1
Introduction
1. Corporate Finance – how decision making affects “value”.
2. Corporate finance is not a number “game”.
3. Focus: (a) practical issues that arise in valuation, (b) taxes, (c) incentives of different stakeholders.
2
Chapter 7 Risk, Return and the Cost of Capital
Final objective: Estimating the opportunity cost of capital.
Explain and calculate Expected return Security risk Diversification Portfolio risk beta.
3
Capital Budgeting Example
• Capital Budgeting Decision– Suppose you had the opportunity to buy a
tbill which would be worth $400,000 one year from today.• Interest rates on tbills are a risk free
7%.– What would you be willing to pay for this
investment?
$400,000 / (1.07) = $373,832
PV today:0 1 2
-$400,000
4
Cost of Capital
• Capital Budgeting Decision– Suppose you are offered a construction
deal with similar cost and payoff.– An important concept in finance is that a
risky dollar is worth less than a safe dollar. – You are told that the risk is quantified by
the cost of capital, which is 12%.
NPV= -350,000+400,000/1.12 = $7,142
5
Calculating Returns
Suppose you bought 100 shares of BCE one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share × 100 shares). At the end of the year, the stock sells for $30. How did you do?
6
Holding Period Returns
The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri:
1)1()1()1(
return period holding
21
nrrr
7
0.1
10
1000
1957 1962 1967 1972 1977 1982 1987 1992 1997 2002
The Future Value of an Investment of $1 in 1957: Evidence from Canada
$42.91
$20.69
17.86$)1()1()1(1$ 200319581957 rrr
Common Stocks
Long Bonds
T-Bills
8
An Investment of $1 in 1900: US evidence
$1
$10
$100
$1,000
$10,000
$100,000
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Start of Year
Dol
lars
Common Stock
US Govt Bonds
T-Bills
15,578
14761
2004
9
$1
$10
$100
$1,000
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Start of Year
Dol
lars
Equities
Bonds
Bills
719
6.81
2.80
2004
Real Returns
An Investment of $1 in 1900: US evidence
10
How does this relate to cost of capital?
• Suppose there is an investment project which you know has the same risk as Standard and Poor’s Composite Index.
• What rate should you use?
11
Rates of Return 1900-2003
Source: Ibbotson Associates
-60%
-40%
-20%
0%
20%
40%
60%
80%
1900 1920 1940 1960 1980 2000
Year
Per
cent
age
Ret
urn
Stock Market Index Returns
12
Measuring Risk
1 14
1012
19
15
24
13
32
0
4
8
12
16
20
24
-50
to -
40
-40
to -
30
-30
to -
20
-20
to -
10
-10
to 0
0 to
10
10 t
o 20
20 t
o 30
30 t
o 40
40 t
o 50
50 t
o 60
Return %
# of Years
Histogram of Annual Stock Market ReturnsHistogram of Annual Stock Market Returns
13
Average Stock Returns and Risk-Free Returns
• The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk.
• One of the most significant observations of stock (and bond) market data is this long-run excess of security return over the risk-free return.
• The historical risk premium was 7.6% for the US.
14
Average Market Risk Premia (by country)
4.3 4.7 5.1 5.3 5.8 5.9 5.9 6.3 6.4 6.67.6 8.1 8.2 8.6
9.3 1010.7
0123456789
1011
Den
mar
k
Bel
giu
m
Sw
itze
rlan
d
Sp
ain
Can
ada
Irel
and
Ger
man
y
UK
Ave
rage
Net
her
lan
ds
US
A
Sw
eden
Sou
th A
fric
a
Au
stra
lia
Fra
nce
Jap
an
Ital
y
Risk premium, %
Country
15
Measuring Risk
Variance - Average value of squared deviations from mean. A measure of volatility.
Standard Deviation – Square root of variance. A measure of volatility.
16
Return Statistics
• The history of capital market returns can be summarized by describing the – average return
– the standard deviation of those returns
T
RRR T )( 1
1
)()()( 222
21
T
RRRRRRVARSD T
17
Average Standard Investment Annual Return Deviation Distribution
Canadian common stocks 10.64% 16.41%
Long Bonds 8.96 10.36
Treasury Bills 6.80 4.11
Inflation 4.29 3.63
Canada Returns, 1957-2003
– 60% + 60%0%
18
Risk Statistics
There is no universally agreed-upon definition of risk. A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
19
Historically – Are Returns Normal?
