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Ch 7 Mini Case
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5/11/2003
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Chapter 7. Mini Case
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Situation
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Sam Strother and Shawna Tibbs are senior vice-presidents 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.
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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. workloads. You are to answer the following questions.
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a. Describe briefly the legal rights and privileges of common stockholders. stockholders.
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Features of Common Stock 1. Common Stock represents ownership 2. Ownership implies control 3. Stockholders elect directors 4. Directors hire management who attempt to maximize stock price.
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Classified Stock Classified Stock carries carries special provisions. For example, shares could be classified classified as founders shares which come with voting rights but dividend restrictions.
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b. (1.) Write out a formula that can can be used to value any stock, regardless of its dividend pattern. pattern.
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THE DISCOUNTED DIVIDEND APPROACH
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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 expects to earn, and so on for different generations of investors. 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.
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Here is the basic dividend valuation equation:
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P0 =
D1 (1+rs)
+
D2 (1+rs)
+
. . . .
2
Dn (1+rs)
n
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The dividend stream theoretically theoretically extends on out forever, i.e., 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.
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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 that they have a constant growth rate.
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(2.) What is a constant growth stock? How are constant growth stocks valued?
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VALUING STOCKS WITH 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 g eneral uncertainty, perhaps our assumption of constant growth is reasonable. It is reasonable to guess that a given will experience 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 firm's life. In addition to assuming a constant growth rate, we will be estimating a long-term required return return for the stock. By assuming these variables are constant, our price equation for common stock simplifies to the following expression: D1 P0 = (rs-g)
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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 likely to fall between 5 and 8 percent a
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year.
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(c.) What happens if a company has a constant g which exceeds r s? Will many stocks have expected g > rs in the short run (i.e., for the next next few years)? In the long run (i.e., forever)? forever)? Answer: See Chapter 7 Mini Case Show
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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,
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and that the market risk premium is 5 percent. What is the required rate of return on the firm’s stock?
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CAPM = rRF + b (rRF-rM) 7% + 1.2(5%) = 13%
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d. Assume that Temp Force 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.
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(1.) What is the firm’s expected dividend stream over the next 3 years? (2.) What is the firm’s current stock price?
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(3.) What is the stock's expected value 1 year from now?
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(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 Infinty Do =2.00 2.12 2 .2 4 7 2 2 .3 8 2 0 1.876 1.760 1.651 Etc. ?? Constant Growth Model: D0= $2.00 g= 6% r s= 13.0%
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P0 =
D1 (rs-g)
P 0=
$30.29
=
D 0 (1+g) (rs-g)
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Stock Price 1 year from now
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P1 =
D2 (rs-g)
P1 =
2.2472 0.07
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P1 =
32.10
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Dividend Yield
D1 P0
C&G Yield
P1-P0 P0
Dividend Yield
2 .1 2 $30.29
C&G Yield
$1.82 $30.29
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Dividend Yield
7.00%
C&G Yield
6.00%
=
$ 2 .1 2 0 .0 7
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Total Yield =
Dividend Yi
Total Yield =
13.00%
+
C&G Yield
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e. Now assume that the stock is currently currently selling at $30.29. What is the expected rate rate of return on the stock?
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Rearrange to rate of return fo rmula
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rs =
D1 P1
+
g
2 .1 2 32.10
+
0 .0 6
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rs =
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rs =
13%
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f. What would the stock price be if its its dividends were expected to to have zero growth?
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EXAMPLE: PREFERRED STOCK (I.E., STOCK WITH ZERO GROWTH) The dividend stream would be a perpetuity.
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P =
PMT
÷
r
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P = P =
$2.00 $15.38
÷
13.00%
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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. rates. There are some special special scenarios when the Gordon DCF constant growth model will not make sense, which will be discussed later.
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g. Now assume that Temp Force is expected 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 expected dividend yield and capital gains yield in Year 1? In Year 4?
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VALUING STOCKS WITH NON-CONSTANT GROWTH
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For many companies, it is unreasonable to assume that 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. dividends. Then, we must estimate a constant long-term growth rate that the firm is expected expected to grow at. Generally, we assume that after a certain 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 short-term growth rate, how long the short-term growth will hold, and the long-term growth rate.
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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 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 summarized as:
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TV N
=
PN =
D N+1 (rs-g)
=
DN (1+g) (rs-g)
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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.
