1. Summary of Previous Lecture Understand why ranking project proposals on the basis of IRR, NPV, and PI methods “may” lead to conflicts in ranking. Describe the situations where ranking projects may be necessary and justify when to use either IRR, NPV, or PI rankings. Understand how “sensitivity analysis” allows us to challenge the single-point input estimates used in traditional capital budgeting analysis. Explain the role and process of project monitoring, including “progress reviews” and “post-completion audits.”

2. Chapter 14 (I) Risk and Managerial (Real) Options in Capital Budgeting

3. Learning Outcomes After studying Chapter 14 you should be able to: Define the "riskiness" of a capital investment project. Understand how cash-flow riskiness for a particular period is measured, including the concepts of expected value, standard deviation, and coefficient of variation. Describe methods for assessing total project risk, including a probability approach and a simulation approach. Judge projects with respect to their contribution to total firm risk (a firm-portfolio approach). Understand how the presence of managerial (real) options enhances the worth of an investment project. List, discuss, and value different types of managerial (real) options.

4. Risk and Managerial (Real) Options in Capital Budgeting The Problem of Project Risk Total Project Risk Contribution to Total Firm Risk: Firm- Portfolio Approach Managerial (Real) Options The Problem of Project Risk Total Project Risk Contribution to Total Firm Risk: Firm- Portfolio Approach Managerial (Real) Options

5. Expectation and Measurement of Dispersion Probability distribution can be explained in two parameters of distribution; (1) The expected Value, (2) the standard deviation. Expected value is the weighted average of possible outcomes, with weights being probabilities of occurrence. Standard deviation is the statistical measurement of the variability of a distribution around its mean.

6. Coefficient of Variation (CV) SD sometime can be misleading in comparing the risk or uncertainty. CV is the ratio of the SD of a distribution to the mean of that distribution. It is a measure of relative risk. Smaller the CV, the lesser the risk. A project with lower CV is better.

7. Discrete and Continuous Distribution In the discrete case, one can easily assign a probability to each possible outcome: when throwing a die, each of the six values 1 to 6 has the probability 1/6. a continuous random variable is the one which can take a continuous range of values — as opposed to a discrete distribution, where the set of possible values for the random variable is at most countable. While for a discrete distribution an event with probability zero is impossible (e.g. rolling 3½ on a standard die is impossible, and has probability zero), this is not so in the case of a continuous random variable. For example, if one measures the width of an oak leaf, the result of 3½ cm is possible http://en.wikipedia.org/wiki/Probability_distribution

8. An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A State Probability Cash Flow Deep Recession.10 $ 3,000 Mild Recession.20 3,500 Normal.40 4,000 Minor Boom.20 4,500 Major Boom.10 5,000 ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A State Probability Cash Flow Deep Recession.10 $ 3,000 Mild Recession.20 3,500 Normal.40 4,000 Minor Boom.20 4,500 Major Boom.10 5,000

9. Probability Distribution of Year 1 Cash Flows.1 Probability 3,000 3,500 4,000 4,500 5,000 Cash Flow ($) Proposal A.2.3.4

10. Expected Value of Year 1 Cash Flows (Proposal A) CF1P1(CF1)(P1) 30000.1300 35000.2700 40000.41600 45000.2900 50000.1500 Σ = 14000 CF =

11. (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 300 (3,000 - 4,000) 2 (.01) 700 (3,500 - 4,000) 2 (.20) 1,600 (4,000 - 4,000) 2 (.40) 9,000 (4,500 - 4,000) 2 (.20) 500 (5,000 - 4,000) 2 (.01) $4,000 (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 300 (3,000 - 4,000) 2 (.01) 700 (3,500 - 4,000) 2 (.20) 1,600 (4,000 - 4,000) 2 (.40) 9,000 (4,500 - 4,000) 2 (.20) 500 (5,000 - 4,000) 2 (.01) $4,000 Variance of Year 1 Cash Flows (Proposal A)

12. (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 300 100000 700 50,000 1,600 0 9,000 50,000 500 100,000 $4,000 300,000 (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 300 100000 700 50,000 1,600 0 9,000 50,000 500 100,000 $4,000 300,000 Variance of Year 1 Cash Flows (Proposal A)

13. Summary of Proposal A The standard deviation = SQRT (300,000) = $548 The expected cash flow = $4,000 Coefficient of Variation (CV) = $548 / $4,000 = 0.14 CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.

14. An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B State Probability Cash Flow Deep Recession.01 $ 2,000 Mild Recession.20 3,000 Normal.40 4,000 Minor Boom.20 5,000 Major Boom.01 6,000 ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B State Probability Cash Flow Deep Recession.01 $ 2,000 Mild Recession.20 3,000 Normal.40 4,000 Minor Boom.20 5,000 Major Boom.01 6,000

15. Probability Distribution of Year 1 Cash Flows.1 Probability 2,000 3,000 4,000 5,000 6,000 Cash Flow ($) Proposal B.2.3.4

16. Expected Value of Year 1 Cash Flows (Proposal B) CF1P1(CF1)(P1) 20000.1 200 30000.2 600 40000.41600 50000.21000 60000.1 600 Σ = 14000 CF1 =

