What are stocks and how to value them

THE MARKET FOR COMMON STOCKS

If a company needs some money it can obtain it by borrowing it for example from banks or it can sell new shares of the company to investors on the market. When a firm sells its own shares on a market the shares are said to be traded in the primary market. When investors trade stocks among each others, the shares are said to be traded in the secondary market. Investors however do not buy shares directly from each others but they are connected and trade with each others thanks to a broker. An investor who wants to sell a share gives the broker the so called market order while an investor who wants to buy will give the broker a limit order specifying the max price at which he is willing to buy the stock.

HOW TO READ THE MOST IMPORTANT DATA ABOUT STOCKS

Consider this screenshot on GE in 2014, as you can see the closing price of the stock in that day was $24.49. This price is the result of the decrease of the price of the previous day by $0.10 or by the 0.41%. The market capitalization of the firm is defined as the price per share times the number of shares available on the market. So by knowing that market capitalization is $245.93billions and that the price of each share is $24.49 we can find the number of shares available: 245.93billions/24.49=10.04billions of shares. The earnings per share (EPS) refer to the earnings the company registered per share available during the last 12 months. The term “ttm” in the brackets means trailing twelve months. The ratio between the price of the share and what the share has earned over the past 12 months (EPS) is called the P/E ratio and it is obviously computed using the past year’s EPS because, in order to compute the future year’s ones, we should guess the future earnings per share. Then we can notice that the company decided to pay $0.88 per share which represent the 3.5% of the price of the share.

DIFFERENT WAYS TO VALUE STOCKS:

An option to value stocks is to use the firm’s book value computed as the total revenues of the firm minus its total costs. The problem with that method is that is that when valuing the company’s we are using their original cost less their depreciation but this gives no actual clue on how much the assets are worth today. Other factors that are not considered in that model are the inflation that modifies the actual value of money, the going concern value, which is the extra value of the company’s asset when they are put together and form an healthy business and most importantly, the book value of a company often does not consider the intangible assets of the company in its valuations. The book value is instead more useful for other purposes like knowing which will be the liquidation value: the money investors receive if the company shuts down and all of its assets are sold.

VALUATE OUR COMPANY USING OTHER COMPANIES VALUES

In order to value a company, financial experts generally compare the firm they want to evaluate with other similar firms that are called comparable firms that are already valued on the market. Because the comparable firms have stocks traded on the market, it is public knowledge how much investors are willing to spend in order to buy their stocks. More specifically, financial managers are interested in how much investors are willing to pay per dollar of earnings or book assets and, by using one of those values they estimate the value of the company. This process is called valuation by comparables. When you consider the firm’s comparables you are considering more than one firm and therefore you should compute the average of the P/E and P/B (which is the price of the share over the book value per share) of those firms. Once you compute that, in order to estimate the price of the share just multiply the average P/E by the estimated future earnings per share or the P/B by the book value of the company. In some cases you could find some outliers (firms having incredibly high or very low performances) among the comparables, in this case, when computing the average you should not consider them. In other cases it could be impossible to estimate the stock price using comparables because, if those firm incurred in negative profits, they do not have a P/E. In most cases this kind of evaluation is never used: investors on the market trade stocks that already have their own prices. This model of evaluation is useful for example when managers have to choose the price for the company’s IPO (initial public offering): the first shares of the company traded on the market.

HOW DIVIDENDS AND STOCK PRICES ARE RELATED

For companies it is not compulsory to pay dividends to shareholders. In many cases, the companies which want to grow fast like startups reinvest their earnings for future projects while established companies generally pay back the earnings to investors. In order to calculate the prices of a share you do not need to consider the dividends it will pay (if any), but also the expected price at which you will be able to sell that same share in one year from now. If we know which is the price of stock today, which will be its price in the future and the amount of dividends it will pay, we can calculate the share’s rate of return (r):

If instead we know the rate of return from other stocks of similar risk, the dividends it will pay and its price in the future we can calculate how much the stock is worth today:

Notice that we did not use the rate of return of the stock, because, in order to calculate it, we would need the stock’s price first. We instead used the so called market capitalization rate or cost of equity capital which simply represents the opportunity cost of investing our money in stocks in the same risk class. If the shares of a company are priced above all the other stocks in its risk class, investors will decide to buy the other firms’ stocks thus making the price of the stocks of the “expensive” firm decrease. If instead the shares of a company are underpriced with respect to the others in the risk class, investors will rush to buy that stock thus making the price rise. This is why all the assets in the same risk classes offer the same expected return.

