Question

A mechanical engineer must recommend a new heating system to a commercial building owner. The owner intends to sell the building in 15 years. A gas fired furnace option has a design life of 5 years, an initial cost of $12,000, a replacement cost of $5,000 and annual operating costs of $3,500, but adds no value to the building when sold. A geothermal heat pump system has a design life of 10 years, an initial cost of $17,000, a replacement cost of $9,000, annual operating costs of $2,500, and increases the value of the building by $4,000, when it is sold at the end of year 15. Determine the PW of costs for the option the engineer should recommend at an interest rate of 7.7%. Express your answer in $ to the nearest $100.

Answer 1

Present worth of the gas furnace = Initial cost+replacement cost in and 10 year+annual operating costs

PW=-12000 - 3500 (P/A, 7.7%, 15) - 5000*(P/F, 7.7%, 5) - 5000*(P/F, 7.7%, 10)

=-12000-3500(8.718528)-5000(0.690115)-5000(0.476259)

=-12000-30514.848-3450.575-2381.295

= -48300

Present worth of the Geothermal heat pump = Initial cost+replacement cost in 10 years+annual operating costs- increase in cost

PW = -17000 - 2500 (P/A, 7.7%, 15) - 9000*(P/F, 7.7%, 10) + 4000 * (P/F, 7.7%, 15)

=-17000-2500(8.718528)-9000(0.476259)+4000(0.328673)

=-17000-21796.32-4286.331+1314.692

=-41700

The geothermal pump should be recommended as its present worth is lower than the gas furnace.