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Business Finance 3220

Creation date：2024-04-30 15:20:21

Belonging category：金融Finance

Tag 3220

Business Finance

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CHAPTER 9 STOCK VALUATION

Business Finance 3220
Discounted Dividend Model
Estimating Dividends: 3 Cases
1. Constant fixed dividend (g=0):
The firm will pay a constant dividend forever
This is like preferred stock: �0 = 1
2. Constant dividend growth:
The firm will increase the dividend by a constant
percent every period:
�0 = 1−
3. Supernormal growth:
Dividend growth is not consistent initially, but settles
down to constant growth eventually
Estimating g
g = growth rate = (1 – payout rate)ROE = (retention rate)ROE
ROE = Return on Invested Capital = Net Earnings/Equity
The more a company retains/reinvests, the higher g will be.
Retention/Reinvestment only good as long as ROE > Equity Cost
of Capital (rS)
Shareholders will be satisfied with foregoing dividends if the company is
able to reinvest at a higher rate of return than the shareholders are
demanding
If rs = 15%, but a new project has an expected return on invested capital
(ROE) of 20%, shareholders will be willing to let the company invest in the
new project rather than giving the shareholders the cash.
Stock Price Sensitivity to Dividend Growth, g
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2
St
oc
k
Pr
ic
e
Growth Rate
D1 = $2; rs = 20%
Using the Discounted Dividend Model to find rs
Start with the Discounted Dividend Model:
1 = 0(1+g)
Rearrange and solve for : = 10 +
= Dividend yield + Cap Gains Yield
�0 = 1 −
Finding the Required Return - Example
• Suppose a firm’s stock is selling for $10.50. They just paid a $1
dividend and dividends are expected to grow at 5% per year.
What is the required return?
1 = 0(1+g) = $1(1+.05) = $1.05
rs = [1.05/10.50] + .05 = 15%
• What is the dividend yield?
1.05/ 10.50 = 10%
• What is the capital gains yield?
g =5%
Constant growth Problem
Laurel Enterprises expects earnings next year of $4/share and
has a 60% payout rate, which it plans to keep constant. Its equity
cost of capital is 10%, which is also its ROE. Its earnings are
expected to grow forever at a rate of 4%/year. If its next dividend
is due in one year, what do you estimate the firm’s current stock
price to be?

To retain more or less?
XTRA Corp. expects earnings next year of $12/share, and it plans
to pay a $3 dividend/share. XTRA will retain $9/share to reinvest
in new projects that have an expected return of 12%/year (ROE).
Suppose XTRA will maintain the same payout rate and ROE.
A. Solve for g, the growth rate in earnings
B. If the cost of equity capital is 15%, what is the stock price?
C. Suppose they decided to pay a $6 dividend and retain only $6/share, and
maintain this payout ratio indefinitely. Is this a good policy or not?

Supernormal growth
McGraw Hill expects to pay a dividend of $4.50/share one year
from today. The growth rate of dividends is expected to be 9%
for the next three years, then 4% thereafter. If McGraw Hill’s
equity cost of capital is 10.5%/year and its dividend payout ratio
remains constant, compute McGraw Hill’s stock price.
Three steps:
1. Find the PV of the dividends during the non-constant growth period (3 years,
in this case)
2. Find the “terminal value” to cover the remaining cash flows on the timeline
(years 4-infinity, in this case). Use the growing perpetuity formula. Remember
that if your first cash flow in your growing perpetuity formula is from year 4, that
means you are solving for the terminal value as of the end of year 3.
3. Discount terminal value back to time 0 and add to your value from step 1.

What if the company doesn’t pay dividends?
• Many small and/or young companies do not pay
dividends—what then?
• Dividend discount models are out, unless you can
anticipate when the company will pay a dividend in
the future (good luck).
• If the company does share repurchases, the value of
the repurchase is effectively the same as a cash
dividend.
• Since dividends are a proxy for equity cash flows, we
can substitute another estimate, such as free cash
flow
• This is what is commonly done in the industry, but requires
much more information and expertise to forecast. Intuition
is the same, however.
Corporate Valuation Model
Firm finances with debt, preferred stock and common stock
WACC is the weighted average cost of capital used to discount
the cash flows
FCF is the cash generated before any payments are made to any
investors; so it must be used to compensate common
stockholders, preferred stockholders and bondholders
Rearrange: MV(Equity) 0 = V0 – Debt0 – Preferred Stock0
P0 = (V0 – Debt0 – Preferred Stock0) / Shares Outstanding0
Corporate Valuation Example
Allied Inc. expects to have the following Free Cash Flows (in
millions) over the next 5 years:
Year 1 2 3 4 5
FCF ($M) 124 122 137 168 182
After that, the free cash flows are expected to grow by 3%/year.
If the WACC is 17%, estimate the Total Corporate Value of the
firm.
If Allied has $100 million in preferred stock, debt of $650 million
and 75 million shares outstanding, estimate its share price.

Valuation based on “comps”
Compare firms by valuation multiples:
1. Price-to-Earnings (P/E): Use firm’s EPS and multiply it by
industry P/E to get estimated price. Assumes firm should be at
industry average P/E.
Forward P/E: use E1. Trailing P/E: use E0
2. Enterprise Multiple: = ()

Overall, comps are a shortcut. Gives us a ballpark estimate. But
need to note the differences between firms. Industry average
may not be applicable to the firm in question.
Comps Example
• After researching the competitors of Merck, you determine
that most comparable firms have the following valuation ratios:
• Merck has EPS of $2, EBITDA of $16 billion, $18 billion in
preferred stock, $27 billion in debt, and 3 billion shares
outstanding. What range of prices is consistent with both sets
of multiples?

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SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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