3.2 Stocks, One

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3.2. Asset Types: Stocks, the First Half

+ Describe a stock in general
+ Understand how the share price reflects the total value of the company
+ Become familiar with the Discounted Dividend valuation method and those similar

Lecture:  Stocks

Part I – What are stocks, or shares?
1. As we saw in the earlier section Corporate Finance – Capital Structure, firms raise capital either by issuing debt, or selling shares in the company as equity.
2. While many companies issues shares, only some companies, usually the larger ones, are publicly traded. Shares of these companies are normally traded on stock exchanges.
3. While most companies issue shares through an IPO, and receive the money from that initial sale, the subsequent trading of shares on stock exchanges by investors, large and small, constitutes the change of ownership of the shares–the company is no longer involved and does not receive any additional money. What most people see as the buying and selling of shares occurs in what is known as the secondary market.
4. Check out the Investopedia webpage describing how the two main US stock markets, NYSE and Nasdaq, work.
5. The market capitalization of a publicly traded company is the price per share times the number of shares outstanding. For example, when trading at $878 per share, Google’s market capitalization is $293billion. That means there was 334million shares outstanding.
6. Companies are usually categorized as small cap (under $2billion, although there is no single rule for deciding on the ranges,) medium cap ($2b to $10b in market capitalization) and large cap (over $10billion.)
7. Google is a large cap company. But, really, how much is Google worth, as a company? The fair market value of Google might be $293b, or it might not…

Part II – Company valuation and share price determination
1. Is the current price of a share of Company X a fair price?
This leads to two obvious questions:
~ How is the price of a share in a company determined?
~ How much is a company worth (and is the current price equal to that?)
2. There are three basic methods used to determine the value of a company.
~1. Asset value: valuing the assets of a company at current market worth
~2. Market comparison: comparing the company with similar companies with known value
~3. Income or Discounted cash flow: taking the present value of the future net income of the company.
3. Prof. Damodaran of NYU offers a nice summary of valuation methods here.

The Discounted cash flow model and the many other methods that are very similar, is based on the idea that owning an asset makes sense if it generates a stream of income, or cash, in the future. Assets are not owned for their own sake, but because they can produce things, provide services or otherwise create value or income. Every method of valuation tries to calculate the present discounted value of the stream of future income generated by the assets belonging to the company and owned by shareholders.

Rather than present the Discounted Cash Flow valuation method here (linked above,) I am going to present the Discounted Dividend Model, which is conceptually equivalent and mathematically very similar (structurally identical.) The basic premise is that the value of a company is the sum of all the profits it will make over its life. Each year, those profits can either be returned to owners in the form of dividends, or re-invested in the company to make higher profits in the future, which will be returned to owners as dividends. At the end of the life of the company, any value not already dispersed as dividends will be captured in the terminal value of the company, which goes to owners. As an owner, a shareholder will share in the profits either through dividends today, or dividends tomorrow. Future dividends are reflected in the price of the shares owned.

According to this model, the value of a company today is the sum of all dividends, D(t) each year from now (t=1) to the end of the company (t=T), discounted by an appropriate factor to obtain present value, V. This is explained in the video below.

Watch Valuation video

Each year the company can pay dividends to shareholders, or decide to retain earnings and reinvest in the company (or some combination of both,) in the expectation that future profits, and hence dividends, will be higher. Owners get the profits now, or later, with the hope that later dividends are larger. To calculate this Value, we would have to predict, or estimate, what each D(t) was, assume some life for the company, T years, and choose a discount factor, d. Unfortunately that’s not simple! One set of assumptions is set out in the Gordon growth model variant of the DDM. Gordon assumed dividends would grow at a constant rate each year of g, and the company would last forever (T is infinity.) With a constant discount rate of d, the present value of the company would be Vg = D1/(r-g) where D1 is the current level of dividends. Note that r must be greater than g for a positive valuation.

Whether using the standard DDM, or the Gordon version, an assumption how profits will be distributed (through dividends or reinvested) must be used, and the discount factor must be chosen. Dividends throughout time can be modeled in many simple (constant, or constant growth) or complicated ways (zero, then increasing once the company is mature, for example.) The company’s cost of capital is often used as the discount factor. The Capital Asset Pricing Model (CAPM) is sometimes used to calculate the cost of capital.

Once the (discounted present) value of the company is calculated, it can be divided by the number of shares outstanding to obtain the value per share, V*. This can then be compared to the current market share price. If the current price, P is greater than V* the company is over-valued, if less then it is under-valued. Note that this is just one of many valuation methods intended to assist investors in deciding if a company’s share is correctly valued by the market. See the Aside below for links to Benjamin Graham’s now famous valuation formula.

What increases the value of a company? The formula suggests that higher dividends, and earlier dividends increase the value, while a lower discount rate also increases value. But many companies don’t pay dividends, or pay lower dividends. The idea being that current profits can be re-invested in the company to produce greater profits and dividends in the future. But a company must be careful not to ask investors to wait too long for those realized and distributed profits!

Part III – Income or Capital Gains?

