Question

You are the design consultant comparing two pump options. The first option has an installation cost of $36,000 and lasts 40 years with $1,000 maintenance every 10 years. The second option has an installation cost of $30,000 and lasts 40 years if a large refurbishment of $15,000 is conducted after 20 years. Assuming a 5% annual interest rate, what is the difference in present value between options 1 and 2? (Option 1 – Option 2)

a.

$1,569

b.

$2,710

c.

$1,711

d.

-$6,000

Answer 1

Interest rate = 5%

Option 1:

First cost = $30,000

Cost every 10 years = 1,000

Present value of cost after 10 years = [1,000 / (1 + 0.05)^¹⁰] = 613.91

Present value of cost after 20 years = [1,000 / (1 + 0.05)^²⁰] = 376.89

Present value of cost after 30 years = [1,000 / (1 + 0.05)^³⁰] = 231.37

Sum of present value of cost = 613.91 + 376.89 + 231.37 = 1,222.18

Option 2:

First cost = $36,000

Cost every 20 years = 15,000

Present value of cost after 20 years = [20,000 / (1 + 0.05)^²⁰] = 5,653.34

Present value of option 1 - option 2 = Initial cost of option 1 + Present value of cost of option 1 - Initial cost of option 2 - Present value of cost of option 2 = 36000 + 1,222.18 - 30,000 - 5,653.34 = 1,568.83 which is rounded to 1,569

Keep in mind that we will not consider cost at the end of 40 year because neither of the option is worthy at the end of 40 years.  

Option A is correct.