Chapter 18

Equity Valuation Models

Models of Equity Valuation
• Balance Sheet Models
– Book Value
• Dividend Discount Models
• Price/Earning Ratios

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Intrinsic Value and Market Price
• Intrinsic Value
– Self assigned Value
– Variety of models are used for estimation
• Market Price (MP)
– Consensus value of all potential traders
• Trading Signal
– IV > MP Buy
– IV < MP Sell or Short Sell
– IV = MP Hold or Fairly Priced

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Dividend Discount Models:
General Model
∞
𝐷𝑡
𝑉0 = 𝑡
1+𝑘
𝑡=1

V0 = Value of Stock
Dt = Dividend
k = required return
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 No Growth Model
𝐷1
𝑉0 =
𝑘

The no growth model would work for common

stocks that have earnings and dividends that
are expected to remain constant (this
assumption is probably not too realistic).

A good example of a claim that has constant

dividends is Preferred Stock
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No Growth Model: Example
𝐷1
𝑉0 =
𝑘
D1 = $5.00
k = 0.15
V0 = $5.00 / 0.15 = $33.33

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The constant growth model
∞
𝐷0 1 + 𝑔 𝑡
𝑉0 =
(1 + 𝑘)𝑡
𝑡=1

Where D1 = D0(1+g)
D2 = D1(1+g) = D0(1+g)2
and so on …..
As long as k > g, the sum will converge to:

𝐷0 (1 + 𝑔) 𝐷1
𝑉0 = =
𝑘−𝑔 𝑘−𝑔

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 Constant Growth Model: Example
𝐷0 (1 + 𝑔) 𝐷1
𝑉0 = =
𝑘−𝑔 𝑘−𝑔

k = 15% D1 = $3.00 g = 8%
(therefore: D0 = 3/1.08)
V0 = 3.00 / (0.15 - 0.08) = $42.86

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Constant growth continued
On the previous slide we computed the intrinsic value as
V0 = 3/(0.15-0.08)=$42.86. Based on the constant growth model, what is
the intrinsic value at t=1, V1?

𝐷2
𝑉1 =
𝑘−𝑔
Because D2 = D1(1+g), we can substitute this value for D2 into the
expression for V1 as follows:

𝐷1 1 + 𝑔 𝐷1
𝑉1 = = 1 + 𝑔 = 𝑉0 (1 + 𝑔)
𝑘−𝑔 𝑘−𝑔
In words, the intrinsic value grows at the same rate, g, as
dividends.
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Constant growth continued
V0 = 3/(0.15-0.08)=$42.86 and V1 = 42.86(1.08) = 46.29
What is the Holding Period Return from t = 0 to t = 1 if prices follow the
DDM?
𝑉1 − 𝑉0 + 𝐷1
𝐻𝑃𝑅 =
𝑉0

𝑉1 − 𝑉0 𝐷1
𝐻𝑃𝑅 = +
𝑉0 𝑉0
𝐻𝑃𝑅 = 8% + 7%
= 15% = k

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Specified Holding Period Model
𝐷1 𝐷2 𝐷𝑁 + 𝑃𝑁
𝑉0 = + 2
+ ⋯+
1+𝑘 1+𝑘 1+𝑘 𝑁
PN = the expected price for the stock at time N
N = the specified number of years the stock is expected to be held
∞
𝐷𝑡
𝑃𝑁 = 𝑡
1+𝑘
𝑡=𝑁+1

𝐷𝑁+1
𝑃𝑁 =
𝑘 − 𝑔2
Where the growth rate during the stage from N+1 to ∞, g2, may
differ from the growth rate used from periods 1 to N.

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 Example of 2-stage model
Assume that the current dividend is D0 = 1.00 and dividends are expected
to grow at 10% for the next 3 years (i.e., from t=0 to t=1, t=1 to t=2, and t=2
to t=3). Starting in year 3, dividends will grow at 4% indefinitely (i.e., from
t=3 to infinity). Calculate the current intrinsic value based on these
assumptions, given k = 8%.
Step 1: Trace out all the dividends
Growth in the first stage, g1 = 10%
D1 = 1.00 x 1.10 = $1.10
D2 = 1.00 x 1.102 = $1.21
D3 = 1.00 x 1.103 = $1.33
D4 = D3 x 1.04 = $1.33 x 1.04 = $1.38 growing at 4% forever.