Investors can own shares for two possible reasons–to receive dividend income at regular intervals or to realize a capital gain on shares owned by “buying low and selling high.” Some companies don’t pay dividends, or wait some time before doing so, but most investors hope the value of their shares will rise over time. Sometimes the value of a share can be affected by a stock split, a reverse-split or a buy back. When a company effectively doubles (or some other factor) the number of shares outstanding by giving shareholders two shares for every one they own, it is a stock split. Companies do this usually to lower the price per share, to make them more affordable to smaller investors, but it does dilute share ownership because more shares are on the market. At the time of the split the market capitalization of the company stays the same, so a shareholder with 100 shares worth $20 each will next day own 200 shares worth $10 each. But after the split some investors might expect to see their shares rise in price. Or not.
arning income from dividends is a reasonable strategy for investors looking for an income stream at some point in their life cycle–in retirement for example. It is common for people to invest in “blue chip” stocks because they pay relatively high dividends. These investors usually “buy and hold” the stock rather than track price movements looking for opportunities to sell when prices go up. More on this when we consider the Strategies topic.
Day trading is the most extreme form of speculation in stocks to realize small, but significant, gains by selling at higher prices than the purchase price. Tax regulations do not favor buying and selling shares within a period of a year as all gains are treated as regular income, rather than capital gains. More on this later.

The Quiz will appear in next week’s section Stock, Two on the Learn website.

Aside: Benjamin Graham’s valuation formula
Benjamin Graham, the so-called father of value investing, wrote a book called the Intelligent Investor (1945), among many other things in his life, and is said to have inspired Warren Buffett, the heralded investor of our times. Despite some controversy as to his motives in presenting the formula, Graham presented a formula in the Intelligent Investor that can be used to price a company’s stock. (The controversy arises because some readers claim Graham intended for his formula to be used to solve for the growth rate of earnings, given the share price, not the other way around.)
The formula as originally specified is pretty simple:
Intrinsic value = V = EPS * (8.5 + 2g)
where EPS is earnings per share, and g is the expected 5-10 year growth rate of earnings.
Graham later revised the equation to include another term: (*4.4/Y), where Y is the yield on AAA rated bonds. The formula is quite similar to the Gordon formula, which is similar to the DDM formula. Actually it would be more surprising if there were a formula for valuing a company that was different!

Aside: Selling short
For most investors, and the general public, the rule is “buy low and sell high.” But there are also opportunities to make money selling high and buying low. Doesn’t seem to make sense, or I said it the wrong way ’round, but actually the important distinction is timing. Brokers actually provide the opportunity for investors to sell shares (they do, or do not, own) at a high price, then buy them back at a lower price some time later. Just as an investor can take advantage of rising share prices by buying low and selling high (called taking a long position in the stock,) they can take advantage of falling share prices by selling high and buying low (called taking a short position in the stock.)

In order to sell a stock short, an investor must have an account with a broker, who lends the investor the shares to sell. The investor’s account is credited the value of the sale, but it also creates a debt–the investor must pay back the original shares, and must pay the broker interest. The broker has set up a margin account for the investor, and the investor has borrowed the shares on margin. Assuming the investor’s expectation of falling prices is correct, the shares can be bought back after some time at a lower price, repaid to the broker with interest, and the investor’s account is up by the difference between sale and purchase price, less interest!

Unfortunately short stocks is risky for a number of reasons, compared to taking a long position on a stock. The price may not fall! If so, the broker may make a margin call, forcing the investor to buy the shares to repay the broker and clear the debt, but at a cost to the investor. The investor will lose money rather than make money. There is some symmetry here–an investor with a long position can lose money if the price goes down, just as an investor with a short position can lose money if the price goes up, but the long investor will never be forced to sell shares to cover a position, but a short investor can be forced to buy shares to cover the position. Extra risk!

Additional Resources/links
Nearly every investor website, such as Investopedia, Yahoo Finance, Motley Fool, provide lots of information about stocks, stock markets, how to trade, and everything else you ever need to know, and some you don’t, about stocks and shares.
1. Investopedia’s entry on Discounted Cash Flow calculation:
2. WIkipedia entry for short selling:
3. Investopedia entry for short selling:
4. Wikipedia entry for Graham’s formula:
Graham’s value formula.

Homework (due Mon Mar 16 – note two weeks includes break)
Write one-two page essay on the following topic.
When might an investor want to short sell a stock? How is this done? Is this part of a “standard” portfolio? Does it increase portfolio risk?

Discuss one, or all of these questions:
1. There are almost as many statistics (numbers) available for a company as there are for a baseball game! There’s the market cap., P/E ratio, Beta, ROE, and many, many more. Are some more important than others? Which ones would you focus on, and why?
2. Many (most) investors don’t know how the stock market works (either how shares are actually traded, or more generally how supply and demand work.) Since you are taking this class, why do you think understanding how D and S work helps people make better investment decisions?
3. There is turmoil all across the world (in the Middle East for example.) Stock markets are influenced by many things, especially people’s predictions of the future. To what extent do you think current stock market prices are influenced by news (both good and bad?) How about the influence of the Presidential election?

Second half of this Topic –>