BASIC STOCK VALUATION Common stock valuation Common stock provides an expected future cash flow stream, and a stock's value is found in the same
manner as the values of other financial assets: as the present value of the expected future cash flow stream. The expected cash flow consists of two elements: 1) the dividends expected in each year 2) the price investors expect to receive when they sell the stock The expected price includes the return of the original investment plus an expected capital gain. Definitions of Terms: Dt = dividend the the stockholder stockholder expects expects to receive at the end end of Year t D0 = the most recent dividend, dividend, which has already already been paid Po = actual market price of the stock stock today = expected price price of the stock stock at the end of each year t D1 / Po =expected dividend yield during the coming year = expected capital capital gain yield during the coming coming year g = expected growth growth rate in dividends as predicted predicted by a marginal investor investor r s s = minimum acceptable, acceptable, or required required rate of return = expected expected rate of return =(D1 / Po )+g = actual or realized, after -the-fact -the-fact rate rate of return = actual dividend dividend yield + actual actual capital gains yield Example: (Tool Kit 5.4.) D 1 = $3.00, P0 = $50, and the expected P at t =1 If D =1 is equal to $52, what is the stock’s expected dividend
yield, expected capital gains yield, and total expected return return for the coming year? Expect Expected ed Divid Dividend end yie yield ld = (D1/ Po)=(3/50)=0.06 Expected Expected Capital Capital gains gains yield yield =
=
(
)
6%
= 0.04 4%
Expect Expected ed total total retur return n = Expect Expected ed Divid Dividend end yield yield + Expec Expected ted Capita Capitall gain gainss yie yield ld = 6%+4 6%+4% % = 10% 1. Dividend Discount Discount Models Models (DDM) The basic model
The basic model of discounted dividends is elementary common stock valuation model, which starts from the the assumpt assumption ion that that the value value of common common stocks stocks equal equal to the prese present nt value value of expected expected future future dividends, with the intention of holding it forever. Value of stock =
= 1
=
(1 +
)
+
(1 +
)
+
(1 +
)
+⋯+
(1 +
)
=
(1 +
)
But what what is is the valu value e of when when we expe expect ct to hold hold the the stoc stockk for a fini finite te per period iod and and then then sell sell it? it? The value of the the stock is again again determined determined by the same equation. equation. Namely, for an individual investor, investor, the the expected cash flows consist consist of expected dividends plus the expected expected price of the stock. However, However, the sale price the current investor receives will depend on the dividends some future investor expects. Therefore, for all present and future investors, investors, expected cash flows must be based on expected future dividends. Example:
What if we plan to hold stock only for two years? In this case our model becomes: becomes:
=
(1 +
)
+
(1 +
)
+
(1 +
)
1.1. Zero growth stock
This model model provide a constant constant dividend dividend forever, forever, meaning meaning D1 = D2 =... =..... = D and g = 0.
= Example: (Tool Kit 5.5.)
A stock is expected expected to pay a dividend of $2 at the the end of the year. The required rate rate of return is r s = 12%. What would the stock’s price be if the growth rate were 0%? D1 = $2.0 $2.00 0 g = 0% r s = 12% 2 = = = 16.67 0.12
1.2. Constant growth model (Gordon model)
It starts from the assumption assumption that future dividends grow at a constant rate of growth growth - g from period to period, indefinitely. indefinitely.
=
∙ ((1 1+ ) = −
A necessa necessary ry condition condition for the validity validity of this this equation equation is that that
− greater greater than g.
2
Expected rate of return on constant growth stock
= Expected dividend yield + Expected capital gains yield = Expected Expected dividend yield yield + Expected Expected growth rate
=
+
Example: (Tool Kit 5.5.)
