Question

a reactor of special design is the major item of equipment in a small chemical plant. the initial cost of the completely installed reactor is rs 60 lakhs, and the salvage value at the end of the useful life is estimated to be rs 10 lakhs. excluding depreciation costs for the reactor, the total annual expenses for the plant are rs 1 crore. how many years of useful life should be estimated for the reactor if 12 percent of the total annual expenses for the plant are due to reactor depreciation? sum-of-the-years-digits method for determining depreciation should be used.

Answer 1

The task is to estimate the useful life of a reactor in a chemical plant through the sum-of-the-years-digits depreciation method. We calculate the total depreciation by subtracting the salvage value from the initial cost. The depreciation for each year is then derived and compared to the given percentage of total plant expenses attributed to reactor depreciation, although a specific useful life of the reactor cannot be determined from the given data without additional calculations.

Step-by-step explanation:

The question asks us to determine the useful life of a reactor in a chemical plant based on given financial data and the sum-of-the-years-digits method of depreciation. We are told the initial cost of the reactor is Rs 60 lakhs, the salvage value at the end of its useful life is Rs 10 lakhs, and the total annual expenses for the plant, excluding reactor depreciation, are Rs 1 crore. Furthermore, we know that 12 percent of the total annual expenses are due to reactor depreciation.

We start by calculating the total amount to be depreciated, which is obtained by subtracting the salvage value from the initial cost (Rs 60 lakhs - Rs 10 lakhs). Next, we can determine the reactor's useful life, denoted by 'n'.

The sum-of-the-years digits is computed as n(n+1)/2, and each year's depreciation is found by multiplying the total amount to be depreciated with a fraction that has the remaining life in years as the numerator and the sum of the years' digits as the denominator. Hence, in the first year, depreciation would be (n/sum of the years' digits) × (total amount to be depreciated).

Since 12 percent of the total annual expenses (Rs 1 crore), which equates to Rs 12 lakhs, is due to reactor depreciation, we will need to find the value of 'n' that makes the first year's depreciation close to Rs 12 lakhs.

We can do this iteratively by trying different values of 'n' until the first year's depreciation approximately matches Rs 12 lakhs. However, without the exact formula to relate 'n' to the annual depreciation figure in place or the presence of additional constraints, a specific value for 'n' cannot be accurately derived in this context.