Chapter 11
Risk-Adjusted
Expected Rates of
Return and the
Dividends Valuation
Approach
Chapter: 11
1
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Inverted Yield Curve
•
•
•
An “inverted yield curve” in the
bond market is a distortion that
has often occurred before U.S.
recessions.
This happens when short-term
bond yields exceed those of
longer-term bonds. It means
investors are worried about the
economy’s long-term
prospects.
The two-year versus 10-year
yield on a U.S. Treasury bond is
generally the most watched by
economists. That curve hasn’t
yet inverted, but another part
of the market did on Monday.
Chapter: 11
2
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duplicated, or posted 01
to a publicly accessible website, in whole2
or in part.
Valuing the Firm
Economic theory teaches us that the value of an
investment is:
n
Projected Future Payoffs t
V0  
t
(1

Discount
Rate)
t 1
Expected future payoffs can be measured in
terms of:
• Dividends
• Cash Flows
• Earnings
Chapter: 11
3
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Approaches to Firm Valuation
Chapter: 11
4
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Risk-Adjusted Expected Rates of Return
(1 of 2)
• Risk-adjusted expected rate of return on
equity capital is used as discount rate to
compute present value of projected future
payoffs.
• To develop discount rates, consider:
• Expected future riskiness of the firm
• Expected future interest rates
• Expected future capital structure
Chapter: 11
5
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Risk-Adjusted Expected Rates of Return
(2 of 2)
• Can use Capital Asset Pricing Model (CAPM) to
develop discount rates.
• Expected rate of return needs to be adjusted if
capital structure changes.
Chapter: 11
6
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Evaluating the Use of the CAPM
• Criticisms of CAPM• Beta estimates are quite sensitive to the time
period and methodology used in computation.
• Return index for a diversified portfolio of assets
that spans the entire economy does not exist.
• The market risk premium is not stable over time.
• Therefore, it is important to analyze the
sensitivity of share value estimates across
different discount rates for common equity.
Chapter: 11
7
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Capital Asset Pricing Model
E[REj ]  E[R F ]  ß j  {E[RM ] – E[RF ]}
Where:
E  expectation
REj  Required return on common equity in firm j
RF  Risk-free rate of return
ß j  Market beta for firm j
RM  Required return on marketwide portfolio
•
For Risk-free rate of return (RF), yield on short- or
intermediate term U.S. government securities can be used.
• {E[RM] – E[RF]} known as “market risk premium.”
Chapter: 11
8
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Cost of Equity Capital and Systematic Risk
Chapter: 11
9
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
More Criticisms of CAPM
Risk Free – So low, what it means?
Beta - Is it a true measure of a stock volatility or
market risk?
Smart Beta
Smart beta defines a set of investment strategies
that emphasize the use of alternative index
construction rules to traditional market capitalizationbased indices. Smart beta emphasizes capturing
investment factors or market inefficiencies in a rulesbased and transparent way.
7/9/2023
Chapter: 11
Chapter: 04
10
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10
Beta
Google’s Beta
Stocks Betas & the S&P Market
Stock
Beta
Last 52-week
FB
1.2
33.05%
MSFT
0.93
54.40%
AMZN
1.32
53.75%
GOOGL
1.06
30.90%
S&P
Chapter: 11
6.72%
11
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The Three-Factor Model Formula
The Fama and French model has three factors:
size of firms, book-to-market values and excess
return on the market. In other words, the three
factors used are SMB (small minus big), HML
(high minus low) and the portfolio's return less the
risk free rate of return.
7/9/2023
Chapter: 11
Chapter: 04
12
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
12
The Three-Factor Model Formula
Where:
r = Expected rate of return
rf = Risk-free rate
ß = Factor’s coefficient (sensitivity)
(rm – rf) = Market risk premium
SMB (Small Minus Big) = Historic excess returns of
small-cap companies over large-cap companies
HML (High Minus Low) = Historic excess returns of
value stocks (high book-to-price ratio) over growth
stocks (low book-to-price ratio)
↋ = Risk
7/9/2023
Chapter: 11
Chapter: 04
13
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13
Arbitrage Pricing Theory (APT)
Arbitrage pricing theory (APT) is a multi-factor asset
pricing model based on the idea that an asset's
returns can be predicted using the linear relationship
between the asset's expected return and a number of
macroeconomic variables that capture systematic
risk.
7/9/2023
Chapter: 11
Chapter: 04
14
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14
Cost of Debt
and Preferred Equity Capital
• Cost of Debt:
• Computed as the yield to maturity on each type of
debt times one minus the statutory tax rate
applicable to income tax deductions for interest.