S&P 500 Return Frequencies
0
2
5
11
16
9
1212
12
110
0
2
4
6
8
10
12
14
16
62%52%42%32%22%12%2%-8%-18%-28%-38%-48%-58%
Annual returns
Ret
urn
fre
qu
ency
Normal approximationMean = 12.8%Std. Dev. = 20.4%
20
Expected Return, Variance, and covariance
Consider the following two risky asset worlds. There is a 1/3 chance of each state of the economy and the only assets are a stock fund and a bond fund.
Rate of ReturnScenario Probability Stock fund Bond fund
Recession 33.3% -7% 17%Normal 33.3% 12% 7%
Boom 33.3% 28% -3%
21
Expected Return, Variance, and Covariance
Stock fund Bond Fund
Rate of Squared Rate of Squared
Scenario Return Deviation Return Deviation Recession -7% 3.24% 17% 1.00%Normal 12% 0.01% 7% 0.00%Boom 28% 2.89% -3% 1.00%Expected return 11.00% 7.00%Variance 0.0205 0.0067Standard Deviation 14.3% 8.2%
22
Rate of ReturnScenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.160%Normal 12% 7% 9.5% 0.003%Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%Variance 0.0205 0.0067 0.0010Standard Deviation 14.31% 8.16% 3.08%
The Return for Portfolios
The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.
)()()( SSBBP rEwrEwrE
23
Rate of ReturnScenario Stock fund Bond fund Portfolio squared deviationRecession -7% 17% 5.0% 0.160%Normal 12% 7% 9.5% 0.003%Boom 28% -3% 12.5% 0.123%
Expected return 11.00% 7.00% 9.0%Variance 0.0205 0.0067 0.0010Standard Deviation 14.31% 8.16% 3.08%
The Variance of a Portfolio
24
Portfolio Risk
1
2
3
4
5
6
N
1 2 3 4 5 6 N
STOCK
STOCKTo calculate portfolio variance add up the boxes
25
Diversification
• The variance (risk) of the security’s return can be broken down into:– Systematic (Market) Risk– Unsystematic (diversifiable) Risk
The Effect of Diversification:– unsystematic risk will significantly diminish in
large portfolios– systematic risk is not affected by
diversification since it affects all securities in any large portfolio
26
Portfolio Risk as a Function of the Number of Stocks in the Portfolio
Nondiversifiable risk; Systematic Risk; Market Risk
Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk
n
In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not.
Thus diversification can eliminate some, but not all of the risk of individual securities.
Portfolio risk
27
Beta and Unique Risk
beta
Expected
return
Expectedmarketreturn
10%10%- +
-10%+10%
stock
Copyright 1996 by The McGraw-Hill Companies, Ic
-10%
1. Total risk = diversifiable risk + market risk2. Market risk is measured by beta, the sensitivity to market changes
28
Beta and Unique Risk
Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio.
29
Definition of Risk When Investors Hold the Market Portfolio
• Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta ()of the security.
• Beta measures the responsiveness of a security to movements in the market portfolio.
)(
)(2
,
M
Mii R
RRCov
30
Chapter 8Risk and Return
• Markowitz Portfolio Theory
• Risk and Return Relationship
• Validity and the Role of the CAPM
31
Markowitz Portfolio Theory
• Given a certain level of risk, investors prefer stocks with higher returns.
• Given a certain level of return, investors prefer less risk.
• By combining stocks into a portfolio, one can achieve different combinations of return & standard deviation.
• Correlation coefficients are crucial for ability to reduce risk in portfolio.
32
Markowitz Portfolio Theory
Exxon Mobil
Coca Cola
Standard Deviation
Expected Return (%)
40% in Coca Cola
Expected Returns and Standard Deviations vary given different weighted combinations of the stocks
33
Efficient Frontier
Example Correlation Coefficient = .4
Stocks % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
34
Efficient Frontier
Standard Deviation
Expected Return (%)
Each half egg shell represents the possible weighted combinations for two stocks.