WHAT IF I DO NOT WANT TO SELL THE STOCK THE NEXT YEAR

When computing the rate of return and the price of the stock today we assumed that the stock would be sold one year after its acquisition. This is not always true. As we expressed the price of the stock in period 0 using period one expected price and dividend, we can express the stock price in period 1 using forecasts about period 2 dividends and price:

Now, we can substitute this relationship for P1 in our equation to find the present price of the stock:

So now we are expressing the price of the stock today based on the dividends it will pay out the first two years and the price it will have two years from now. But we can once again write period 2 price as a function of period 3 dividends and price. If keep substituting each year price in terms of the subsequent year’s dividends and price, we will find:

This formula is called the dividend discount model (DCF). The first part of the equation is the sum of the dividends paid from period 1 to period H while the second part is simply the price at which you will be able to sell the stock in period H. If H is a period which is infinite the present value of the price in the future will approach 0 and therefore the price of the stock will depend only on the dividends it will pay out:

As time passes the present value of the future price of the share will become lower and lower while the future value of the dividends paid will become higher and higher.

WHAT IF DIVIDENDS ARE EXPECTED TO GROW

If the dividends paid by a company are expected to grow each year at a constant rate g, then we can consider them simply as a growing perpetuity. So we can write present value of our stock as:

We can use this formula when r>g . The more g is close to r, the more the price of the stock will tend to infinite. The formula can be obviously used in the opposite way to find r:

The first part of the equation is the dividend yield.

HOW MUCH OF THE EARNINGS PER STOCK ARE DISTRIBUTED

If you want to calculate the percentage of earnings per share distributed via dividends you are asking yourself which is the stock’s payout ratio and it is computed as DIV/EPS. The percentage of earnings that are not distributed constitute the plowback ratio and they are simply computed as 1-DIV/EPS. The return on the firm experiences per book share is called the return on equity (ROE) and it is computed as: EPS/bo

ok equity per share. If a company earns 10% of book equity during one year and reinvests 50% of this income, then the book equity will increase by 0.1*0.5=0.05. Also earnings and dividends per share will increase by 0.05. We can then express the dividend growth rate (g) as:

g = plowback ratio * ROE

in reality it is important to remember that saying that a firm will grow by a certain factor g forever is just an assumption that will only rarely be true.

HOW STOCK PRICE AND EARNINGS PER SHARE ARE LINKED

Generally investors distinguish among growth stocks, stocks that are expected to grow in the future and therefore to give them earnings thanks to the increase in the value of the stock itself and income stocks, stocks that are not expected to grow that much but that regularly pay dividends. The expected return on stocks held just for dividends and therefore never sold is: DIV/r. The returns for growth stocks can be computed as future price of the stock/price of the stock in the present. Suppose that a firm has stock price $100 and that in the past 12 months it has produced an EPS of $10. The firm is considering in the present an investment of $10 that will in the future leave stockholders without dividends in period 1 but will increase future dividends by $1 per share. If we suppose that other assets in the same risk class offer a return of 10% (market cap rate), the net present value per share in period 1 can be computed as:

Net present value at period 1 = -10 + 1/0.1 = 0

The first part is the cost incurred while the second part is the 1 euro in perpetuity. As you can see, the NPV is 0 meaning that the reduction of the dividends this year for the future investment will not produce any future earnings. The rate of return of the investment is exactly equal to the one single investors could achieve in the market by receiving the dividend in period 1:

Earnings-price ratio measured with future expected earnings are equal to the market capitalization rate r when the investment considered has NPV=0. The stock price can be considered as the sum of earnings that are not used for growth and therefore distributed and the net present value of the investment made with the earnings not distributed called net present value of growth opportunities (PVGO):

So the earning price ratio can be written as: