Lecture 11
Investing in Risky Projects
Thermo Fisher Scientific
Start or
acquire new
lines of
business
Benefits
Turn them into
independent
public
companies with
their own
publicly traded
shares
Helps the company’s
managers make better
capital allocation
decisions
Financial Markets and Corporate Strategy, David Hillier
Benefits
Managers are highly
motivated to make
decisions that maximize
share price
Tracking Portfolios and Real Asset
Valuation
Asset Pricing Models and the Tracking Portfolio Approach
How to Use Tracking Portfolios for Valuation
State
Probability
Good state
.4
Average state
.4
Bad state
.2
Tracking Error and Present Values
Cash Flow Next Year of
Hilton
Market Portfolio
Hotel/Casino
(per $1 invested)
(in $ millions)
$12.3
$1.40
11.3
1.20
9.3
.80
Result 11.1
Whenever a tracking portfolio for the future cash flows of a project generates tracking error with
zero systematic (or factor) risk and zero expected value, the market value of the tracking portfolio is
the present value of the project’s future cash flows
Financial Markets and Corporate Strategy, David Hillier
Implementing the tracking portfolio
approach
•Estimating Tracking Portfolios without
Expected Cash Flows or Returns
•Using the Market Portfolio or Factor
Portfolios in Computing the Tracking
Portfolio
•Linking Financial Asset Tracking to Real
Asset Valuation with the SML
Financial Markets and Corporate Strategy, David Hillier
Exhibit 11.1 Real Assets and the
Securities Market Line
Financial Markets and Corporate Strategy, David Hillier
Defining and Implementing the Risk-Adjusted
Discount Rate Method with Given Betas
Result 11.2
To find the present value of next period’s cash flow using the riskadjusted discount rate method:
1. Compute the expected future cash flow next period ;
2. Compute the beta of the return of the project, ;
3. Compute the expected return of the project by substituting the beta
calculated in step 2 into the tangency portfolio risk-expected return
equation;
4. Divide the expected future cash flow in step 1 by one plus the
expected return from step 3.
In algebraic terms
~
E (C )
PV 
1  r f   ( RT  r f )
Financial Markets and Corporate Strategy, David Hillier
The Effect of Leverage on Comparisons
Exhibit 11.2 Balance Sheet for an All-Equity-Financed Firm
Assets
A
Liabilities and Equity
Debt
0 (i.e., D = 0)
Equity
E
Exhibit 11.3 Balance Sheet for a Firm with Leverage
Assets
A
Liabilities and Equity
Debt
D (D > 0)
Equity
E
Financial Markets and Corporate Strategy, David Hillier
The Right-Hand Side of the Balance Sheet
as a Portfolio


D
 A
E
Equity risk measure:
 E  1 
Return on Assets:
 D ~  E ~
~
rA  
rD  
rE
DE
DE
Result 11.3
Increasing the firm’s debt (raising D and reducing E)
increases the (beta and standard deviation) risk per unit of
equity investment. It will increase linearly in the D/E ratio if
the debt is risk free.
Financial Markets and Corporate Strategy, David Hillier
Distinguishing risk-free debt from defaultfree debt
Asset beta :

D


E

A  
 D  
 E
DE
DE
Exhibit 11.4 Equity Beta as a Function of the Firm’s Leverage Ratio
Financial Markets and Corporate Strategy, David Hillier
The Cost of Equity, Cost of Debt, and Cost of
Capital as a Function of the Leverage Ratio
The cost of equity for a firm is the expected return required by investors to
induce them to hold the equity.
Result 11.4
The cost of equity
~
rE  ~
rA  D / E ~
rA  ~
rD 
increases as the firm’s leverage ratio D/E increases. It will increase linearly
in the ratio D/E if the debt is default free and if , the expected return of the
firm’s assets, does not change as the leverage ratio increases.
