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 $11,000, a replacement cost of $6,000 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 $10,000, 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 equivalent uniform annual cost (EUAC) of costs for the option the engineer should recommend at an interest rate of 5.6%. Express your answer in $ to the nearest $10.

Answer 1

MARR = 5.6%

gas-fired furnace option

the initial cost of 11,000

the replacement cost of 6,000 (Will be replaced at end of 5th and 10th year as life is only 5 yrs)

annual operating costs of 3,500

life = 5 years

Present value for a study period of 15 years = -11000 - 3500 *(P/A, 5.6%,15) - 6000 *(P/F, 5.6%,5)- 6000 *(P/F, 5.6%,10)

= -11000 - 3500 *9.9712077 - 6000 *0.7615184 - 6000*0.5799102

= -53947.80

Annual worth = -53947.80 *(A/P, 5.6%,15)

= -53947.80 *0.10028875 = -5410.36

= -5410 (rounding to nearest 10)

geothermal heat pump system

initial cost of 17,000

replacement cost = 10,000 (will be replaced in 10th year as live is only 10 years)

annual operating costs = 2,500

increases the value of the building by 4,000, when it is sold at the end of year 15

Present value for a study period of 15 years = -17000 -10000 *(P/F, 5.6%,10) - 2500 *(P/A, 5.6%,15) + 4000 * (P/F, 5.6%,15)

= -17000 -10000 *0.5799102 - 2500 *9.9712077 + 4000 * 0.4416123

= -45960.67

Annual worth = -45960.67 *(A/P, 5.6%,15)

= -45960.67 *0.10028875 = -4609.34

= -4610 (rounding to nearest 10)

We should choose geothermal heat pump system as its Equivalent annual cost id less