Calculate deferred tax liability

CFA Level I FRA
#1

Hi everyone,

I’m going through some quizzes I found online for the Income Taxes Chapter. I taught I mastered the chapter, but I got a mediocre result on the end of chapter questions, so I turned to some additional quizzes found online. I know this kind of resource can be of doubtful reliability and accuracy, so I would need your help.

One quiz goes like: a company buys new equipment with 5 yrs useful life for 25,352. For accounting purposes the asset is depreciated with the straight line method, while for tax purposes it’s depreciated of 35% of its historic cost for the first 2 years and 30% of its historic cost on year 3. Annual revenues of the company are 14,384 constant over the next 5 years. The tax rate will change on years 4 and 5 from 41% to 31%. What is the deferred tax liability at the end of year 3?

I personally would have solved this by calculating the carrying amount and tax base, taking the difference and multiplying it by 41% to get a DTL of 4,158.

However, on the solutions the depreciation for accounting and tax purposes is calculated, then for each of the 3 years the difference between the income and the depreciation is calculated (again for tax and reporting purposes), then the cumulative difference between the accounting and tax reporting incomes for 3 years is calculated and, finally this difference is multiplied for the 31% tax rate to get to a DTL of 3,144. The whole process shown in the solution doesn’t make any sense to me. Also, I believe the tax rate of 41% should be used, given that the change in tax rate will occur in Y4 and Y5.

Am I missing something? Or is the solution actually correct?

Thanks in advance to anyone who will try and help me on this.

#2

The only difference between your approach and theirs is the tax rate; if you had used a 31% tax rate you would have gotten 3,144 as they did.

The correct rate to use is 31%, because that’s the rate that will apply when the remainder of the difference in carrying amounts is resolved: in years 4 and 5.

#3

The answer is correct.
The way to solve this is to simply get the carrying value at end of Year 3 as it is already fully tax depreciated. Apply the expected tax rate: 10,141 x 31% = 3,144.(see yellow cells in the image below).

Tax Rate from Standards:
IFRS (use enacted or substantively enacted by the end of the reporting period)
US GAAP (use enacted tax rate expected to apply)

Here is the lifetime accounting of DTL:
DTLTaxRateChange