Question

Answer the following multiple-choice question. You have to select the correct option and provide a complete correct solution.

d. A remotely situated fuel cell has an installed cost of $2,000 and will reduce existing surveillance expenses by $350 per year. The border security agency's MARR is 10%. What is the approximate minimum useful life that makes the fuel cell purchase break even? i. 8.52 ii. 8.63 iii. 8.77 iv. 8.89

Answer 1

Please rate the answer
Answer (iv) 8.89 years

TO make the purchase break even , the present value of the savings should be equal to the cost
PV of the savings can be calculated using P/A factor for 10 %

We can calculate the value of n at which it will break even.

2000 $ = 350 $ * P/A_{( 10%,n)}
5.71429 =  P/A_{( 10%,n)}
5.71429 = (1-(1+0.1)^-n) / 0.1
0.57146 = (1-(1.1)^-n
1.1^-n = 0.42854

Taking log both sides
-n log (1.1) = log ( 0.42854)
-n (0.04139) = -0.3680
n = 0.3680 / 0.04139
= 8.89