1. 14-1 Chapter 14 Risk and Managerial Options in Capital Budgeting © 2001 Prentice-Hall, Inc. Fundamentals of Financial Management, 11/e Created by: Gregory A. Kuhlemeyer, Ph.D. Carroll College, Waukesha, WI

2. 14-2 Risk and Managerial Options in Capital Budgeting u The Problem of Project Risk u Total Project Risk u Contribution to Total Firm Risk: Firm-Portfolio Approach u Managerial Options u The Problem of Project Risk u Total Project Risk u Contribution to Total Firm Risk: Firm-Portfolio Approach u Managerial Options

3. 14-3 An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A ProbabilityCash Flow State Probability Cash Flow Deep Recession.05 $ -3,000 Mild Recession.25 1,000 Normal.40 5,000 Minor Boom.25 9,000 Major Boom.05 13,000 ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A ProbabilityCash Flow State Probability Cash Flow Deep Recession.05 $ -3,000 Mild Recession.25 1,000 Normal.40 5,000 Minor Boom.25 9,000 Major Boom.05 13,000

4. 14-4 Probability Distribution of Year 1 Cash Flows.40.05.25 Probability -3,000 1,000 5,000 9,000 13,000 Cash Flow ($) Proposal A

5. 14-5 CF 1 P 1 CF 1 )(P 1 ) CF 1 P 1 (CF 1 )(P 1 ) $ -3,000.05 $ -150 1,000.25 250 5,000.40 2,000 9,000.25 2,250 13,000.05 650  1.00 CF 1 $5,000  =1.00 CF 1 =$5,000 CF 1 P 1 CF 1 )(P 1 ) CF 1 P 1 (CF 1 )(P 1 ) $ -3,000.05 $ -150 1,000.25 250 5,000.40 2,000 9,000.25 2,250 13,000.05 650  1.00 CF 1 $5,000  =1.00 CF 1 =$5,000 Expected Value of Year 1 Cash Flows (Proposal A)

6. 14-6 CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) 2 (.05) $ -150 ( -3,000 - 5,000) 2 (.05) 2 (.25) 250 ( 1,000 - 5,000) 2 (.25) 2 (.40) 2,000 ( 5,000 - 5,000) 2 (.40) 2 (.25) 2,250 ( 9,000 - 5,000) 2 (.25) 2 (.05) 650 (13,000 - 5,000) 2 (.05) $5,000 CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) 2 (.05) $ -150 ( -3,000 - 5,000) 2 (.05) 2 (.25) 250 ( 1,000 - 5,000) 2 (.25) 2 (.40) 2,000 ( 5,000 - 5,000) 2 (.40) 2 (.25) 2,250 ( 9,000 - 5,000) 2 (.25) 2 (.05) 650 (13,000 - 5,000) 2 (.05) $5,000 Variance of Year 1 Cash Flows (Proposal A)

7. 14-7 Variance of Year 1 Cash Flows (Proposal A) CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 *(P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 *(P 1 ) $ -150 3,200,000 250 4,000,000 2,000 0 2,250 4,000,000 650 3,200,000 $5,000 14,400,000 CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 *(P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 *(P 1 ) $ -150 3,200,000 250 4,000,000 2,000 0 2,250 4,000,000 650 3,200,000 $5,000 14,400,000

8. 14-8 Summary of Proposal A standard deviation $3,795 The standard deviation = SQRT (14,400,000) = $3,795 expected cash flow $5,000 The expected cash flow = $5,000

9. 14-9 An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B ProbabilityCash Flow State Probability Cash Flow Deep Recession.05 $ -1,000 Mild Recession.25 2,000 Normal.40 5,000 Minor Boom.25 8,000 Major Boom.05 11,000 ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B ProbabilityCash Flow State Probability Cash Flow Deep Recession.05 $ -1,000 Mild Recession.25 2,000 Normal.40 5,000 Minor Boom.25 8,000 Major Boom.05 11,000

10. 14-10 Probability Distribution of Year 1 Cash Flows.40.05.25 Probability -3,000 1,000 5,000 9,000 13,000 Cash Flow ($) Proposal B

11. 14-11 Expected Value of Year 1 Cash Flows (Proposal B) CF 1 P 1 CF 1 )(P 1 ) CF 1 P 1 (CF 1 )(P 1 ) $ -1,000.05 $ -50 2,000.25 500 5,000.40 2,000 8,000.25 2,000 11,000.05 550  1.00 CF 1 $5,000  =1.00 CF 1 =$5,000 CF 1 P 1 CF 1 )(P 1 ) CF 1 P 1 (CF 1 )(P 1 ) $ -1,000.05 $ -50 2,000.25 500 5,000.40 2,000 8,000.25 2,000 11,000.05 550  1.00 CF 1 $5,000  =1.00 CF 1 =$5,000

