A company has decided to gradually phase out an old machine with a new machine.

Question

A company has decided to gradually phase out an old machine with a new machine. It will take 2 years to gradually make this transition so the company does not reduce its annual production output and they will still be able to ship all of their customer orders on time. Therefore the costs and savings during the first two years will balance one another out and there will be no extra costs or savings during the initial 2 year period. However, beginning in year 3 the company will begin saving $18,000 per year and these savings will continue through year 12. Determine the equivalent annual worth of these savings (years 1 through 12) using an interest rate of 7% per year.

Please use shifted uniform series to solve problem.

Explanation / Answer

Present value of annuity in year 2 = 18,000*(1-(1+0.07)^-10)/0.07

= 126424.47

Present value of amount in year 0 = 126424.478*(1+0.07)^-2

110424.03

=> EAW = 110424.03/((1-(1+0.07)^-12)/0.07)

$13902.60

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