On January 3, 2006, Lopez Co.purchased machinery.The machinery has an estimated useful life of eight years and an estimated salvage value of $30,000.The depreciation applicable to this machinery was $65,000 for 2008, computed by the sum-of-the-years'-digits method.The acquisition cost of the machinery was

Question

Quizplus · Accepted Answer

The sum-of-the-years'-digits method is a depreciation method that allocates a higher amount of depreciation in the earlier years of an asset's life and a lower amount in the later years. To use this method, you need to calculate the sum of the digits for the number of years in the asset's useful life.

For this machinery, the sum of the digits is: 1+2+3+4+5+6+7+8 = 36

To calculate the annual depreciation under this method, you divide the remaining useful life by the sum of the digits. 
Year 1 depreciation: (8/36) x (cost - salvage value) = (8/36) x (cost - 30,000) 
Year 2 depreciation: (7/36) x (cost - salvage value) = (7/36) x (cost - 30,000) 
Year 3 depreciation: (6/36) x (cost - salvage value) = (6/36) x (cost - 30,000) 
And so on...

We know that the depreciation for 2008 was $65,000, which means it was the sum of the depreciation for years 1-3 (since 8-3=5). 
$65,000 = (8/36)(cost-30,000) + (7/36)(cost-30,000) + (6/36)(cost-30,000) 
$65,000 = (21/36)cost - (21/36)30,000 
$65,000 = (21/36)cost - 12,500 
(21/36)cost = 77,500 
cost = $420,000

Therefore, the acquisition cost of the machinery was $420,000.