A village on is planning a new water supply scheme, and is considering two options:

a) A 15-year system with an initial cost of $400,000. The system will have to be supplemented with a similar system in year 15. Supporting equipment will be replaced every 30 years for a total cost of $75,000. For the first 15 years, operating costs will be $31,000 per year, then will increase to $62,000 per year. They will also be expected to increase by $1000 per year after year 21.

b) A one-time system with an initial cost of $550,000. The system will be operated at half-capacity in the first 15 years, incurring operating costs of $35,000 per year. These will increase to $55,000 per year in year 15, when the system will move to full-capacity operation. Supplementary equipment will have to be replaced every 30 years at a cost of $150,000.

Do the following:

a) Based on a rate of return for the village of 10%, make a recommendation to the village on which system to use based on a life-cycle analysis.