Session 4, Monday, April 3 rd (4:00-5:00)

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Session 4, Monday, April 3 rd (4:00-5:00) Applied Statistical Tools: Risk and Capital

3 Main Point of Risk Adjustments By specifying a range of possible values for an investment s cash flows, and the associated probabilities, the user can better assess expected return and risk v Association for Financial Professionals. All rights reserved. Session 12-3

5 NPV Scenario Analysis Assume that your group has identified three potential NPV scenarios for a possible investment. Best Case NPV = $842, Base Case NPV =$409, Worst Case NPV = -$315, If each scenario is equally likely, what is the expected value of the investment s NPV? v Association for Financial Professionals. All rights reserved. Session 12-5

6 Probability Adjusted NPV Economic Scenarios Probability of Economic Scenario NPV Associated w/ Economic Scenario Best Case $842, Base Case $409, Worst Case $315,099 v Association for Financial Professionals. All rights reserved. Session 12-6

7 Calculating Expected Value of the NPV Expected Value for NPV = (0.333*$842,888.05) +(0.333*$409,090.91)+(0.333*-$315,099) = $311, Interpretation: This would be the average NPV earned if replication was possible. Expected values are great, but only one 7of the three possibilities will be realized. v Association for Financial Professionals. All rights reserved. Session 12-7

9 Probability-Adjusted NPV, pg. 139 The setup: An investment will produce a 5-year annuity cash flow stream of either -$20M, $80M, or $140M. Since the upfront cost and discount rate are assumed to be know, the question becomes, what is the expected value/probability adjusted cash flow stream? Expected value/probability adjusted cash flow stream= (0.30*-$20)+(0.5*80)+(0.2*140)= $62M v Association for Financial Professionals. All rights reserved. Session 12-9

11 What About Risk? In the context of the previous problems, we would find the probability adjusted standard deviation helpful This topic is not discussed here, but is described in Chapter 14, page IIC-90. Note error in text v Association for Financial Professionals. All rights reserved. Session 12-11

12 Calculating a Probability Adjusted Standard Deviation Prob. Adjusted Standard Deviation of X = Σ Prob i X i Exp. Value of X Where Prob i = the probability of a given scenario for the variable X X i = the specific value of X for each scenario 12 v Association for Financial Professionals. All rights reserved. Session 12-12

13 Application: Problem from Earlier Example Prob. Adjusted Standard Deviation of the NPV = [{0.333*(842, ,981) 2 } + {0.333*(409, ,981) 2 } + {0.333*(-315, ,981) 2 } ] 0.5 Standard Deviation of the NPV = $477, Interpretation? The typical deviation from the expected value of the NPV is $477, A higher deviation implies more variability/risk 13 v Association for Financial Professionals. All rights reserved. Session 12-13

15 CV = $477,437 $311,981 = Assessing Relative Risk Interpretation: This investment has 1.53 units of risk for each 1 unit of return. Or, the standard deviation is 1.53 times the return. Why is the CV needed? When mutually exclusive investments are compared. Increased variability in CFs may lead to a larger NPV. So if we choose just based on the probability adjusted NPV, then we are ignoring the variability in the CFs. The CV takes both return and risk into account. v Association for Financial Professionals. All rights reserved. Session 12-15

16 Using the CV Suppose that the firm can make an alternative investment (Project X) that has a CV of 2. Which investment has more relative risk? Project X has more relative risk as a CV of 2 exceeds a CV of 1.53 Please note: CV is not covered in the Learning System. Still, it may be important 16 v Association for Financial Professionals. All rights reserved. Session 12-16

17 Flexible Options OPTION A Invest OPTION B Not invest Continue Abandon Expand Not expand Contract Not contract Continue Delay v Association for Financial Professionals. All rights reserved. Session 12-17

19 The Option to Continue or Abandon See Exhibit 12.3, page 143 Building on the previous example, suppose that if the Worst Case scenario is apparent at the end of Year 1, we can abandon the investment and sell PPE for a net cash flow of $50M at the end of year 2. Now, the Worst Case CF stream would be -$20M, $50M, $0, $0, $0 and the Best Case remains unchanged v Association for Financial Professionals. All rights reserved. Session 12-19

20 The Option to Continue or Abandon NPV Worst Case = $200M + $20M $50M = $ NPV Best Case = $ NPV Expected Case = 0.5 $ $ = $11.54M 20 v Association for Financial Professionals. All rights reserved. Session 12-20

21 The Value of the Abandonment Option Moving from Exhibit 12.2 to Exhibit 12.3, note that the PV of the Worst Case Scenario changes from -$59.81M to $18.06M Where does the difference come from? The abandonment option Note that 50%*(18.06-(-59.81)) = $38.94M This is identical to the difference in the Expected Value of the NPV (with and without Abandonment) -$11.54-(-$50.47) = $38.94M v Association for Financial Professionals. All rights reserved. Session 12-21

Session 2, Monday, April 3 rd (11:30-12:30)

Session 2, Monday, April 3 rd (11:30-12:30) Capital Budgeting Continued and the Cost of Capital v2.0 2014 Association for Financial Professionals. All rights reserved. Session 3-1 Chapters Covered Internal