Hi @Alanbrotz! Thanks for reaching out.
As much as it might seem some simple algebra might work for this question, I think that’s what’s throwing you off. You’re right with the first part:
Long margin accts is LMV - Debit = Equity
Short Margin accts is Credit - SMV= Equity
However, avoid making the two equivalent. Meaning:
LMV - Debit ≠ Credit - SMV
Many times, we segregate the long equity formula (LMV - Debit = Equity) from the short equity formula (Credit - SMV = Equity). Test questions tend to focus on one or the other, when in the real world investors can utilize both long and short positions in the same margin account.
Let’s work with an example using these numbers:
- LMV = $20,000
- Debit = $10,000
- Credit = $15,000
- SMV = $10,000
In this scenario, this would be our equity formula:
$20,000 LMV - $10,000 Debit + $15,000 credit - $10,000 SMV = $15,000 Equity
It’s quite possible an investor could have a $20,000 LMV and a $10,000 SMV simultaneously. Let’s put these numbers back in the original formula you quoted:
LMV - Debit = Credit - SMV (your formula)
$20,000 LMV - $10,000 Debit = $15,000 Credit - $10,000 SMV
$10,000 = $5,000 ??
Do you see how it doesn’t work that way? Instead, combine the two “non-equity” sides together like this:
LMV - Debit = Equity
Credit - SMV = Equity
LMV - Debit + Credit - SMV = Equity
The simplest way to approach it is by ensuring the positive figures stay positive, and the negative figures stay negative. Meaning:
Positive (+) figures = LMV and Credit
Negative (-) figures = Debit and SMV
There are numerous ways to rewrite the equity formula, and they’re all correct as long as the LMV and Credit are positive, while the Debit and SMV are negative, including:
LMV - Debit - SMV + Credit = Equity
-Debit - SMV + Credit + LMV = Equity
-SMV + Credit + LMV - Debit = Equity
Credit + LMV - SMV - Debit = Equity
All are correct because they maintain the right figures as positive (LMV and Credit) and negative (Debit and SMV).
I hope this helps!