12. 14-12 CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) 2 (.05) $ -50 ( -1,000 - 5,000) 2 (.05) 2 (.25) 500 ( 2,000 - 5,000) 2 (.25) 2 (.40) 2,000 ( 5,000 - 5,000) 2 (.40) 2 (.25) 2,000 ( 8,000 - 5,000) 2 (.25) 2 (.05) 550 (11,000 - 5,000) 2 (.05) $5,000 CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) 2 (.05) $ -50 ( -1,000 - 5,000) 2 (.05) 2 (.25) 500 ( 2,000 - 5,000) 2 (.25) 2 (.40) 2,000 ( 5,000 - 5,000) 2 (.40) 2 (.25) 2,000 ( 8,000 - 5,000) 2 (.25) 2 (.05) 550 (11,000 - 5,000) 2 (.05) $5,000 Variance of Year 1 Cash Flows (Proposal B)

13. 14-13 Variance of Year 1 Cash Flows (Proposal B) CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ -50 1,800,000 500 2,250,000 2,000 0 2,000 2,250,000 550 1,800,000 $5,000 8,100,000 CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) (CF 1 )(P 1 ) (CF 1 - CF 1 ) 2 (P 1 ) $ -50 1,800,000 500 2,250,000 2,000 0 2,000 2,250,000 550 1,800,000 $5,000 8,100,000

14. 14-14 Summary of Proposal B Proposal B < Proposal A. ( $2,846 < $3,795 ) The standard deviation of Proposal B < Proposal A. ( $2,846 < $3,795 ) standard deviation $2,846 The standard deviation = SQRT (8,100,000)= $2,846 expected cash flow $5,000 The expected cash flow = $5,000

15. 14-15 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

16. 14-16 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.

17. 14-17 Probability Tree Approach initial cost $900 Year 1 Basket Wonders is examining a project that will have an initial cost today of $900. Uncertainty surrounding the first year cash flows creates three possible cash-flow scenarios in Year 1. -$900

18. 14-18 Probability Tree Approach $1,200 Node 1: 20% chance of a $1,200 cash-flow. $450 Node 2: 60% chance of a $450 cash-flow. -$600 Node 3: 20% chance of a -$600 cash-flow. -$900 $1,200 (.20) $1,200 -$600 (.20) -$600 $450 (.60) $450 Year 1 1 2 3

19. 14-19 Probability Tree Approach Year 2 branch Each node in Year 2 represents a branch of our probability tree. conditional probabilities The probabilities are said to be conditional probabilities. -$900.20$1,200 (.20) $1,200.20-$600 (.20) -$600 60$450 (.60) $450 Year 1 1 2 3 $1,200 (.60) $1,200 $ 900 (.30) $ 900 $2,200 (.10) $2,200 $ 900 (.35) $ 900 $ 600 (.40) $ 600 $ 300 (.25) $ 300 $ 500 (.10) $ 500 -$ 100 (.50) -$ 100 -$ 700 (.40) -$ 700 Year 2

20. 14-20 Joint Probabilities [P(1,2)].02 Branch 1.12 Branch 2.06 Branch 3.21 Branch 4.24 Branch 5.15 Branch 6.02 Branch 7.10 Branch 8.08 Branch 9 -$900.20$1,200 (.20) $1,200.20-$600 (.20) -$600 60$450 (.60) $450 Year 1 1 2 3 $1,200 (.60) $1,200 $ 900 (.30) $ 900 $2,200 (.10) $2,200 $ 900 (.35) $ 900 $ 600 (.40) $ 600 $ 300 (.25) $ 300 $ 500 (.10) $ 500 -$ 100 (.50) -$ 100 -$ 700 (.40) -$ 700 Year 2

21. 14-21 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 i P i NPV =  (NPV i )(P i ) NPV i NPV i = CF 1 R f 1 (1 + R f ) 1 R f 2 (1 + R f ) 2 CF 2 ICO - ICO + i = 1 z

22. 14-22 NPV for Each Cash-Flow Stream at 5% Risk-Free Rate $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79 -$ 199.32 -$ 1,017.91 -$ 1,562.13 -$ 2,106.35 -$900.20$1,200 (.20) $1,200.20-$600 (.20) -$600 60$450 (.60) $450 Year 1 1 2 3 $1,200 (.60) $1,200 $ 900 (.30) $ 900 $2,200 (.10) $2,200 $ 900 (.35) $ 900 $ 600 (.40) $ 600 $ 300 (.25) $ 300 $ 500 (.10) $ 500 -$ 100 (.50) -$ 100 -$ 700 (.40) -$ 700 Year 2

23. 14-23 NPV on the Calculator Remember, we can use the cash flow registry to solve these NPV problems quickly and accurately!

