Ch 7 Mini Case 5/11/2003

Chapter 7. Mini Case

Situation

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

Features of Common Stock

Classified Stock

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

THE DISCOUNTED DIVIDEND APPROACH

Here is the basic dividend valuation equation:

+ + . . . .

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

VALUING STOCKS WITH A CONSTANT GROWTH RATE

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, theNorthwestern Municipal Alliance, 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.

1. Common Stock represents ownership 2. Ownership implies control 3. Stockholders elect directors 4. Directors hire management who attempt to maximize stock price.

Classified Stock carries special provisions. For example, shares could be classified as founders shares which come with voting rights but dividend restrictions.

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

P 0 =D 1 D 2 D n

( 1 + r s ) ( 1 + r s ) 2 ( 1 + r s ) n

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 a tremendously 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.

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In this stock valuation model, we first assume that the dividend and stock will grow forever at a constant growth rate. 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, our price equation for common stock simplifies to the following expression:

P 0 =D 1

( r s - g )

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.

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7% + 1.2(5%) = 13%

(1.) What is the firm’s expected dividend stream over the next 3 years? (2.) What is the firm’s current stock price? (3.) What is the stock's expected value 1 year from now?

(4.) What are the expected dividend yield, the capital gains yield, and the total return during the first year?EXAMPLE: CONSTANT GROWTH

0 1 2 3 Continue to InfintyDo =2.00 2.12 2.2472 2.3820

1.8761.7601.651Etc.??

Constant Growth Model:

$2.00 g = 6%

13.0%

= =$2.12

0.07

$30.29

Stock Price 1 year from now

2.24720.07

32.10

Dividend Yield C&G Yield

Dividend Yield 2.12 C&G Yield $1.82$30.29 $30.29

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.

(c.) What happens if a company has a constant g which exceeds 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: See Chapter 7 Mini Case Show

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?

CAPM = rRF + b (rRF-rM)

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 0 =

r s =

P 0 =D 1 D 0 (1+g)

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

P 0 =

P 1 =D 2

( r s - g )

P1 =

P1 =

D1 P1-P0

P0 P0

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Dividend Yield 7.00% C&G Yield 6.00%

Total Yield = Dividend Yi + C&G Yield

Total Yield = 13.00%

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

Rearrange to rate of return formula

+ g

2.12 + 0.06

32.10

13%

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

EXAMPLE: PREFERRED STOCK (I.E., STOCK WITH ZERO GROWTH)The dividend stream would be a perpetuity.

P = PMT ÷ r

P = $2.00 ÷ 13.00%P = $15.38

VALUING STOCKS WITH NON-CONSTANT GROWTH

rs =D1

P1

rs =

rs =

An important consideration to be made is that this kind of constant growth assumption only makes sense if you are valuing a mature firm with somewhat stable growth rates. There are some special scenarios when the Gordon DCF constant growth model will not make sense, which will be discussed later.

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 in Year 1? In Year 4?

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:

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=

$2.00

13.0%

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

6% Long-run g; for Year 4 and all following years.30% 6%

TV N = P N =D N+1 DN (1+g)

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

This condition holds 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.

D 0

r s

gs

gL

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Year 0 1 2 3 4Dividend $2.00 2.6 3.38 4.394 4.6576

PV of dividends$2.3009

2.64703.0453 4.6576

$7.9932 P4 = 66.5377 = Terminal value =

$46.1140 7.0%

$54.1072

Dividend and C&G Yields at t=0 Dividend and C&G Yields at t=4P4 = 66.5377143

Dividend 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%

DO STOCK PRICES REFLECT LONG-TERM OR SHORT-TERM CASH FLOWS?

$46.1140Current price: $54.1072

85.2%

For most stocks, the percentage of the current price that is due to long-term cash flows is over 80%.

$2.00

13.0%

0%

6%0% 6%

Year 0 1 2 3 4Dividend $2.00 $2.00 $2.00 $2.00 2.1200

= r - gL

= P0

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 3 years in the future.

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 3 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):

Percent of current price that is due to long-term cash flows

(PV of terminal value / Current price):

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?

D 0

r s

g 1-3

g 4

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PV of dividends$1.7699

1.56631.3861 2.1200

$4.7223 P4 = 30.2857 = Terminal value =

$20.9895 7.0%

$25.7118

$2.00 g = -6%

13.0%

= =$1.88

0.19

$9.89

C & G Yield = -6.00%

Dividend Yield 19.00%

Total Return = 13.0%

2.00g = 5.0%

10.0%

= =$2.10

0.05

$42.00

Resulting Resulting % growth Last Price Last Price

$42.00 $42.00 4% Dividend, D0 $34.67 9% Dividend, D0 $52.505% Dividend, D0 $42.00 10% Dividend, D0 $42.006% Dividend, D0 $53.00 11% Dividend, D0 $35.00

= r - g4

= P0

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?

D 0 =

r s =

P 0 =D 1 D 0 (1+g)

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

P 0 =

k. What is market multiple analysis? Answer: See Chapter 7 Mini Case Show

l. 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 of 6 percent? If rs is 9 percent or 11 percent?

D 0 =

r s =

P 0 =D 1 D 0 (1+g)

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

P 0 =

in D0 Dividend, D0 rs Dividend, D0

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m. What does market equilibrium mean?

Market Equilibrium

Achieving equilibrium

+ g >

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

o. What is the Efficient Markets Hypothesis, what are its three forms, and what are its implications?

Efficient Market Hypothesis

Weak form EMH

Semistrong form EMH

In equilibrium, stock prices are stable. There is no general tendency for people to buy or sell. The expected price must equal the actual price. In other words, the fundamental value must be the same as the price. In equilibrium, expected returns must equal required returns.

If: rs =D1

rsP0

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.

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

States that one cannot profit by looking at past trends. A recent decline is no reason to think stocks will go up or down in the future.

All publicly available information is reflected in stock prices. It does not pay to pore over annual reports looking for undervalued stocks.

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Strong form EHMAll information, including inside information, is reflected in stock prices.

Preferred Stock

Vps = 50Dividend = 5

PMTP

550

10%

p. Schmid Company 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?

rps =

rps =

rps =

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