A firm acquires an asset for $ 1 20,000 with a 4-year useful life and no salvage value. • The asset will generate 50,000 of cash flow for all four years. • The tax rate is 40% each year. • The firm will depreciate the asset over three years on a straight-line (SL) basis for tax purposes and over four years on a SL basis for financial reporting purposes. 1/ Calculate the Differred Tax liability (DTL) at the end of year 1 and at the end of year 2 2/ Suppose the tax rate rises **during year 2** to 50%. At the end of year 2, what is the DTL? ------------------------------------------------------ ------------------------------------------------------ My solution is: Tax return ----------------- Year 1 Year2 Year3 Year4 Sales(k€) 50 50 50 50 Depreciation 40 40 40 0 Taxable income 10 10 10 50 Taxe rate x0.4 x0.4 x0.4 x0.4 Tax payable 4 4 4 20 Income statement ----------------- Year 1 Year2 Year3 Year4 Sales(k€) 50 50 50 50 Depreciation 30 30 30 30 Pre-tax income 20 20 20 20 Taxe rate x0.4 x0.4 x0.4 x0.4 Tax payable 8 8 8 8 **For the question 1,** I found: DTL year 1 = 8 -4 = 4 DTL year 2 = DTL\_1 + (8-4) = 4+4 = 8 k For the question 2 , because the tax rate is changed during year 2 (not year 1), so, I just adjust the tax rate of year 2. (Ithe depreciation and sales aren’t impacted by the change of tax rate, are they?) Tax return ----------------- Year 1 Year2 Year3 Year4 Sales(k€) 50 50 50 50 Depreciation 40 40 40 0 Taxable income 10 10 10 50 Taxe rate x0.4 x0.5 x0.5 x0.5 Tax payable 4 5 5 25 Income statement ----------------- Year 1 Year2 Year3 Year4 Sales(k€) 50 50 50 50 Depreciation 30 30 30 30 Pre-tax income 20 20 20 20 Taxe rate x0.4 x0.5 x0.5 x0.5 Tax payable 8 10 10 10 Same method for the question 1, I have: DTL_year2 = DTL_year1 + (10-5) = 4+5 = 9 k$ ---------------------------------------------------------- The problem is that: after my Schewer, DTL_year2 is equal 10k$ for the question 2. Here is the solution in the book: Question 1: At the end of year 2, the tax base is $40,000 ($1 20,000 cost - $80,000 accumulated tax depreciation) and the carrying value is $60,000 ($120,000 cost - $60,000 accumulated financial depreciation). Since the carrying value exceeds the tax base, a DTL of $8,000 (($60,000 carrying value - 40,000 tax base) x 40%] is reported. Question2: The deferred tax liability is now 10,000 [($60,000 carrying value - $40,000 tax base) X 50%). In my opinion, the solution of book show implicitly that the rate change at beginning of year 1 , not during year 2. Which is not correct. I don’t familize with the method using (“carring value” - “tax base”) * tax rate. I found the first method I used is more comprehensive. But I don’t know whether this method is good? Sorry for my long question 
and thanks in advance for your help.
Your problem is how they come up with DTL_Year2 = 10. right?
If you remember, when tax rate changes, DTL and DTA also need to be arranged to new tax rate.
so in your equation, your DTL_year1 is still carrying DTL in year 2 which gets adjusted due to new tax rate in year 2 as
(4/0.4)*0.5 = 5K
I believe, at the beginning of year 2 the firm already knows that their tax rate has changed so they adjust their DTL in the beginning itself.
not 100% sure on that though…
Yes, my question is how they have DTL_Year2 = 10k in Schweser book.
As you said, the deferred taxe occurs during year 2 (only) is 5k. So, the total DTL of year 2 = DTL_year1 + 5k = 9k.
We don’t have same result as in Schweser book but I didn’t find anything wrong in the calculation.
DTL_year1 is at 40% rate, which just became 50%.
So DTL_Year1 would need to be revalued as 4K/0.4 * 0.5 = 5K
- 5 K of the 2nd year = 10K total.