Remember use:
Incremental Cash Flows
•
•
•
•
•
Discount incremental cash flows
Include All Indirect Effects
Forget Sunk Costs
Include Opportunity Costs
Beware of Allocated Overhead Costs
Incremental
Cash Flow
=
cash flow
with project
-
cash flow
without project
Sequence of Firm Decisions
Capital Budget - The list of planned
investment projects.
The Decision Process
1 - Develop and rank all investment projects
2 - Authorize projects based on:
•
•
•
•
Govt regulation
Production efficiency
Capacity requirements
NPV (most important)
Capital Budgeting Process
• Capital Budgeting Problems
–
–
–
–
Consistent forecasts
Conflict of interest
Forecast bias
Selection criteria (NPV and others)
How To Handle Uncertainty
Sensitivity Analysis - Analysis of the effects
of changes in sales, costs, etc. on a project.
Scenario Analysis - Project analysis given a
particular combination of assumptions.
Simulation Analysis - Estimation of the
probabilities of different possible outcomes.
Break Even Analysis - Analysis of the level of
sales (or other variable) at which the
company breaks even.
Sensitivity Analysis
Example
Given the expected cash flow
forecasts listed on the next
slide, determine the NPV of
the project given changes in
the cash flow components
using an 8% cost of capital.
Assume that all variables
remain constant, except the
one you are changing.
Sensitivity Analysis
Example - continued
Year 0
Investment
Years 1 - 12
- 5,400
Sales
16,000
Variable Costs
13,000
Fixed Costs
2,000
Depreciation
450
Pretax profit
550
. Taxes @ 40%
220
Profit after tax
330
Operating cash flow
780
Net Cash Flow
- 5,400
780
NPV= $478
Sensitivity Analysis
Example - continued
Possible Outcomes
Range
Variable Pessimistic Expected Optimistic
Investment(000s)
6,200
5,400
5,000
Sales(000s)
14,000
16,000
18,000
Var Cost (% of sales)
83%
81.25%
80%
Fixed Costs(000s)
2,100
2,000
1,900
Sensitivity Analysis
Example - continued
NPV Calculations for Pessimistic Investment Scenario
Year 0
Investment
Years 1 - 12
- 6,200
Sales
16,000
Variable Costs
13,000
Fixed Costs
2,000
Depreciation
450
Pretax profit
550
. Taxes @ 40%
220
Profit after tax
330
Operating cash flow
780
Net Cash Flow
- 6,200
780
NPV= ($121)
Sensitivity Analysis
Example - continued
NPV Possibilities
NPV (000s)
Variable Pessimistic
Expected Optimistic
Investment(000s)
- 121
478
778
Sales(000s)
- 1,218
478
2,174
Var Cost (% of sales)
- 788
478
1,382
Fixed Costs(000s)
26
478
930
Break Even Analysis
Example
Given the forecasted data
on the next slide,
determine the number of
planes that the company
must produce in order to
break even, on an NPV
basis. The company’s cost
of capital is 10%.
Break Even Analysis
Year 0 Years 1 - 6
Investment
Sales
$900
15.5xPlanes Sold
Var. Cost
8.5xPlanes Sold
Fixed Costs
175
Depreciation
900 / 6 = 150
Pretax Profit
(7xPlanes Sold) - 325
Taxes (50%)
(3.5xPlanes Sold) - 162.5
Net Profit
(3.5xPlanes Sold) - 162.5
Net Cash Flow - 900
(3.5xPlanes Sold) - 12.5
Break Even Analysis
Answer
The break even point, is the # of Planes
Sold that generates a NPV=$0.
The present value annuity factor of a 6
year cash flow at 10% is 4.355
Thus,
NPV = -900 + 4355
. (3.5xPlanes Sold - 12.5)
Break Even Analysis
Answer
Solving for “Planes Sold”
0 = -900 + 4355
.
(3.5xPlanes Sold - 12.5)
Planes Sold = 63
Flexibility & Options
Decision Trees - Diagram of sequential decisions
and possible outcomes.