Financial Markets and Corporate Strategy, David Hillier
Exhibit 11.5 Cost of Debt, Equity, and
Capital as a Function of D/E
Financial Markets and Corporate Strategy, David Hillier
Implementing the risk-adjusted discount rate
formula with comparison firms
•The CAPM, the Comparison Method, and Adjusting for Leverage
•Weighting the Betas of Comparison Firms
•An Illustration of the Necessary Leverage Adjustment without Taxes.
Example 11.2: Using the Comparison Approach to Obtain Beta and
Returning to the BA Cityflyer example (Example 11.1), we must identify comparison
firms that have similar business models and operations. BA Cityflyer is a British
company and operates from the UK, so where possible we must choose comparison
firms from the same country. As of 2011, there were 12 British airlines that could be
used as comparisons. These are Air Southwest, BMIBaby, easyJet, First Choice,
flybe, flythomascook Jet2.com, Monarch, Ryanair, Thomsonfly, TUIfly and Wizzair.
Unfortunately, only two of the comparison firms, Ryanair and easyJet, are traded on
the London Stock Exchange. Even more unluckily, Ryanair shares are denominated in
Euros and it operates out of Dublin, so we must concentrate only on easyJet. easyJet
has an equity beta of 0.71, a market capitalization of equity (E) equal to £2.62 billion,
and book value of debt (D) equal to £0.46 billion.
Financial Markets and Corporate Strategy, David Hillier
Implementing the risk-adjusted discount rate
formula with comparison firms - continue
Assume that the risk-free rate is 6 percent per year, the risk premium on the
market portfolio is 8.4 percent per year, the CAPM holds and the debt of
Easyjet is risk free. Estimate the cost of capital for BA Cityflyer.
Answer: Using equation (11.2a), , we first find Easyjet’s asset beta:
A 
E
2.62
E 
0.71  0.604
DE
2.62  0.46
Applying the CAPM risk-expected return equation, using the .603 estimate of
Easyjet’s asset beta gives BA Cityflyer’s cost of capital, 11.07 percent per year:
.1107 = .06 + .71(.084)
Financial Markets and Corporate Strategy, David Hillier
Obtaining a Cost of Capital from the
Arbitrage Pricing Theory (APT)
•The Multifactor APT Version of the Risk-Adjusted Discount
Rate Formula
~
E (C )
PV 
1  r f  1  1  2  2     K  K
•Arbitrage Pricing Theory versus Capital Asset Pricing
Model
Financial Markets and Corporate Strategy, David Hillier
A five factor APT model used by firms
Short-term
inflation
(SINF)
The monthly
Gross
Domestic
Product
(GDP)
A fivefactor
APT
model
The
premium for
default risk
(PREM)
Financial Markets and Corporate Strategy, David Hillier
Long-term
inflation
(LINF)
The level of
short-term
interest
rates (INT)
Exhibit 11.6 Cost of Equity Capital
CAPM
Equity
Firm
Beta
Ericsson
Nordea
SHB
Skandia
Telia
H&M
1.03
0.60
1.24
1.52
1.05
0.98
Arbitrage Pricing Theory (APT)
Premiums from Sensitivity to Five
Equity
Equity
Factors
Expected Expected
Returns
Returns (%)
SINF LINF INT PREM GDP
(%)
11.42
12.61
0.83 1.25 1.39
0.95
1.22
9.57
10.41
0.52 0.76 0.86
0.56
0.74
12.34
11.89
0.57 1.13 1.24
0.82
1.15
13.56
11.79
0.39 1.16 1.31
0.69
1.26
11.53
8.95
0.03 0.54 0.61
0.22
0.64
11.19
8.54
0.07 0.45 0.49
0.17
0.52
Financial Markets and Corporate Strategy, David Hillier
Exhibit 11.7 CAPM and APT Costs of Capital
with Leverage Ratios (D/E) for Six Firms
Firm
Ericsson
Nordea
SHB
Skandia
Telia
H&M
Debt to
CAPM
Cost
Equity Ratio
of Capital
(%)
6.36
46.90
51.31
778.74
0.00
27.50
(%)
11.02
7.93
9.85
5.65
11.53
10.12
Financial Markets and Corporate Strategy, David Hillier
APT Cost
Difference
between APT
of Capital and CAPM Cost of
