# Debt-to-Equity Ratio to Debt Ratio

Debt ratio (i.e. debt to assets ratio) can be calculated directly from debt-to-equity ratio or equity multiplier. It equals (a) debt to equity ratio divided by (1 plus debt to equity ratio) or (b) (equity multiplier minus 1) divided by equity multiplier.

Many financial information websites such as Yahoo Finance, Morningstar, etc. list only debt to equity ratio and/or equity multiplier. Debt to equity ratio is very useful because it tells you the size of a company’s debt in number of times the company’s equity. If its 1, it means equity and debt are equal, if its higher than 1, it means there is more debt than equity. Similarly, equity multiplier equals total assets divided by total equity, it tells you the size of assets in terms of the equity. However, there might be a situation in which you need the proportion of debt in terms of assets. For example, in calculating the weighted average cost of capital, the weight of debt capital equals total debt divided by total capital which is approximated by total assets.

## Formula

Instead of going back to the balance sheet and manually working out debt to assets ratio, you can use the following formula to directly covert debt to equity ratio or equity multiplier to debt to assets ratio:

$$ Debt\ to\ Assets\ Ratio=\frac{Debt\ to\ Equity\ Ratio}{1+Debt\ to\ Equity\ Ratio} $$

$$ Debt\ to\ Assets\ Ratio=\frac{Equity\ Multiplier\ -\ 1}{Equity\ Multiplier} $$

### Derivation from Debt to Equity Ratio

Let’s see how we arrived at the above equation. A stands for assets, D stands for debt and E stands for equity. Let’s say x represent D/E ratio The accounting equation tells us that assets are equal to sum of debt plus equity:

A = D + E

It follows that D/E ratio (x) can be written as:

x = D/E

E = D/x

Substituting E in the accounting equation with E = D/x, we get the following:

A = D + D/x

A = (xD + D)/x

A = D × (1 + x)/x

x/(1+x) = D/A

x represented debt to equity ratio, so

$$ Debt\ to\ Assets\ Ratio=\frac{Debt\ to\ Equity\ Ratio}{1+Debt\ to\ Equity\ Ratio} $$

### Derivation from Equity Multiplier

Equity multiplier (let’s represent it by e) equals assets (A) divided by equity (E):

e = A/E

From accounting equation, we know E = A – D, so:

e = A/(A – D)

e × (A – D) = A

eA – eD = A

eA – A = eD

A ( e – 1) = eD

(e – 1)/e = D/A

Since e represented equity multiplier, debt to assets ratio can be written as (equity multiplier – 1)/equity multiplier:

## Example

Let’s demonstrate if the above formulas work. Let’s say you company have $100 in assets, $30 in equity and $70 in debt. Its debt to equity ratio is 2.33 (=$70/$30), and its equity multiplier is 3.33 (=$100/$30). You can directly observe debt to assets ratio. It is 0.7 (=$70/$100). What if you didn’t have the actual figures for debt and just the debt to equity ratios and equity multiplier.

The following formulas illustrate how we can work out D/A ratio from D/E:

$$ Debt\ to\ Assets\ Ratio=\frac{2.33}{1+2.33}=0.7 $$

It can also be worked out from equity multiplier:

$$ Debt\ to\ Assets\ Ratio=\frac{3.33\ -\ 1}{3.33}=0.7 $$