Amortization expense

CFA Level I FRA
#1

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

#2

You need to start with year 1 and work your way to year 4 like this.

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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#3

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. :bulb: :nerd_face:

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#4

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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