17. (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 200 (2,000 - 4,000) 2 (.10) 600 (3,000 - 4,000) 2 (.20) 1,600 (4,000 - 4,000) 2 (.40) 1,000 (5,000 - 4,000) 2 (.20) 600 (6,000 - 4,000) 2 (.10) $4,000 (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 200 (2,000 - 4,000) 2 (.10) 600 (3,000 - 4,000) 2 (.20) 1,600 (4,000 - 4,000) 2 (.40) 1,000 (5,000 - 4,000) 2 (.20) 600 (6,000 - 4,000) 2 (.10) $4,000 Variance of Year 1 Cash Flows (Proposal B)

18. (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 200 400,000 600 200,000 1,600 0 1,000 200,000 600 400,000 $4,000 1,200,000 (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ 200 400,000 600 200,000 1,600 0 1,000 200,000 600 400,000 $4,000 1,200,000 Variance of Year 1 Cash Flows (Proposal B)

19. Summary of Proposal B The standard deviation of A < B ($548< $1,095), so “A” is less risky than “B”. The coefficient of variation of A < B (0.14<0.27), so “A” has less relative risk than “B”. The standard deviation = SQRT (1,200,000) = $1,095 The expected cash flow = $4,000 Coefficient of Variation (CV) = $1,095 / $4,000 = 0.27

20. Total Project Risk Projects have risk that may change from period to period. Projects are more likely to have continuous, rather than discrete distributions. Cash Flow ($) 123 1 2 3 Year

21. Probability Tree Approach A graphic or tabular approach for organizing the possible cash-flow streams generated by an investment. The presentation resembles the branches of a tree. Each complete branch represents one possible cash-flow sequence.

22. Probability Tree Approach initial cost $240 Year 1 A project that has an initial cost today of $240. Uncertainty surrounding the first year cash flows creates three possible cash-flow scenarios in Year 1.

23. Probability Tree Approach $500 Node 1: 25% chance of a $500 cash-flow. $200 Node 2: 50% chance of a $200 cash-flow. -$100 Node 3: 25% chance of a -$100 cash-flow. -$240 $500 (.25) $500 -$100 (.25) -$100 $200 (.50) $200 Year 1 1 2 3

24. Probability Tree Approach Each node in Year 2 represents a branch of our probability tree. The probabilities are said to be conditional probabilities. -$240.25$500 (.25) $500.25-$100 (.25) -$100 50$200 (.50) $200 Year 1 1 2 3 $500 (.40) $500 $200 (.20) $200 $800 (.40) $800 $500 (.20) $500 $200 (.60) $200 -$100 (.20) -$100 $200 (.20) $200 -$100 (.40) -$100 -$400 (.40) -$400 Year 2

25. Joint Probabilities [P(1,2)].01 Branch 1.01 Branch 2.05 Branch 3.10 Branch 4.30 Branch 5.10 Branch 6.05 Branch 7.10 Branch 8.10 Branch 9 -$240.25$500 (.25) $500.25-$100 (.25) -$100 50$200 (.50) $200 Year 1 1 2 3 $500 (.40) $500 $200 (.20) $200 $800 (.40) $800 $500 (.20) $500 $200 (.60) $200 -$100 (.20) -$100 $200 (.20) $200 -$100 (.40) -$100 -$400 (.40) -$400 Year 2

26. Project NPV Based on Probability Tree Usage risk-free The probability tree accounts for the distribution of cash flows. Therefore, discount all cash flows at only the risk-free rate of return. NPV for branch i The NPV for branch i of the probability tree for two years of cash flows is NPV =  (NPV i )(P i ) NPV i = CF 1 (1 + R f ) 1 (1 + R f ) 2 CF 2 - ICO + i = 1 z

27. NPV for Each Cash-Flow Stream at 8% Risk-Free Rate $ 909 $ 652 $ 394 $ 374 $ 117 -$ 141 -$ 161 -$ 418 -$ 676 -$240.25$500 (.25) $500.25-$100 (.25) -$100 50$200 (.50) $200 Year 1 1 2 3 $500 (.40) $500 $200 (.20) $200 $800 (.40) $800 $500 (.20) $500 $200 (.60) $200 -$100 (.20) -$100 $200 (.20) $200 -$100 (.40) -$100 -$400 (.40) -$400 Year 2

28. Calculating the Expected Net Present Value (NPV) Branch NPV i Branch 1 $ 909 Branch 2 $ 652 Branch 3 $ 394 Branch 4 $ 374 Branch 5 $ 117 Branch 6 -$ 141 Branch 7 -$ 161 Branch 8-$ 418 Branch 9 -$ 676 P(1,2) NPV i x P(1,2).10 $ 91.10 $ 65.05 $ 20.10 $ 37.30 $ 35.10 -$ 14.05 -$ 08.10 -$ 42.10 -$ 68 Weighted Average = $ 116=NPV

29. Calculating the Variance of the Net Present Value P(1,2) (NPV i - NPV ) 2 [P(1,2)].10 $ 62,885.10 $ 28,730.05 $ 3,864.10 $ 6,656.30 $ 0.30.10 $ 6,605.05 $ 3,836.10 $ 28,516.10 $ 62,726 Variance = $203,819 NPV i $ 909 $ 652 $ 394 $ 374 $ 117 -$ 141 -$ 161 -$ 418 -$ 676

30. Summary of the Decision Tree Analysis The standard deviation = SQRT($20,3819) = $451 The expected NPV= $ 116

31. Summary We covered following topics in today’s lecture; Define the "riskiness" of a capital investment project. Understand how cash-flow riskiness for a particular period is measured, including the concepts of expected value, standard deviation, and coefficient of variation. Describe methods for assessing total project risk, including a probability approach.