• Decision trees help companies determine their
Options by showing the various choices and
outcomes.
• The Option to avoid a loss or produce extra profit
has value.
• The ability to create an Option thus has value that
can be bought or sold.
Decision Trees
Success
Test (Invest
$200,000)
Pursue project
NPV=$2million
Failure
Stop project
Don’t test
NPV=0
NPV=0
Decision Tree: Example
• You invest in a dot com company.
• At the start of each year for 3 years, it
requires £1 million to continue.
• The future value of a successful dot.com in
at the beginning of the 4th year is £10
million.
• Each year it has a 50% of surviving.
• What is the NPV of this investment at r=.1?
You want to be a millionaire
• You have no life-lines and are risk neutral. For
simplicity assume if you answer wrong you get
£0.
• If your are at £500,000, at what certainty would
you guess for the million?
• Given your previous answer. Before seeing the
question your certainty of answering correctly the
£500,000 is either 25% or 75% with equal
chance.
• At what certainty at £250,000, would you go for
it?
Risk
•
•
•
•
•
Rates of Return
73 Years of Capital Market History
Measuring Risk
Risk & Diversification
Thinking About Risk
The value of a $1 investment in 19266
Index
1000
10
Common Stocks
Long T-Bonds
T-Bills
Source: Ibbotson Associates
Year End
19
90
19
98
19
80
19
70
19
60
19
50
19
40
19
30
0.1
Rates of Return
Percentage Return
60
40
20
0
-20
Common Stocks
Long T-Bonds
T-Bills
-40
-60 26
30
35
40
45
Source: Ibbotson Associates
50
55
60
Year
65
70
75
80
85
90
95
Expected Return
Expected market
return
interest rate on
normal risk
=
+
Treasury bills
premium
(1981) 23.3%
=
14
+
9.3
(1999) 14.1%
=
4.8
+
9.3
Equity Premium Puzzle.
• In 1985, a pair of economists, Rajnish Mehra and
Edward Prescott, examined almost a century of
returns for American shares and bonds. After
adjusting for inflation, equities had made average
real returns of around 7 a year, compared with
only 1% for Treasury bonds-a 6% point equity
premium. Given that shares are riskier (in the
sense that their prices bounce around more) there
should have been some premium. But theory
suggested it should not have been much more than
1 point. The extra five points seemed redundant-evidence of some inexplicable market inefficiency
Measuring Risk
Variance - Average value of squared deviations from
mean. A measure of volatility.
Standard Deviation – Square-Root of Variance. A
measure of volatility.
Measuring Risk
Coin Toss Game-calculating variance and standard deviation
(1)
(2)
(3)
Percent Rate of Return Deviation from Mean Squared Deviation
+ 40
+ 30
900
+ 10
0
0
+ 10
0
0
- 20
- 30
900
Variance = average of squared deviations = 1800 / 4 = 450
Standard deviation = square of root variance =
450 = 21.2%
Risk and Diversification
Diversification - Strategy designed to reduce risk
by spreading the portfolio across many
investments.
Unique Risk - Risk factors affecting only that firm.
Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that
affect the overall stock market. Also called
“systematic risk.”
Risk and Diversification
Deviation from
Average Return
-23.44
12.68
-1.6
8.61
3.83
Squared
Deviation
549.43
160.78
2.82
74.13
14.67
801.84
Year
Rate of Return
1994
1.31
1995
37.43
1996
23.07
1997
33.36
1998
25.58
Total
123.75
Average rate of return = 123.75/5 = 24.75
Variance = average of squared deviations = 801.84/5=160.37
Standard deviation = squared root of variance = 12.66%
Portfolio standard deviation
Risk and Diversification
Unique
risk
Market risk
0
5
10
15
Number of Securities
What does this tell you about mutual funds (unit trusts)?
Topics Covered
•
•
•
•
•
Measuring Beta
Portfolio Betas
CAPM and Expected Return
Security Market Line
Capital Budgeting and Project Risk
Measuring Market 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.
