How equity value from EV works

Equity value is enterprise value minus net debt:

$$E = EV - (D - C) = EV - D + C$$

On $100,000,000 of equity, $40,000,000 of debt and $10,000,000 of surplus cash, net debt is $30,000,000 and EV is $130,000,000. Against $10,000,000 of EBITDA that is 13 times. Start at that $130,000,000, take off the $40,000,000 of debt, put back the $10,000,000 of cash, and the residual is $100,000,000.

A buyer of the whole firm pays the equity holders, takes on the debt, and inherits the cash. The cheque that prices the operations is the $130,000,000. The cheque that prices the residual is the $100,000,000. This page is the walk from the first cheque to the second.

The enterprise value calculator on this page is that identity. Its first screen is the teaching default: EV of $130,000,000 at 13 times. How enterprise value works owns $E + D - C$. How net debt works owns $D - C$. This page owns the rearrangement.

Enterprise value against equity value is the pair on one sheet: what this $30,000,000 of net debt does to the gap, and which multiple belongs on which number.

Keep equity at $100,000,000, debt at $40,000,000 and EBITDA at $10,000,000. Set cash to $0. Net debt is the full $40,000,000. EV is $140,000,000. The multiple is 14 times. Walk back: $140,000,000 minus $40,000,000 plus $0 is still $100,000,000 of equity.

The $10,000,000 of cash on the first sheet had been subtracted in full, so putting it back raises EV by exactly that amount and leaves equity where it was. That is the teaching convention: surplus cash is not an operating asset. Cash a firm needs to run the operations is not surplus, and subtracting it would understate EV.

Type the cash your sheet is treating as surplus. The formula will add back whatever you type.

Back to $100,000,000 of equity, $40,000,000 of debt and $10,000,000 of cash, so EV is still $130,000,000 and the residual is still $100,000,000. Raise EBITDA to $13,000,000. The multiple is 10 times.

Equity did not move. EV did not move. Both are stock identities. The flow in the denominator moved. A lower EV/EBITDA here is a more profitable year, not a smaller residual claim.

How EV/EBITDA works owns that 13 and that 10. This page is the $100,000,000 those multiples sit above.

It is not enterprise value. EV is the operations. Equity is what is left after net debt.

It is not a P/E. P/E divides a share price by a year's profit after interest. This page never takes a share price or an EPS figure, so it does not print an earnings multiple.

It is not a claim about book against market. Type book equity or market equity, but say which. The identity does not know the difference.

Interest-bearing debt is loans, bonds and, in a full bridge, lease liabilities. Trade payables are not usually in this $D$, because they are already inside working capital.

Surplus cash is cash you could hand back tomorrow without changing the forecast. Restricted cash and cash that has to sit in the till are not surplus. Adding them back would overstate equity recovered from EV.

How DCF works produces enterprise value from unlevered cash flows. Subtract this net debt from that EV to get equity value. Mixing a DCF of the operations with equity value double-counts the $30,000,000, or ignores it, depending on which way you drifted.

It is not a full net-debt bridge, not a P/E engine, and not a recommendation about what multiple a firm should trade on. The three sheets are equity of $100,000,000 inside EV of $130,000,000 at 13 times, the same $100,000,000 inside EV of $140,000,000 when cash is $0, and the same $100,000,000 when EBITDA is $13,000,000 and the multiple is 10 times. This is educational material, not financial advice.