(%)
12.14
8.51
9.55
5.45
8.95
8.04
Capital (%)
1.12
0.58
0.30
0.20
2.58
2.08
Costs of capital computed with alternatives to
CAPM and APT: Dividend discount models
•Impediments to using the CAPM and APT
•The dividend discount model
•Gordon growth model
S0 
div1
(rE  g )
•Using analyst forecasts to estimate the expected dividend growth rate
•Using the plowback ratio formula to estimate the expected dividend growth rate where
g  b  ROE
b = the plowback ratio, the fraction of earnings retained in the firm
ROE = book return on equity, that is, earnings divided by last year’s (midyear) book
equity
Financial Markets and Corporate Strategy, David Hillier
Assumptions and Pitfalls of the Dividend
Discount Model
1
2
3
• The earnings growth forecasts, whether from
analysts or equation (11.6), are unbiased; that is,
they do not tend to systematically underestimate or
overestimate the earnings growth rate
• The earnings growth forecasts are based on the
same information that investors use to value the
firm’s stock.
• The firm’s earnings and dividends grow at the same
constant rate, forever.
Financial Markets and Corporate Strategy, David Hillier
Pitfalls in using the comparison method
•Project Betas Are Not the Same as Firm Betas
•Growth Opportunities Are Usually the Source of High Betas
•Multiperiod Risk-Adjusted Discount Rates
The
Approach
Used by
Practitioners
Estimate the equity beta
from a comparison firm
using historical data,
typically of weekly or
monthly frequency.
Usually, the comparison
firm is the firm doing the
project.
Compute the expected
return using the riskexpected return formula of
choice (CAPM or APT)
with parameters estimated
from historical data.
Use the cost of capital as
a single discount rate for
each period in the way
that we used the risk-free
rate (assuming a flat term
structure) in Chapter 10 to
discount multiperiod cash
flows.
Adjust for leverage and
taxes to obtain a cost of
capital.
Financial Markets and Corporate Strategy, David Hillier
Example 11.4 Applying a one-period cost of
capital to multiyear cash flows
Example 11.2 identified Easyjet as a comparison firms for BA Cityflyer and from these
estimated 11.07 percent per year as the cost of capital for BA Cityflyer. Assume that
BA Cityflyer is expected to produce £25 million in cash flows at the end of this year
and that this number will grow by
5 percent per year forever. At what price would British Airways be willing to sell BA
Cityflyer?
Answer: The present value, using a risk-adjusted discount rate of 11.07 percent per
year, is
£25million £25million (1.05)
£25million (1.05) 2
PV 


L
2
3
1.1107
1.1107
1.1107
Recognizing this as a growing perpetuity (see equation 9.10), BA Cityflyer’s value
would be
£25million
PV 
 £411.86million
0.1107  0.05
Financial Markets and Corporate Strategy, David Hillier
Empirical Failures of the CAPM and APT
Exhibit 11.8 Gross Returns of the Project and Its Tracking Portfolio for Example 11.5
Outcome
Probability
Project Return + 100%
Tracking Portfolio
Return + 100%
Recovery
Recession
Depression
3
4
3
16
1
16
150% 
€150,000
€100,000
€150,000
PV
35% 
€35,000
€100,000
€35,000
PV
5% 
€5,000
€100,000
€5,000
PV
Result 11.5
The betas of the actual returns of projects equal the project’s profitability index times the
appropriate beta needed to compute the true present value of the project. Since the profitability
index exceeds 1 for positive NPV projects and is below 1 for negative NPV projects, this error in
beta computation does not affect project selection in the absence of project selection constraints.
