mba 253 sensitivity and scenario analysis 2012-13

8/10/2019 MBA 253 Sensitivity and Scenario Analysis 2012-13

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Sensitivity and Scenario

Analysis



Financial Modeling

Any model we use has the potential to haveerror

How do we account for the uncertaintyassociated with our inputs into the model?



Three Types of Risk

Stand Alone Risk

Views project in isolation

With-in firm (Corporate Risk)Looks at the firms portfolio of projects and howthey interact

Market Risk

Risk from the view of a well diversified investor.



Definitions

Risk

Exposure to a chance of injury or loss

ProbabilityThe likelihood an event occurs

Risk vs. Uncertainty

Risk – the probability of the outcome is known

Uncertainty – includes judgment concerning theprobability



Definitions and Terms Continued

Objective Prob –can measure prob. precisely

Subjective Prob. – Includes judgment or

opinion Variation Risk – We want to look at a rangeof possible outcomes



Issues in Risk Measurement

1. Stand Alone Risk is the easiest to measure

2. Market Risk is the most important to the shareholder

3. To evaluate risk you need three things

i. Standard deviation of the projects forecastedreturns

ii. Correlation of the projects forecasted returns withthe firms other assets

iii. Correlation of the projects forecasted returns withthe market



Issues in Risk Management con’t

4. Using the numbers in 3) you can find the corporatebeta and market beta coefficient (equal to ((s/s)r)

5. Most projects have a + correlation with otherprojects and a coefficient < 1

6. Most projects are positively correlated with themarket with coefficient < 1

7. Corporate risk should also be examined1. More important to small business

2. Investors may look at things other than market risk

3. Firm Stability is important to creditors, suppliers etc



Stand Alone Risk (Review)

The easiest approach to measuring stand alonerisk is to use the standard deviation of theprojects returns.

Just like security analysis you need to be carefullooking at only standard deviation – don’t forgetcoefficient of variation



Measuring Stand Alone Risk

Sensitivity Analysis

Scenario Analysis

Monte Carlo Simulation




Looks at the change in your decision variablewhen one input changes.

Examples:what happens to the value of a project if salesare 10% higher than expected.

What happens to the cost of capital if the riskfree rate increases.



Example 1

Basic time value of money problem.

Assume you believe you need 2,000,000 when

you retire and you are now 25 years old.How much will you need to deposit each year atthe end of the year if your account earns 8%each year?

$27,357.56



Example 1 Change ONLYExpected return

What if your estimated rate of return is of by 10% of thebase (What if your account earns 8.8% each year?Or 7.2% each year)?

Rate Payment

7.2% $24,322.44

8% $27,357.56

8.8% $30,724.44



Example 2: change ONLY Amount Needed for Retirement

Now assume that the amount you need for retiremetnmay be off either way by 10%

Savings Needed Payment

1,800,000 $24,621.80

2,000,000 $27,357.56

2,200,000 $30,093.31




Usually the results are represented in a tablewhere the response of the decision variable tochanges in more than one individual variableare reported.

Then you can compare across variables to seewhich one has the largest impact on your

decision



Example Results

Change in Payment needed for RetirementSavings Needed Expected Return

+10% $24,621.80 $24322.44

Base $27,357.56 $27,357.56

-10% $30,093.31 $30,724.49




Benefits

a. Easy to Calculate and Understand

b. Measures risk associated with individual inputs

Weaknesses

a. Ignores probability of event

b. Ignores interaction among the variables

c. Ignores gains from diversification



Scenario Analysis

Differences from Sensitivity Analysis

Allows you to change more than one variable ata time

Look at a group of scenarios (best case, basecase, and worst case) for example worst case – what if all variables change against us by 20%….

Includes probability estimates of each scenario



Scenario Analysis

Now let both the future cash flows and the cost ofcapital change.

Worst Case Scenario Best Case Scenario

(Savingsh Returni) (Savingsi Returnh)

Need $2,200,000 Need $1,800,000

Return = 7.2% Return = 8.8%

PMT = 33,796.89 PMT = $21,890.20



Scenario Analysis

Given the NPV and Probability you can findthe expected NPV and standard deviation

Scenario NPV Prob. NPV(Prob)Worst $33,796.89 .33 $11,265.63

Base $27357.56 .33 $ 9,119.17

Best $21,890.20 .33 $ 7,296.73Expected NPV $27,681.55

Standard Deviation $ 5,959.95



Interpreting the Results

The project has an expected return on4204.94 with standard deviation of 741.38

This implies a 68 % confidence interval of(3463.56 to 4946.32) a large range ofpossible outcomes

The coefficient of variation would be .1763

(you are accepting .1763 units of risk foreach unit of return)



Scenario Analysis

Benefits

1. More than one variable changes at a time

2. Accounts for probability3. Easy to perform

Weaknesses

1. Small number of scenarios is unrealistic2. Probability distributions difficult to estimate




A more advanced form of scenario analysis

Utilizes the computer to make random choices

for each variable input then calculate theexpected return and standard deviation



Mont Carlo Simulation

1. Construct a model of the firms cash flows andNPV’s

2. Specify a probability distribution for each

uncertain variable (characterized by mean andstandard dev) and correlation among variables.

3. Allow computer to select a random draw form thedistribution for each variable

4. Calculate NPV (this is one scenario).5. Repeat 3) an 4) (10,000 or 100,000 times) equal

chance of each scenario –Calculate expected NPVand standard deviation.




Benefits

1. More realistic selection of variables

2. Easy to understand resultsWeaknesses

1. Only as good as probability estimate andcorrelation of variables



Quick Review

Sensitivity Analysis Scenario Analysis andMonte Carlo Simulation were all used tomeasure stand alone risk

Each is designed to provide more informationabout the uncertainty associated with theproject – they do not provide a clear cut

decision rule.

mba 253 sensitivity and scenario analysis 2012-13

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