Question

There are various depreciation methods that require an adjustment to Cost for the asset's estimated residual value. These are 1) Straight-line, 2) Units-of-Production, and 3) Sum-of-the-years-digits.

For Double-Declining, no adjustment to cost is made. The residual value is left un-depreciated at the end.

A New Truck had a cost of $35,000 and was expected to operate for five years. It is estimated to be worth $3,000 at the end of it's useful life of 100,000 miles. The truck was used 25,000 miles in year one and 20,000 in year two.

A) Under each of these methods what will be the book value of the truck at the end of it's useful life?
B) How much is year one's depreciation using sum-of-the year digits, unit-of-production and double-declining balance.

Answer 1

• Answer ‘A’

Under every method, the book value of the truck at the end of its useful life WILL BE EQUAL TO ITS RESIDUAL VALUE or SLAVAGE VALUE.

This is because ‘Cost – Salvage value’ amount is depreciated over the useful life of assets, and at the end only the residual value remains un depreciated.

Hence, answer = Book Value at the end of useful life = $ 3,000 FOR ALL METHODs

• Answer ‘B’

Working:

Depreciable base = Cost – Salvage value = 35000 – 3000 = $ 32,000

--Sum of Year Digit method

Sum of digits of year of useful life = 1 + 2 + 3 + 4 + 5 = 15

Year #1 Depreciation = 32000 x 5/15 = $ 10,666.67 or $ 10,667

--Units of production Method

Depreciation per mile = $ 32,000 / 100000 miles = $ 0.32 miles

Year #1 Depreciation = 25000 miles x $ 0.32 = $ 8,000

---Double Declining balance method

A	Cost	$            35,000.00
B	Residual Value	$              3,000.00
C=A - B	Depreciable base	$            32,000.00
D	Life [in years]	5
E=C/D	Annual SLM depreciation	$              6,400.00
F=E/C	SLM Rate	20.00%
G=F x 2	DDB Rate	40.00%

Year #1 depreciation = $ 35000 x 40% = $ 14,000