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# Berkshire Hathaway Inc. Message Board

• mr_dryesdale mr_dryesdale Dec 19, 2003 2:18 PM Flag

## Help with math ?

Can someone show the actual numbers for the example? I must be pushing the wrong button and can not come up a number that agrees with what has been posted. Thanks

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• With regard to message # 199506:

Trepanne,

Congratulations, you're right.

I stand corrected.

I calculated the 12/23/2003 year-to-date total returns for two dividend paying stocks using the IRR function (method # 1) and your "stop the clock" geometrically linked, incremental, total return procedure (method # 2).

Your calculation results match the YTD %TR reported by Morningstar.

Summary:
................... 12/23/2003 YTD %TR
Stock Symbol ..... FUN ....... LZ
Moringstar ........... 39.6 .... 11.0
Method # 1 .......... 40.7 .... 11.2
Method # 2 .......... 39.6 .... 11.0

Calculation Details: Historical Data from Yahoo!
==========================================
Cedar Fair, L.P. (FUN)
Method # 1
Date ........... NCF
12/31/02 ... (23.60)
01/02/03 ..... 0.42
04/01/03 ..... 0.44
06/01/03 ..... 0.44
10/01/03 ..... 0.44
12/23/03 ... 30.79
..... XIRR = 40.66%

Method # 2
Date ... Closing P/s ... Dividend/s ... Inc %TR ... YTD %TR
12/31/02 ... 23.60
01/02/03 ... 23.50 ............. 0.42 ........ 1.36% ...... 1.36%
04/01/03 ... 24.50 ............. 0.44 ........ 6.13% ...... 7.57%
06/01/03 ... 27.39 ............. 0.44 ...... 13.59% ..... 22.19%
10/01/03 ... 27.54 ............. 0.44 ........ 2.15% ..... 24.82%
12/23/03 ... 30.79 ..... ...................... 11.80% .... 39.55%

==========================================
Lubrizol Corp. (LZ)
Method # 1
Date ........... NCF
12/31/02 ... (30.50)
02/06/03 ..... 0.26
05/07/03 ..... 0.26
08/06/03 ..... 0.26
11/06/03 ..... 0.26
12/23/03 ... 32.75
..... XIRR = 11.24%

Method # 2
Date ... Closing P/s ... Dividend/s ... Inc %TR ... YTD %TR
12/31/02 ... 30.50
02/06/03 ... 29.14 ............. 0.26 ...... -3.61% ........ -3.61%
05/07/03 ... 31.44 ............. 0.26 ....... 8.79% ......... 4.86%
08/06/03 ... 32.88 ............. 0.26 ....... 5.41% ....... 10.53%
11/06/03 ... 30.39 ............. 0.26 ...... -6.78% ......... 3.04%
12/23/03 ... 32.75 ............................. 7.77% ........ 11.04%

Thanks for the clarification!

• solving for the IRR as indicated in jad1148's post is not best practice for calculating investment performance - reason being it assumes cash inflows/outflows compound at the IRR, which simplifies the calculation but is unrealistic.

what is instead recommended by the AIMR is that you "stop the clock" and value the portfolio at each cash inflow & outflow. compute the ratio of the port's ending value over the beginning value. then add or subtract the cash flow from the last period's ending value, and use the post-cashflow valuation as the starting value for the next period. stop the clock again at the next cashflow, and again take the ratio of ending value over starting value.

multiply all such ratios together for the whole year, then subtract one. voila - you have a geometrically-linked, time-weighted rate of return as advocated by AIMR.

i just got through doing this, and boy does it suck when there are a lot of cashflows. you have to look up a WHOLE lot of historic stock prices.

trp

PS i agree about getting TI's financial calculator over the HP-12C. it is actually called the BA-II.

• LOL!

I guess that's Yahoo's way of saying "enough already!"

