Equipment costing $40,000 is to be depreciated over 15 years,at which time it will be sold for scrap for $4,000.Let R_s = depreciation expense for the 6^th year under the straight line method and R_c = depreciation expense for the 6^th year under the constant percentage method with rate of depreciation d = 20%.What is | R_s -R_c |?

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Quizplus · Accepted Answer

Under the straight-line method, the annual depreciation expense is calculated as (Cost - Salvage Value) / Useful Life. Therefore, for the equipment costing $40,000 with a salvage value of $4,000 over 15 years, the annual depreciation expense is ($40,000 - $4,000) / 15 = $2,400. Thus, R_s = $2,400.For the constant percentage method (also known as the declining balance method) with a rate of depreciation of 20%, the depreciation expense for any year is calculated as the book value at the beginning of the year times the rate of depreciation. The book value decreases each year as it is depreciated. The formula for the book value at the beginning of year n is: Initial Cost * (1 - d)^(n-1), where d is the rate of depreciation (expressed as a decimal).To find the depreciation expense for the 6th year under the constant percentage method, we first calculate the book value at the beginning of the 6th year and then apply the 20% depreciation rate.The book value at the beginning of the 6th year is $40,000 * (1 - 0.20)^(6-1) = $40,000 * (0.8)^5 ≈ $10,485.76.The depreciation expense for the 6th year under the constant percentage method is then 20% of this book value, which is $10,485.76 * 0.20 ≈ $2,097.15. Thus, R_c ≈ $2,097.15.The difference between the two depreciation expenses is |$2,400 - $2,097.15| ≈ $302.85.

Equipment Costing $40,000 Is to Be Depreciated Over 15 Years,at