Ratios: Suppose your debt ratio is

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:

$DR = {TL \over TA}$
$0.4 = {\$400,000 \over \$1,000,000 }$
$0.4 = 0.4$

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