# Amortization expense

A company acquires a patent with an expiration date in six years for ¥100 million. The company assumes that the patent will generate economic benefits that will decline over time and decides to amortize the patent using the double-declining balance method. The annual amortization expense in Year 4 is closest to:

1. ¥6.6 million.
2. ¥9.9 million.
3. ¥19.8 million.

#### Solution

B is correct. As shown in the following calculations, under the double-declining balance method, the annual amortization expense in Year 4 is closest to ¥9.9 million.

Annual amortization expense = 2 × Straight-line amortization rate × Net book value.

Amortization expense Year 4 = 33.3% × ¥29.6 million = ¥9.9 million.

I dont really understand the calculation. How did they come up with the NBV of 29.6 million? Thank you

Begin Amort End
100.0 33.3 66.7
66.7 22.2 44.5
44.5 14.8 29.7
29.7 9.9 19.8
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You can even do this on the BAII with the DEPR worksheet!!! Works like a charm!!!

100,000,000 * (1 - 2/6)^3 = 100,000,000 * 0.296296 = 29,629,600.

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Below are the calculations for Depreciation and Year-end Book Value for Years 1, 2, and 3. I trust that it’s self-explanatory, but I welcome any questions(s) you might have.

Year 1: Deprec. = 100 * .3333 = 33.3 | Year-end Book Value = 100.0 - 33.3 = 66.7
Year 2: Deprec. = 66.7 * .3333 = 22.2 | Year-end Book Value = 66.7 - 22.2 = 44.5
Year 3: Deprec. = 44.5 * .3333 = 14.8 | Year-end Book Value = 44.5 - 14.8 = 29.6
Year 4: etc.

I trust that this is helpful. Good luck on the exam!

Warren Miller, CPA, CFA
Lexington, Virginia
USA

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