Suppose your debt ratio is 0.4 and you have $600000 in owner equity. What are your total assets?

### Problem Statement

We are given:

- Debt Ratio (
*DR*) = 0.4 - Owner Equity (
*OE*) = $600,000

And we must find **Total Assets ( TA)**.

### Relevant Information

We have two relevant equations:

From the **Accounting Ratios** section:

$Debt Ratio (DR) = {Total Liabilities (TL) \over Total Assets (TA)}$

or more concisely $DR = {TL \over TA}$

From The **Accounting Documents - Balance Sheet** section:

$Total Assets (TA) = Total Liabilities (TL) + Owner Equity (OE)$

or more concisely $TA = TL + OE$

### Algebra

We can manipulate the first equation as such:

1. $DR = {TL \over TA}$

2. $(DR)(TA) = TL$

3. $TA = {TL \over DR}$

Now that both equations equal *TA*, set them equal to each other and solve for the other unknown, *TL*, in terms we are given (i.e. *DR* and *OE*):

1. ${TL \over DR} = TL + OE$

2. $TL = (DR)(TL + OE)$

3. $TL = (DR)(TL) + (DR)(OE)$

4. $TL - (DR)(TL) = (DR)(OE)$

5. $(TL)(1 - DR) = (DR)(OE)$

6. $TL = {(DR)(OE) \over (1 - DR)}$

### Substitute Known Values

Now we can substitute the given values:

- Debt Ratio (
*DR*) = 0.4 - Owner Equity (
*OE*) = $600,000

$TL = {(DR)(OE) \over (1 - DR)}$

$TL = {(0.4)(600000) \over (1 - 0.4)}$

$TL = \$400,000$

Then replace *TL* in one of the original equations to get *TA*:

$TA = TL + OE$

$TA = \$400,000 + \$600,000$

$TA = \$1,000,000$

### Result

So the Total Assets (*TA*) are **$1,000,000**.

### Confirmation

Check the answer with the other equation:

$DR = {TL \over TA}$

$0.4 = {\$400,000 \over \$1,000,000 }$

$0.4 = 0.4$ ✔