Top Banner
The Definition of a Stock Plain and simple, stock is a share in the ownership of a company. Stock represents a claim on the company's assets and earnings. As you acquire more stock, your ownership stake in the company becomes greater. Whether you say shares, equity, or stock, it all means the same thing. In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally potential market prices, and thus to profit from price movement – stocks that are judged undervalued (with respect to their theoretical value) are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall. The Definition of Stock Valuation In the view of fundamental analysis, stock valuation based on fundamentals aims to give an estimate of their intrinsic value of the stock, based on predictions of the future cash flows and profitability of the business. Fundamental analysis may be replaced or augmented by market criteria – what the market will pay for the stock, without any necessary notion of intrinsic value. These can be combined as "predictions of future cash flows/profits (fundamental)", together with "what will the market pay for these profits?". These can be seen as "supply and demand" sides – what underlies the supply (of stock), and what drives the (market) demand for stock? In the view of others, such as John Maynard Keynes, stock valuation is not a prediction but a convention, which serves to facilitate investment and ensure that stocks are liquid, despite being underpinned by an illiquid business and its illiquid investments, such as factories. Being an Owner
33
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: The Definition of a Stock Vol 2

The Definition of a Stock

Plain and simple, stock is a share in the ownership of a company. Stock represents a claim on the company's assets and earnings. As you acquire more stock, your ownership stake in the company becomes greater. Whether you say shares, equity, or stock, it all means the same thing.

In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally potential market prices, and thus to profit from price movement – stocks that are judged undervalued (with respect to their theoretical value) are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.

The Definition of Stock Valuation

In the view of fundamental analysis, stock valuation based on fundamentals aims to give an estimate of their intrinsic value of the stock, based on predictions of the future cash flows and profitability of the business. Fundamental analysis may be replaced or augmented by market criteria – what the market will pay for the stock, without any necessary notion of intrinsic value. These can be combined as "predictions of future cash flows/profits (fundamental)", together with "what will the market pay for these profits?". These can be seen as "supply and demand" sides – what underlies the supply (of stock), and what drives the (market) demand for stock?

In the view of others, such as John Maynard Keynes, stock valuation is not a prediction but a convention, which serves to facilitate investment and ensure that stocks are liquid, despite being underpinned by an illiquid business and its illiquid investments, such as factories.

Being an Owner

Holding a company's stock means that you are one of the many owners (shareholders) of a company and, as such, you have a claim (albeit usually very small) to everything the company owns. Yes, this means that technically you own a tiny sliver of every piece of furniture, every trademark, and every contract of the company. As an owner, you are entitled to your share of the company's earnings as well as any voting rights attached to the stock.

A stock is represented by a stock certificate. This is a fancy piece of paper that is proof of your ownership. In today's computer age, you won't actually get to see this document because your brokerage keeps these records electronically, which is also known as holding shares "in street name". This is done to make the shares easier to trade. In the past, when a person wanted to sell his or her shares, that person physically took the certificates down to the brokerage. Now, trading with a click of the mouse or a phone call makes life easier for everybody.

Page 2: The Definition of a Stock Vol 2

Being a shareholder of a public company does not mean you have a say in the day-to-day running of the business. Instead, one vote per share to elect the board of directors at annual meetings is the extent to which you have a say in the company. For instance, being a Microsoft shareholder doesn't mean you can call up Bill Gates and tell him how you think the company should be run. In the same line of thinking, being a shareholder of Anheuser Busch doesn't mean you can walk into the factory and grab a free case of Bud Light!

For ordinary shareholders, not being able to manage the company isn't such a big deal. After all, the idea is that you don't want to have to work to make money, right? The importance of being a shareholder is that you are entitled to a portion of the company’s profits and have a claim on assets. Profits are sometimes paid out in the form of dividends. The more shares you own, the larger the portion of the profits you get. Your claim on assets is only relevant if a company goes bankrupt. In case of liquidation, you'll receive what's left after all the creditors have been paid. This last point is worth repeating: the importance of stock ownership is your claim on assets and earnings. Without this, the stock wouldn't be worth the paper it's printed on.

