Deferred Taxes when tax rates change

CFA Level I FRA
#1

From a Schweser question:

A company purchases a new pizza oven for $12,675. It will work for 5 years and have no salvage value. The company will depreciate the oven over 5 years using the straight-line method for financial reporting, and over 3 years for tax reporting. If the tax rate for years 4 and 5 changes from 41% to 31%, the deferred tax liability as of the end of year 3 is closest to:

a) $1,570

b) $2,080

c) $1,040

Why is the answer a?

From my understanding, the depreciation under financial reporting is $2,535 and under tax reporting is $4,225. Thus:

End of Year 1 asset base (FR) = $10,140

Tax Expense = $10,140 x 0.41 = $4,157.40

End of Year 1 tax base = $8,450

Tax Payable = $8,450 x 0.41 = $3,464.50

Tax Expense - Tax Payable = DTL (Year 1) = $4,157.40 - $3,464.50 = $692.90

The same process for Year 2 gives DTL (Year 2) = $1,385.75

And for Year 3, DTL = $2,078.70

Therefore, the total DTL at the end of year 3 should be $692.9 x 3 = $2,078.7 as in answer b. Can someone shed some light on why this is not the case please?

#2

Hello,

Initially I got B as the answer too; but if you recall, tax change will require you to recompute deferred taxes from the prior periods as the temporary differences when reveresed in the future will be based on the new tax rates. See it this way, if your 1st 3 years is based on old tax rate of 41% and the remaining 2 years based on new tax rate of 31%; the temporary differences during the day of reversal will be based on 31%; the deferred tax amounts do not tally right?

The differences between carrying value of the machine and tax base of the machine will be 1,690 for the 1st 3 years, so by the end of year 3 total DTL created will be:

1,690 x 0.41 x 3 = 2,078.70

To change it to the new tax rate of 31% we can do the following:

(2,078.70/0.41)*0.31 = 1,571.70

Hope this helps.

Cheers,

Ernest