Required return calculation question first, next, providing, Recently, question

JRossSter

Hi Guys, I had two questions below on how to correctly calculate required return - I’ve made up the below examples to illustrate my questions:
1. Assume the case below:
- John Smith
- Recently Retired
- Has a portfolio of $5,000,000
- Smith estimates she will need $50,000 the first year of retirement, and likes to keep 6 months of living expenses on hand.
- He also will support his son by providing him with $20,000 next year.
- Both figures are expected to increase each year at the inflation rate, which is 2%
What is Smith’s required return over the coming year?
The way I would solve it:
($50,000 + $25,000 + $20,000)/$5,000,000 = 1.9%
1.9% + 2% inflation = 3.9%
The way it should be solved based on the text:
($50,000 + $20,000)/$5,000,000 = 1.4%
1.4% + 2% inflation = 3.4%
So basically, the difference is that the emergency fund, which would be ($50,000/2) since he keeps six-months on hand, is omitted in the second one. Shouldn’t this be part of the return calculation? Or, alternatively, shouldn’t it be subtracted from the $5,000,000 before any calculations are done as it is not an investable amount?
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2. Assuming the below case:
- Jerry Jones
- Retired, time horizon of 25 years.
- Portfolio of $3,000,000
- Will need to take out $70,000 each year for the rest of his life, indexed to inflation, starting next year.
- Plans to leave a bequest of $3,500,000 (in today’s dollars) at death to charity.
- 2% inflation
What is Jerry’s return objective?
The way it would be solved based on the text:
N = 25; PMT = 70,000; FV = 3,500,000; PV = –3,000,000; IRR = 2.80%
2.80% + 2% inflation = 4.80%
My problem with this is:
a) It doesn’t seem right to me to add 2% inflation in to the required return at the end, given how each withdrawal of $70k is being increased by the inflation amount each year - so the second year withdrawal would be ($70,000 x 1.02 = $71,400), and so on. How can the above be right seeing how it does not take this gradual increase in withdrawal into account?
b) The first $70,000 withdrawal isn’t happening until one year from now - doesn’t the calculation above ignore this fact - in other words, would this calculation be different if the first $70k was coming out next week, as opposed to next year? I have some doubts about whether this answer is right, but if it’s wrong I’m not quite sure how to solve it correctly!
If anyone can shed some light on these two, I’d really appreciate it - thank you!!

defour44

cpk123 wrote:
in return terms - Q6
Part a: Income: 0.02 * .75 = 0.015
Part b: Cap Gains: 0.12 * (1-0.15*.75) = .1065
Net = .1065 + .015 = 0.1215
You double counted the .12 portion inside as well.
Oh I see…thank you for the explanation, yes the numbers check out with the calculation above. I was confused because the text says that the Capital Gains Tax is to be calculated as (price appreciation * .15 * turnover rate), so I thought that this was the calculation for the actual cap gain tax RATE as opposed to the actual percentage tax charged…poor wording in the text I guess.
Any idea on Q2? I fear that this kind of confusion about when the inflation rate should/shouldn’t be subtracted will lead to unnecessarily lost points on the return calculations for IPS on the exam..

irlfaan7

in return terms - Q6
Part a: Income: 0.02 * .75 = 0.015
Part b: Cap Gains: 0.12 * (1-0.15*.75) = .1065
Net = .1065 + .015 = 0.1215
You double counted the .12 portion inside as well.

