Question

A 2,500 square foot house in New Jersey costs $2,000 each winter to heat with its existing oil-burning furnace. For an investment of $6,000, a natural gas furnace can be installed, and the winter heating bill is estimated to be $1,200. If the homeowner's MARR is 8% per year, what is the discounted payback period of this proposed investment? Choose the correct answer below. A. The discounted payback period of this proposed investment is 9 years. B. The discounted payback period of this proposed investment is 8 years. C. The discounted payback period of this proposed investment is 12 years. D. The discounted payback period of this proposed investment is 10 years.

Answer 1

Annual savings after installation of natural gas furnace = 2000 - 1200 = 800

Initial cost = 6000

MARR = 8%

Let the payback be n yrs

6000 = 800 * (P/A, 8%,n)

(P/A, 8%,n) = 6000 / 800 = 7.5

((1 + 0.08)^n-1)/(0.08 * (1 + 0.08)^n) = 7.5

((1.08)^n-1)/(0.08 * (1.08)^n) = 7.5

((1.08)^n-1) = 7.5 * (0.08 * (1.08)^n)

((1.08)^n-1) = 0.6 * (1.08)^n

(1.08)^n = 1 / (1 - 0.6) = 1 / 0.4 = 2.5

n = log 2.5 / log 1.08 = 11.91 yrs

Payback period = 12 yrs (option c)