Tom Sewell has gathered data on the relative costs of a solar water heater system and a conventional electric water heater. The data are based on statistics for a mid-American city and assume that during cloudy days an electric heating element in the solar heating system will provide the necessary heat. The installed cost of a conventional electric water tank and heater is $200. A family of four uses an average of 300 liters of hot water a day, which takes $230of electricity per year. The glass-lined tank has a 20-year guarantee. This is probably a reasonable estimate of its actual useful life. The installed cost 'of two solar panels, a small electric pump, and storage tank with auxiliary electric heating element is $1400. It will cost $60-a year for electricity to run the pump and heat water on cloudy days. The solar system will require $180 of maintenance work every 4 years. Neither the conventional electric water heater nor the solar water heater will have any salvage value at the end of their useful lives.
(a) Using Tom's data what is the payback period if the solar water heater system is installed, rather than the conventional electric water heater?
(b) Chris Cook studied the same situation and decided that the solar system will not require the $180 of maintenance every 4 years. Chris believes future replacements of either the conventional electric water heater or the solar water heater system can be made at the same costs and useful lives as the initial installation. Based on a 10% interest rate, what must be the useful life of the solar system to make it no more expensive than the electric water heater system?