Different Types Of Stocks

There are two main types of stocks: common stock and preferred stock.

Common Stock

Common stock is, well, common. When people talk about stocks they are usually referring to this type. In fact, the majority of stock is issued is in this form. We basically went over features of common stock in the last section. Common shares represent ownership in a company and a claim (dividends) on a portion of profits. Investors get one vote per share to elect the board members, who oversee the major decisions made by management.

Over the long term, common stock, by means of capital growth, yields higher returns than almost every other investment. This higher return comes at a cost since common stocks entail the most risk. If a company goes bankrupt and liquidates, the common shareholders will not receive money until the creditors, bondholders and preferred shareholders are paid.

Preferred Stock

Preferred stock represents some degree of ownership in a company but usually doesn't come with the same voting rights. (This may vary depending on the company.) With preferred shares, investors are usually guaranteed a fixed dividend forever. This is different than common stock, which has variable dividends that are never guaranteed.

Another advantage is that in the event of liquidation, preferred shareholders are paid off before the common shareholder (but still after debt holders). Preferred stock may also be callable, meaning that

Page 3: The Definition of a Stock Vol 2

the company has the option to purchase the shares from shareholders at anytime for any reason (usually for a premium).

Some people consider preferred stock to be more like debt than equity. A good way to think of these kinds of shares is to see them as being in between bonds and common shares.

Different Classes of Stock

Common and preferred are the two main forms of stock; however, it's also possible for companies to customize different classes of stock in any way they want. The most common reason for this is the company wanting the voting power to remain with a certain group; therefore, different classes of shares are given different voting rights. For example, one class of shares would be held by a select group who are given ten votes per share while a second class would be issued to the majority of investors who are given one vote per share.

When there is more than one class of stock, the classes are traditionally designated as Class A and Class B. Berkshire Hathaway (ticker: BRK), has two classes of stock. The different forms are represented by placing the letter behind the ticker symbol in a form like this: "BRKa, BRKb" or "BRK.A, BRK.B".

What Causes Stock Prices To Change?

Stock prices change every day as a result of market forces. By this we mean that share prices change because of supply and demand. If more people want to buy a stock (demand) than sell it (supply), then the price moves up. Conversely, if more people wanted to sell a stock than buy it, there would be greater supply than demand, and the price would fall.

Understanding supply and demand is easy. What is difficult to comprehend is what makes people like a particular stock and dislike another stock. This comes down to figuring out what news is positive for a company and what news is negative. There are many answers to this problem and just about any investor you ask has their own ideas and strategies.

That being said, the principal theory is that the price movement of a stock indicates what investors feel a company is worth. Don't equate a company's value with the stock price. The value of a company is its market capitalization, which is the stock price multiplied by the number of shares outstanding.

For example, a company that trades at $100 per share and has 1 million shares outstanding has a lesser value than a company that trades at $50 that has 5 million shares outstanding ($100 x 1 million = $100 million while $50 x 5 million = $250 million). To further complicate things, the price of a stock doesn't only reflect a company's current value, it also reflects the growth that investors expect in the future.

Page 4: The Definition of a Stock Vol 2

So, why do stock prices change? The best answer is that nobody really knows for sure. Some believe that it isn't possible to predict how stock prices will change, while others think that by drawing charts and looking at past price movements, you can determine when to buy and sell. The only thing we do know is that stocks are volatile and can change in price extremely rapidly.

The important things to grasp about this subject are the following:

1. At the most fundamental level, supply and demand in the market determines stock price.

2. Price times the number of shares outstanding (market capitalization) is the value of a company. Comparing just the share price of two companies is meaningless.

3. Theoretically, earnings are what affect investors' valuation of a company, but there are other indicators that investors use to predict stock price. Remember, it is investors' sentiments, attitudes and expectations that ultimately affect stock prices.

4. There are many theories that try to explain the way stock prices move the way they do. Unfortunately, there is no one theory that can explain everything.