• Cost of Preferred Capital:
• It is the dividend rate on the preferred stock. In
case of convertible preferred stock the cost will be
a blending of cost of non-convertible stock and
common stock.
Chapter: 11
15
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Capital Asset Pricing Model
𝐸 𝑅𝐸𝑗 = 𝐸 𝑅𝐹 + ß𝑗 × 𝐸 𝑅𝑀 – 𝐸 𝑅𝐹
Re = 𝑅𝑓 + ß𝑗 (Rm− Rf)
Rm- Rf = Market Risk Premium
Rp = Dp/Pp
Rd = YTM, RD af = Rd bt x (1- Tax)
Chapter: 11
16
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Weighted Average Cost of Capital
• WACC: Considers debt, preferred, and equity
capital used to finance
• Calculated as:
RA  [wD  RD  ( 1 – tax rate)]  [wP  RP ]  [wE  RE ]  [Wnci  R nci ]
Where:
wD  wP  wE  wNCI  1
R is cost of each type of capital
w is proportion of each type of capital
Tax rate is rate applicable to debt costs
Chapter: 11
17
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Adjusting Market Equity Beta
to Reflect a New Capital Structure
• The market beta reflects operating leverage, financial leverage,
variability of sales and earnings, and other firm characteristics.
Current Levered Market Beta  Unlevered Market Beta x [1  (1  Income Tax Rate)
 (Current Market Value of Debt/Current Market Value of Equity)]
• The analyst can “unlever” the current market beta by adjusting it
to remove the effects of leverage
Unlevered Market Bet
= Current Levered Market Beta / [1 + (1 − Income Tax Rate)
× (Current Market Value of Debt/Current Market Value of Equity)]
βu =βl /[(1+(1-Tax) x D/E]
• Then relever it by adjusting leverage under the new capital structure.
New Levered Market Beta  Unlevered Market Beta x [1  (1  Income Tax Rate)
 (New Market Value of Debt/New Market Value of Equity)]
Chapter: 11
18
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Country Risk Premium
There are three approaches for incorporating a Country Risk
Premium into the CAPM so as to derive an Equity Risk
Premium that can be used to assess the risk of investing in a
company located in a foreign country.
1.The first approach assumes that every company in the
foreign country is equally exposed to country risk. While this
approach is commonly used, it makes no distinction between
any two companies in the foreign country, even if one is a
huge export-oriented firm and the other is a small local
business. In such cases, CRP would be added to the mature
market expected return, so that CAPM would be:
Re​=Rf​+β(Rm​−Rf​)+CRP​
7/9/2023
Chapter: 11
Chapter: 04
19
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19
Country Risk Premium
The second approach assumes that a company's exposure
to country risk is similar to its exposure to other market risk.
Thus,
Re​=Rf​+β(Rm​−Rf​+CRP)​
The third approach considers country risk as a separate risk
factor, multiplying CRP with a variable (generally denoted by
lambda or λ). In general terms, a company that has
significant exposure to a foreign country - by virtue of getting
a large percentage of its revenues from that country, or
having a substantial share of its manufacturing located there
- would have a higher λ value than a company that is less
exposed to that country.
20
Chapter: 11
7/9/2023
Chapter: 04
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
20
Country Risk Premium
Example:
CRP for Country A=7.0%
Rf = risk-free rate=2.5%
Rm =expected market return=7.5%
Project Beta=1.25
A)
Cost of equity=Rf +β(Rm −Rf) +CRP
Cost of equity=2.5%+1.25 (7.5%−2.5%)+7.0
Cost of equity=17.0%
B)
Cost of equity=Rf +β(Rm −Rf +CRP)
Cost of equity=2.5%+1.25 (7.5%−2.5%+7.0)
Cost of equity=17.5%
7/9/2023
Chapter: 11
Chapter: 04
21
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21
Country Risk Premium
COUNTRIES WITH THE HIGHEST CRP – AS OF JANUARY 2019
Country
Total Equity Risk
Premium
Country Risk Premium
Venezuela
28.10%
22.14%
Barbados
19.83%
13.87%
Mozambique
19.83%
13.87%
Congo (Republic of)
18.46%
12.50%
Cuba
18.46%
12.50%
El Salvador
16.37%
10.41%
Gabon
16.37%
10.41%
Iraq
16.37%
10.41%
Ukraine
16.37%
10.41%
Zambia
16.37%
10.41%
Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/ctryprem.html
7/9/2023
Chapter: 11
Chapter: 04
22
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22
Dividends-Based Valuation:
Rationale and Basic Concepts
• Dividends
• All cash flows between the firm and the common
equity shareholders
• Ways shareholders receive cash
• Quarterly or annual dividend payments
• Payment when the firm repurchases shares or
when another firm acquires all of the outstanding
shares in a merger or acquisition
• Final “liquidating” dividend
Chapter: 11
23
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Measuring Dividends Using Clean
Surplus Accounting
• Formula for Dividends
BVt  BVt -1  CI t  Dt
Dt  CI t  BVt -1  BVt
• CI = Net Income (Sustainable) + Unusual Items
Chapter: 11
24
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Measuring Dividends Using Clean
Surplus Accounting
Unusual Items:
• 1-Unrealized Gains and Losses on Securities
Held for Sale: Under Financial Accounting Standards
Board (FASB) Summary Statement No. 115, companies are
required to report any unrealized gains and losses on any
securities they are holding for sale.
