Is that front loading washer worth it?

As my wife noted, our washer celebrated the new year by giving in to gravity, dumping several soapy gallons of water on our newly-painted laundry room floor. So we're in the market for a new washer, and were told by the salesman last night that a front loading washer is better because it will save us $100 in utilities, get clothes cleaner, and do our taxes.

"Great," says I, "but this EnergyGuide tag suggests it's more like $20 a year."

"That's not counting the expense of heating the water," says Slick, "that's the real expense."

But $100? Let's do the math.

Assumptions:

• Two washers, one top-load and one front-load. The former uses 450 kWh per year (and 40 gallons per wash load) and the latter 150 kWh per year (and around 21 gallons per load) for operations. These are typical figures according to the federal Dept of Energy.
• The top-load washer costs $300, the front load washer costs $600.
  
• Water is heated with natural gas. It takes 706 btus or 0.007 therms of natural gas to heat 1 gallon of water from 55 Fahrenheit to 140 Fahrenheit.
• Electricity costs 8.3 cents per kWh, the national average.
  
• Natural gas costs $0.91 per therm, the rate from my local utility.
  
• The water itself costs $0.003 per gallon, the municipal rate in my hometown.
  

So, the typical top-load wash consumes 40 gallons of water, for a cost of 11.4 cents for the water. Heating the water consumes 40*706=28,280 btus or 0.28 therms, for a cost of 25.7 cents. So, the water and heat cost 37.1 cents per load.

The front-load washer consumes 21 gallons of water, for a cost of 6.1 cents. The energy used to heat the water is 21*706=14,826 btus or 0.148 therms, for a cost of 13.5 cents. So, the front load water and heat cost 19.6 cents per load.

My wife and I average 2 loads a week (104 a year), plus a few bonus loads. Let's call it a round 120 loads.

Since the government provides the electricity use figures on the yellow tag, I'm using those even though they aren't adjusted per load. So each year, the top load washer uses 450 kWh @ 8.3 cents/kWh = $37.35. The front loader uses 150 kWh @ 8.3 cents/kWh = $12.45.

So, our total costs look like this:
Top loader: 120 loads * ($0.371 water/heat per load) + $37.35 for electricity = $81.87 annual operating cost
Front loader: 120 loads * ($0.196 water/heat per load) + $12.45 for electricity = $35.97

Front load annual savings: $45.90 (simple payback = 6.5 years)

Slick clearly doesn't understand that a couple with no kids doesn't run the washer 4 times a week.

For those curious, here's a chart showing the annual cost of each washer based on the number of loads done each week, with the dotted line showing the annual savings.