A stock is expected to pay a dividend dividend of $2 at the end of the year. The required rate rate of return is rs = 12%. What would the stock’s price be if the growth rate were 4%? D1 = $2,0 $2,00 0 g = 4% r s = 12% 2 = = = 25 − 0.12 0.12 − 0.04 0.04 Example: (Tool Kit 5.6.) D 0 = $4.00, r s = 9 % and If D and g = 5 % for a constant constant growth growth stock, stock, what is the the stock’s stock’s price, price, the stock’s stock’s
expected dividend yield, capital gains yield, and total expected return for the coming year? D0 = $4.00 r s = 9 % g=5% ∙ (1 (1 + ) 4 ∙ ((1 1 + 0.0 0.05) 4.2 = = = = 105 − 0.09 0.09 − 0.05 0.05 0.04 Expect Expected ed Divid Dividend end yie yield ld = (D1/ Po)=(4.2/105)=0.04
4%
Expected Expected Capital Capital gains gains yield yield = growth growth rate rate = 5% Expect Expected ed total total retur return n = Expect Expected ed Divid Dividend end yield yield + Expec Expected ted Capita Capitall gain gainss yie yield ld = 4%+5 4%+5% % = 9% Exerci Exercise: se: 1
Boehm Incorporated is expected to pay $1.50 per share dividend at the end of the year ( D1=1.50).The dividend is expected to grow at a constant rate of 7% a year. The required rate of return on the stock, r s, is 15%. What is the the value per share of the company's company's stock? Exerci Exercise: se: 2
Brushy Mountain's sales are falling and its costs are rising. As a result, the company's earnings and dividends are declining at the constant rate of 4% per year. If D0=$5 and r s=15%, what is the value of this company stock? Exercise: 3
The beta coefficient for Stock C i bc=0,4, whereas that for Stock D is bd =-0,5. a) if the risk-free rate is 9% and the expected rate of return on an average stock is 13%, what are required rates rates of return on stocks stocks C and D?
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b) for stock C, suppose the current price, is $25; the next expected dividend D 1 is $1,5 and the stock's expected constant growth rate is 4%. Is the stock in equilibrium? equilibrium? Explain, and describe what will happen if the stock is not in equilibrium. equilibrium. Exerci Exercise: se: 4
Woidtke Manufacturing's stock currently sells for $20 a share. The stock just paid a dividend of $1.00 a share. The dividend is expected to grow at a constant rate of 10% a year. What stock price is expected 1 year from now? What is the required rate of return on the company's stock? Exerci Exercise: se: 5
A stock is trading at $80 per share. The stock is expected to have a year-end dividend of $4 per share, which is expected to grow at some constant rate g throughout time. The stock's required rate of return g? is 14%. If you are an analyst who believes in efficient markets, what is your forecast of g Exercise: 6
You are considering an investment in the common stock of Cookware. The stock is expected to pay a dividend of $2 a share at the end of the the year. The stock has a beta equal to 0.9. 0.9. The risk-free rate is 5.6% and the market risk premium is 6%. The stock's dividend is expected to grow at some constant rate g. the stock is currently sells for $25 a share. Assuming the market is in equilibrium, equilibrium, what does the market believe will be the stock price at the end of 3 years? Exercise: 7
You buy a share of LC corporation for $21.40. You expect it to pay dividends of $1.07, $1.1449 and $1.2250 in Years 1, 2 and 3, respectively, and you expect to sell it at a price of $26.22 at the end of 3 years. a) calculate the growth rate rate in dividends b) calculate the expected dividend yield c) assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth growth rate to get the expected total total rate of return. What is this stock's expected total total rate of return? Exercise: 8
Suppose a firm's common stock paid a dividend of $2 yesterday. You expect the dividend to grow at the rate of 5% per year for the next 3 years and if you buy the stock, you plan to hold it for 3 years and then sell it: a) find the expected dividend for each of the next 3 years b) given that the appropriate discount rate is 12% and that the fisrt of these dividend payment will occur D1, D2 adn D3 1 year from now. Find the present value of the dividens stream; that is calculate calculate the PV of D and then sum these PVs c) you expect expect the the price price of the the stock stock 3 years years from from now to to be $34.73; $34.73; that that is you expect expect to equal equal $34.73 $34.73 d) if you plan to buy the stock, hold it for 3 years, and then sell it for $34.73, what is the most you should pay for for it it ? e) calculate present value of this stock, assume that g = 5%, and it is constant. f) is the value of this stock stock dependent on on how long you plan to hold hold it ?
