The City of Prattsville is comparing two plans for supplying water to a newly developed subdivision:
• Plan A will take care of requirements for the next 15 years, and at the end of this time, the initial cost of $400,000 will have to be duplicated to meet the requirements of subsequent years. The facilities installed at dates 0 and 15 may be considered permanent. However, certain supporting equipment will have to be replaced every 30 years from the installation dates at a cost of $75,000. Operating costs are $31,000 a year for the first 15 years and $62,000 thereafter, although they are expected to increase by $1,000 a year beginning in the 21st year.
• Plan B will supply all requirements for water indefinitely into the future, although it will be operated only at half capacity for the first 15 years. Annual costs over this period will be $35,000 and will increase to $55,000 beginning in the 16th year. The initial cost of Plan B is $550,000. The facilities can be considered permanent, although it will be necessary to replace $150,000 worth of equipment every 30 years after the initial installation.
The city will charge the subdivision for the use of water on the basis of the equivalent annual cost. At an interest rate of 10%, determine the equivalent annual cost for each plan, and make a recommendation to the city.