The last paragraph:

If you do decide to buy a financial calculator check out the Texas Instruments Financial Analyst II. I believe I've seen it at Walmart for about \$30. I used to push Hewlett-Packard's stuff, but, IMHO, the quality (or lack therein) no longer supports the premium price they ask. I'll stick with RPN only because I've been using it for more than 25 years now and think it is the best "language" for a calculator. I wish I felt the same way about hp's hardware.

Hope that helps.

• << If I invested an amount of \$10000 at the beginning of the year and contributed \$1000 at the end of each month for the next 12 months and at the end of year if I have total \$Y including principle and profit/loss, what's my rate of return for the year? >>

When payments are involved you'll need a "root finder" to solve for "i", the interest rate, in the TVM, Time Value of Money, equation.

You can either purchase a financial calculator that has the TVM equation in firmware or use spreadsheet software that supports the IRR, Internal Rate of Return, function. The good news is that every piece of spreadsheet software I've every played with supports the IRR function.

Let's work Neb2000us's example using the Microsoft Works spreadsheet.

Mth# ... NCF
0 ..... -10000
1 ...... -1000
2 ...... -1000
3 ...... -1000
4 ...... -1000
5 ...... -1000
6 ...... -1000
7 ...... -1000
8 ...... -1000
9 ...... -1000
10 .... -1000
11 .... -1000
12 ... 23000

IRR = 0.010240622
Annualized 0.130050706
13.0%

Notes:

Mth# ... is the month number.

NCF ... is the Net Cash Flow to you.

If you made a contribution, you paid cash OUT and it is a negative number.

If you can received or withdraw cash it is a positive number.

The "root finder" behind the IRR function will fail or give you the wrong answer if you get the signs of the cash flows wrong.

Specifics:

You contributed (paid out) \$10,000 at the END of month number # 0, (if it's easier, think of this as the BEGINNING of month # 1, for example: 31-Dec-2002 ~ 1-Jan-2003).

At the end of months # 1 .. # 12 (Jan .. Dec) you contributed (paid out) \$1,000.

At the end of month # 12 you can withdraw (at least on paper) \$24,000. So the NET cash flow to you for the end of month # 12 is \$23,000 { + \$24,000 - \$1,000 }.

The calculated IRR, internal rate of return, is based on the period between net cash flows, in this case, one month.
So an IRR = 0.010240622 is a monthly interest rate (or total return) of 1.024%.

To annualized the monthly rate: add one to it, raise that to the twelve power (12 months to a year) and subtract one.

Annualized = [ ( 1 + 0.010240622 ) ^ 12 ] - 1 = 0.1301 = 13.01%

Full feature spreadsheet software (Microsoft Excel and Lotus123) support yet another variant of IRR called XIRR. XIRR takes two argument lists; an array of NCFs and an array of dates, as input and calculates an annualized internal rate of return for irregular periods. Very nice, your contributions don't have to be made exactly one month apart.

OK, the same problem on a financial calculator.

I'm currently playing around with an Aurora Financial Manager FN1000, a ~\$25 cheapie Chinese knock off of Hewlett-Packard's HP12C (which sells for ~\$69).

[SHIFT] [CLEAR FIN] ... clears the financial registers.
[SHIFT] [END] ... payments occur at the end of the period.
12 [n] ... there will be twelve payments.
10000 [+/-] [PV] ... stores -\$10,000 as the present value.
1000 [+/-] [PMT] ... stores -\$1,000 as the periodic (monthly) payments.
24000 [FV] ... stores +\$24,000 as the future value.
[i] ... calculates the periodic (monthly) interest rate.
... nine seconds later ...
1.0241
That's the monthly return in percent.

Annualize it. (Warning, this is in RPN, Reverse Polish Notation).
1 [X<->Y] [%] [+] 12 [Y^X] 1 [-]

If you do decide to buy a financial calculator check out the Texas Instruments Financial Analyst II. I believe I've seen it at Walmart for about \$30. I used to push Hewlett-Packard's stuff, but, IMHO, the quality (or lack therein) no longer supports the premium price they ask. I'll stick with RPN only because I've been using it for more than 25 years now and think it is the best "language" f

• A pretty simple way to calculate ROR is:

(Ending value - beginning value - cash flows)
divided by (beginning value plus 1/2 of cash flows).

