simplification comes in the form of valuing stocks on the premise that they have a constant growth rate.
(2.) What is a constant growth stock? How are constant growth stocks valued?
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A B C D E F G H I J
12/9/2012
Situation
Features of Common Stock
Classified Stock
THE DISCOUNTED DIVIDEND APPROACH
D1D2DN
( 1 + rs ) ( 1 + rs ) 2 ( 1 + rs ) N
Sam Strother and Shawna Tibbs are senior vice presidents of 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
+
+
. . . .
Chapter 7 Mini Case
b. (1.) Write out a formula that can be used to value any stock, regardless of its dividend pattern.
1. Common Stock represents ownership. 2. Ownership implies control. 3. Stockholders elect directors. 4. Directors hire
management who attempt to maximize stock price.
Here is the basic dividend valuation equation:
Classified Stock carries special provisions. For example, shares could be classified as founders’ shares which come with
voting rights but dividend restrictions.
a. Describe briefly the legal rights and privileges of common stockholders.
𝐏𝟎=
who will make the actual presentation, have asked you to help them.
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A B C D E F G H I J
VALUING STOCKS WITH A CONSTANT GROWTH RATE
D1
( rs – g )
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
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% a year.
𝐏𝟎=
D1CG Yield = P1 – P0
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A B C D E F G H I J
Constant Growth Model:
INPUTS:
D0 = $2.00
g = 6%
rs =13.0%
Stock Price 1 year from now:
D2
( rs – g )
D2 = D1 (1+g) = $2.2472
(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 PowerPoint file.
c. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7.0%, and that the
market risk premium is 5%. What is the required rate of return on the firm’s stock?
P1 =
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% rate.
expected during Years 1, 2, and 3.
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A B C D E F G H I J
Total Yield =
Dividend
Yield
+
CG
Yield
INPUTS:
P0 = $30.29
D0 = $2.00
g = 6%
rs =13.0%
For most stocks, the percentage of the current price that is due to long-term cash flows is over 80%.
The first step is to forecast the dividends for the next 3 years. Then we find the present value of these dividends
and compare that PV with the current stock price, which reflects the PV of all future dividends.
f. Why are stock prices volatile? Using Temp Force as an example, what is the impact on the estimated stock price if g
falls to 5% or rises to 7%? If rs changes to 12% or to 14%?
INPUTS:
P0 = $30.29
D0 = $2.00
g = 6%
rs =13.0%
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A B C D E F G H I J
Estimated Price for Changes in Inputs
Growth Rate: g Required Return: rs
11.0% 12.0% 13.0% 14.0% 15.0%
5% $35.00 $30.00 $26.25 $23.33 $21.00
Rearrange to rate of return formula
Process for Finding the Value of a Nonconstant Growth Stock
INPUTS:
D0 = $2.00 Last dividend the company paid.
rs = 13.0% Stockholders’ required return.
For many companies, it is unreasonable to assume that it grows at a constant growth rate. Hence, valuation for these
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
h. Now assume that Temp Force’s dividend is expected to experience nonconstant growth of 30% from Year 0 to Year 1,
25% from Year 1 to Year 2, and 15% from Year 2 to Year 3. After Year 3, dividends will grow at a constant rate of 6%. What
is the stock’s intrinsic value under these conditions? What are the expected dividend yield and capital gains yield during
the first year? What are the expected dividend yield and capital gains yield during the fourth year (from Year 3 to Year 4)?
g. Now assume that the stock is currently selling at $30.29. What is its expected rate of return?
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Dividend Yield = 0.0%
CG Yield = 13.0%
Total Return = 13.0%
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A B C D E F G H I J
gL = 6% Constant long-run growth rate for all years after Year 3.
Growth rate 30% 25% 15% 6% 6%
Year 0 1 2 3 4
Dividends $2.6000 $3.2500 $3.7375
Expected Dividend and CG Yields at t = 0
Dividend Yield = 5.6%
CG Yield = 7.4%
Total Return = 13.0%
i. What is free cash flow (FCF)? What is the weighted average cost of capital? What is the free cash flow valuation model?
Answer: See Chapter 7 Mini Case Show
j. Use a pie chart to illustrate the sources that comprise a hypothetical company’s total value. Using another pie chart,
show the claims on a company’s value. How is equity a residual claim? Answer: See Chapter 7 Mini Case Show
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Minus Value of Preferred Stock $50.0
Intrinsic Value of Equity $270.0
(3) What is its estimated intrinsic value of equity?
to common stockholders.
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A B C D E F G H I J
11%
5%
$100.0
$200.0
$50.0
Number of shares of stock 10.0
(1) What is its estimated value of operations?
0.06
Vop = $420.00
Value of Operation $420.0
Plus Value of Non-operating Assets $100.0
Total Corporate Value $520.0
Intrinsic Value of Equity $270.0
Divided by number of shares 10.0
Intrinsic price per share $27.00
(2) What is its estimated total corporate value?
(4) What is its estimated intrinsic stock price per share?
Marketable securities
Debt
Preferred stock
WACC
Growth
Estimating the Value of R&R’s Stock Price (Millions, Except for Per
Share Data)
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− Preferred stock 50.00
Estimated value of equity $270.00
÷ Number of shares 10.00
Estimated stock price per share = $27.00
B&B’s Value of Operations (Millions of Dollars)
INPUTS:
gL = 5.00%
WACC = 11.00%
Year 0 1 2 3 4
FCF −$10.00 $20.00 $35.00
↓ ↓ ↓
INPUTS:
(1.) What is its horizon value (i.e., its value of operations at year three)? What is its current value of operations (i.e., at
time zero)?
Estimating the Value of R&R’s Stock Price (Millions, Except for Per
Share Data)
Projections
(2.) What is its value of equity on a price per share basis?
l. You have just learned that B&B has undertaken a major expansion that will change its expected free cash flows to −$10
million in 1 year, $20 million in 2 years, and $35 million in 3 years. After 3 years, free cash flow will grow at a rate of 5%. No
new debt or preferred stock were added, the investment was financed by equity from the owners. Assume the WACC is
unchanged at 11% and it that there are still has 10 million shares of stock outstanding.
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The dividend stream would be a perpetuity.
o. What is preferred stock? Suppose a share of preferred stock pays a dividend of $2.10 and investors require a return of
7%. What is the estimated value of the preferred stock?
m. Compare and contrast the free cash flow valuation model and the dividend growth model. Answer: See Chapter 7
Mini Case Show
n. What is market multiple analysis? Answer: See Chapter 7 Mini Case Show