Calculations also assume 100% efficiency of heat transfer to the water, so probably need to adjust a little for that.
Can't believe you electricity is so much cheaper, we will be paying around 18c / kwH here in the UK...
Since we're talking about electrical resistance heating here,
all of the energy used by the heater itself is transferred to the water. It has nowhere else to go! It isn't like a heat exchanger in a furnace where there is some heat loss in the combustion gasses. However, there are transmission losses in the wiring between your utility meter and the hot tub's heater that must be considered. Provided the wiring is appropriately sized, these losses will be about 40 watts for a 50-foot run to a hot tub with a 6,000-watt heater - about $2 per month if the heater ran continuously, which it does not. The real-world cost for this transmission loss might be a nickel or a dime at most - even less when you consider some of the heat generated by the wire's resistance might be in your wall and some gets transferred into your home which offsets home heating costs. Point being, the amount of transmission loss is minuscule and not even worthy of discussion in this application.
Electricity is always "cheap" here. My 1,600 sq. ft. home built in 2012 is "all-electric". My electric bill averages $95 per month. Water is a different story - I'm on a municipal water system owned by the tiny, incorporated "city" I live in. There are only a few hundred customers, so we pay quite a premium for our award-winning water.
