I've been reading the Rosenbaum textbook and am currently on the 1st chapter. It went over the enterprise value and equity value formulas, but I wanted to get a more in depth understanding of how it works.

I looked at this guide: https://samples-breakingintowallstreet-com.s3.amaz...
The guide essentially says to look at EV and EqV questions conceptually based on the definitions. They define equity value as the value of everything a company has(all assets) but only to equity investors. They define enterprise value as the value of the business's core operating assets but to all investors. Anything that affects common stock(issuance, repurchase, and dividends) would change equity value, and anything that would affect business core operations would change enterprise value.

I looked at two scenarios I found online which asked how EV and EqV would be affected:
1. Company issues out \$100 in dividends
2. Company finds \$100 in the street and keeps it in their bank account

Now for #1, dividends is related to common stock, so equity value changes according to the guide. It falls by \$100. There's nothing operations-related here, so enterprise value doesn't change. I was confused when trying to check this answer with the formula though. If equity value is market price * # of shares outstanding, then why would issuing dividends change it? I understand that dividends declared and paid out decrease cash and decrease retained earnings. However, isn't equity value based off paid-in capital accounts and not retained earnings(earned capital)? Do we assume that there is a corresponding decrease in the price per share after dividend issuance that causes EqV to fall by the amount of the dividend? If so, then it would check out because cash falls by \$100 and EqV falls by \$100 leading to no change in EV.

I had a similar confusion with #2 based on the definition of EqV. EV doesn't change because cash isn't a core operating asset. Using the formula, if cash increases by \$100, then something else in the formula would have to increase by \$100 to balance it out. I guess the only one that would make sense is EV, but that's where I get confused again. I get cash would be debited and retained earnings credited, but why does equity value change based off retained earnings? Per its definition, EqV doesn't factor in retained earnings directly. I suppose it indirectly would be affected because increase in retained earnings would probably increase the price of shares in the market, but how would that be immediately reflected in EqV after the company pocketing the cash? Is there some hidden thing I am missing from EV including retained earnings?

Here are my questions(in case you didn't want to read the post):
1. Why is EV defined as the value of only the core business operations to all investors? If EqV is the value of all assets to equity investors, why doesn't EV also include all value of all assets since it includes every single investor group?
2. Is EqV different from total stockholders' equity on the balance sheet? If so, why do things that affect retained earnings(like dividends) affect EqV by the exact same amount? Do we assume a perfect/efficient market?
3. EV of 0 does not mean you can purchase the company for nothing correct? My understanding is that EqV is the purchase price to acquire the company, and EV is like factoring in the net transaction price based on the operating assets of the company acquired. Although, the guide from M&I says not to think about it as a takeover price. For example, say a person invested \$50 cash and started a company, and you decided to purchase it. Assume no debt. The equity value is \$50 and that would be the purchase price to acquire the company. However, EV would be 0 because you have \$50 after buying the company, so in effect the net transaction price based on the assets of the business is 0. Is that correct?
4. For shares outstanding in EqV calculation, does that include preferred stock shares or no?
5. For EPS calculation, are preferred stock shares included in outstanding shares in the denominator?
6. What is the best way to truly understand EV or EqV? Do you think the M&I guide in this post is the best way to think about it, or just remember the formulas? What has worked for you to master this concept?

Sorry for the long post; I'm a noob to IB and actually want to understand the material instead of just memorizing. Thanks for taking the time to read this post and respond!

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Thanks for this link. I'm still having trouble understanding how fluctuations in retained earnings and dividend issuance directly change EqV since it should only be based on price/share and outstanding shares. If you could take a look at the 2 scenarios I outline in the post, that would be super helpful. Those are the ones that are giving me trouble

1. When you do a unlevered DCF, the values arrives as an enterprise value. Why? because the unlever FCF has not attribute any money to any investors yet. (remember UFCF is before interest so debt holder is not getting paid yet). UFCF also doesn't include side business like investment income, interest income from cash, or other non-core gains because they are after operating income. Enterprise value is value of the CORE business operation. Everything after EBIT should be non-core. Equity Value only include common shareholder's equity (so preferred stock, noncontrolling don't count, they are not common shareholders).
2. Eqv reflects anything that affects the common stockholders, so stock repurchase, dividend issuance, and so on.
3. Market EV can 0 or negative but does not mean you can buy that company for nothing. assuming your market eqv is great than 0, you can have a company with only cash but no debt.
4. no, Eqv is only common stockholders, don't get confused with book value of shareholder's equity
5. no
6. not sure. figuring this out too

Thanks for your response. I understand all your answers, but I'm still confused why dividend issuance and increased net income/retained earnings affects EqV? If you could take a look at the 2 scenarios I outlined in the post, that would be extremely helpful. I'm having trouble understanding how fluctuations in retained earnings directly change EqV since it should only be based on price/share and outstanding shares.

i think re your question number 6, the best way to think about it is enterprise value is the present value of all future operating cash flows of the business (unlevered cash flows if you want to get more technical). just think really generally, a company is an asset that generates cash from its operations. enterprise value is the present value of that cash. another, equivalent way to think about this is it's the value of all claims to those cash flows. so that could be debt claims, equity claims, claims generated through options, convertible notes (etc. etc. etc.) really anything that gives the holder a right to value produced by the company. the commonly recited enterprise value formula is a way to more simply get to this value, but it's kind of a commonly accepted (and accurate, usually) shortcut in a lot of ways. this link explains this similarly, maybe better:
https://alphaarchitect.com/2020/05/01/whats-the-st...
equity value, conceptually, is what's left over for equity holders after paying the other claimants to a company's cash flows.

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Thanks for your detailed response and the link you provided. I'm still having trouble understanding how fluctuations in retained earnings and dividend issuance directly change EqV since it should only be based on price/share and outstanding shares. If you could take a look at the 2 scenarios I outline in the post, that would be super helpful. Those are the ones that are giving me trouble.

"Do we assume that there is a corresponding decrease in the price per share after dividend issuance that causes EqV to fall by the amount of the dividend? If so, then it would check out because cash falls by \$100 and EqV falls by \$100 leading to no change in EV."

Yes, that's correct. Your equity value would be reduced by the amount of the dividend. Your price per share would fall by the decrease in equity value divided by shares outstanding

Not sure I understand the second core question you asked. Equity value included retained earnings. Earnings belong to shareholders (equityholders). Earnings can be reinvested in the business (i.e., held by the business and used to acquire assets, fund operations, etc.) or they can be distributed to shareholders via dividends (or buybacks)

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I think where you're tripping up is the empirical vs theoretical aspect. Equity value and Enterprise value derived from a DCF are theoretical concepts. The way that I understand it (feel free to correct me if I am wrong) is that EqV decreases by the amount of the dividend because shareholders actually received that \$100, so it shouldn't be reflected in the stock price anymore. Retained earnings belong to the shareholders, so they are accounted for in the market value of equity; once you decrease retained earnings, shareholders are no longer entitled to that amount (it does not exist anymore, its been paid out), so market value of equity decreases to reflect that. So cash and equity value both go down by 100, EntV remains the same. The same is true with finding \$100. Cash goes up by 100, RE (which belongs to the shareholders) increases by 100 so EqV increases by 100. EntV remains the same.

Again this is a theoretical concept, not an empirical concept. Finance is as much an art as it is a science, you have to learn to distinguish between theoretical and empirical concepts.

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Ah this was exactly what I was looking for. I think you described my confusion perfectly. Thanks!

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