24. 14-24 Actual NPV Solution Using Your Financial Calculator Solving for Branch #3: Step 1:PressCF key Step 2:Press2 nd CLR Workkeys Step 3: For CF0 Press -900 Enter  keys Step 4: For C01 Press 1200 Enter  keys Step 5: For F01 Press 1 Enter  keys Step 6: For C02 Press 900 Enter  keys Step 7: For F02 Press 1 Enter  keys

25. 14-25 Actual NPV Solution Using Your Financial Calculator Solving for Branch #3: Step 8: Press   keys Step 9: PressNPV key Step 10: For I=, Enter 5Enter  keys Step 11: PressCPT key Result:Net Present Value = $1,059.18 You would complete this for EACH branch!

26. 14-26 Calculating the Expected Net Present Value (NPV) NPV i Branch NPV i Branch 1 $ 2,238.32 Branch 2 $ 1,331.29 Branch 3 $ 1,059.18 Branch 4 $ 344.90 Branch 5 $ 72.79 Branch 6 -$ 199.32 Branch 7 -$ 1,017.91 Branch 8-$ 1,562.13 Branch 9 -$ 2,106.35 P(1,2) NPV i P(1,2) P(1,2) NPV i * P(1,2).02 $ 44.77.12 $159.75.06 $ 63.55.21 $ 72.43.24 $ 17.47.15 -$ 29.90.02 -$ 20.36.10 -$156.21.08 -$168.51 Expected Net Present Value -$ 17.01 Expected Net Present Value = -$ 17.01

27. 14-27 Calculating the Variance of the Net Present Value NPV i NPV i $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79 -$ 199.32 -$ 1,017.91 -$ 1,562.13 -$ 2,106.35 P(1,2) (NPV i NPVP(1,2) P(1,2) (NPV i - NPV ) 2 [P(1,2)].02 $ 101,730.27.12 $ 218,149.55.06 $ 69,491.09.21 $ 27,505.56.24 $ 1,935.37.15 $ 4,985.54.02 $ 20,036.02.10 $ 238,739.58.08 $ 349,227.33 Variance $1,031,800.31 Variance = $1,031,800.31

28. 14-28 Summary of the Decision Tree Analysis standard deviation $1,015.78 The standard deviation = SQRT ($1,031,800) = $1,015.78 expected NPV -$ 17.01 The expected NPV = -$ 17.01

29. 14-29 Simulation Approach An approach that allows us to test the possible results of an investment proposal before it is accepted. Testing is based on a model coupled with probabilistic information.

30. 14-30 Simulation Approach Market analysis u Market analysis u Market size, selling price, market growth rate, and market share Investment cost analysis u Investment cost analysis u Investment required, useful life of facilities, and residual value Operating and fixed costs u Operating and fixed costs u Operating costs and fixed costs Factors we might consider in a model:

31. 14-31 Simulation Approach Each variable is assigned an appropriate probability distribution. The distribution for the selling price of baskets created by Basket Wonders might look like: $20 $25 $30 $35 $40 $45 $50.02.08.22.36.22.08.02 The resulting proposal value is dependent on the distribution and interaction of EVERY variable listed on slide 14-30.

32. 14-32 Simulation Approach internal rate of return distribution Each proposal will generate an internal rate of return. The process of generating many, many simulations results in a large set of internal rates of return. The distribution might look like the following: INTERNAL RATE OF RETURN (%) PROBABILITY OF OCCURRENCE

33. 14-33 diversification Combining projects in this manner reduces the firm risk due to diversification. Contribution to Total Firm Risk: Firm-Portfolio Approach CASH FLOW TIME Proposal A Proposal B Combination of Proposals A and B

34. 14-34 NPV P =  ( NPV j ) NPV P is the expected portfolio NPV, NPV j is the expected NPV of the jth NPV that the firm undertakes, m is the total number of projects in the firm portfolio. NPV P =  ( NPV j ) NPV P is the expected portfolio NPV, NPV j is the expected NPV of the jth NPV that the firm undertakes, m is the total number of projects in the firm portfolio. Determining the Expected NPV for a Portfolio of Projects m j=1

