Question

Which of the following alternatives is superior over a 30 year period, if the interest rate is 5%? Determine the EUAC for each alternative, and also calculate the Capitalized Cost for each. a. Green roof costing $50,000 with a life of 30 years; utility costs $12,000/year b. Standard roof costing $20,000 with life of 10 years; utility costs $18,000/year

Answer 1

time period = 30 years , i = 5%

Alternative A:

Capitalized cost = 50000 + 12000/(1 + 5%) + .... + 12000/(1 + 5%)³⁰

Capitalized cost = $ 234469.41

EUAC = A (PV of A for 30 years at 5% = 234469.41)

A/1.05 + .... + A/1.05³⁰ = 234469.41

EUAC = A = $ 15252.57

Alternative B:

Capitalized cost = 20000 + 18000/(1 + 5%) + .... + 18000/(1 + 5%)¹⁰ + 20000/1.05¹⁰ + 18000/(1 + 5%)¹¹ + .... + 18000/(1 + 5%)²⁰ + 20000/1.05²⁰ + 18000/(1 + 5%)²¹ + .... + 18000/(1 + 5%)³⁰

Capitalized cost = $ 316520.17

EUAC = B (PV of B for 30 years at 5% = 316520.17)

B/1.05 + .... + B/1.05³⁰ = 316520.17

EUAC = B = $ 20590.09

Alternative A has a lower cost and should be chosen over alternative B.