Financial Markets and Corporate Strategy, David Hillier
Estimating Beta from Scenarios: The
Certainty Equivalent Method
•Defining the Certainty Equivalent Method
•Identifying the Certainty Equivalent from Models of Risk and Return
Result 11.6. To obtain a certainty equivalent, subtract the product of the cash
flow beta and the tangency portfolio risk premium from the expected cash
flow; that is
where
~
~
CE(C )  E (C )  b( RT  r f )
b
~ ~
cov( C , RT )
 T2
Financial Markets and Corporate Strategy, David Hillier
Result 11.7 - The certainty equivalent
present value formula
PV, the present value of next period’s cash flow, can be found
~
by (1) computing E (C ) ,the expected future cash flow and the
beta of the future cash flow, (2) subtracting the product of this
beta and the risk premium of the tangency portfolio from the
expected future cash flow, and (3) dividing by (1 + the risk-free
return); that is
PV 
~
E (C )  b( RT  r f )
1  rf
Financial Markets and Corporate Strategy, David Hillier
Example 11.7: Computing the Cost of
Capital
Each share of BA Cityflyer, a wholly owned subsidiary of International Airlines Group plc, first seen in Example
11.1, has a cash flow beta (b) of £5.125 when computed against the tangency portfolio. One year from now,
this subsidiary has a .9 probability of being worth £5 per share and a .1 probability of being worth £4 per share.
The risk-free rate is 6 percent per year. The tangency portfolio has an expected return of 14 percent per year.
What is the present value of BA Cityflyer, assuming no dividend payments to the parent firm in the coming
year?
Answer: The expected value of BA Cityflyer one year from now is
£4.90 per share = .9(£5) + .1(£4)
The numerator in the certainty equivalent formula, the certainty equivalent, is thus
£4.49 = £4.90  £5.125(.14  .06)
The subsidiary’s present value is its certainty equivalent divided by 1 plus the risk-free rate or approximately
£4.24 per share 
Financial Markets and Corporate Strategy, David Hillier
£4.49
1.06
The CAPM, Scenarios, and the Certainty
Equivalent Method
•The APT and the certainty equivalent method
~
E (C )  (1b1  2b2  K  K bK )
PV 
1  rf
•The relation between the certainty equivalent formula
and the tracking portfolio approach
Financial Markets and Corporate Strategy, David Hillier
Obtaining certainty equivalents with risk-free
scenarios
A Description of the Risk-Free Scenario Method
•Distributions for Which the Risk-Free Scenario Method Works
•Inputs for the Risk-Free Scenario Method
•Conditional expected cash flows
•Obtaining PVs with the Risk-Free Scenario Method
•Advantages of the Risk-Free Scenario Method
~
~
r  r     ( R  r )  ~
f
T
f
Result 11.8
(Estimating the certainty equivalent with a risk-free scenario.) If it is possible to estimate the
expected future cash flow of an investment or project under a scenario where all securities are
expected to appreciate at the risk-free return, then the present value of the cash flow is
computed by discounting the expected cash flow for the risk-free scenario at the risk-free rate.
Financial Markets and Corporate Strategy, David Hillier
Example 11.9: Valuation with the Risk-Free
Scenario Method
You are asked to evaluate a project with a one-year life that has an
uncertain cash flow at the end of the first year. Your managers estimate
that the project will generate a cash flow of €100,000 at the end of year 1
under a scenario where all securities are expected to earn the risk-free
return of 5 percent per year. What is the present value of this risky
project? For what costs should the project be accepted or rejected?
Answer:
€100,000 is the certainty equivalent of the future cash flow. Discounting
this at a rate of 5 percent yields €100,000/1.05 or €95,238. Therefore, if
the project costs less than €95,328, your managers should accept it. If it
costs more than €95,328, they should reject it.
Financial Markets and Corporate Strategy, David Hillier
Computing certainty equivalents from prices
in financial markets
•Forward prices
•Example 11.11 Present values with certainty
equivalents from futures prices
•Tracking portfolios that contain forward contracts
Financial Markets and Corporate Strategy, David Hillier
Thank You