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D0 rs gs gL
$2.00 13.0% 30% Short-run g; for Years 1-3 only. 6% Long-run g; for Year 4 and all following years. 3 0% 6%
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Year Dividend
0 $2.00
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2 3.38
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PV of dividends $2.3009 2.6470 3.0453 $7.9932 $46.1140
4.6576 P4 =
66.5377
= Terminal value = 7.0%
= r - gL
$54.1072 = P0
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h. Is the stock price based more on long-term or short-term 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.
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Divid ivideend and and C&G C&G Yie Yields lds at at t=0
Divi Divide dend nd and and C& C&G Yi Yields elds at t=4 P4 = 66.5377143
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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%
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h. Is the stock price based more on long-term or short-term 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.
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DO STOCK PRICES REFLECT LONG-TERM OR SHORT-TERM CASH FLOWS?
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Managers often claim that stock p rices 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.
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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 the present value of all dividends that will be paid in year 4 and beyond. This PV represents represents the part of the current current stock price that that is due to long-term cash flows.
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Stock price due to long-term cash flows (PV of terminal value): Current price: long-term cash flows (PV of terminal value / Current price):
$46.1140 $54.1072 85.2%
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For most stocks, the percentage of the current price that is due to long-term cash flows is over 80%.
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i. Suppose Temp Force is expected to experience zero growth during the first 3 years and then to resume its steadystate growth of 6 percent in the fourth fourth year. What is the stock's value now? What is its expected dividend dividend yield and its capital gains yield in Year 1? In Year 4?
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D0 rs g 1-3 g4
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Year Dividend
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PV of dividends
$2.00 13.0% 0% 6% 0% 0 $2.00
1 $2.00
2 $2.00
6% 3 $2.00
4 2.1200
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$1.7699 1.5663 1.3861 $4.7223 $20.9895
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$25.7118 = P0
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2.1200 P4 =
30.2857
= Terminal value = 7.0%
= r - g4
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Finally, assume that Temp Force’s Force’s earnings and dividends are expected expected to decline by a constant 6 percent per year,
that is, g = -6%. -6%. Why would anyone be willing to buy such a stock stock and at what price should it sell? What would be the dividend yield and capital gains yield in each year?
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D0= g= r s=
$2.00 -6% 13.0%
P0 =
D1 (rs-g)
P 0=
$9.89
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=
D 0 (1+g) (rs-g)
=
$ 1 .8 8 0.19
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C & G Yield =
-6.00%
Dividend Yield
19.00%
Total Return =
13.0%
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k. What is market market multiple analysis? Answer: See Chapter 7 Mini Case Show
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l. Why do stock prices change? change? Suppose the expected expected D1 is $2, the growth rate 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 percent of 6 percent? If rs is 9 percent or 11 percent?
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D0= g= r s=
2 .0 0 5.0% 10.0%
P0 =
D1 (rs-g)
P 0=
$42.00
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=
D 0 (1+g) (rs-g)
=
$ 2 .1 0 0.05
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% growth in D0 4% 5% 6%
Last Dividend, D0 Dividend, D Dividend, D Dividend, D
Resulting Price $42.00 $34.67 $42.00 $53.00
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m. What does market equilibrium mean? mean?
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Market Equilibrium
rs 9% 10% 11%
Last Dividend, D ividend, D ividend, D ividend, D
Resulting Price $42. $42.00 00 $52.50 $42.00 $35.00
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In equilibrium, stock prices prices are stable. There is no general tendency for people to 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.
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Achieving equilibrium D1 If: rs = P0
+
g
>
rs
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P0 is too low If the price is lower than than the fundamental value, then the stock is a bargain. Buy orders will exceed sell orders orders and the price will be bid up.
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n. If equilibrium does not exist, how will it be established? established?
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o. What is the Efficient Markets Markets Hypothesis, what are its three forms, forms, and what are its implications?
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Efficient Market Hypothesis Securities are normally in equilibrium and are "fairly priced." One cannot "beat the market" except through luck or good inside information.
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Weak form EMH States that one cannot profit by looking at past trends. A recent decline decline is no reason to think stocks will go up or down in the future.
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Semistrong form EMH All publicly available information is reflected reflected in stock prices. prices. It does not pay to pore over annual reports looking for undervalued stocks.
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Strong form EHM All information, including inside information, is reflected in stock prices.
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p. Schmid Company recently recently issued preferred preferred stock. It pays an annual dividend of $5, and the issue issue price was $50 per share. What is the expected return to an investor on this preferred stock?
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Preferred Preferre d Stock
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Vps = Dividend =
50 5
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rps =
PMT P
rps =
5 50
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rps =
10%
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