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 $13,000, 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 $9,000, annual operating costs of $2,500, and increases the value of the building by $7,000, 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 6.4%. Express your answer in $ to the nearest $10.

Answer 1

We have the following information

	Gas Fired Furnace	Geothermal Heat Pump
Initial Cost	$13,000	$17,000
Replacement Cost	$6,000	$9,000
Annual Operating Cost	$3,500	$2,500
Benefit	$0	$7,000
Life	5 Years	10 Years

Interest rate (i) = 6.4% per annum or 0.064

Gas Fired Furnace

Equivalent annual worth = 13,000(A/P, i, n) + 6,000(A/P, i, n) + 3,500

Equivalent annual worth = 13,000(A/P, 6.4%, 5) + 6,000(A/P, 6.4%, 5) + 3,500

Equivalent annual worth = 13,000[0.064(1 + 0.064)⁵/((1 + 0.064)⁵ – 1)] + 6,000[0.064(1 + 0.064)⁵/((1 + 0.064)⁵ – 1)] + 3,500

Equivalent annual worth = 3,119.81 + 1,439.91 + 3,500

Equivalent annual worth of Gas Fired Furnace = $8,059.72

Geothermal Heat Pump

Equivalent annual worth = 17,000(A/P, i, n) + 9,000(A/P, i, n) + 2,500 – 7,000(A/F, i, n)

Equivalent annual worth = 17,000(A/P, 6.4%, 10) + 9,000(A/P, 6.4%, 10) + 2,500 – 7,000(A/F, 6.4%, 15)

Equivalent annual worth = 17,000[0.064(1 + 0.064)¹⁰/((1 + 0.064)¹⁰ – 1)] + 9,000[0.064(1 + 0.064)¹⁰/((1 + 0.064)¹⁰ – 1)] + 2,500 – 7,000[0.064/((1 + 0.064)¹⁵ – 1)]

Equivalent annual worth = 2,353.73+1,246.09+2,500–291.69

Equivalent annual worth of Geothermal Heat Pump = $5,808.13

Since, the equivalent annual worth of Geothermal Heat Pump is lower, so, it should be selected.