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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%

Why are the investable assets 1,120,000 and not 1, 020,000 seeing as Christa uses up 100,000 to establish a reserve fund ( for the case  where her living expenses are 100,000 pa)? 

Assets = 1,020,000 + 75,000 + 25,000 = 1,120,000

Reserve fund = 100,000

ie. Investable assets = 1,020,000 

Because they are looking for the required return for the next year and the emergency reserve can be used for the next year, and the returns from the emergency reserve can be used for the next year. 

If they were looking at required return needed for retirement, and then stated that current emergency reserves would be spent by the time of retirement, then you would exclude it.