# What is my annual return?



## skc (3 February 2010)

Dump question.

How would you determine the annual return if I:

Started in Jan with $25K.
Made profit of $10K in the first 6 months.

Added new capital of $20K to the account in 1 Jul (so account is now $55K)
Made profit of $10K in the next 3 months.

Added new capital of $20K to the account in 1 Oct (account now $75K)
Made profit of $10K in the last 3 months.

Here are 3 possible solutions:

1. Total profit = $30K. Total capital put in = $65K. Return = 46.2%
2. Total profit = $30K. Time weighted capital = $40K. Return = 75%
3. Time weighted average of annualised return for each period. So period 1 = 40% over 6 months, period 2 = $10k/$55K over 3 months, period 3 = $10K / $75K over 3 months. Average to be ~71.5%
4. Similar to 3 above but exclude the compounding profits in calculating the annualised returns. This works out to be ~77.7%

Any others?

I know this is mostly academic, but just wondering if there's an usual way of looking at it.


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## SusanW (3 February 2010)

skc said:


> How would you determine the annual return if I:
> 
> Here are 3 possible solutions:
> 
> ...




No. 1 isn't an annualized return because all principal wasn't in for 12mths. 
No. 2 isn't an annualized return because you don't time weight receipt of returns.
No. 3 is compromised because you presume your profit comes in equally over each month of each period. 

Some other ways:

1.  annual return calculated monthly
set up a xls thus:
Col A  month  
B cash injections
C monthly net profit loss
D cumulative cash injections
E monthly return on investment (C/D)  
annual return = Sum(E:E)

2. Internal rate of return
make Column G net monthly cash flows, where cash injections are negative amounts (-B+C), except for month 12, which gives back cash injections (-B+C+D)

use excel IRR function thus   =IRR(G:G)  where G:G are the rows in col g for the 12 mths. 
IRR figure is average return per month.
Multiply by 12 to get annualized return.


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## skc (3 February 2010)

SusanW said:


> No. 1 isn't an annualized return because all principal wasn't in for 12mths.
> No. 2 isn't an annualized return because you don't time weight receipt of returns.
> No. 3 is compromised because you presume your profit comes in equally over each month of each period.
> 
> ...




Thanks Susan... you didn't join ASF just to answer my question, did you?

For the record, using the method you suggested above, the numbers are 77.6% and 91.%.


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## Mr J (3 February 2010)

The last three months has starting capital of 85k, not 75k.


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## SusanW (3 February 2010)

skc said:


> Thanks Susan... you didn't join ASF just to answer my question, did you?
> 
> For the record, using the method you suggested above, the numbers are 77.6% and 91.%.




I've been a lurker for a few days, and joined so I could search the forums better. 

I got an IRR of 81.3%


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## Timmy (3 February 2010)

skc said:


> Dump question.




Wrong forum dude.


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## skc (3 February 2010)

SusanW said:


> I've been a lurker for a few days, and joined so I could search the forums better.
> 
> I got an IRR of 81.3%




Depends on how you divide the profit through the months.

If all lumped at the end of the periods, it's 81.3%

I divided it up evenly within each period, and that computes to 91.3%


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## peterh (3 February 2010)

XIRR might be a better Excel function to use. That way the intervals don't matter.


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## MITCH027 (3 February 2010)

80+% looks too high. I haven't used that excel formula much outside of uni so don't know a lot about how it works (and it was quite basic at uni - I wasn't a finance major). As you guys know, when you put the capital in would have a large effect on the rate of return

I got 69.9425%. Might not be exactly that figure but its close

You made a 80% pa return for the first six months (10x2/25)
You made 72.72% pa for the next 3 months (10x4/55)
You made 47.65% pa for the last 3 months (10x4/85)

How do you check? Work backwards:

Starting capital: $25K
$25K * 0.69425 / 2 + $25K (for principal) = $33,678
$53,678 * 0.69425 / 4 + $53,678 = $62,994
$82,994 * 0.69425 / 4 + $82,994 = $97,398

Ending capital from your post = $95,000

Not exactly equal but I would put that discrepancy down to rounding. I also used a hand calculator

Any of these calculations work off your capital base, you don't separate profit from capital/principal base

If you were to put in an average return of 80%+, you'll find that the mismatch would be larger


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## skc (4 February 2010)

MITCH027 said:


> 80+% looks too high. I haven't used that excel formula much outside of uni so don't know a lot about how it works (and it was quite basic at uni - I wasn't a finance major). As you guys know, when you put the capital in would have a large effect on the rate of return
> 
> I got 69.9425%. Might not be exactly that figure but its close
> 
> ...




I think it's a matter of choice whether you include the profit in calculation.

A very simple way of thinking about it... you started the year with $50K, and ended the year with $20K profit, you will just say you made 40%. You will not go break it down further on the distribution of the $20K through the year and consider profits in the first half to be compounding.

On the other hand, you can also make a case that leaving the profit in the account is a conscious decision and is no different to injecting additional capital.

So neither here nor there imo.


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## yonnie (4 February 2010)

Is not the profit % derived over a year from inputted capital over a year?

so number 2 is correct: 6 months of 25k, 3 months of 45k and 3 months of 65k = 40k of capital used on average throughout the year.
the profit gained with this average capital is 30k for the year = 75% return per year on capital used.


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## SusanW (4 February 2010)

the importance of returns timing is even moreso if you are reinvesting those returns....

rather than use IRR (or XIRR), it is more apt to use MIRR.


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## MITCH027 (4 February 2010)

skc said:


> I think it's a matter of choice whether you include the profit in calculation.
> 
> A very simple way of thinking about it... you started the year with $50K, and ended the year with $20K profit, you will just say you made 40%. You will not go break it down further on the distribution of the $20K through the year and consider profits in the first half to be compounding.
> 
> ...




yeah this is a good point


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## Huskar (13 October 2011)

I just stumbled across this. I have struggled with the same problem. A better way of calculating your annual returns and disregarding cash inflows or outflows is by using a "time-weighted internal rate of return" (TWIRR). This is just a fancy way of saying pretend you are a mutual fund and calculate your net asset value. The explanation can be found at the motley fool with a sample spreadsheet here: http://www.fool.co.uk/stockideas/2005/si050720.htm.

Happy days

h


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