arithmetic versus geometric

[InvGrp2]

I've got a simple rate of return question but I think the answer may not be as simple.

25 years ago I invested $5,000 into a privately owed company. The company just sold I got a check for $85,000 (I received no return, no dividends, nothing during the entire 25 years)....my account was always worth $5,000.

In calculating the return I took the $85,000 - $5,000 initial investment = $80,000 profit / 25 years = $3,200 per year / $5,000 = 64% annual return.....I've been told this is the "arithmetic" way to calculate things AND its incorrect.

I've been told if I used the geometric way to calculate the return its more like 12%.

I totally understand compounded returns BUT in the above case there wasn't a compounded return......it was always worth $5,000 until the 25th year and in the 25th is when the big return was realized.

I tried to explain this to a friend (not really a friend) and he just could not believe the return was 64%...he kept saying my return was only 12%.

I even tried presenting it another way:

Say, I lent $5,000 to a company at 64% annual interest (simple interest and no compounding). This would return: $5,000 x 64% = $3,200 x 25 years = $80,000 in profits and he still said my return was only 12%.

Since my background is real estate my method of calculation seems correct BUT then again it may be wrong.

I was wondering if anyone could shed some light on this matter.

Thanks.

Bruce

[deadlyduck]

Your friend is correct!

You can use Excel to solve for the annual rate of return on your initial investment as follows:

Cell A1: Enter a guesstimated annual rate of return eg 15% (or 64% if you wish). Format this cell to display 2 decimal places
Cell B1:Enter the number of years you had your investment ie 25
Cell C1: Enter the value of settlement cheque/ initial investment (as a formula) ie =80000/5000

Cell A4: Enter the following formula: =(1+a1)^b1. Excel calculates a value.

Now you can use 'Goal seek' [Tools | Goal seek...] to calculate the actual rate of return (from the 'Goal seek' dialog box which appears):

Set cell A4 | To value c1 | By changing cell: A1

Excel calculates that A1 should be 11.73% ie a 12% return pa.

[InvGrp2]

Excel calculates that A1 should be 11.73% ie a 12% return pa.

I've used a compounding calculator and it comes out the same 11.73% (so, I must think if the excel formula comes out with the same numbers (11.73%)....would it not also be using compounding).

So, if we didn't have any compounding should it not be 64%?

I may be a bit thick here but if I use the 2nd example:

Say, I lent $5,000 to a company at 64% annual interest (simple interest and no compounding). They would owe me $3,200 per year in interest. This $3,200 is not added to principle it just accrues and earns no interest. At the end of 25 years the would owe me $3,200 x 25 = $80,000. Since he was paying me 64% per year would not my return be 64% per year?

[deadlyduck]

Yes- without compounding (ie simple interest) you'd be getting 3200 pa on average or 64% of your initial investment.

To be honest, it doesn't really make sense to NOT do the calculation using compound interest.