A manager’s actions affect both the stream of income to investors and the riskiness of that stream. Therefore, managers need to know how alternative actions are likely to affect stock prices. At this point we develop some models to help show how the value of a share of stock is determined. We begin by defining the following terms:

Page 5: The Definition of a Stock Vol 2
Page 6: The Definition of a Stock Vol 2

Stock Valuation Methods

Stocks have two types of valuations. One is a value created using some type of cash flow, sales or fundamental earnings analysis. The other value is dictated by how much an investor is willing to pay for a particular share of stock and by how much other investors are willing to sell a stock for (in other words, by supply and demand). Both of these values change over time as investors change the way they analyze stocks and as they become more or less confident in the future of stocks.

The fundamental valuation is the valuation that people use to justify stock prices. The most common example of this type of valuation methodology is P/E ratio, which stands for Price to Earnings Ratio. This form of valuation is based on historic ratios and statistics and aims to assign value to a stock based on measurable attributes. This form of valuation is typically what drives long-term stock prices.

The other way stocks are valued is based on supply and demand. The more people that want to buy the stock, the higher its price will be. And conversely, the more people that want to sell the stock, the lower the price will be. This form of valuation is very hard to understand or predict, and it often drives the short-term stock market trends.

There are many different ways to value stocks. The key is to take each approach into account while formulating an overall opinion of the stock. If the valuation of a company is lower or higher than other similar stocks, then the next step would be to determine the reasons.

Earnings Per Share (EPS).

EPS is the total net income of the company divided by the number of shares outstanding. They usually have a GAAP EPS number (which means that it is computed using all of mutually agreed upon

Page 7: The Definition of a Stock Vol 2

accounting rules) and a Pro Forma EPS figure. The most important thing to look for in the EPS figure is the overall quality of earnings. Make sure the company is not trying to manipulate their EPS numbers to make it look like they are more profitable. Also, look at the growth in EPS over the past several quarters / years to understand how volatile their EPS is, and to see if they are an underachiever or an overachiever.

The EPS number that most analysts use is the pro forma EPS. To compute this number, use the net income that excludes any one-time gains or losses and excludes any non-cash expenses like stock options or amortization of goodwill. Then divide this number by the number of fully diluted shares outstanding.

Price to Earnings (P/E).

Now that you have several EPS figures (historical and forecasts), you'll be able to look at the most common valuation technique used by analysts, the price to earnings ratio, or P/E. To compute this figure, take the stock price and divide it by the annual EPS figure. For example, if the stock is trading at $10 and the EPS is $0.50, the P/E is 20 times. To get a good feeling of what P/E multiple a stock trades at, be sure to look at the historical and forward ratios.

Historical P/Es are computed by taking the current price divided by the sum of the EPS for the last four quarters, or for the previous year. You should also look at the historical trends of the P/E by viewing a chart of its historical P/E over the last several years (you can find on most finance sites like Yahoo Finance). Specifically you want to find out what range the P/E has traded in so that you can determine if the current P/E is high or low versus its historical average.

Forward P/Es reflect the future growth of the company into the figure. Forward P/Es are computed by taking the current stock price divided by the sum of the EPS estimates for the next four quarters, or for the EPS estimate for next calendar of fiscal year or two.

P/Es change constantly. If there is a large price change in a stock you are watching, or if the earnings (EPS) estimates change, the ratio is recomputed.

Like all financial assets, equilibrium stock prices are the present value of a stream of cash flows. What are the cash flows that corporations provide to their stockholders? First, think of yourself as an investor who buys a stock with the intention of holding it (in your family) forever. In this case, all that you (and your heirs) will receive is a stream of dividends, and the value of the stock today is calculated as the present value of an infinite stream of dividends:

Page 8: The Definition of a Stock Vol 2

CONSTANT GROWTH STOCKS

Equation 5-1 is a generalized stock valuation model in the sense that the time pattern of Dt can be anything: Dt can be rising, falling, fluctuating randomly, or it can even be zero for several years, and Equation 5-1 will still hold. With a computer spreadsheet we can easily use this equation to find a stock’s intrinsic value for any pattern of dividends.5 In practice, the hard part is getting an accurate forecast of the future dividends. However, in many cases, the stream of dividends is expected to grow at a constant rate. If this is the case, Equation 5-1 may be rewritten as follows:

EXPECTED RATE OF RETURN ON A CONSTANT GROWTH STOCK

VALUATING NON CONSTANT GROWTH STOCKS

For many companies, it is inappropriate to assume that dividends will grow at a constant rate. Firms typically go through life cycles. During the early part of their lives, their growth is much faster than that of the economy as a whole; then they match the economy’s growth; and finally their growth is slower than that of the economy.

