A steam boiler has a first cost of $50,000. Use the sum-of-years digits (SOYD) depreciation accounting method with a $5,000 salvage value and a 10-year depreciation life; determine the boiler's book value at the end of year eight.

$2,425

Explanation:

Sum of the digits = 10 + 9 + 8+7 +6 + 5+ 4+ 3+ 2 +1  = 55

Depreciation expense :

1st year = 10/55 x $45,000 = $8,182

2nd year = 9/55 x $45,000 = $7364

3rd year = 8/55 x $45,000 = $6,545

4th year = 7/55 x $45,000 = $5,757

5th year = 6/55 x $45,000 = $4,909

6th year = 5/55 x $45,000 = $4,091

7th year = 4/55 x $45,000 = $3,273

8th year = 3/55 x $45,000 = $2,454

Total depreciation               = $42,575

Book Value = $45,000 - $42,575 = $2,425

the boiler's book value at the end of year eight is $2,425

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