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

Chapter 14 Risk and Managerial (Real) Options in Capital Budgeting. Learning Objectives. After studying Chapter 14, you should be able to: Define the "riskiness" of a capital investment project.

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

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

  2. Learning Objectives 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.

  3. Topics • The Problem of Project Risk • Total Project Risk • Contribution to Total Firm Risk: Firm-Portfolio Approach • Managerial (Real) Options

  4. An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A StateProbabilityCash Flow Deep Recession .10$ 3,000 Mild Recession .203,500 Normal .404,000 Minor Boom .204,500 Major Boom .10 5,000

  5. Probability Distribution of Year 1 Cash Flows (Proposal A) .40 Probability .20 .10 3,000 4,000 5,000 Cash Flow ($)

  6. Expected Value of Year 1 Cash Flows (Proposal A) CF1P1(CF1)(P1) $ -3,000.10$ 300 1,000.20700 5,000.401,600 9,000.20900 13,000.10500 S=1.00CF1=$4,000

  7. Variance of Year 1 Cash Flows (Proposal A) (CF1)(P1)(CF1 - CF1)2(P1) $ 300( 3,000 - 4,000)2 (.10)= 100,000 700 ( 3,500 - 4,000)2(.20)= 50,000 1,600 ( 4,000 - 4,000)2(.40)= 0 900 ( 4,500 - 4,000)2(.20)= 50,000 500 ( 5,000 - 4,000)2 (.10)= 100,000 $4,000 300,000

  8. Summary of Proposal A Standard deviation = SQRT (300,000)=$548 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.

  9. An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B StateProbabilityCash Flow Deep Recession .10$ 2,000 Mild Recession .203,000 Normal .404,000 Minor Boom .205,000 Major Boom .106,000

  10. Probability Distribution of Year 1 Cash Flows (Proposal B) .40 .20 Probability .10 2,000 3,000 4,000 5,000 6,000 Cash Flow ($)

  11. Expected Value of Year 1 Cash Flows (Proposal B) CF1P1 (CF1)(P1) $ 2,000.10 $ 200 3,000.20600 4,000.401,600 5,000.201,000 6,000.10600 S=1.00CF1=$4,000

  12. Variance of Year 1 Cash Flows (Proposal B) (CF1)(P1)(CF1 - CF1)2(P1) $ 200( 2,000 - 4,000)2 (.10) = 400,000 600( 3,000 - 4,000)2(.20) = 200,000 1,600( 4,000 - 4,000)2(.40) = 0 1,000( 5,000 - 4,000)2(.20) = 200,000 600( 6,000- 4,000)2 (.10) = 400,000 $4,000 1,200,000

  13. Summary of Proposal B Standard deviation = SQRT (1,200,000) = $1,095 Expected cash flow = $4,000 Coefficient of Variation (CV) = $1,095 / $4,000 = 0.27

  14. Comparison of Proposal A & B The standard deviation of B > A($1,095 > $548), so “B” is morerisky than “A”. The coefficient of variation of B > A (0.27 < 0.14), so “B” has higherrelative risk than “A”.

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

  16. 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. Probability Tree Approach

  17. Basket Wonders is examining a project that will have an initial cost today of $240. Uncertainty surrounding the first year cash flows creates three possible cash-flow scenarios in Year 1. Probability Tree Approach -$240

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

  19. Each node in Year 2 represents a branch of our probability tree. The probabilities are said to be conditional probabilities. Probability Tree Approach (.40) $800 (.25) $500 (.40)$500 1 (.20) $200 (.20)$ 500 (.50) $200 (.60)$ 200 -$240 2 (.20) -$ 100 (.20)$ 200 (.25) -$100 (.40)-$ 100 3 (.40)-$ 400 Year 1 Year 2

  20. .10 Branch 1 .10 Branch 2 .05 Branch 3 .10 Branch 4 .30 Branch 5 .10 Branch 6 .05 Branch 7 .10 Branch 8 .10 Branch 9 Joint Probabilities [P(1,2)] (.40) $800 (.25) $500 (.40) $500 1 (.20) $200 (.20) $500 (.50) $200 (.60) $400 -$240 2 (.20) -$100 (.20) $200 (.25) -$100 (.40)-$100 3 (.40)-$400 Year 1 Year 2

  21. The probability tree accounts for the distribution of cash flows. Therefore, discount all cash flows at only the risk-free rate of return. The NPV for branch iof the probability tree for two years of cash flows is Project NPV Based on Probability Tree z NPV = S (NPVi)(Pi) i = 1 CF1 CF2 NPVi = + (1 + Rf)1 (1 + Rf )2 - ICO

