16. an asset has a cost of $50,000, with a residual value of $10,000. it has a life of 5 years and was…

16. an asset has a cost of $50,000, with a residual value of $10,000. it has a life of 5 years and was purchased on january 1. under double - declining - balance, what’s the asset’s fourth full year of depreciation expense?

16. an asset has a cost of $50,000, with a residual value of $10,000. it has a life of 5 years and was purchased on january 1. under double - declining - balance, what’s the asset’s fourth full year of depreciation expense?

Answer

Explanation:

Step1: Calculate the straight - line depreciation rate

The asset has a useful life of 5 years. The straight - line depreciation rate $r_{sl}=\frac{1}{5}=0.2$ or 20%.

Step2: Calculate the double - declining - balance rate

The double - declining - balance rate $r = 2\times r_{sl}=2\times0.2 = 0.4$ or 40%.

Step3: Calculate the depreciation for each year

  • Year 1: The beginning book value (BV) is the cost of the asset, $BV_0=$50,000$. Depreciation expense $DE_1=r\times BV_0 = 0.4\times50000=$20,000$. The ending book value $BV_1=BV_0 - DE_1=50000 - 20000=$30,000$.
  • Year 2: $DE_2=r\times BV_1=0.4\times30000=$12,000$. $BV_2=BV_1 - DE_2=30000 - 12000=$18,000$.
  • Year 3: $DE_3=r\times BV_2=0.4\times18000=$7,200$. $BV_3=BV_2 - DE_3=18000 - 7200=$10,800$.

Step4: Calculate the depreciation for Year 4

In the double - declining - balance method, we do not depreciate below the residual value. The maximum depreciation in year 4 is $BV_3-\text{Residual Value}=10800 - 10000=$800$. So the depreciation expense in the fourth year is $$800$.

Answer:

$800$