Question

A shovel costing (P) Rs. 20 crores has a salvage value (S) of Rs. 2 crores with a useful life (n) of 10 years. The annual depreciation is evaluated using the declining balance method as given by
\[ \text{Depreciation rate} = 1 - (S/P)^{1/n} \]
The depreciated cost of the shovel, in crores, in its 2nd year is Rs. . (rounded off to two decimal places)

Hint:

Find the yearly declining-balance depreciation rate from S, P and n, then apply it twice to shrink the book value down to the end of year 2.

Answer 1

Correct Answer: 12.62

Step 1: Find the annual depreciation rate.
In the declining balance (reducing balance) method, the book value drops by a fixed percentage every year, instead of a fixed rupee amount. That percentage is given by
\[ r = 1 - (S/P)^{1/n} = 1 - (2/20)^{1/10} \]
\[ (0.1)^{1/10} = 0.7943 \]
\[ r = 1 - 0.7943 = 0.2057, \text{ about } 20.57\% \text{ per year} \]

Step 2: Apply this rate twice to bring the book value down to the end of year 2.
Each year the shovel loses 20.57% of whatever value it still has, so the value remaining gets multiplied by \((1-r) = 0.7943\) each time.
Book value at the end of year 1:
\[ BV_1 = P(1-r) = 20 \times 0.7943 = 15.89 \text{ crores} \]
Book value at the end of year 2:
\[ BV_2 = P(1-r)^2 = 20 \times (0.7943)^2 = 20 \times 0.6310 = 12.62 \text{ crores} \]

Final Answer:
The depreciated cost of the shovel at the end of its 2nd year is about Rs. 12.62 crores. \[ \boxed{Rs.\ 12.62 \text{ crores}} \] A different reading of "depreciated cost in its 2nd year" takes it as the amount of value lost during year 2 alone, not the value left over. That amount is \(BV_1 - BV_2 = 15.89 - 12.62 = 3.27\) crores. Both numbers come from the same rate and the same two book values, they just answer slightly different questions, and this solution takes the remaining book value as the answer.