  22. $ 909 $ 652 $ 394 $ 374 $ 117 -$ 141 -$ 161 -$ 418 -$ 676 NPV for Each Cash-Flow Stream at 8% Risk-Free Rate (.40) $ 800 (.25) $500 (.40) $ 500 1 (.20) $ 200 (.20) $ 500 (.50) $200 (.60) $ 200 -$240 2 (.20) -$ 100 (.20) $ 200 (.25) -$100 (.40)-$ 100 3 (.40)-$ 400 Year 1 Year 2

  23. BranchNPVi 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) NPVi* P(1,2) .10 $ 91 .10 $ 65 .05 $ 20 .10 $ 37 .30 $ 35 .10 -$ 14 .05 -$ 8 .10 -$ 42 .10 -$ 68 Calculating the Expected Net Present Value (NPV) Expected Net Present Value = $116

  24. NPVi $ 909 $ 652 $ 394 $ 374 $ 117 -$ 141 -$ 161 -$ 418 -$ 676 P(1,2) (NPVi- NPV )2[P(1,2)] .10 $ 62,884.90 .10 $ 28,729.60 .05 $ 3,864.20 .10 $ 6,656.40 .30 $ 0.30 .10 $ 6,604.90 .05 $ 3,836.45 .10 $ 28,515.60 .10 $ 62,726.40 Calculating the Variance of the Net Present Value Variance = $203,818.75

  25. Calculating the Variance of the Net Present Value

  26. Summary of the Decision Tree Analysis Standard deviation = SQRT ($203,697) = $451.33 Expected NPV = $116.65

  27. 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. Simulation Approach

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

  29. 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. Simulation Approach

  30. Each proposal will generate aninternal 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: Simulation Approach PROBABILITY OF OCCURRENCE INTERNAL RATE OF RETURN (%)

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

  32. Determining the Expected NPV for a Portfolio of Projects NPVPis the expected portfolio NPV, NPVj is the expected NPV of the jth NPV that the firm undertakes, m is the total number of projects in the firm portfolio.

  33. Determining Portfolio Standard Deviation sjkis the covariance between possible NPVs for projects j and k, sjk = sj sk rjk. sjis the standard deviation of project j, skis the standard deviation of project k, rjkis the correlation coefficient between projects j& k.

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

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

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

  37. Node 1: 25% chance of a $1Mcash-flow. Node 2: 50% chance of a $2Mcash-flow. Node 3: 25% chance of a $3Mcash-flow. Probability Tree Approach (.25) $1M 1 (.50) $2M -$3M 2 (.25) $3M 3 Year 1

  38. Assume that this project can be abandoned at the end of the first year for $1.5M. What is the project worth? Example without Project Abandonment (.25) $ 0 (.25) $1M (.50) $ 1M 1 (.25) $ 2M (.25) $ 1M (.50) $2M (.50) $ 2M -$900 2 (.25) $ 3M (.25) $ 2M (.25) $3M (.50)$ 3M 3 (.25)$ 3.5M Year 1 Year 2

  39. Example without Project Abandonment

  40. p1 D1 C1 p2 Outcome Node Decision Node D2 Chance Node C2 py DX CY Pruned Branch Decision Trees • Decision tree graphically displays all decisions in a complex project and all the possible outcomes with their probabilities.

  41. 7. CF1=$1.5M 2. Volume for New Product • Build New • Product No 3. $0 Decision Tree (14.3)(New Product Development – with Abandonment) Terminate 8.CF2=$0 (.25) Low Volume P=0.25 4. CF1=$1M 9.CF2=$1M (.5) Continue 10.CF2=$2M (.25) Med. Vol. P=0.5 11.CF2=$1 (.25) 5. CF1=$2M 12.CF2=$2M (.5) Continue 13.CF2=$3M (.25) Yes First cost=$3M High Volume P=0.25 14.CF2=$2 (.25) Continue 15.CF2=$3M (.5) 6. CF1=$3M 16.CF2=$3.5M (.25) Expand t=2, …, t=1 t=0

  42. 7. CF1=$1.5M 2. Volume for New Product • Build New • Product No 3. $0 Decision Tree (14.4)(New Product Development – with Abandonment) Terminate 8.CF2=$0 (.25) Low Volume P=0.25 4. CF1=$1M 9.CF2=$1M (.5) Continue 10.CF2=$2M (.25) EV(CF1)=.909M Med. Vol. P=0.5 EV(CF2)=1M 11.CF2=$1 (.25) 12.CF2=$2M (.5) Continue 5. CF1=$2M 13.CF2=$3M (.25) Yes First cost=$3M 14.CF2=$2 (.25) Continue 15.CF2=$3M (.5) High Volume P=0.25 16.CF2=$3.5M (.25) 6. CF1=$3M Expand t=2, …, t=1 t=0

  43. Example with Project Abandonment

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