Question

Alternative A has an initial acquisition cost of $10,000 and an annual average operating and maintenance cost of $1402 per down time. Alternative B has a higher acquisition cost of $20,000, but has a lower annual average operating and maintenance cost of $500 per down time. With an expected lifetime of 5 years for both alternatives, and an annual interest of 5%, determine the break even number of down times per year.

please show all work

Answer 1

Total cost for A = initial acquisition cost + (annual cost*5)

= 10,000 + (5*1402) = 17,010

Total Cost for B = 20,000 + (5*500) = 22,500

Let the no. of years for breakeven be n

Thus for A, 10,000(1+5/100)ⁿ = 20,000. The left hand side is equated to 20,000 because 20,000 is double of 10,000 and thus when the total revenue reaches 20,000, only then there will be a breakeven

(105/100)ⁿ = 2

n = 14

Thus, 14 years will be taken to breakeven

In the second case, left-hand side equation will be equated to 40,000. The explanation is the same as given above.

20,000(1+5/100)ⁿ = 40,000

(1+5/100)ⁿ = 2

n = 14