35. 14-35  P  P =   jk  jk is the covariance between possible NPVs for projects j and k   r  jk =  j  k r  jk.  j is the standard deviation of project j,  k is the standard deviation of project k, r jk is the correlation coefficient between projects j and k.  P  P =   jk  jk is the covariance between possible NPVs for projects j and k   r  jk =  j  k r  jk.  j is the standard deviation of project j,  k is the standard deviation of project k, r jk is the correlation coefficient between projects j and k. Determining Portfolio Standard Deviation m j=1 m k=1

36. 14-36 E: Existing Projects 8 Combinations EEE EE EE EE + 1 E + 1 + 2 E + 2 E + 1 + 3 E + 3 E + 2 + 3 E E + 1 + 2 + 3 ABC dominating A, B, and C are dominating combinations from the eight possible. Combinations of Risky Investments A B C E Standard Deviation Expected Value of NPV

37. 14-37 Managerial (Real) Options Management flexibility to make future decisions that affect a project’s expected cash flows, life, or future acceptance. Project Worth = NPV + Option(s) Value

38. 14-38 Managerial (Real) Options Expand (or contract) u Allows the firm to expand (contract) production if conditions become favorable (unfavorable).Abandon u Allows the project to be terminated early.Postpone u Allows the firm to delay undertaking a project (reduces uncertainty via new information).

39. 14-39 Previous Example with Project Abandonment $200 Assume that this project can be abandoned at the end of the first year for $200. project worth What is the project worth? -$900.20$1,200 (.20) $1,200.20-$600 (.20) -$600 60$450 (.60) $450 Year 1 1 2 3 $1,200 (.60) $1,200 $ 900 (.30) $ 900 $2,200 (.10) $2,200 $ 900 (.35) $ 900 $ 600 (.40) $ 600 $ 300 (.25) $ 300 $ 500 (.10) $ 500 -$ 100 (.50) -$ 100 -$ 700 (.40) -$ 700 Year 2

40. 14-40 Project Abandonment Node 3 Node 3: 500 -100 -700 (500/1.05)(.1)+ (-100/1.05)(.5)+ (-700/1.05)(.4)= ($476.19)(.1)+ -($ 95.24)(.5)+ -($666.67)(.4)=-($266.67) -$900.20$1,200 (.20) $1,200.20-$600 (.20) -$600 60$450 (.60) $450 Year 1 1 2 3 $1,200 (.60) $1,200 $ 900 (.30) $ 900 $2,200 (.10) $2,200 $ 900 (.35) $ 900 $ 600 (.40) $ 600 $ 300 (.25) $ 300 $ 500 (.10) $ 500 -$ 100 (.50) -$ 100 -$ 700 (.40) -$ 700 Year 2

41. 14-41 Project Abandonment -$900.20$1,200 (.20) $1,200.20-$600 (.20) -$600 60$450 (.60) $450 Year 1 1 2 3 $1,200 (.60) $1,200 $ 900 (.30) $ 900 $2,200 (.10) $2,200 $ 900 (.35) $ 900 $ 600 (.40) $ 600 $ 300 (.25) $ 300 $ 500 (.10) $ 500 -$ 100 (.50) -$ 100 -$ 700 (.40) -$ 700 Year 2 Year 1 $200 The optimal decision at the end of Year 1 is to abandon the project for $200. $200 $200 >-($266.67) “new” What is the “new” project value?

42. 14-42 Project Abandonment $ 2,238.32 $ 1,331.29 $ 1,059.18 $ 344.90 $ 72.79 -$ 199.32 -$ 1,280.95 -$900.20$1,200 (.20) $1,200.20-$400* (.20) -$400* 60$450 (.60) $450 Year 1 1 2 3 $1,200 (.60) $1,200 $ 900 (.30) $ 900 $2,200 (.10) $2,200 $ 900 (.35) $ 900 $ 600 (.40) $ 600 $ 300 (.25) $ 300 $ 0 (1.0) $ 0 Year 2 *-$600 + $200 abandonment

43. 14-43 Summary of the Addition of the Abandonment Option * For “True” Project considering abandonment option standard deviation* $857.56 The standard deviation*= SQRT (740,326) = $857.56 expected NPV* $ 71.88 The expected NPV* = $ 71.88 NPV* Abandonment Option NPV* = Original NPV + Abandonment Option Thus, $71.88 Option Thus, $71.88 = -$17.01 + Option Abandonment Option $ 88.89 Abandonment Option = $ 88.89