So, if you finished the year with \$24k, as a example:

\$24k - 10k - 12k (1k per month) = \$2k

divided by (10k + 1/2(12k) = \$16k

ROR = 12.5% (if the math is correct)

The result is a dollar weighted return, which approximates a time weighted return, and used to be, don't know if it still is, an accepted return calculation by the financial analysts society.

• I am trying to calculate my rate of return in the following situtaion and am not sure how to go about it.

If I invested an amount of \$10000 at the beginning of the year and contributed \$1000 at the end of each month for the next 12 months and at the end of year if I have total \$Y including principle and profit/loss, what's my rate of return for the year?

Thanks!!

• Well, I really didn't mean to attack calculators or spreadsheets, I use them all the time. And Buffett and Munger wax enthusiastic about this stuff and imo they're right in context ... but I betcha Buffett pays somebody with an adding machine to make sure he doesn't get shortchanged. Right tool for the job.

I only wanted to make the "telescope" point. It's very easy to be hypnotized by precision instruments, and to forget that we're only human. For every gain in detail ("magnification") we suffer a corresponding blindness ("reduced field of view"). For me personally, "blindness" type errors seem to be self-concealing and so especially treacherous ... as Yossarian says to Appleby in Catch-22: "you have flies in your eyes ... that's why you can't see them."

• Oh yea if you have to do math to see if something is cheap, then you should just move on.

The 1st post had alright made his invest decision and was trying to see how they did. If you are trying to find a real return then you need inflation figures, which dont exist. You can guess at them, but you dont know them.

By the way, you dont need a calculator. Just do it by hand. Batteries cost money so that would lower your return. You can find some paper trash and some pen you got for voting for someone. :)

30bpp is a lot. You have the inflation problem if you make 10% or 10.3%. So the inflation doesnt change the fact that 30bpps makes a difference. Actually inflation would make the real return difference higher.

Is it worth the time to do it by hand? Looks like to me it isnt that many more steps. I dont know. One is an est of return and one is the exact return.

SWUSC

• (apologies ... this is a big bee-in-bonnet issue for me)

Well ... sure, the rules are only approximations. But imo that isn't the real issue. Why are we even talking about 30 bpp per year for 30 years when we don't know next year's inflation (or maybe even last year's) to within 2 percentage points? Here's why, imo: the tool we use quickly comes to frame our outlook. If our only tool is a calculator, then we start to ignore anything the calculator can't show us.

Here's a seemingly silly example. There are telescopes for looking at the moon and eyeglasses for driving your car. On paper, one might be able to sell the idea that a telescope is a "next-generation driving tool": you can read road signs 40 blocks away, etc. And here's the dangerous part: all that is true. Nevertheless the magnification would be suicidal (or at least homicidal) in practice.

So the point isn't "don't use a calculator." The point is "don't RELY ON a calculator." The danger isn't that your batteries will go dead or something, the danger is that so often your biggest uncertainties aren't visible though the narrow frame of one model. And this is something Munger & Buffett say that really resonates with experiences I've had.

I only have so many brain cells; if I immediately put them on the 3rd and 4th decimal places, my risk of calculating entirely the wrong number goes way up.

• but they dont answer the first question

which was is my return. the rule of 72 got close but it was off by 3% when you are compounding the difference between 10 and 10.3% is noticable.

so why waste time on these 72 rule when you can get it right?

8% doubles in nine years? 1.08^9=1.999
7.2 doubles in ten years? 1.072^=2.004231

pretty close if you are close to nine to ten years. 1% doubles in 72 years? 2.047

I becomes less correct as you leave that 9-10 range.

72% it should double in a year? 1.72^1= 1.72

SWUSC

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