Page 9: The Definition of a Stock Vol 2
Page 10: The Definition of a Stock Vol 2

First, we assume that the dividendwill grow at a nonconstant rate (generally a relatively high rate) for N periods, after which it will grow at a constant rate, g. N is often called the terminal date,or horizon date.We can use the constant growth formula, Equation 5-2, to determine what the stock’s horizon, or terminal, value will be N periods from today:

The stock’s intrinsic value today, Pˆ 0, is the present value of the dividends during the nonconstant growth period plus the present value of the horizon value:

To implement Equation 5-5, we go through the following three steps:

1. Estimate the expected dividends for each year during the period of nonconstant growth.

2. Find the expected price of the stock at the end of the nonconstant growth period, at which point it has become a constant growth stock.

3. Find the present values of the expected dividends during the nonconstant growth period and the present value of the expected stock price at the end of the nonconstant growth period. Their sum is the intrinsic value of the stock, Pˆ 0.

Page 11: The Definition of a Stock Vol 2

Stocks and Their Valuation

MINI CASE

Sam Strother and Shawna Tibbs are senior vice presidents of the Mutual of Seattle. They are co-directors of the company’s pension fund management division, with Strother having responsibility for fixed income securities (primarily bonds) and Tibbs being responsible for equity investments. A major new client, the Northwestern Municipal League, has requested that Mutual of Seattle present an investment seminar to the mayors of the represented cities, and Strother and Tibbs, who will make the actual presentation, have asked you to help them.

To illustrate the common stock valuation process, Strother and Tibbs have asked you to analyze the Temp Force Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following questions.

a. Describe briefly the legal rights and privileges of common stockholders.

Answer: The common stockholders are the owners of a corporation, and as such, they have certain rights and privileges as described below.

1. Ownership implies control. Thus, a firm’s common stockholders have the right to elect its firm’s directors, who in turn elect the officers who manage the business.

2. Common stockholders often have the right, called the preemptive right, to purchase any additional shares sold by the firm. In some states, the preemptive right is automatically included in every corporate charter; in others, it is necessary to insert it specifically into the charter.

b. 1. Write out a formula that can be used to value any stock, regardless of its dividend pattern.

Answer: The value of any stock is the present value of its expected dividend stream:

P̂0 =

D1

(1+r s)t+

D2

(1+rs )+

D3

(1+rs )3+⋯+ D∞

(1+rs )∞ .

However, some stocks have dividend growth patterns which allow them to be valued using short-cut formulas.The value of any financial asset is equal to the present value of future cash flows provided by the asset. When an investor buys a share of stock, he or she typically expects to receive cash in the form of dividends and then, eventually, to sell the stock and to receive cash from the sale. Moreover, the price any investor receives is dependent upon the dividends the next investor expects to earn, and so on for different generations of investors. Thus, the stock's value ultimately depends on

Page 12: The Definition of a Stock Vol 2

the cash dividends the company is expected to provide and the discount rate used to find the present value of those dividends.

The dividend stream theoretically extends on out forever, i.e., n = infinity. Obviously, it would not be feasible to deal with an infinite stream of dividends, but fortunately, an equation has been developed that can be used to find the PV of the dividend stream, provided it is growing at a constant rate.

Naturally, trying to estimate an infinite series of dividends and interest rates forever would be an extremely difficult task. Now, we are charged with the purpose of finding a valuation model that is easier to predict and construct. That simplification comes in the form of valuing stocks on the premise that they have a constant growth rate.

b. 2. What is a constant growth stock? How are constant growth stocks valued?

Answer: A constant growth stock is one whose dividends are expected to grow at a constant rate forever. “Constant growth” means that the best estimate of the future growth rate is some constant number, not that we really expect growth to be the same each and every year. Many companies have dividends which are expected to grow steadily into the foreseeable future, and such companies are valued as constant growth stocks.