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1.3. Stocks that have a non-constant growth rate
Companies Companies that generat generate e above-aver above-average age grow growth th rates rates over a number number of years years cannot cannot be evalua evaluated ted based on the model of constant growth growth dividend because because the periods of super normal growth growth are inconsistent with the assumptions of this model. Two-phase and three phase models of growth imply that after several years of exceptional growth period, ie above average growth is expected that the growth rate falls and return to average growth rates, and to stabilize at a level consistent with the model of constant growth. growth. Two-stage growth model: we have one an above-average growth growth rate of dividends
=
∙ (1 + ) (1 + )
+
∙ (1 + ) 1 ∙ ( − ) (1 + )
whereby:
=
∙ (1 +
)
gs = rate of growth during the the supernormal growth growth period N = years of superno supernorma rmall growth growth gn = rate of normal, constant constant growth after the supernormal supernormal period Exerci Exercise: se: 9
Thress Industries just paid a dividend of $1.50 a share ( D0=1.50). The dividend is expected to grow 5% a year for the next 3 years, and then 10% a year thereafter. What is the expected dividend per share for each of the next 5 years? Exercise: 10
Simpkins Corporation is expanding rapidly, and it currently needs to retain all of its earnings; hence it does not pay any dividends. However, investors investors expect Simpkins to begin paying dividends, with with the first dividend of $1.0 $1.0 coming 3 years from from today. The dividend should grow rapidly rapidly - at a rate of 50% per per year-during Years 4 and 5. After Year 5, the company should grow at a constant rate of 8% per year. If the required return return on the stock is 15%. What is the the value of the stock today? Exerci Exercise: se: 11
A company currently pays a dividend of $2 per share. It is estimated that the company's dividend will grow at a constant rate of of 20% per year for the next next 2 years, and then the the dividend will grow grow at a constant rate of 7% thereafter. The company's stock has a beta equal 1.2, the risk-free rate is 7.5% and the market risk premium is 4%. What is your estimate of the stock's current price?
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Three-stage growth model: we we have two above-average above-average growth growth rates rates of dividends dividends
∙ ((1 1+ ) (1 + )
=
∙ ((1 1+ ) + (1 + )
+
∙ (1 + ) 1 ∙ ( − ) (1 + )
whereby:
=
= ∙ (1 + ) ∙ (1 + ) ∙ (1 +
)
gs = first rate of growth growth during the the supernormal supernormal growth period period which takes for N years gb = second rate of growth growth during the the supernormal supernormal growth period period which takes for (B-N) year yearss gn = rate of normal, constant constant growth after the supernormal supernormal period Example: (Tool Kit 5.7.)
Suppose D0 = $5.00 and rs = 10 percent. percent. The expected expected growth rate from Year Year 0 to Year 1 ( g0 to 1) = 20 percent, the expected growth rate from Year 1 to Year 2 (g1 to 2) = 10 percent, and the constant rate beyond Year 2 is gn = 5 percent. What are the expected dividends for Year 1 and Year 2? What is the expected horizon value price at Year 2? What is the expected P0? D0 = $5.00 r s = 10% g1 = 20% N=1 g2 = 10% B=1 gn = 5%
Expected dividends for Year 1 and Year 2: D1 = D0 ∙ ((1 1 + ) = 5 ∙ (1 + 0.2) = 6 D2 = D0 ∙ (1 (1 + ) ∙ (1 (1 + ) = 5 ∙ (1 + 0.2) ∙ (1 + 0.1) = 6. 6.6
Horizon Horizon value value =
=
=
∙(
)
=
. ∙( ( .
. .
