DDB

What is the fifth-year DDB depreciation charge for a machine whose first cost is $50,000 and estimated salvage value at the end of its 8-year useful life is $2,000?

Question

DDB

What is the fifth-year DDB depreciation charge for a machine whose first cost is $50,000 and estimated salvage value at the end of its 8-year useful life is $2,000?

Accepted Answer

Since we need to determine the depreciation charge for a specific (fifth) year only, the use of equation will be simpler than the first-principles. The latter would have required determining depreciation for the previous years too to get the book value for year 5. The relevant formula, Equation (10.4), is

jth year depreciation [latex]=({2P}/{N})({1-2}/{N})^{j-1}[/latex]

for [latex]P=\$ 50,000 , N = 8 years, and j = 5[/latex] , we get

5th year depreciation [latex]= (2 imes {\$50,000}/{8})(1-{2}/{8})^{5-1}[/latex]

[latex]=(\$12,000) imes (1-0.25)^{4}[/latex]

[latex]=\$12,500 imes 0.75^{4}[/latex]

[latex]=\$12,500 imes 0.3164[/latex]

[latex]=\$3,955[/latex]

Using Equation (10.4), two more equations are derived in the following two subsections. These equations are handy in determining specific year-end cumulative declining balance and the asset book value.

Question 10.6: DDB What is the fifth-year DDB depreciation charge for a ma...

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