Measuring Market Risk
Example - Turbo Charged Seafood has the
following % returns on its stock, relative to
the listed changes in the % return on the
market portfolio. The beta of Turbo Charged
Seafood can be derived from this
information.
Measuring Market Risk
Example - continued
Month Market Return % Turbo Return %
1
+ 1
+ 0.8
2
+ 1
+ 1.8
3
+ 1
- 0.2
4
- 1
- 1.8
5
6
- 1
- 1
+ 0.2
- 0.8
Measuring Market Risk
Example - continued
• When the market was up 1%, Turbo average
% change was +0.8%
• When the market was down 1%, Turbo
average % change was -0.8%
• The average change of 1.6 % (-0.8 to 0.8)
divided by the 2% (-1.0 to 1.0) change in
the market produces a beta of 0.8.
• Beta is a measure of risk with respect to the
market (covariance). Can be additional risk!
• Betting on Israel vs. Austria WC game.
Measuring Market Risk
Example - continued
Turbo
return %
1
0.8
0.6
0.4
Market Return %
0.2
0
-0.2-0.8 -0.6 -0.4 -0.2
-0.4
-0.6
-0.8
0
0.2
0.4
0.6
0.8
1
Portfolio Betas
• Diversification decreases variability from
unique risk, but not from market risk.
• The beta of your portfolio will be an
average of the betas of the securities in the
portfolio.
• If you owned all of the S&P Composite
Index stocks, you would have an average
beta of 1.0
Measuring Market Risk
Market Risk Premium - Risk premium of market
portfolio. Difference between market return and
return on risk-free Treasury bills.
Measuring Market Risk
Market Risk Premium - Risk premium of market
portfolio. Difference between market return and
return on risk-free Treasury bills.
14
Expected Return (%) .
12
Market
Portfolio
10
8
6
4
2
0
0
0.2
0.4
0.6
Beta
0.8
1
Measuring Market Risk
CAPM - Theory of the relationship between risk and
return which states that the expected risk premium
on any security equals its beta times the market
risk premium.
Market risk premium = rm - rf
Risk premium on any asset = r - rf
Expected Return = rf + B(rm - rf )
Measuring Market Risk
Security Market Line - The graphic representation
of the CAPM.
Expected Return (%) .
20
Rm
Security Market Line
Rf
0
0
1
Beta
Problems with CAPM
• Plotting average return vs. Beta, a zero Beta
beats Risk-free rate.
• Short term doesn’t do so well.
• Unstable Betas.
• Tough to test. Will the real market portfolio
stand up?
• Beta is not a very good predictor of future
returns.
However, Jagannathan & Wang do find support with adjustments.
Capital Budgeting & Project Risk
• The project cost of capital depends on the
use to which the capital is being put.
Therefore, it depends on the risk of the
project and not the risk of the company.
Capital Budgeting & Project Risk
Example - Based on the CAPM, ABC Company has a cost
of capital of 17%. (4 + 1.3(10)). A breakdown of the
company’s investment projects is listed below. When
evaluating a new dog food production investment, which
cost of capital should be used?
1/3 Nuclear Parts Mfr.. B=2.0
1/3 Computer Hard Drive Mfr.. B=1.3
1/3 Dog Food Production B=0.6
Capital Budgeting & Project Risk
Example - Based on the CAPM, ABC Company has a cost
of capital of 17%. (4 + 1.3(10)). A breakdown of the
company’s investment projects is listed below. When
evaluating a new dog food production investment, which
cost of capital should be used?
R = 4 + 0.6 (14 - 4 ) = 10%
10% reflects the opportunity cost of capital on an
investment given the unique risk of the project.
You should use this value in computing that project’s NPV!!
Wait a second!
• A project has a NPV=£10,000 when r=.05
and a NPV=-£10,000 when r=.1 and the
company can borrow at 5%. Why shouldn’t
the company invest even if the cost of
capital is 10% because of a beta?
• Shouldn’t a project that is risky but has
Beta=0 be considered worse than a project
that is safe and has Beta=0?