# before tax return vs after tax return

What is the nominal before tax return next year? Why are these 2 approaches not coming to the same answer?

Portfolio next year = \$1,000,000

Expenses next year = \$300,000

Before tax Income next year = \$200,000

Tax rate = 25%

After tax income next year = \$150,000

Inflation = 2%

Approach 1:

After tax income needed = 300,000 - 150,000 = 150,000

nominal after tax return = 150,000/1,000,000 = 15% + 2% = 17%

nominal before tax return needed = 17% / (1-T) = 22.67%

Approach 2:

Before tax income needed = 300,000 - 100,000 = 200,000

nominal before tax return = 200,000/1,000,000 = 20% + 2% = 22%

nominal before tax return needed = 22%

Your example actually shows the return requirement (\$100k expenses) being met by the post tax income (\$150k). Hence, if there’s a question on return requirement, you should take \$100k as the numerator i.e. 10%, + adjustment for inflation 2% to maintain asset base purchasing power + tax gross up to get 16% pretax nominal requirement. Means the asset base must generate a 16% pretax return at any given year in order to meet expenses needs \$100k, taxes, and still maintain its end-of-period value of \$1mil. Since the person is earning \$200k pretax, or 20% pretax, his salary is meeting his pretax nominal requirement.

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Thanks. I changed the numbers.