Financial Mathematics Text

Monday, February 18, 2013

Understanding Enterprise Value

There's a procedure used when evaluating stocks of subtracting cash or subtracting "net cash". I don't think it's well understood so I'll give a brief presentation here.

The procedure is actually based upon two observations:

1) Modigliani-Miller Theorem - This states, roughly, that the firm value is independent of its capital structure. It's valid under certain restraints but I think it's useful approximation.

The way it typically gets states is for V being the value of the firm, E is the value of the equity and D is the value of the debt:

$$V = E + D$$

Realistically we should factor in things like preferred shares and the like but we'll keep matters simple.

2) This one is based on the idea that the value of the firm is related to the value of the assets where the assets are Operating Assets and Non-Operating Assets. This is true given the law of excluded middle.

Often we replace "operating assets" with Enterprise Value (EV) and "non-operating assets" with Cash (C). This isn't entirely accurate. Some non-operating assets are not "cash" while some cash may be required for operations. But it's a close enough simplification. This gives us:

$$V = EV + C$$

If we combine these equations we can get several relationships. There are two that are most useful:

$$E = EV + C - D$$

This often gets used to first apply a discounted future cash flow to arrive at enterprise value, then add in the cash (or non-operating assets) and then subtract out the debt (and preferred shares, etc) to arrive at the value of the equity claim.

The second important relationship is this one:

$$EV = E + D - C$$

The way this gets used is that it takes the market value of equity and debt and subtracts out the cash to arrive at EV. Then EV is compared to, say, EBIT (Earnings Before Interest and Taxes) or some other appropriate figure.

This technique gets misused frequently. Some incorrectly subtract cash without adding in the debt. Others assume equity multiples remain constant (what remains constant, per Modigliani-Miller should be the EV multiple not equity multiple).

I think it's important to understand where the technique comes from as it will help prevent one from misapplying it.  Hopefully this brief presentation adds to that understanding.

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