For a constant growth stock:

D1 = D0(1 + g), D2 = D1(1 + g) = D0(1 + g)2, and so on.

Naturally, assuming a constant growth rate for the rest of eternity is a rather bold statement. However, considering the implications of imperfect information, information asymmetry, and general uncertainty, perhaps our assumption of constant growth is reasonable. It is reasonable to guess that a given will experience ups and downs throughout its life. By assuming constant growth, we are trying to find the average of the good times and the bad times, and we assume that we will see both scenarios over the firm's life. In addition to assuming a constant growth rate, we will be estimating a long-term required return for the stock. By assuming these variables are constant, the general stock valuation model can be simplified to the following very important equation:

P̂0 =

D1

rs−g =

D0(1+g )r s−g .

This is the well-known “Gordon,” or “constant-growth” model for valuing stocks. Here D1, is the next expected dividend, which is assumed to be paid 1 year from now, rs is the required rate of return on the stock, and g is the constant growth rate.

In this equation, the long-run growth rate (g) can be approximated by multiplying the firm's return on assets by the retention ratio. Generally speaking, the long-run growth rate of a firm is likely to fall between 5 and 8 percent a year.

Page 13: The Definition of a Stock Vol 2

b. 3. What happens if a company has a constant g which exceeds its rs? Will many stocks have expected g > rs in the short run (i.e., for the next few years)? In the long run (i.e., forever)?

Answer: The model is derived mathematically, and the derivation requires that rs > g. If g is greater than rs, the model gives a negative stock price, which is nonsensical. The model simply cannot be used unless (1) rs > g, (2) g is expected to be constant, and (3) g can reasonably be expected to continue indefinitely.

Stocks may have periods of supernormal growth, where gs > rs; however, this growth rate cannot be sustained indefinitely. In the long-run, g < rs.

c. Assume that temp force has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7 percent, and that the market risk premium is 5 percent. What is the required rate of return on the firm’s stock?

Answer: Here we use the SML to calculate temp force’s required rate of return:

rs = rRF + (rM – rRF)bTemp Force = 7% + (12% - 7%)(1.2)= 7% + (5%)(1.2) = 7% + 6% = 13%.

d. Assume that Temp Force is a constant growth company whose last dividend (D0, which was paid yesterday) was $2.00, and whose dividend is expected to grow indefinitely at a 6 percent rate.

d. 1. What is the firm’s expected dividend stream over the next 3 years?

Answer: Temp Force is a constant growth stock, and its dividend is expected to grow at a constant rate of 6 percent per year. Expressed as a time line, we have the following setup. Just enter 2 in your calculator; then keep multiplying by 1 + g = 1.06 to get D1, D2, and D3:

0 1 2 3 4 | | | | |

D0 = 2.00 2.12 2.247 2.382

1.88 1.76 1.65 . . .

rs = 13%

g = 6%

Page 14: The Definition of a Stock Vol 2

d. 2. What is the firm’s current stock price?

Answer: We could extend the time line on out forever, find the value of Temp Force’s dividends for every year on out into the future, and then the PV of each dividend, discounted at r = 13%. For example, the PV of D1 is $1.76106; the PV of D2 is $1.75973; and so forth. Note that the dividend payments increase with time, but as long as rs > g, the present values decrease with time. If we extended the graph on out forever and then summed the PVs of the dividends, we would have the value of the stock. However, since the stock is growing at a constant rate, its value can be estimated using the constant growth model:

D 0 = $2,00 g = 6%r s = 13,0%

P̂0 =

D1

rs−g =

$2 .120 .13−0 .06 =

$2 . 120 .07 = $30.29.

d. 3. What is the stock’s expected value one year from now?

Answer: After one year, D1 will have been paid, so the expected dividend stream will then be D2, D3, D4, and so on. Thus, the expected value one year from now is $32.10:

P̂1 =

D2

(r s−g ) =

$2 .247(0 . 13−0 . 06 ) =

$2 . 2470 .07 = $32.10.

