Question

Federal income tax allows a deduction for any state tax paid during the year. In addition, the state of Alabama allows a deduction from its state income tax for any federal tax paid during the year. The federal corporate income tax is equivalent to a flat rate of 34% and the Alabama state tax rate is a flat 5%.

Both the Alabama and the federal taxable income for a corporation is $1,000,000 before either tax is paid. Because each tax is deductible on the other return, the taxable income will differ for the state and federal taxes (assume for this problem that the company has no other deductions to consider). One procedure often used by tax accountants to find the tax due in this and similar situations is called iteration and it’s described by the following steps:

Make an estimate of the federal taxes due by assuming no state tax is due, deduct this estimated federal tax due from the state taxable income and calculate an estimate of the state taxes due on the basis of this assumption.

Deduct the estimated state tax as computed in (1) from the federal taxable income and calculate a new estimate of the federal tax due under this assumption.

Deduct the new federal tax due as computed in (2) from the state taxable income and calculate a new estimate of the state taxes due on the basis of these calculations.

Repeat the process in (2) and (3) until the federal tax changes from one repetition to another by less than $1.

QUESTION 1

Use Excel (or your favorite spreadsheet application) to model the above iteration process. Then complete the table, using as many rows as needed (until the change in federal tax is less than $1). Please include a print-out of your table rather than filling in the one below (this is just the sample)

	Federal Taxable Income (Taxable Income - State Tax Deduction)	Federal Tax (34%)	State Taxable Income (Taxable Income - Fed Tax Deduction)	State Tax (5%)
1st Iteration	1,000,000	340,000	660,000	33,000
2nd Iteration	1,000,000-33,000= 967,000
3rd Iteration

(Hint: this process will not take a lot of iterations – be careful how you apply the deductions at each step, and keep in mind that the taxable income is always $1,000,000.)

QUESTION 2

We can model the above situation via a system of linear equations.

What are the unknowns in this system? (Hint: What do you want to find out?)

x=

y=

Write down two linear equations that describe this taxation situation.

Find the augmented matrix that corresponds to this system:

A=

Find the solutions of this system of linear equations (they better match what you found in Question 1 – you are computing the same thing!)

x=

y=

What is the effective tax rate that this corporation pays to each government?

Answer 1

Q-1

		Federal Tax	State Taxable Income	State Tax
	Federal Taxable Income	-34%	(Taxable Income - Fed Tax Deduction)	-5%
	(Taxable Income - State Tax Deduction)
1stIteration	10,00,000	3,40,000	6,60,000	33,000
2ndIteration	9,67,000	3,28,780	6,38,220	31,911
3rdIteration	9,68,089	3,29,150	6,38,939	31,947
4th Iteration	9,68,053	3,29,138	6,38,915	31,946
5th Iteration	9,68,054	3,29,138	6,38,916	31,946

Q-2

x= Federal tax

y= State tax

Effective Tax Rate = Federal = 32.91%(329138/1000000)

State Tax = 3.19%(31946/1000000)