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L30: Methods of Handling Project Risk

L30: Methods of Handling Project Risk. ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences. Probability Concepts for Investment Decisions. Random variable : variable that can have more than one possible value

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L30: Methods of Handling Project Risk

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  1. L30: Methods of Handling Project Risk ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences

  2. Probability Concepts for Investment Decisions • Random variable: variable that can have more than one possible value • Discrete random variables: Any random variables that take on only isolated values • Continuous random variables: any random variables can have any value in a certain interval • Probability distribution: the assessment of probability for each random event

  3. Expected Return/Risk Trade-off

  4. Measure of Expectation (discrete case) (continuous case)  xf(x)dx

  5. Expected Return Calculation

  6. Measure of Variation Standard Deviation

  7. Variance Calculation

  8. Estimating the amount of Risk involved in an Investment Project Probabilistic Cash Flow Approach Risk-Adjusted Discount Rate Approach

  9. 1. Probabilistic Cash Flow Approach

  10. Example

  11. Present Worth Distribution • If we can assume that PW(i) is a normal distribution with mean E[PW] and variance V[PW], we can make a more precise probabilistic statement of PW for the project.

  12. 2. Risk-Adjusted Discount Rate Approach • An alternate approach to consider the risk elements in project evaluation is to adjust the discount rate to reflect the degree of perceived investment risk. • The most common way to do this is to add an increment to the discount rate, that is, discount the expected value of the risky cash flows at a discount rate that includes a premium for risk. • The size of risk premium naturally increases with the perceived risk of the investment

  13. Example • You are considering a $1 million investment promising risky cash flows with an expected value of $250,000 annually for 10 years. What is the investment’s NPW when the risk-free interest rate is 8% and management has decided to use a 6% risk premium to compensate for the uncertainty of the cash flows

  14. Solution • Given: initial investment = $1 million, expected annual cash flow = $250,000, N = 10 years, r = 8%, risk premium = 6% • Find: net present value and is it worth investing? • First find the risk adjusted discount rate = 8% + 6% = 14%. Then, calculate the NPW using this risk-adjusted discount rate: • PW(14%) = -$1 million + $250,000 (P/A, 14%, 10) = $304,028 • Because the NPW is positive, the investment is attractive even after adjusting for risk.

  15. Comparing Risky Investment Projects - Comparison Rule • If EA > EB and VA VB, select A. • If EA = EB and VA VB, select A. • If EA < EB and VA VB, select B. • If EA > EB and VA> VB, Not clear. Model 2 vs. Model 3  Model 2 >>> Model 3 Model 2 vs. Model 4  Model 2 >>> Model 4 Model 2 vs. Model 1  Can’t decide

  16. Investment Strategies • Trade-Off between Risk and Reward • Cash: the least risky with the lowest returns • Debt: moderately risky with moderate returns • Equities: the most risky but offering the greatest payoff • Broader diversification reduces risk • Broader diversification increase expected return

  17. Broader Diversification Reduces Risk

  18. Broader Diversification Increases Return

  19. 1

  20. Summary Project risk—the possibility that an investment project will not meet our minimum requirements for acceptability and success. Our real task is not to try to find “risk-free” projects—they don’t exist in real life. The challenge is to decide what level of risk we are willing to assume and then, having decided on your risk tolerance, to understand the implications of that choice.

  21. Three of the most basic tools for assessing project risk are as follows: • 1. Sensitivity analysis– a means of identifying the project variables which, when varied, have the greatest effect on project acceptability. • 2. Break-even analysis– a means of identifying the value of a particular project variable that causes the project to exactly break even. • 3. Scenario analysis-- means of comparing a “base –case” or expected project measurement (such as NPW) to one or more additional scenarios, such as best and worst case, to identify the extreme and most likely project outcomes.

  22. Sensitivity, break-even, and scenario analyses are reasonably simple to apply, but also somewhat simplistic and imprecise in cases where we must deal with multifaceted project uncertainty. Probability concepts allow us to further refine the analysis of project risk by assigning numerical values to the likelihood that project variables will have certain values. The end goal of a probabilistic analysis of project variables is to produce a NPW distribution.

  23. From the NPW distribution, we can extract such useful information as the expected NPW value, the extent to which other NPW values vary from , or are clustered around, the expected value, (variance), and the best- and worst-case NPWs. • All other things being equal, if the expected returns are approximately the same, choose the portfolio with the lowest expected risk (variance).

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