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).

	Federal Taxable Income (Income-State Tax Deduction)	Federal Tax (34%)	State Taxable I ncome (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

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=