# Ratios

Can anyone explain why ROA is always lower than ROE when net income is positive and debt is present?

Because if there is debt, then Assets > Equity.

I believeIt is easier to think of your fundamental relationship :

ASSETS = LIABILITIES + EQUITY

This answers the question “How did I buy my assets?” Well 1) equity and 2) debt (liability).

You can see that assets are at least greater or equal than equity. If we add any amount to debt (which is a liability), equity will immediately become less than assets.

Now, of course since ROA is going to be the smaller figure (due to the larger denominator) in absolute terms, if you add a negative sign in front of these ratios then ROE is going to be lower - that is why this relationship is true for a positive net income only.

Example

Assets = 10 | Equity = 5 | Liabilities = 5 (lets assume the only liability is debt for simplicity)

Net income = 1 (I saw an other post of yours , remember net income is a low (indeed even negative) value because it is all that is left after we remove all the expenses from revenues/sales)

10 = 5 + 5

Return on Equity -> Net Income/ Equity -> 1/5 (0.2)

Return on Assets -> Net Income/ Assets -> 1/10 (0.1)

Notice that if net income is NEGATIVE, then indeed ROE (-0.2) is going to be lower than ROA (-0.1)

Hope I’ve helped!!