Flok

Interesting debate – according to the CFAI text, what CPK is saying appears to be the right way to approach the question. Thanks for all the feedback!
I’ve been doing the EOC for this reading (Reading 10), and did have two more related questions that would help shed this light on some whole thing. These are Q2 and Q6 from Pg. 195 (answers starting on Pg 205) of the Vol 2 CFAI text. By the way - I know we can’t post any exam info but are we able to post CFAI question text here? If we can then I’ll edit in the questions.
Q2:
- The way they calculate the return requirement here is (100,000 - 50,000)/1,120,000 = 4.46% (real return)
- The way they calculate the portfolio return is 82,500/1,120,000 = 7.4% - 3% inflation = 4.4% (real return)
- Based on the above two, the text states that the portfolio return doesn’t meet the portfolio return.
What I don’t get about this is why is the return requirement assumed to be in real terms and thus inflation need not be subtracted, but portfolio return is not? Wouldn’t inflation act on both of these percentages?
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Q6:
The way the text determines the answer here is by converting the return/tax percentages into dollar amounts, and then doing the calculations. I did the same thing in percentages, so the answer should be the same, but it’s not:
- For the high growth income fund, for instance, the book calculates the net investment gain as [(20,000 - 5,000) + (120,000 - 13,500)] = 121,500
- But if you do the same calculation in return terms: [(.02 * .75) + (.12 * (1 - (.12 * .15 * .75))] = 1.5% + 11.83% = 13.33%, and (1,000,000 * .1333) = $133,300, NOT $121,500
What’s causing this discrepancy - shouldn’t the dollar return calculated in either manner be the same?
Thanks - this has been stumping me all afternoon!

Colum

I don’t think so. This is a very common mistake L3 candidates commit when calculating required rate of return for individual investors.
Mr Smith thinks in nominal terms about his retirement needs - CURRENTLY, in Year 0 ! This means his 50 grands will be not 50 grands in one year but 2% cheaper. Thus, to keep the client’s needs constant in power purchasing terms you should adjust the 50 grands by 2% - at the year 1 beginning the real money are 50,000 x 1.02, and the 20 grands are as well.
Then, to calculate the required rate of return THE portfolio needs to provide in Year 1, you need further to adjust the return for nominal terms - this is required for the investor must be provided by the return figure at the beginning of investment period.
It is explained by Schweser in the Practice Tests.

Darien

the needs are in the first year of retirement.  - so they should remain 70K and not 71.4K
He is retiring at the end of this year - when he would have 5 Mill$ in investable assets.
the 6 months need - is a liquidity requirement - which as has been stated above is needed for the SAA portion and to determine Cash needs in the portfolio.
So the Required Return that ua_bender calculated has been inflated an additional 2%.

leonardus

brafique
You must draw a line between Required needs and Desired needs. The required ones determine the required rate of return.
Next step is to look at whether money are in real terms or nominal terms.
Your problem indicates that John Smith doesnot know what real money are meant to be - hence, he’s considering in nominal terms and his portfolio is also expressed in nominal terms.
Year 0. Required needs: (50,000 + 20,000) x 1.02 = 71,400 at the beginning of Year 1.
Required return (real) = 74,400/5,000,000 = 1.428%
Year 1. Nominal required return: 1.428 x 1.02 = 3.457%
Correct me please if i made a mistake.

mkytz15

cirkon wrote:
brafique wrote:
So basically, the difference is that the emergency fund, which would be ($50,000/2) since he keeps six-months on hand, is omitted in the second one. Shouldn’t this be part of the return calculation? Or, alternatively, shouldn’t it be subtracted from the $5,000,000 before any calculations are done as it is not an investable amount?
Isn’t this 6-month reserve just a liquidity requirement (not impacting the required return, but rather impacting acceptable asset allocation?).
That’s what I’d say. $25k should be kept in cash, but it doesn’t need to be $25k in addition to the $5,000,000. He ought to at least be earning interest on that $25k.

ryanlb

brafique wrote:
So basically, the difference is that the emergency fund, which would be ($50,000/2) since he keeps six-months on hand, is omitted in the second one. Shouldn’t this be part of the return calculation? Or, alternatively, shouldn’t it be subtracted from the $5,000,000 before any calculations are done as it is not an investable amount?
Isn’t this 6-month reserve just a liquidity requirement (not impacting the required return, but rather impacting acceptable asset allocation?).

kasinkei

for the 2nd case, draw a timeline
now is time 0
starting end of this year - a withdrawal of 70K, which is indexed to inflation is happening.
and this will happen for 25 years. So your PV / FV/ N / PMT method is set up right.
If by the same token - the first 70K withdrawal had happened NOW - the 71.4K (70 * 1.02) would need to have become the PMT term for the next 25 years.