Page 15: The Definition of a Stock Vol 2

d. 4. What are the expected dividend yield, the capital gains yield, and the total return during the first year?

Answer: The expected dividend yield in any year n is

Dividend Yield =

DnP̂n−1 ,

While the expected capital gains yield is

Capital Gains Yield =

( P̂n−P̂n−1)

P̂n−1 = r -

DnPn−1 .

Thus, the dividend yield in the first year is 10 percent, while the capital gains yield is 6 percent:

Dividend Yield = D1

C&G Yield = P1-P0

P0 P0

Dividend Yield = 2,12

C&G Yield = $1,82

$30,29 $30,29

Dividend Yield = 7,00%

C&G Yield = 6,00%

Total Yield =Dividend Y. +

C&G Yield

Total Yield = 13,00%

Total return = 13.0%Dividend yield = $2.12/$30.29 = 7.0%

Capital gains yield = 6.0%

Page 16: The Definition of a Stock Vol 2

e. Now assume that the stock is currently selling at $30.29. What is the expected rate of return on the stock?

Answer: The constant growth model can be rearranged to this form:

r¿

s=

D1

P0

+g.

Here the current price of the stock is known, and we solve for the expected return. For Temp Force:

r¿

s= $2.12/$30.29 + 0.060 = 0.070 + 0.060 = 13%.

Page 17: The Definition of a Stock Vol 2

f. What would the stock price be if its dividends were expected to have zero growth?

Answer: If Temp Force’s dividends were not expected to grow at all, then its dividend stream would be a perpetuity. Perpetuities are valued as shown below:

0 1 2 3 | | | |

2.00 2.00 2.00

1.77 1.57 1.39 . . .

P0 = 15.38

P0 = PMT/r = $2.00/0.13 = $15.38.

Note that if a preferred stock is a perpetuity, it may be valued with this formula. Also, this kind of constant growth assumption only makes sense if you are valuing a mature firm with somewhat stable growth rates.

g. Now assume that Temp Force is expected to experience supernormal growth of 30 percent for the next 3 years, then to return to its long-run constant growth rate of 6 percent. What is the stock’s value under these conditions? What is its expected dividend yield and capital gains yield be in year 1? In year 4?

Answer: For many companies, it is unreasonable to assume that it grows at a constant growth rate. Hence, valuation for these companies proves a little more complicated. The valuation process, in this case, requires us to estimate the short-run non-constant growth rate and predict future dividends. Then, we must estimate a constant long-term growth rate that the firm is expected to grow at. Generally, we assume that after a certain point of time, all firms begin to grow at a rather constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how long the short-term growth will hold, and the long-term growth rate.

Specifically, we will predict as many future dividends as we can and discount them back to the present. Then we will treat all dividends to be received after the convention of constant growth rate with the Gordon constant growth model described above. The point in time when the dividend begins to grow constantly is called the horizon date. When we calculate the constant growth dividends, we solve for a terminal value (or a continuing value) as of the horizon date. The terminal value can be summarized as:

rs = 13%

g = 0%

Page 18: The Definition of a Stock Vol 2

TV N =P N =

D N+1 =DN (1+g)

( r s - g ) ( r s - g )

This condition is true, where N is the terminal date. The terminal value can be described as the expected value of the firm in the time period corresponding to the horizon date.

So we know now that the Temp Force is no longer a constant growth stock, so the constant growth model is not applicable. Note, however, that the stock is expected to become a constant growth stock in 3 years. Thus, it has a nonconstant growth period followed by constant growth. The easiest way to value such nonconstant growth stocks is to set the situation up on a time line as shown below:

D 0 $2,00

r s 13,0%

gs 30% Short-run g; for Years 1-3 only.

gL 6%Long-run g; for Year 4 and all following years.

