Project ForgePlant Design & Economics
Profitability Analysis
GATE 2011
Hard
A process plant has a life of 7 years and its salvage value is 30%. For what MINIMUM fixed-percentage factor will the depreciation amount for the second year, calculated by declining balance method, be EQUAL to that calculated by the straight line depreciation method?
- A0.1
- 0.113
- C0.527
- D0.887
Explanation
Straight-line 2nd-year depreciation=(1−0.30)V0/7=0.10V0 (same each year). Declining-balance 2nd-year depreciation=f(1−f)V0. Setting equal: f(1−f)=0.10 ⟹ f²−f+0.10=0 ⟹ f=[1±√0.6]/2, giving roots 0.887 and 0.113. The MINIMUM of the two roots is 0.113.
Source: GATE CH 2011 (2011)
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