Not sure if using correct formula - dealing w/ redemptions in a growth/investment account

[bbsinc]

Long story short -

Our company handles investments, and we track the initial investments as well as the value according to the quarterly fund statements.

Using this information, we create a spreadsheet that shows the growth their investments have made, taking into account any money they've invested since the initial investment.

When a client withdraws money from their account, we use a formula to calculate the withdrawal in proportion to the initial investment (example: Someone invests $1,000.00 at the beginning of 2011. It grows to $1,100.00 at the end of 2012, at which point they withdraw $500.00. We want to show them what proportion of the original $1,000.00 that $500.00 withdrawal represents.

We are currently using the following formula: (A/B)*C = D

A = The ACTUAL SHARE VALUE withdrawn

B = The TOTAL SHARE VALUE in the account prior to the withdrawal

C = The TOTAL DOLLAR VALUE invested prior to the withdrawal (the initial amount, not taking any growth into account).

D = The end result

Does anyone see an issue with this formula? The reason I ask is we've been doing it this way for years, but recently noticed that, while one particular client's investments had actually declined in value over time, the actual withdrawal was GREATER than the result we calculated. It seems to me that it would be the other way around.

Sorry for the lengthy post, just needed to explain the concept.

Thanks in advance for any help!

[Pauleyb]

What values are causing the issue? Seems to me, you are saying that A>D when the account declined (i.e. B<C). A must be <= B (unless you allow people to overdraft), so A/B ranges from 0 to 1, which would mean C <= D. So, A<=B<C<=D. I agree, that A>D seems incorrect.

I do have other issues with your formula though. As an investor, I want a better grasp of my return over time. This just seems way too simplistic. What if I put in $1000, make no gain, remove $500, the market doubles (so I have $1000, again), then I put in the $500, and then withdraw $500 after no gain?
Seems to me, it should report $500 in and $500 out. You would actually say (500/1500)*1000 = $333?
What if instead of $500 as the last withdrawal it was $600? How do you account for the $500 of no growth and $100 that was originally $50? I'd think it should report $550, but you would calculate (600/1500)*1000 = $400?