Project ForgePlant Design & Economics
Profitability Analysis
GATE 2019
Hard
Equipment A: capital Rs.80,000, operating Rs.20,000/yr, life 4 years. Equipment B: capital Rs.1,60,000, operating Rs.15,000/yr, life n years. At 10% compound interest, for B to be the cheaper option (by equivalent annual cost), its minimum life n (years, rounded to next higher integer) is
8 years
Explanation
EAC_A=80000×CRF(10%,4)+20000=80000×0.3155+20000=45,238. For B: 160000×CRF(n)+15000≤45238 ⟹ CRF(n)≤0.189. Solving 0.10(1.1)^n/((1.1)^n−1)=0.189 gives (1.1)^n=2.124, n=ln(2.124)/ln(1.1)=7.90, rounded up to 8 years.
Source: GATE CH 2019 (2019)
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