The composite of all stock sets constitutes the efficient frontier
35
Efficient Frontier
Example Correlation Coefficient = .4
Stocks % of Portfolio Avg Return
ABC Corp 28 60% 15%
Big Corp 42 40% 21%
Portfolio 28.1 17.4%
Let’s Add stock New Corp to the portfolio
36
Efficient Frontier
Example Correlation Coefficient = .3
Stocks % of Portfolio Avg Return
Portfolio 28.1 50% 17.4%
New CorpNew Corp 3030 50%50% 19% 19%
New Portfolio 23.43 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION
42
Riskless Borrowing and Lending
Now investors can allocate their money across the T-bills and a balanced mutual fund
100% bonds
100% stocks
rf
retu
rn
Balanced fund
CML
44
100% bonds
100% stocks
retu
rn
First Optimal Risky Portfolio
Second Optimal Risky Portfolio
CML 0 CML 1
0fr
1fr
Changes in Riskfree Rate
45
Security Market LineReturn
.
rf
Risk Free
Return =
Efficient Portfolio
Market Return = rm
BETA1.0
48
Estimating with regression
Sec
uri
ty R
etu
rns
Sec
uri
ty R
etu
rns
Return on Return on market %market %
RRii = = ii + + iiRRmm + + eeii
Slope = Slope = iiCharacte
ristic
Line
Characteris
tic Line
49
Estimates of Beta for Selected Stocks
Stock Beta
Research in Motion 3.04
Nortel Networks 3.61
Bank of Nova Scotia 0.28
Bombardier 1.48
Investors Group. 0.36
Maple Leaf Foods 0.25
Roger Communications
1.17
Canadian Utilities 0.08
TransCanada Power 0.08
50
CAPM versus Reality
1. Do investors care about mean and variance?
2. Is there a security that is risk-free?
3. Short selling?
4. Transaction costs?
5. Most important: homogeneous expectations?
51
Testing the CAPM
Avg Risk Premium 1931-2002
Portfolio Beta1.0
SML30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
52
Testing the CAPM
Avg Risk Premium 1931-65
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
53
Testing the CAPM
Avg Risk Premium 1966-2002
Portfolio Beta1.0
SML
30
20
10
0
Investors
Market Portfolio
Beta vs. Average Risk Premium
54
Invest in project
Chapter 9 (part 1)Capital Budgeting and Risk
Firm withexcess cash
Shareholder’s Terminal
Value
Pay cash dividend
Shareholder invests in financial
asset
Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk.
A firm with excess cash can either pay a dividend or make a capital investment
55
Company Cost of Capital
• A firm’s value can be stated as the sum of the value of its various assets
PV(B)PV(A)PV(AB) valueFirm
56
Company Cost of Capital
10%nologyknown tech t,improvemenCost
COC)(Company 15%business existing ofExpansion
20%products New
30%Ventures eSpeculativ
RateDiscount Category
57
Company Cost of Capital (COC) is based on the average beta of the assets
The average Beta of the assets is based on the % of funds in each asset
Example1/3 New Ventures B=2.01/3 Expand existing business B=1.31/3 Plant efficiency B=0.6
AVG B of assets = 1.3
Company Cost of Capitalsimple approach
58
Company Cost of Capital
If the firm is all equity financed, A company’s cost of capital can be compared to the CAPM required return
Required
return
Project Beta1.26
Company Cost of Capital
13
5.5
0
SML
59
Example
• Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100-percent equity financed.
• Assume a risk-free rate of 5-percent and a market risk premium of 10-percent.
• What is the appropriate discount rate for an expansion of this firm?
60
Example (continued)Suppose Stansfield Enterprises is evaluating the following non-mutually exclusive projects. Each costs $100 and lasts one year.
Project Project Project’s Estimated Cash Flows Next Year
IRR NPV at 30%
A 2.5 $150 50% $15.38
B 2.5 $130 30% $0
C 2.5 $110 10% -$15.38
61
Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects
Pro
ject
IRR
Firm’s risk (beta)
SML
5%
Good projects
Bad projects
30%
2.5
A
B
C
62
Capital Structure - the mix of debt & equity within a company
Expand CAPM to include CS (common shares)
R = rf + B ( rm - rf )
becomes
Requity = rf + B ( rm - rf )
Capital Structure
63
Capital Structure & COC (company cost of capital)
COC = rportfolio = rassets
rassets = rdebt (D) + requity (E)
(V) (V)
Bassets = Bdebt (D) + Bequity (E)
(V) (V)
requity = rf + Bequity ( rm - rf )
IMPORTANT
E, D, and V are all market values
64
0
20
0 0.2 0.8 1.2
Capital Structure & COC
Expected return (%)
Bdebt Bassets Bequity
Rrdebt=8
Rassets=12.2
Requity=15
Expected Returns and Betas prior to refinancing
65
Suppose the Conglomerate Company has a cost of capital, based on the CAPM, of 17%. The risk-free rate is 4%, the market risk premium is 10%, and the firm’s beta is 1.3.
