senstivity analysis.ppt

43
Remember use: Incremental Cash Flows Discount incremental cash flows Include All Indirect Effects Forget Sunk Costs Include Opportunity Costs Beware of Allocated Overhead Costs Incremen tal Cash Flow cash flow with project cash flow without project = -

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Page 1: Senstivity Analysis.ppt

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= -

Page 2: Senstivity Analysis.ppt

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)

Page 3: Senstivity Analysis.ppt

Capital Budgeting Process

• Capital Budgeting Problems– Consistent forecasts– Conflict of interest– Forecast bias– Selection criteria (NPV and others)

Page 4: Senstivity Analysis.ppt

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.

Page 5: Senstivity Analysis.ppt

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.

Page 6: Senstivity Analysis.ppt

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

Page 7: Senstivity Analysis.ppt

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

Page 8: Senstivity Analysis.ppt

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)

Page 9: Senstivity Analysis.ppt

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

Page 10: Senstivity Analysis.ppt

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%.

Page 11: Senstivity Analysis.ppt

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

Page 12: Senstivity Analysis.ppt

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)

Page 13: Senstivity Analysis.ppt

Answer

Solving for “Planes Sold”0 4355 35= - 900 + . ( . l d - 12. 5)xPl anes So

Pl anes Sol d = 63

Break Even Analysis

Page 14: Senstivity Analysis.ppt

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.

Page 15: Senstivity Analysis.ppt

Decision Trees

NPV=0

Don’t test

Test (Invest $200,000)

Success

Failure

Pursue project NPV=$2million

Stop project

NPV=0

Page 16: Senstivity Analysis.ppt

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?

Page 17: Senstivity Analysis.ppt

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?

Page 18: Senstivity Analysis.ppt

Risk

• Rates of Return

• 73 Years of Capital Market History

• Measuring Risk

• Risk & Diversification

• Thinking About Risk

Page 19: Senstivity Analysis.ppt

The value of a $1 investment in 19266

Source: Ibbotson Associates

0.1

10

1000

Common StocksLong T-BondsT-Bills

Inde

x

Year End

Page 20: Senstivity Analysis.ppt

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

Page 21: Senstivity Analysis.ppt

Expected Return

9.3+4.8=14.1% (1999)

9.3+14=23.3% (1981)

premium

risk normal+

billsTreasury

on rateinterest =

return

market Expected

Page 22: Senstivity Analysis.ppt

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

Page 23: Senstivity Analysis.ppt

Measuring Risk

Variance - Average value of squared deviations from mean. A measure of volatility.

Standard Deviation – Square-Root of Variance. A measure of volatility.

Page 24: Senstivity Analysis.ppt

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%

Page 25: Senstivity Analysis.ppt

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.”

Page 26: Senstivity Analysis.ppt

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%

Page 27: Senstivity Analysis.ppt

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)?

Page 28: Senstivity Analysis.ppt

Topics Covered

• Measuring Beta

• Portfolio Betas

• CAPM and Expected Return

• Security Market Line

• Capital Budgeting and Project Risk

Page 29: Senstivity Analysis.ppt

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.

Page 30: Senstivity Analysis.ppt

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.

Page 31: Senstivity Analysis.ppt

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

Page 32: Senstivity Analysis.ppt

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

Page 33: Senstivity Analysis.ppt

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 %

Page 34: Senstivity Analysis.ppt

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

Page 35: Senstivity Analysis.ppt

Measuring Market RiskMarket Risk Premium - Risk premium of market

portfolio. Difference between market return and return on risk-free Treasury bills.

Page 36: Senstivity Analysis.ppt

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

Page 37: Senstivity Analysis.ppt

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

Page 38: Senstivity Analysis.ppt

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

Page 39: Senstivity Analysis.ppt

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.

Page 40: Senstivity Analysis.ppt

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.

Page 41: Senstivity Analysis.ppt

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

Page 42: Senstivity Analysis.ppt

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!!

Page 43: Senstivity Analysis.ppt

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?