double-declining balance method

CFA Level I FRA
#1

Q: A company acquires an intangible asset for $100,000 and expects it to have a value of $20,000 at the end of its 5-year useful life. If the company amortizes the asset using the double-declining balance method, amortization expense in year 4 of the asset’s useful life is closest to: ?

A: $1,600. Net book value at the end of year 3 is $100,000 × 3/5 × 3/5 × 3/5 = $21,600. DDB amortization in year 4 of 2/5 × $21,600 = $8,640 would amortize the asset below its salvage value, so amortization expense is the remaining $1,600 that will amortize net book value to $20,000.

My question is: where do the "3/5"s in the calculation come from? Thanks in advance.

#2

Hey dnv05,

You DDB rate is 40% so you end up keeping 60% (3/5) of the assets value at the end of each year. Initial book value of the assets multiplied by (3/5)3 gives your value at the end of year 3. In year 4 you depreciate 1,600 because you cannot go below salvage value when dealing with DDB.

Hope this helps!