, (delivering ~15MBTU to the water/year)
10 year cost: $3000.
20 year cost $6000
Solar system capitilalizaon: $5000, assume zero mainenance for 20+ years, 80% solar fraction.
Solar backup power: 20% of 15MBTU, or 3mbtu/year, which is 3x 293kwh/mbtu= 879kwh/year, so x $0.12/kwh= $105/year, $1050/decade
10 year cost: $6050 (more than the 20 year cost of the cheapo tank)
20 year cost: $7100
But simple analysis doesn't reflect the real world in two important respects:
1> The $4500 up-front different in cost between a cheapo tank and a cheapo solar could be invested very conservatively to return 5% after taxes, the proceeds of which could be applied to the higher utility costs of the tank. The tank uses $250 (in gas), the solar system uses $105 in electricity, for a difference of $145 in operational cost. With the returns on the cash applied to the utilites that's now reduced to a ~$100/year cost difference.
2> The price of natural gas (and electricity) are not static, and some assumptions have to be made about the future costs of each if we're looking out 5+ years. With the ramping up of production in the Allegheny shale formations predictions of natural gas prices INCREASING dramaticaly over the next 20 years are very dubious indeed, and fraught with many many impossible-to-know factors. Will the US start taxing carbon emissions
heavily, driving electricity production to shift from coal to gas quicker than the gas production can increase? If yes prices will indeed rise on average, but how much requires a crystal ball. If not, we could be looking at decades of lower NG pricing relative to the upramp of the 1900s and early part of this century. At the same time, if electricity is ever increasingly supplied by the same natural gas burners, the price of electricity will also rise.
This is not simple to model, and by no means a no-brainer at $5KUSD. In a net-present-value analysis the underlying assumptions for discount & fuel/electricity inflation rates are likely to have large errors, and it could fall far to either side of the cost effectiveness in a 20 year term, but there's no way it can be demonstrably cost effective in a shorter years than that without some fairly wild assumptions.
It's dead-obvious 10 years at $3K up front though.
But if you have a better analysis (or can point me to one online) let's have it. The math will tell you "the truth".