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.