an expenditure of $16,00 was made to modify the production line of a local manuf

Question

an expenditure of $16,00 was made to modify the production line of a local manufacture .The modification will save the company $1000 the first year,$3000 the second year and $4000 from then on. How many years must the system last to pay for itself if a 12% MARR is used? There will be no salvage value for the system at the end of its life.

Explanation / Answer

let n be the required no. of years NPV = -1600 + 1000/(1+r) + 3000/(1+r)^2 + 4000/(1+r)^3 + 4000/(1+r)^4 + 4000/(1+r)^5 ......... + 4000/(1+r)^n r = 0.12 To pay for itself, NPV = 0 => 16 = 10/1.12 + 30/1.12^2 + 40/1.12^3(1 + (1/1.12)^2 + ...... + (1/1.12)^(n-3)) if the system last for one year, NPV = -1600 + 1000/1.12 = -707.14 -ve if the system last for two years, NPV = -1600 + 1000/1.12 + 3000/(1.12)^2= 1684.44 which is +ve so system should last atleast two years to pay for itself.

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