• This process is called mark-to-market accounting and takes
place every time an income statement is created. These
unrealized gains and losses are then recorded in the
company's income statement at year-end.
Chapter: 11
25
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Measuring Dividends Using Clean
Surplus Accounting
Unusual Items:
• 2- Foreign Currency Translation Gains and
Losses: When a company has a controlling interest in a foreign
controlled subsidiary, the consolidated income statement will include
translating the subsidiary's financial statements into the same currency
the controlling parent uses. A forex gain or loss calculation might not
accurately capture the costs of doing business internationally.
• 3- Pension Funds Liabilities
Chapter: 11
26
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Measuring Dividends Using Clean
Surplus Accounting
Unusual Items:
• 4- Gains and Losses on Derivative Assets and
Liabilities: According to FASB 133, companies are required
to report any gains or losses associated with derivatives used
to hedge future transactions. Under FASB 133, derivatives are
marked to market on every balance sheet date. These gains
and losses are also unrealized every reporting period, which
can make their inclusion in net income questionable from the
perspective of some analysts and investors.
Chapter: 11
27
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Measuring Dividends Using Clean
Surplus Accounting
Unusual Items:
• 5- Employee Stock Options: A Hidden Dirty
Surplus Item: Although known dirty surplus items are
easily dealt with, hidden dirty surplus items are much more
difficult. The major hidden dirty surplus item is employee stock
options (ESOs).
• A company grants a call option to a qualified employee while the
option is at-the-money. When the employee exercises the call
option as long as it is now in-the-money. Therefore, the
company receives the strike price for the underlying stock, and
the employee will receive the stock for less than what it costs in
the open market.
Chapter: 11
28
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Measuring Dividends (1 of 2)
• Assume clean surplus accounting is followed.
• Under U.S. GAAP and IFRS, clean surplus is
measured by other comprehensive income as well
as net income.
Chapter: 11
29
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Measuring Dividends (2 of 2)
• Effects of transactions between firm and
common shareholders are included in book
value.
• Thus, accounting for common equity is
represented by:
BVt  BVt -1  CI t  Dt
Dt  CI t  BVt -1  BVt
Chapter: 11
30
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Forecast Horizon
• Represented by periods 1 through T in the dividends
valuation equation.
• Depending on:
• The industry
• Firm’s maturity
• Expected growth and stability
• Should be until firm reaches steady-state
equilibrium.
• Difficult for young, high-growth firms.
Chapter: 11
31
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Continuing Value of Future
Dividends
• Represented by last term of equation on slide
14.
• Use long-term growth rate assumption (1+ g)
uniformly on the year T+1 income statement
and balance sheet projections to derive the
dividends for the year T+1 correctly.
• Thus: DT 1  CIT 1  BVT – BVT 1
 [CIT  ( 1  g)]  BVT – [BVT  ( 1  g)]
Chapter: 11
32
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Dividends-Based Valuation
(Screen 1 of 4)
• The rationale for using expected dividends in
valuation is two fold:
• Dividends measure the cash that investors
ultimately receive from investing in an equity
share.
• Cash serves as a measurable common
denominator for comparing the future benefits of
alternative investment opportunities.
Chapter: 11
33
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Dividends-Based Valuation
(Screen 2 of 4)
Dividends include all cash flows between firm
and shareholders:
•
•
•
•
Periodic dividend payments
Stock buybacks
The liquidating dividend
And “negative dividend” when firm initially issues
stock
Chapter: 11
34
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Dividends-Based Valuation
(Screen 3 of 4)
Dividends valuation model:

Dt
t
(
1

R
)
t 1
E
V0  
D1
D2
DT
VT


 .... 