17% = 4% + 1.3 × [14% – 4%]
This is a breakdown of the company’s investment projects:1/3 Automotive retailer = 2.0
1/3 Computer Hard Drive Mfr. = 1.3
1/3 Electric Utility = 0.6
average of assets = 1.3
When evaluating a new electrical generation investment, which cost of capital should be used?
The Firm versus the Project
66
Capital Budgeting & Project RiskP
roje
ct
IRR
Firm’s risk (beta)
SML
17%
1.3 2.00.6r = 4% + 0.6×(14% – 4% ) = 10%
10% reflects the opportunity cost of capital on an investment in electrical generation, given the unique risk of the project.
10%
24% Investments in hard drives or auto retailing should have higher discount rates.
67
Capital Budgeting & Project Risk
Pro
ject
IR
R
Firm’s risk (beta)
SML
rf
FIRM
Incorrectly rejected positive NPV projects
Incorrectly accepted negative NPV projects
Hurdle rate
)( FMFIRMF RRβR
The SML can tell us why:
68
Theoretically, the calculation of beta is straightforward:
2)(
),(
M
im
M
Mi
σ
σ
RVar
RRCovβ
Problem 1: Betas may vary over time.
Measuring Betas
69
Measuring Betas
Dell Computer
Slope determined from plotting the line of best fit.
Price data: May 91- Nov 97
R2 = .10
B = 1.87
70
Measuring Betas
Dell Computer
Slope determined from plotting the line of best fit.
Price data: Dec 97 - Apr 04
R2 = .27
B = 1.61
71
Measuring Betas
General Motors
Slope determined from plotting the line of best fit.
R2 = .07
B = 0.72
Price data: May 91- Nov 97
72
Measuring Betas
General Motors
Slope determined from plotting the line of best fit.
GM
return (%)R2 = .29
B = 1.21
Price data: Dec 97 - Apr 04
73
Estimated Betas
Beta equity
Standard Error
Burlington Northern & Santa Fe 0.53 0.2
CSX Transportation 0.58 0.23Norfolk Southern 0.47 0.28
Union Pacific Corp 0.47 0.19Industry portfolio 0.49 0.18
74
Beta Stability
% IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER
10 (High betas) 35 69
9 18 54
8 16 45
7 13 41
6 14 39
5 14 42
4 13 40
3 16 45
2 21 61
1 (Low betas) 40 62
Source: Sharpe and Cooper (1972)
75
Using an Industry Beta
• It is frequently argued that one can better estimate a firm’s beta by involving the whole industry.
• If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta.
• If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta.
76
Problems with Industry Beta
One must make sure that the firm is comparable to other industry both in its operation and its financing.
Question: Consider Grand Sport, Inc., which is currently all-equity and has a beta of 0.90. The firm has decided to lever up to a capital structure of 50% debt and 50% equity. Since the firm will remain in the same industry, its asset beta should remain 0.90.
Assuming a zero beta for its debt, what should the equity beta be?
77
Beware of Fudge Factors
• Common practice to make adjustments to discount rate to offset worries.
Example:
1) A new drug won’t get FDA approval and won’t be able to go on the market.
2) Unexpected weather condition would hurt the crop.
78
Determinants of Beta
• Business Risk– Cyclicality of Revenues
– Operating Leverage
• Financial Risk– Financial Leverage
79
Cyclicality of Revenues
• Highly cyclical stocks have high betas.– Empirical evidence suggests that retailers
and automotive firms fluctuate with the business cycle.
– Transportation firms and utilities are less dependent upon the business cycle.
80
Operating Leverage
• The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs.
• Operating leverage increases as fixed costs rise and variable costs fall.
• Operating leverage magnifies the effect of cyclicality on beta.
• The degree of operating leverage is given by:
Salesin Change
Salesin Change
EBIT
EBITDOL
81
Operating Leverage
Volume
$
Fixed costs
Total costs
EBIT
Volume
Operating leverage increases as fixed costs rise and variable costs fall.
