The Balance Sheet Identity

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, as well as 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:

\(A \equiv L + SE\)

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.

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 \(A - L\).

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