30% 6%Year 0 1 2 3 4

Dividend $2,00 2,6 3,38 4,394 4,6576

PV of dividends$2,30092,64703,0453 4,6576

P3 = 66,5377 = Terminal value =

$46,1140 7,0% = r - gL

$54,1072 = P0

Dividend and C&G Yields at t=0 Dividend and C&G Yields at t=4

P3 = 66,53771Dividend Yield = 4,8% Dividend Yield = 7,0%

C & G Yield = 8,2% C & G Yield = 6,0%

Total Return = 13,0% Total Return = 13,0%

Page 19: The Definition of a Stock Vol 2

Simply enter $2 and multiply by (1.30) to get D1 = $2.60; multiply that result by 1.3 to get D2 = $3.38, and so forth. Then recognize that after year 3, Temp Force becomes a constant growth stock, and at that point can be found using the constant growth model. is the present value as of t = 3 of the dividends in year 4 and beyond.

With the cash flows for D1, D2, D3, and shown on the time line, we discount each value back to year 0, and the sum of these four PVs is the value of the stock today, P0 = $54.109.

The dividend yield in year 1 is 4.80 percent, and the capital gains yield is 8.2 percent:

Dividend yield = = 0.0480 = 4.8%.

Capital gains yield = 13.00% - 4.8% = 8.2%.

During the nonconstant growth period, the dividend yields and capital gains yields are not constant, and the capital gains yield does not equal g. However, after year 3, the stock becomes a constant growth stock, with g = capital gains yield = 6.0% and dividend yield = 13.0% - 6.0% = 7.0%.

h. Is the stock price based more on long-term or short-term expectations? Answer this by finding the percentage of Temp Force current stock price based on dividends expected more than three years in the future.

Managers often claim that stock prices are "short-term" in nature in the sense that they reflect what is happening in the short-term and ignore the long-term. We can use the results for the non-constant model to test this claim.The terminal value, or price at year 3, reflects the value of all dividends from year 4 and beyond, discounted back to year 3. Therefore, the PV of the terminal value is the present value of all dividends that will be paid in year 4 and beyond. This PV represents the part of the current stock price that is due to long-term cash flows.

Stock price due to long-term cash flows (PV of terminal value): $46,1140

Current price: $54,1072Percent of current price that is due to long-term cash

flows (PV of terminal value / Current price): 85,2%

Page 20: The Definition of a Stock Vol 2

Answer:

$ 46 .116$54 .109 = 85.2%.

Stock price is based more on long-term expectations, as is evident by the fact that over 85 percent of temp force stock price is determined by dividends expected more than three years from now.For most stocks, the percentage of the current price that is due to long-term cash flows isover 80%.

i. Suppose Temp Force is expected to experience zero growth during the first 3 years and then to resume its steady-state growth of 6 percent in the fourth year. What is the stock’s value now? What is its expected dividend yield and its capital gains yield in year 1? In year 4?

Answer: Now we have this situation:

0 1 2 3 4 | | | | |

2.00 2.00 2.00 2.00 2.12

1.77 1.57 1.3920.99

25.72 = P̂0

During year 1:

Dividend Yield =

$2 . 00$25 . 72 = 0.0778 = 7.78%.

Capital Gains Yield = 13.00% - 7.78% = 5.22%.

Again, in year 4 temp force becomes a constant growth stock; hence g = capital gains yield = 6.0% and dividend yield = 7.0%.

rs = 13%

g = 0% g = 0% g = 0% g = 6%

P̂3 = 30.29 =

2 .120 .07

Page 21: The Definition of a Stock Vol 2

j. Finally, assume that Temp Force’s earnings and dividends are expected to decline by a constant 6 percent per year, that is, g = -6%. Why would anyone be willing to buy such a stock, and at what price should it sell? What would be the dividend yield and capital gains yield in each year?

Answer: The company is earning something and paying some dividends, so it clearly has a value greater than zero. That value can be found with the constant growth formula, but where g is negative:

P0 =

D1

rS−g =

D0(1+g )r S−g =

$2 .00 (0 .94 )0 .13−(−0 .06) =

$1 . 880 .19 = $9.89.

Since it is a constant growth stock:

g = Capital Gains Yield = -6.0%,

hence:

Dividend Yield = 13.0% - (-6.0%) = 19.0%.

As a check:

Dividend Yield =

$ 1. 88$ 9. 89 = 0.190 = 19.0%.

The dividend and capital gains yields are constant over time, but a high (19.0 percent) dividend yield is needed to offset the negative capital gains yield.

