Project ForgePlant Design & Economics
Profitability Analysis
GATE 2019
Medium
A taxi-car costs Rs.10 lakhs (zero salvage), earning Rs.3 lakhs/year net income. At 9% compound interest, the discounted payback period (years, rounded to next higher integer) is
5 years
Explanation
300000×[1−(1.09)^−n]/0.09=1000000 ⟹ 1−(1.09)^−n=0.3 ⟹ (1.09)^−n=0.7 ⟹ n=−ln(0.7)/ln(1.09)=4.14. Since full payback isn't reached until between year 4 and 5, round up to 5 years.
Source: GATE CH 2019 (2019)
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