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 2-stage model continued
Step 2: Compute the horizon value at t = 3
The second stage is infinite and dividends grow at g2 = 4%

Because dividends grow at 4% forever (and 4% < k=8%), we can use

the constant growth dividend discount model to value the dividends
from t=4 onward.
𝐷4
With D4 = $1.38, we can calculate P3 as follows: 𝑃3 =
𝑘−𝑔

P3 = $1.38/(0.08 – 0.04) = $34.5

Step 3: Compute overall intrinsic value at t=0
We can now use the holding period version of the dividend discount
model to calculate the intrinsic value, V0.
𝐷1 𝐷2 𝐷3 + 𝑃3
𝑉0 = + +
1+𝑘 1+𝑘 2 1+𝑘 3

1.10 1.21 1.33 + 34.50

𝑉0 = + + = $30.50
1.08 1.082 1.083
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 2-stage model continued
If the current market price is P0 = $30.50, and we buy the stock,
then we should expect to earn a holding period return of 8% from
t=0 to t =1 (as long as actual prices follow the DDM). Let’s see
why.
Under this model, the expected selling price at t = 1, P1, is the
present value of the dividends, D2 and D3, and the expected price
at t=3, P3. Let’s calculate P1 as follows:
1.21 1.33 + 34.50
𝑃1 = + = $31.84
1.08 1.082

Note the price does not grow by the initial 10% growth rate,
since the initial calculation for the price does not depend on a
single growth rate. The growth in price = 31.84/30.50 = 1.044
or growth rate in price = 4.4%
We can now compute the holding period return from t=0 to t=1

𝑃1 − 𝑃0 + 𝐷1 31.84 − 30.50 + 1.10

𝐻𝑃𝑅 = = = 8% 14
𝑃0 30.50
 Estimating Dividend Growth Rates

𝑔 = 𝑅𝑂𝐸 × 𝑏

g = growth rate in dividends

ROE = Return on Equity for the firm
b = plowback or retention percentage rate
(1- dividend payout percentage rate)

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Partitioning Value: Example
ROE = 20%, b = 40% and (1-b) = 60%

E1 = $5.00 D1 = $3.00 k = 15%

g = 0.20 x 0.40 = 0.08 or 8%

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 Partitioning Value: Example

3.00
𝑉0 = = $42.86
0.15 − 0.08

5.00
𝑁𝐺𝑉0 = = $33.33
0.15

𝑃𝑉𝐺𝑂 = 42.86 − 33.33 = $9.52

V0= value with growth

NGV0 = no growth component value
PVGO = Present Value of Growth Opportunities
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 Price Earnings Ratios
• P/E Ratios are a function of two factors
– Required Rates of Return (k)
– Expected growth in Dividends
• Uses
– Relative valuation
– Extensive Use in industry

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P/E Ratio: No Expected Growth
𝐸1
𝑃0 =
𝑘

𝑃0 1
=
𝐸1 𝑘

E1: expected earnings for next year

E1 is equal to D1 under no growth
k: required rate of return

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P/E Ratio with Constant Growth
𝐷1 𝐸1 1 − 𝑏
𝑃𝑜 = =
𝑘 − 𝑔 𝑘 − (𝑏 × 𝑅𝑂𝐸)

𝑃0 1−𝑏
=
𝐸1 𝑘 − 𝑏 × 𝑅𝑂𝐸

b = retention ratio
ROE = Return on Equity

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Numerical Example: No Growth

E0 = $2.50 g=0 k = 12.5%

P0 = D/k = $2.50/0.125 = $20.00

PE = 1/k = 1/0.125 = 8

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Numerical Example with Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = $2.50 (1 + (0.6)(0.15)) = $2.73
D1 = $2.73 (1-0.6) = $1.09
k = 12.5% g = 9%
P0 = 1.09/(0.125-0.09) = $31.14
PE = 31.14/2.73 = 11.4
PE = (1 - 0.60) / (0.125 - 0.09) = 11.4×

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Table 18.3 Effect of ROE and Plowback on Growth
and the P/E Ratio

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 Free Cash Flow Approach
• Discount the free cash flow for the firm
• Discount rate is the firm’s cost of capital
• Components of free cash flow
– After tax EBIT
– Depreciation
– Capital expenditures
– Increase in net working capital

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Value Line Investment Example for Honda (May 25, 2012)
(see pages 605 – 607 in the text ). Value Line report is the last slide in
this. You can get Value Line reports from the UNL Library
(http://libraries.unl.edu/).
Log onto your My.UNL Account; Choose E-resources, Browse under the
letter V.
Relevant information for late 2009 (row is indicated by letters A – E)

Beta (row A) = 0.95

Recent Price (row B) = $32.88
Dividends (row C) = $1.00 (forecast for 2016)
ROE (row D) = 10%
Dividend payout ratio (row E) = 25%

Growth = g = ROE x b = 10.0% x (1-0.25) = 7.50%

We will use an investment horizon of 2016 and the intrinsic value will be
computed as the PV of the dividends for 2013, 2014, 2015, 2016 and
the horizon price for 2016 (i.e., P2016)

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Honda example, continued

P2016= D2017 / (k – g) = $1.00 (1.075)/(k-0.075)

Now we need an estimate of k and we will use the CAPM

Inputs given are as follows:

r(f) = 2.0% and suppose the market risk premium is 8.0%

k = 2.0% + 0.95(10.0 – 2.0) = 9.6%

P2016 = 51.19 ; D(2013) = 0.78, D(2014) = 0.85, D(2015) = 0.92, and

D(2016) = 1.00,

The intrinsic value for 2012, V(2012) is now the present value of the
stream of dividends and the horizon value (all discounted at 9.6%%).

V(2012) = $38.29

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