Fixed costs
Total costs
82
Chapter 9: Q5
The following table shows estimates of the risk of two well-known Canadian Stocks
STD R^2 Beta STD Beta
Alcan 24 0.15 0.69 0.21
Inco 29 0.22 1.04 0.26
a. What proportion was market risk, and what proportion unique risk?
b. What is the variance of market and unique variance of each stock?
c. What is the confidence level of the Inco’s beta?
d. What is expected return of Alcn if Rf=5% and market return=12%?
e. Suppose next year the market provides a zero return. What return to you expect for each stock?
83
Chapter 9: Q9You run a perpetual encabulator machine, which generates revenues averaging $20 million per year. Raw material costs are 50 percent of revenues. These costs are variable – they are always proportional to revenues. There are no other operating costs. The cost of capital is 9 percent. Your firm’s long-term borrowing rate is 6 percent. Now you are approached by Studebaker Capital Corp., which proposes a fixed-price contract to supply raw materials at $10 million per year for 10 years.
a. What happens to the operating leverage and business risk of the encabulator machine if you agree to this fixed-price contact?
b. Calculate the present value of the encabulator machine with and without the fixed-price contract?
85
Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?
86
Risk,DCF and CEQ
Example
Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?
%12
)8(75.6
)(
fmf rrBrr
240.2 PVTotal
71.21003
79.71002
89.31001
12% @ PV FlowCashYear
AProject
87
Risk,DCF and CEQ
ExampleProject B cash flow is 94.6, 89.6, 84.8 in year 1-3 respectively. However, these cash flows are RISK FREE. What is Project’s B PV?
240.2 PVTotal
71.284.83
79.789.62
89.394.61
6% @ PV FlowCashYear
Project B
240.2 PVTotal
71.21003
79.71002
89.31001
12% @ PV FlowCashYear
AProject
88
Risk,DCF and CEQ
240.2 PVTotal
71.284.83
79.789.62
89.394.61
6% @ PV FlowCashYear
Project B
240.2 PVTotal
71.21003
79.71002
89.31001
12% @ PV FlowCashYear
AProject
Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.
89
Risk,DCF and CEQ
ExampleProject A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?
The difference between the 100 and the certainty equivalent (94.6) is 5.7%…this % can be considered the annual premium on a risky cash flow
flow cash equivalentcertainty flow cashRisky
057.1
90
Long lived assets and discount rates
Example (from text): The scientists at Vegetron have come up with an electric mop and are ready to go ahead with pilot production. The preliminary phase will take one year and costs $125k. Management feels that there is only a 50% chance that the pilot production will be successful. If the project fails, the project will be dropped. If the project succeeds Vegetron will build a $1million plant that would generate an expected annual cash flow in perpetuity of $250k. Rf=7%, Risk Premium=9%. Regular projects of the firm have a beta of 0.33, however due to the 50% probability of failure management assumes a beta of 2 for the project.
1. What is NPV? 2. Is management correct about its approach for the NPV
calculation?
91
International Projects
• Investment projects abroad may be safer than similar domestic investments.
• Remember: Beta measures risk relative to investor’s portfolio (a good question would be to ask who is the investor of the company?)
• Not clear why home bias persists so strongly (perhaps information, transaction costs, etc.)
92
What is Liquidity?
• The idea that the expected return on a stock and the firm’s cost of capital are positively related to risk is fundamental.
• Recently a number of academics have argued that the expected return on a stock and the firm’s cost of capital are negatively related to the liquidity of the firm’s shares as well.
• The trading costs of holding a firm’s shares include brokerage fees, the bid-ask spread, and market impact costs.
93
Liquidity, Expected Returns, and the Cost of Capital
• The cost of trading an illiquid stock reduces the total return that an investor receives.
• Investors thus will demand a high expected return when investing in stocks with high trading costs.
• This high expected return implies a high cost of capital to the firm.
94
Liquidity and the Cost of Capital
Cos
t of
Cap
ital
LiquidityAn increase in liquidity, i.e., a reduction in trading costs, lowers a firm’s cost of capital.
95
Liquidity and Adverse Selection
• There are a number of factors that determine the liquidity of a stock.
• One of these factors is adverse selection.• This refers to the notion that traders with better
information can take advantage of specialists and other traders who have less information.
• The greater the heterogeneity of information, the wider the bid-ask spreads, and the higher the required return on equity.
96
What the Corporation Can Do
• The corporation has an incentive to lower trading costs since this would result in a lower cost of capital.