) )
=138.60
Expected Po
=
D ∙ (1 + ) D ∙ (1 (1 + ) ∙ (1 (1 + ) D ∙ (1 (1 + ) ∙ (1 + ) ∙ (1 (1 + ) 1 + + ∙ ( 1 + r s) (1 + rs) (1 + ) (rs − ) 5 ∙ (1 + 0.2) 5 ∙ (1 + 0.2) ∙ (1 + 0.1) 0.1) 5 ∙ (1 + 0.2) ∙ (1 + 0 . 1) 1) ∙ (1 + 0.05) = + + (1 + 0.1) (1 + 0.1) 0.1) (0.1 (0.1 − 0.05 0.05)) 1 ∙ = 5.4 5.454 54 + 5.45 5.454 4 + 114. 114.55 55 = 125 125.4 .45 5 (1 + 0.1)
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Exercise: 12
Assume that the average firm in your company's industry is expected to grow at a constant rate of 6% and its dividend yield is 7%. Your company company is about as risky as the average firm in the industry, industry, but it has just successfully completed completed some R&D work that leads you to expect expect that its earnings and dividends dividends will grow at a rate of 50% this year and 25% the following following year, after which which growth should match the 6% industry average rate. The last dividend paid was $1. What is the value per share of your firm's stock? D0 = $1, r S = 7% + 6% = 13%, g1 = 50%, g2 = 25%, gn = 6%
2. Stock valuation by the free cash-flow approach
=
( + ) −
FCF = the cash flow available for distribution to all of the firm's investors, not just the shareholders
WACC = the average rate of return required by all of the firm's investors, not just shareholders. V = the value of the entire entire firm's firm's operations Example:
Suppose a firm had a free cash flow of $200 million million at the end of the most recent recent year. Let's assume assume that the firm's FCF s are expected to grow at a constant rate of 5% per year forever. Let's assume that the firm's WACC is 9%. ∙ (1 + ) 200 200 ∙ (1.0 (1.05) 5) = = = $5.250 $5.250 million million − 0.09 0.09 − 0.05 0.05 If the firm had any non-operating assets, such us short-term investments, we would add them to V to find the total value. This company has no non-operating non-operating assets. If the value of debt and preferred stock stock equals $2.000 million, then the the firm's equity has value of $5.250-$2.000 $5.250-$2.000 = $3.250 million. million. If 325 million million shares of stock are outstanding, outstanding, then the intrinsic intrinsic value $3.250/325 $3.250/325 = $10 per share. share.
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3. Market multiple analyses
This method of stock valuation applies a market-determined market-determined multiply to net income, earnings earnings per share (EPS), sales, and book value or, for business such as cable TV or cellular telephone systems, systems, the number of subscribers.
=
ℎ
(
1) ∙
Market multiple shows how much investor is willing to pay per unit of earnings meaning how many times the stock price is higher than the earnings per share.
Preferred stock valuation Preferred stock is a hybrid – it is similar to bonds bonds in some respects respects and to common stock stock in others. It has
a par value and a fixed amount of dividends that must be paid before dividends can be paid on the common stock. stock. Although, preferred stock has a fixed fixed payment payment like bonds, a failure to to make this payment will not lead to bankruptcy.
= = the value of the preferred stock =the preferred dividend = required rate of return = = expected rate of return Example: Example: (Tool (Tool Kit 5.10.) 5.10.)
A preferred stock has an annual dividend of $5. The required return is 8 percent. What is the Vps? Dps=$5.00 Rps=8%
=
5 = 62.50 0.08
Exerci Exercise: se: 13
Nick's Incorporated has a preferred stock outstanding that pays a dividend of $5 at the end of each year. The preferred stock sells for $50 a share. What is the preferred stock's required rate of return?
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Exerci Exercise: se: 14
What will be the nominal rate of return on a preferred stock with a $100 par value, a stated dividend of 8% of par and a curren currentt market price price of: a) $60 b) $80 c) $100 d) $140 Exercise: 15
Rolen Ridders issued preferred stock with a stated dividend of 10% of par. Preferred stock of this type currently yields 8% and the par value is $100. Assume dividends are paid annually: a) what is the value value of Rolen's preferred preferred stock? b) suppose interest rate levels rise to the point where the preferred stock now yields 12%,What would be the value of Rolen's preferred stock?
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