Page 22: The Definition of a Stock Vol 2

k. What is market mutliple analysis?

Answer: Analysts often use the P/E multiple (the price per share divided by the earnings per share) or the P/CF multiple (price per share divided by cash flow per share, which is the earnings per share plus the dividends per share) to value stocks. For example, estimate the average P/E ratio of comparable firms. This is the P/E multiple. Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price. The entity value (V) is the market value of equity (# shares of stock multiplied by the price per share) plus the value of debt. Pick a measure, such as EBITDA, sales, customers, eyeballs, etc. Calculate the average entity ratio for a sample of comparable firms. For example, V/EBITDA, V/customers. Then find the entity value of the firm in question. For example, multiply the firm’s sales by the V/sales multiple, or multiply the firm’s # of customers by the V/customers ratio. The result is the total value of the firm. Subtract the firm’s debt to get the total value of equity. Divide by the number of shares to get the price per share. There are problems with market multiple analysis. (1) It is often hard to find comparable firms. (2) The average ratio for the sample of comparable firms often has a wide range. For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?

l. Temp Force recently issued preferred stock. It pays an annual dividend of $5, and the issue price was $50 per share. What is the expected return to an investor on this preferred stock?

Answer:Preferred Stock

Vps = 50Dividend = 5

rps = PMTP

rps = 550

rps = 10%

m. Why do stock prices change? Suppose the expected D1 is $2, the growth rate is 5 percent, and rs is 10 percent. Using the constant growth model, what is the impact on stock price if g is 4 percent or 6 percent? If rs is 9 percent or 11 percent?

Answer: Using the constant growth model, the price of a stock is P0 = D1 / (rs – g). If estimates of g change, then the price will change. If estimates of the required return on stock change, then the stock price will change. Notice that rs = rRF +

Page 23: The Definition of a Stock Vol 2

(rpm)bi, so rs will change if there are changes in inflation expectations, risk

aversion, or company risk. The following table shows the stock price for various levels of g and rs.

g g grs 4% 5% 6%

9% 40.00 50.00 66.6710% 33.33 40.00 50.0011% 28.57 33.33 40.00

n. What does market equilibrium mean?

Answer: Equilibrium means stable, no tendency to change. Market equilibrium means that prices are stable--at its current price, there is no general tendency for people to want to buy or to sell a security that is in equilibrium. Also, when equilibrium exists, the expected rate of return will be equal to the required rate of return:

r¿

= D1/P0 + g = r = rRF + (rM - rRF)b.P0 is too low:

If the price is lower than the fundamental value, then the stock is a bargain.Buy orders will exceed sell orders and the price will be bid up.

Efficient Market Hypothesis:Securities are normally in equilibrium and are "fairly priced." One cannot "beat the market" except through luck or good inside information.

o. If equilibrium does not exist, how will it be established?

Answer: Securities will be bought and sold until the equilibrium price is established.

p. What is the efficient markets hypothesis, what are its three forms, and what are its implications?

Answer: The EMH in general is the hypothesis that securities are normally in equilibrium, and are “priced fairly,” making it impossible to “beat the market.”

Weak-form efficiency says that investors cannot profit from looking at past movements in stock prices--the fact that stocks went down for the last few days is no reason to think that they will go up (or down) in the future. This form has been proven pretty well by empirical tests, even though people still employ “technical analysis.”

Page 24: The Definition of a Stock Vol 2

Semistrong-form efficiency says that all publicly available information is reflected in stock prices, hence that it won’t do much good to pore over annual reports trying to find undervalued stocks. This one is (I think) largely true, but superior analysts can still obtain and process new information fast enough to gain a small advantage.

Strong-form efficiency says that all information, even inside information, is embedded in stock prices. This form does not hold--insiders know more, and could take advantage of that information to make abnormal profits in the markets. Trading on the basis of insider information is illegal.

r. Temp Force recently issued preferred stock. It pays an annual dividend of $5, and the issue price was $50 per share. What is the expected return to an investor on this preferred stock?

Answer: r¿

ps =

DpsV ps

=

$5$50

= 10%.