# DTL vs. DTA Question

Could someone explain how the numbers in the answer is derived for the following question?

Q) Company faced a 50% marginal tax rate last year and showed the following info:

• DTA of \$1,000

• DTL of \$5,000

Based on this info and the news that the tax rate will decline to 40%,

Answer: DTL will be reduced by \$1,000 and income tax expense will be reduced by \$800.

Thanks so much!

Is there some other part of the question?

From what I know… when tax rate declines, both DTA and DTL will decrease.

Also… Income Tax Expense = Taxes payable + Change in DTL - Change in DTA.

So im assuming you use that formula to get the answer…

When the tax rate changes, you need to determine the amount of the temporary change that led to the DTA or DTL, then multiply that temporary change by the new tax rate to get the new DTA or DTL value. To calculate the value of the temporary change, you divide the DTA or DTL by the old tax rate. Thus, for the DTA:

Temporary change = \$1,000 ÷ 50% = \$2,000

New DTA = \$2,000 × 40% = \$800

ΔDTA = \$800 – \$1,000 = -\$200

For the DTL:

Temporary change = \$5,000 ÷ 50% = \$10,000

New DTL = \$10,000 × 40% = \$4,000

ΔDTL = \$4,000 – \$5,000 = -\$1,000

Therefore,

ΔIncome tax expense = ΔDTL – ΔDTA

= -\$1,000 – (-\$200)

= -\$800

The new DTL =\$5000÷0.5*0.4=4000.

and new DTA=\$1000÷0.5*0.4=800

it’s obviously the DTL reduced by 5000-4000=1000.DTA reduced by 200.

we can conclude that income tax expense will reduced by 800 as result of offseting

Exactly correct.