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
Year 0 Year s 1 - 12
I nvest ment - 5, 400
Sal es 16, 000
Var i abl e Cost s 13, 000
Fi xed Cost s 2, 000
Depr eci at i on 450
Pr et ax pr ofi t 550
. Taxes @ 40% 220
Pr ofi t af t er t ax 330
Oper at i ng cash fl ow 780
Net Cash Fl ow - 5, 400 780
Example - continued
NPV= $478
Sensitivity AnalysisExample - continued
Possible OutcomesRange
Var i abl e Pessi mi st i c Expect ed Opt i mi st i c
I nvest ment( 000s) 6, 200 5, 400 5, 000
Sal es( 000s) 14, 000 16, 000 18, 000
Var Cost ( % of sal es) 83% 81. 25% 80%
Fi xed Cost s( 000s) 2, 100 2, 000 1, 900
Sensitivity AnalysisExample - continuedNPV Calculations for Pessimistic Investment Scenario
Year 0 Year s 1 - 12
I nvest ment - 6, 200
Sal es 16, 000
Var i abl e Cost s 13, 000
Fi xed Cost s 2, 000
Depr eci at i on 450
Pr et ax pr ofi t 550
. Taxes @ 40% 220
Pr ofi t af t er t ax 330
Oper at i ng cash fl ow 780
Net Cash Fl ow - 6, 200 780
NPV= ($121)
Sensitivity AnalysisExample - continued
NPV PossibilitiesNPV s
Var i abl e Pessi mi st i c Expect ed Opt i mi st i c
I nvest ment
( )000
( 000s) - 121 478 778
Sal es( 000s) - 1, 218 478 2, 174
Var Cost ( % of sal es) - 788 478 1, 382
Fi xed Cost s( 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 Year s 1 - 6
I nvest ment $900
Sal es 15. 5xPl anes Sol d
Var . Cost 8. 5xPl anes Sol d
Fi xed Cost s 175
Depr eci at i on 900 / 6 = 150
Pr et ax Pr ofi t ( 7xPl anes Sol d) - 325
Taxes ( 50%) ( 3. 5xPl anes Sol d) - 162. 5
Net Pr ofi t ( 3. 5xPl anes Sol d) - 162. 5
Net Cash Fl ow - 900 ( 3. 5xPl anes Sol d) - 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 xPl anes So= - 900 + 435535. ( . l d - 12. 5)
Answer
Solving for “Planes Sold”0 4355 35= - 900 + . ( . l d - 12. 5)xPl anes So
Pl anes Sol d = 63
Break Even Analysis
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
NPV=0
Don’t test
Test (Invest $200,000)
Success
Failure
Pursue project NPV=$2million
Stop project
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
Source: Ibbotson Associates
0.1
10
1000
Common StocksLong T-BondsT-Bills
Inde
x
Year End
Rates of Return
Source: Ibbotson Associates
-60
-40
-20
0
20
40
60
26 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Common Stocks
Long T-Bonds
T-Bills
Year
Per
cent
age
Ret
urn
Expected Return
9.3+4.8=14.1% (1999)
9.3+14=23.3% (1981)
premium
risk normal+
billsTreasury
on rateinterest =
return
market Expected
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 RiskCoin 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 SquaredYear Rate of Return Average Return Deviation
1994 1.31 -23.44 549.431995 37.43 12.68 160.781996 23.07 -1.6 2.821997 33.36 8.61 74.131998 25.58 3.83 14.67Total 123.75 801.84
Average rate of return = 123.75/5 = 24.75Variance = average of squared deviations = 801.84/5=160.37Standard deviation = squared root of variance = 12.66%
Risk and Diversification
05 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
dev
iati
on
Market risk
Uniquerisk
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
Month Market Return % Turbo Return %
1 + 1 + 0.8
2 + 1 + 1.8
3 + 1 - 0.2
4 - 1 - 1.8
5 - 1 + 0.2
6 - 1 - 0.8
Example - continued
Measuring Market Risk
• 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.
Example - continued
Measuring Market Risk
Example - continued
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Market Return %
Turbo return %
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 RiskMarket Risk Premium - Risk premium of market
portfolio. Difference between market return and return on risk-free Treasury bills.
Measuring Market RiskMarket Risk Premium - Risk premium of market
portfolio. Difference between market return and return on risk-free Treasury bills.
0
2
4
6
8
10
12
14
0 0.2 0.4 0.6 0.8 1
Beta
Exp
ecte
d R
etu
rn (
%)
. Market Portfolio
Measuring Market RiskCAPM - 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 = r - r
Risk premium on any asset = r - r
Expected Return = r + B(r - r )
m f
f
f m f
Measuring Market RiskSecurity Market Line - The graphic representation
of the CAPM.
0
20
0 1Beta
Exp
ecte
d R
etu
rn (
%)
.
Rf
Rm Security Market Line
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?