1
2
T
( 1  RE ) ( 1  RE )
( 1  RE ) ( 1  RE )T
With Growing Perpetuity:
D1
D2
[NIT  ( 1  g)]  BVT  [BVT  ( 1  g)]


 .... 
1
2
( 1  RE ) ( 1  RE )
(RE - g)  ( 1  RE )T
Chapter: 11
35
© 2018 Cengage. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Dividends-Based Valuation
(Screen 4 of 4)
Involves measuring the following three
elements:
• Dividend (Discount rate = RE)
• Expected future dividends (Dt) for periods 1
through T over forecast horizon
• Continuing or final (DT+1), and long-run growth
rate (g)
Chapter: 11
36
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Sensitivity Analysis
Once valuation model is applied, then
• Conduct sensitivity analysis:
•
•
•
•
Vary cost of equity capital rate (RE)
Vary long-run growth rate (g)
Discount rate assumptions
Vary these parameters and assumptions
individually and jointly
Chapter: 11
37
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Evaluation of the Dividends Valuation
Method (1 of 2)
• Advantages:
• Dividends provide a classical approach to valuing
shares as they reflect the payoffs that
shareholders can consume.
• Reflect the implications of analyst’s expectations
for the future operating, investing, and financing
decisions of a firm.
Chapter: 11
38
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Evaluation of the Dividends Valuation
Method (2 of 2)
• Disadvantages:
• Continuing value estimates are sensitive to
assumptions made about growth rates after the
forecast horizon and discount rates.
• The projection can be time-consuming for the
analyst.
Chapter: 11
39
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WACC Example
Chapter: 11
40
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WACC Example 1 - Solution
Re = Rf + b(Rm-Rf)
Re = 13%
E = $2 * 1,600,000 = $3,200,000
D = $2,500,000
Rd = $300,000/$2,500,000 = 12%
W = E + D = $3,200,000 + $2,500,000 = 5,700,000
We = 3,200,000/5,700,000 = 56%
Wd = 2,500,000/5,700,000 = 44%
WACC = We*Re + Wd*Rd*(1-Tax)
WACC = 56% * 13% + 44%*12%*(1-40%) = 10.45%
7/9/2023
Chapter: 11
Chapter: 04
41
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41
WACC Example 2
You are calculating the cost of capital for ABC corp. The firm’s equity
has a book value of $600 million and a market value of $1 billion. The
firm’s debt consists of operating leases with a debt value of $500
million and two bonds. The first bond is a straight 30-year bond with
book value equal to $200 million and market value equal to $125
million. The second bond is a zero-coupon convertible bond with 10years to maturity, a face value of $500 million, and a market value of
$400million. The firm has a debt rating of BBB+ and has a marginal
tax rate of 35%. You assume a market risk premium of 10% and
estimate the Beta of the firm to be 1.8.
Based on the 10-year Treasury Bond yield, you assume a risk-free
rate of 3.0%. Using the default spreads described below, calculate the
cost of Capital for this firm.
Chapter: 11
42
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WACC Example 2
Chapter: 11
43
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WACC Example 2 - Solution
Bond 1
FV = 200,000,000
PV = 125,000,000
N= 30 years
Coupon = (1.341% + 3% = 4.341%)
PMT = 4.341%*200,000,000 = $8682000 per
year
FV
200000000
PV
125000000
N
Tax= 35%
MRP = Rm – Rf = 10%
Rf = 3%
Beta = 1.8
Re = 3% + 1.8*10% = 21%
30
PMT
8682000
YTM
7.52%
Chapter: 11
44
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WACC Example 2 - Solution
Bond 2
FV = $500,000,000
PV = $400,000,000
N= 10 years
PMT = 0
We =65.57%
=(1,000000000)/(1000000000+125000000+400000000)
Wd1 =8.197%
=125000000/(1000000000+125000000+400000000) =
Wd2 =26.230%
=400000000/(1000000000+125000000+400000000)
FV
500000000
WACC =
We*Re + (Wd*Rd* + Wd2*Rd2) *(1- T) = WeRe +
PV
400000000
WACC = 65.57%* 21% + (8.197%*7.52% +
26.230%*2.26%)* (1- 35%) = 14.56%
N
10
PMT
0
YTM
2.26%
Chapter: 11
45
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