• A stock split would increase the liquidity of the shares.
• A stock split would also reduce the adverse selection costs thereby lowering bid-ask spreads.
• This idea is a new one and empirical evidence is not yet in.
97
What the Corporation Can Do
• Companies can also facilitate stock purchases through the Internet.
• Direct stock purchase plans and dividend reinvestment plans handled on-line allow small investors the opportunity to buy securities cheaply.
• The companies can also disclose more information, especially to security analysts, to narrow the gap between informed and uninformed traders. This should reduce spreads.
98
Summary and Conclusions• The expected return on any capital budgeting
project should be at least as great as the expected return on a financial asset of comparable risk. Otherwise the shareholders would prefer the firm to pay a dividend.
• The expected return on any asset is dependent upon .
• A project’s required return depends on the project’s .
• A project’s can be estimated by considering comparable industries or the cyclicality of project revenues and the project’s operating and financial leverage.
99
Jones Family Mini-Case
Executive summary:• The wildcat oil well is going to cost $5 million.• The Jones geologists says there’s only 30% chance of a dry hole.• If oil is found, the expectation is for 300 barrels of crude oil per day
(at a price of $25 per barrel)• Sales will start next year.• Production and shipping costs are $10 per barrel (Mr. Jones argues
that they are fixed).• Production will start declining at 5% every year.• Oil prices expected to grow at 2.5% per year, and pumping will
continue for 15 years.• The interest rate is 6%, the beta is 0.8, and the risk premium is 7%.
100
Chapter 10: Decision Trees• A fundamental problem in NPV analysis is
dealing with uncertain future outcomes.• There is usually a sequence of decisions in
NPV project analysis.• Decision trees are used to identify the
sequential decisions in NPV analysis.• Decision trees allow us to graphically represent
the alternatives available to us in each period and the likely consequences of our actions.
• This graphical representation helps to identify the best course of action.
101
Example of Decision Tree
Do not study
Study finance
Open circles represent decisions to be made.
Filled circles represent receipt of information
e.g., a test score in this class.
The lines leading away from the circles represent
the alternatives.
“C”
“A”
“B”
“F”
“D”
Pay wizard $1000?
102
Stewart Pharmaceuticals • The Stewart Pharmaceuticals Corporation is considering
investing in developing a drug that cures the common cold.• A corporate planning group, including representatives from
production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase.
• This preliminary phase will last one year and cost $1 billion. Furthermore, the group believes that there is a 60% chance that tests will prove successful.
• If the initial tests are successful, Stewart Pharmaceuticals can go ahead with full-scale production. This investment phase will cost $1,600 million. Production will occur over the next four years.
103
Stewart Pharmaceuticals NPV of Full-Scale Production following Successful Test
Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0.
Investment Year 1 Years 2-5
Revenues $7,000
Variable Costs (3,000)
Fixed Costs (1,800)
Depreciation (400)
Pretax profit $1,800
Tax (34%) (612)
Net Profit $1,188
Cash Flow -$1,600 $1,588
75.433,3$)10.1(
588,1$600,1$
4
1
t
tNPV
104
Stewart Pharmaceuticals NPV of Full-Scale Production following Unsuccessful Test
Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0.
Investment Year 1 Years 2-5
Revenues $4,050
Variable Costs (1,735)
Fixed Costs (1,800)
Depreciation (400)
Pretax profit $115
Tax (34%) (39.10)
Net Profit $75.90
Cash Flow -$1,600 $475
461.91$)10.1(
90.475$600,1$
4
1
t
tNPV
105
Decision Tree for Stewart Pharmaceutical
Do not test
Test
Failure
Success
Do not invest
Invest
Invest
The firm has two decisions to make:To test or not to test.To invest or not to invest.
0$NPV
NPV = $0
mNPV 461.91$
mNPV 75.433,3$
106
Stewart Pharmaceutical: Decision to Test
• Let’s move back to the first stage, where the decision boils down to the simple question: should we invest?
• The expected payoff evaluated at date 1 is:
failuregiven
Payoff
failure
Prob.
successgiven
Payoff
sucess
Prob.
payoff
Expected
25.060,2$0$40.75.433,3$60.payoff
Expected
95.872$10.1
25.060,2$000,1$ NPV
• The NPV evaluated at date 0 is:
So we should test.
107
Real Options
• One of the fundamental insights of modern finance theory is that options have value.
