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# The Balance Sheet Identity

## How do we Buy Assets?

You issue financial assets (stocks and bonds) to get the money to buy real assets. These financial assets then have a claim on the assets, and the cash flows generated by those assets.

• The type of financial assets determines the nature (risk/return) of the claim.

• Bond and stock valuation deals with the claim on the cash flows. Here we’ll discuss the claim on the underlying assets themselves.

## The Balance Sheet Identity

The balance sheet identity:

A \equiv L + SE

where A denotes assets, L liabilities, and SE stockholders' equity. You read this identity as "assets are defined to be liabilities plus stockholders' equity."

• This is a result of equity being a residual claim on the assets/cash flows of the firm. Equity receives whatever is left over.

• So the "identity" is saying all the firm's assets are claimed by someone—debtholders first, and then equityholders get everything else.

## The Difference Between Identities and Equations

We call the Balance Sheet relationship an identity rather than an equation because it always holds (because equity just gets whatever is left over).

• Conversely, an equation only holds for certain values. For example, consider the equation x^2 - 1 = 0. This is only true for x = \pm 1

• A \equiv L + SE is always true because SE is simply defined as A - L.

## Interactive App

The following interactive app graphically shows the balance sheet identity. The original asset value is $100, and you can set the proportion of those assets financed by debt. For example, if you set it equal to 0.55, then$55 of the assets was financed via debt. You can then set the new value of assets.

• If the new value of assets increases above $100 all the value goes to equityholders, and if the value of assets drops below$100 equityholders absorb the losses (with no debt value lost).

• If the new value of assets drops below the value of debt, then debtholders incur losses, and the value of equity is negative.

• Note this is an accounting relationship—because of limited liability equity can never have a negative value.

## Credits and Collaboration

Click the following links to see the codeline-by-line contributions to this presentation, and all the collaborators who have contributed to 5-Minute Finance via GitHub.