Chapter 12: Risk and Capital Budgeting

1
Chapter 12 Risk and Capital Budgeting

• Skip Exhibits. 12-3, 4, and 5
• How to incorporate Risk into the model Monte
  Carlo Simulation
• Real Option Application of Black-Scholes Option
  pricing model to capital budgeting

2
Basic Statistics and Excel functions

• Expected Return Average ( )
• Variance VAR ( )
• Standard Deviation STDEV ( )
• Covariance COVAR ( , )
• Correlation CORREL ( , )
• Probability Distribution Possible events (Cash
  flow) and its probability

3
Basic Statistics and Excel functions

• Expected Return
• Variance
• Probability Distribution Possible events (X
  Cash flow) and its probability ( P )

4
Basic Statistics and Excel functions

• Standard Deviation Squared Root of Variance
• These are expected numbers. In practice we use
  the estimated numbers (sample mean, sample
  variance, etc.)

5
Basic Statistics (Estimates) and Excel functions

• Expected Return Average ( )
• Variance VAR ( )
• Standard Deviation STDEV ( )
• Covariance COVAR ( , )
• Correlation (Rho) CORREL ( , )

6
Simulation

• 1. Start with the standard capital budgeting
  problem
• 2. We add uncertainty into the problem. What if
  some of input variables change in the future?
• A. Sensitivity how the result changes with
  respect to a change in some variables. Sometimes
  it is sensitive, sometimes not. We focus on the
  variables to which the results are sensitive.
  Skip Exhibit 12-3, 4, and 5.
• B. Scenario Analysis (review this in Chapter 11)
• C. Monte Carlo Simulation Full-scale scenario
  with probability distribution You need to install
  ExcSim Add-ins on the Website. Also may skip page
  383-385.

7
Monte Carlo simulation

• Assume possible probability distribution on some
  input variables (fish sales, variable cost, price
  in the Frozen Fish example)
• Normal Uniform Triangle distribution
• Given each random input from each distribution,
  calculate NPV or IRR Do this many times to
  obtain the whole distribution of NPVs.
• What is the probability of having negative NPVs?
• NORMSDIST ( )

8
Normal Distribution(mean, standard deviation)
9
Triangular(min., mean, Max)
10
Uniform(Min and Max)