• The phrase “We are out of options” is surely a sign of trouble.
• Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation.
108
Options
The Option to Expand• Static analysis implicitly assumes that the scale of the
project is fixed.• If we find a positive NPV project, we should consider the
possibility of expanding the project to get a larger NPV.• For example,the option to expand has value if demand
turns out to be higher than expected.• All other things being equal, we underestimate NPV if we
ignore the option to expand.The Option to Delay• Has value if the underlying variables are changing with a favourable trend.
109
The Option to Expand: Example
• Imagine a start-up firm, Campusteria, Inc. which plans to open private (for-profit) dining clubs on university campuses.
• The test market will be your campus, and if the concept proves successful, expansion will follow nationwide.
• Nationwide expansion, if it occurs, will occur in year four.
• The start-up cost of the test dining club is only $30,000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus).
110
Campusteria pro forma Income Statement
Investment Year 0 Years 1-4
Revenues $60,000
Variable Costs ($42,000)
Fixed Costs ($18,000)
Depreciation ($7,500)
Pretax profit ($7,500)
Tax shield 34% $2,550
Net Profit –$4,950
Cash Flow –$30,000 $2,550
We plan to sell 25 meal plans at $200 per month with a 12-month contract.
Variable costs are projected to be $3,500 per month.
Fixed costs (the lease payment) are projected to be $1,500 per month.
We can depreciate (straight line) our capitalized leaseholder improvements.
84.916,21$)10.1(
550,2$000,30$
4
1
t
tNPV
111
The Option to Expand: Valuing a Start-Up
• Note that while the Campusteria test site has a negative NPV, its negativity is relatively small.
• If we expand, we project opening 20 Campusterias in year four and the size of the project may grow 20 folds.
• The value of the project is in the option to expand. • If we hit it big, we will be in a position to score large.• We won’t know if this has value if we do not try. Thus, it
seems that we may want to take on this test project and see what it delivers.
112
Discounted Cash Flows and Options
• We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project.
M = NPV + Opt
A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time the more versatile machine is more valuable because it comes with options.
113
The Option to Abandon: Example• The option to abandon a project has value if demand
turns out to be lower than expected.• Suppose that we are drilling an oil well. The drilling rig
costs $300 today and in one year the well is either a success or a failure.
• The outcomes are equally likely. The discount rate is 10%.
• The PV of the successful payoff at time one is $575.• The PV of the unsuccessful payoff at time one is $0.
114
The Option to Abandon: Example (continued)
Traditional NPV analysis would indicate rejection of the project.
NPV = = –$38.641.10
$287.50–$300 +
Expected Payoff
= (0.50×$575) + (0.50×$0) = $287.50
=Expected Payoff
Prob. Success
× Successful Payoff
+ Prob. Failure
× Failure Payoff
115
The Option to Abandon: Example
The firm has two decisions to make: drill or not, abandon or stay.
Do not drill
Drill
0$NPV
300$
Failure
Success: PV = $575
Sell the rig; salvage value
= $250
Sit on rig; stare at empty hole:
PV = $0.
Traditional NPV analysis overlooks the option to abandon.
116
• When we include the value of the option to abandon, the drilling project should proceed:
NPV = = $75.001.10
$412.50–$300 +
Expected Payoff
= (0.50×$575) + (0.50×$250) = $412.50
=Expected Payoff
Prob. Success
× Successful Payoff
+ Prob. Failure
× Failure Payoff
The Option to Abandon: Example (continued)
117
Valuation of the Option to Abandon
• Recall that we can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. OptNPVM
Opt 64.3800.75$
Opt 64.3800.75$
64.113$Opt
118
The Option to Delay: Example
• Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remain constant at $25,000, but since costs are declining the NPV at the time of launch steadily rises.
• The best time to launch the project is in year 2—this schedule yields the highest NPV when judged today.
Year Cost PV NPV t
0 20,000$ 25,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 2 17,100$ 25,000$ 7,900$ 3 16,929$ 25,000$ 8,071$ 4 16,760$ 25,000$ 8,240$
2)10.1(
900,7$529,6$
Year Cost PV NPV t NPV 0
0 20,000$ 25,000$ 5,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 6,364$ 2 17,100$ 25,000$ 7,900$ 6,529$ 3 16,929$ 25,000$ 8,071$ 6,064$ 4 16,760$ 25,000$ 8,240$ 5,628$