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R10 EOC2 - Real Return

Q: Christa’s portfolio is worth $1,120,000 with an expected return of $82,500/year. She has $100,000/year expenses and $50,000 income. Assumption is that inflation averages 3 percent annually.

The solutions explain her required real return is $50,000(income of $50,000 less $100,000 expenses) or 4.5 percent as a rate of return on her portfolio. Based on the current expected real return of 4.47%(82,500/1,120,000 minus rate of inflation) the portfolio is not expected to meet the return requirement.

Without a defined time frame or the investor’s specific required rate of return, how can we arrive at the 4.5% required real return stated above? The expected portfolio return of $82,500 just by looking at numbers should be more than enough to cover her return requirement of $50,000 even in hyperinflation.

Can someone please help?

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Inflation catches up to you very fast. Eyeballing the number is a sure way to get the question wrong. Does the question mention anything about taxes too? The key is that you want the principal to grow at 3% to preserve purhcasing power. If the problem stated you would eat into capital, than maybe the income will be fine.

50K income need is 4.5%. With inflation, that is an additional 3% or 7.598%.

If her income is 82,500, that is only 7.36% (82500/1.12M). The income is too low,.

Thank you very much for your reply. I am still very confused, more from the way the question was structured. “50K income need is 4.5%” you mentioned was actually what I was asking. How did you come up with the 4.5% with the given information? (numerator/denominator?) Or did you just take it as given?

50000/1120000 = 4.46%