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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. • 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. Topics • The Problem of Project Risk • Total Project Risk • Contribution to Total Firm Risk: Firm- Portfolio Approach • Managerial (Real) Options 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 Probability Distribution of Year 1 Cash Flows (Proposal A) .40 Probability .20 .10 3,000 4,000 5,000 Cash Flow ($) Expected Value of Year 1 Cash Flows (Proposal A) CF1 P1 (CF1)(P1) $ -3,000 .10 $ 300 1,000 .20 700 5,000 .40 1,600 9,000 .20 900 13,000 .10 500 S=1.00 CF1=$4,000 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 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. An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B State Probability Cash Flow Deep Recession .10 $ 2,000 Mild Recession .20 3,000 Normal .40 4,000 Minor Boom .20 5,000 Major Boom .10 6,000 Probability Distribution of Year 1 Cash Flows (Proposal B) .40 Probability .20 .10 2,000 3,000 4,000 5,000 6,000 Cash Flow ($) Expected Value of Year 1 Cash Flows (Proposal B) CF1 P1 (CF1)(P1) $ 2,000 .10 $ 200 3,000 .20 600 4,000 .40 1,600 5,000 .20 1,000 6,000 .10 600 S=1.00 CF1=$4,000 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 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 Comparison of Proposal A & B Proposal A Proposal B Standard deviation $548 $1,095 Expected cash flow $4,000 $4,000 Coefficient of Variation (CV) 0.14 0.27 The standard deviation of B > A ($1,095 > $548), so “B” is more risky than “A”. The coefficient of variation of B > A (0.27 < 0.14), so “B” has higher relative risk than “A”. Total Project Risk Projects have risk that may change from period to period. Projects are more Cash Flow ($) likely to have continuous, rather than discrete distributions. 1 2 3 Year 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. Probability Tree Approach Basket Wonders is examining a project that will have an initial cost today of $240. -$240 Uncertainty surrounding the first year cash flows creates three possible cash-flow scenarios in Year 1. Probability Tree Approach (.25) $500 1 Node 1: 25% chance of a $500 cash-flow. (.50) $200 -$240 2 Node 2: 50% chance of a $200 cash-flow. (.25) -$100 3 Node 3: 25% chance of a -$100 cash-flow. Year 1 Probability Tree Approach (.40) $800 Each node in (.25) $500 (.40) $500 1 Year 2 (.20) $200 represents a branch of our (.20) $ 500 probability tree. (.50) $200 (.60) $ 200 -$240 2 (.20) -$ 100 The probabilities (.20) $ 200 are said to be (.25) -$100 (.40) -$ 100 conditional 3 (.40) -$ 400 probabilities. Year 1 Year 2 Joint Probabilities [P(1,2)] (.40) $800 .10 Branch 1 (.25) $500 (.40) $500 1 .10 Branch 2 (.20) $200 .05 Branch 3 (.20) $500 (.50) $200 .10 Branch 4 (.60) $400 -$240 2 .30 Branch 5 (.20) -$100 .10 Branch 6 (.20) $200 .05 Branch 7 (.25) -$100 (.40) -$100 3 .10 Branch 8 (.40) -$400 .10 Branch 9 Year 1 Year 2 Project NPV Based on Probability Tree z The probability NPV = iS1 (NPVi)(Pi) = tree accounts for the distribution of The NPV for branch i of the cash flows. probability tree for two years Therefore, of cash flows is discount all cash flows at only the CF1 CF2 risk-free rate of NPVi = + (1 + Rf )1 (1 + Rf )2 return. - ICO NPV for Each Cash-Flow Stream at 8% Risk-Free Rate (.40) $ 800 $ 909 (.25) $500 (.40) $ 500 1 $ 652 (.20) $ 200 $ 394 (.20) $ 500 (.50) $200 $ 374 (.60) $ 200 -$240 2 $ 117 (.20) -$ 100 -$ 141 (.20) $ 200 -$ 161 (.25) -$100 (.40) -$ 100 3 -$ 418 (.40) -$ 400 -$ 676 Year 1 Year 2 Calculating the Expected Net Present Value (NPV) Branch NPVi P(1,2) NPVi * P(1,2) Branch 1 $ 909 .10 $ 91 Branch 2 $ 652 .10 $ 65 Branch 3 $ 394 .05 $ 20 Branch 4 $ 374 .10 $ 37 Branch 5 $ 117 .30 $ 35 Branch 6 -$ 141 .10 -$ 14 Branch 7 -$ 161 .05 -$ 8 Branch 8 -$ 418 .10 -$ 42 Branch 9 -$ 676 .10 -$ 68 Expected Net Present Value = $116 Calculating the Variance of the Net Present Value NPVi P(1,2) (NPVi - NPV )2[P(1,2)] $ 909 .10 $ 62,884.90 $ 652 .10 $ 28,729.60 $ 394 .05 $ 3,864.20 $ 374 .10 $ 6,656.40 $ 117 .30 $ 0.30 -$ 141 .10 $ 6,604.90 -$ 161 .05 $ 3,836.45 -$ 418 .10 $ 28,515.60 -$ 676 .10 $ 62,726.40 Variance = $203,818.75 Calculating the Variance of the Net Present Value Prob Prob Joint (CF1) CF1 (CF2) CF2 Prob. NPV EV(NPV) Var(NPV) 0.25 500 0.4 800 0.1 $908.83 $90.88 62755.08 0.25 500 0.4 500 0.1 $651.63 $65.16 28620.30 0.25 500 0.2 200 0.05 $394.43 $19.72 3858.02 0.5 200 0.2 500 0.1 $373.85 $37.39 6615.27 0.5 200 0.6 200 0.3 $116.65 $35.00 0.00 0.5 200 0.2 -100 0.1 ($140.55) ($14.05) 6615.27 0.25 -100 0.2 200 0.05 ($161.12) ($8.06) 3858.02 0.25 -100 0.4 -100 0.1 ($418.33) ($41.83) 28620.30 0.25 -100 0.4 -400 0.1 ($675.53) ($67.55) 62755.08 $116.65 $203,697.35 Summary of the Decision Tree Analysis Standard deviation = SQRT ($203,697) = $451.33 Expected NPV = $116.65 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. Simulation Approach Factors we might consider in a model: – 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 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 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: OF OCCURRENCE PROBABILITY INTERNAL RATE OF RETURN (%) Contribution to Total Firm Risk: Firm-Portfolio Approach Combination of Proposal A Proposal B Proposals A and B CASH FLOW TIME TIME TIME Combining projects in this manner reduces the firm risk due to diversification. Determining the Expected NPV for a Portfolio of Projects m NPVP NPV j j 1 NPVP is 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. Determining Portfolio Standard Deviation m m sp s j 1 k 1 jk sjk is the covariance between possible NPVs for projects j and k, s jk = s j s k r jk . sj is the standard deviation of project j, sk is the standard deviation of project k, rjk is the correlation coefficient between projects j & k. Combinations of Risky Investments E: Existing Projects C 8 Combinations B Expected Value of NPV E E+1 E+1+2 E+2 E+1+3 E E+3 E+2+3 E+1+2+3 A A, B, and C are dominating combinations from the eight possible. Standard Deviation 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 Managerial (Real) Options 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). Probability Tree Approach (.25) $1M 1 Node 1: 25% chance of a $1M cash-flow. (.50) $2M -$3M 2 Node 2: 50% chance of a $2M cash-flow. (.25) $3M 3 Node 3: 25% chance of a $3M cash-flow. Year 1 Example without Project Abandonment (.25) $ 0 Assume that (.25) $1M (.50) $ 1M 1 this project can (.25) $ 2M be abandoned at the end of (.25) $ 1M the first year (.50) $2M (.50) $ 2M -$900 2 for $1.5M. (.25) $ 3M What is the (.25) $ 2M project worth? (.25) $3M (.50) $ 3M 3 (.25) $ 3.5M Year 1 Year 2 Example without Project Abandonment Prob Prob Joint (CF1) CF1 (CF2) CF2 Prob. NPV EV(NPV) Var(NPV) 0.25 1000000 0.25 0 0.0625 ($2,090,909.09) ($130,681.82) 402005778400.55 0.25 1000000 0.5 1000000 0.125 ($1,264,462.81) ($158,057.85) 365388853433.85 0.25 1000000 0.25 2000000 0.0625 ($438,016.53) ($27,376.03) 48759756953.93 0.5 2000000 0.25 1000000 0.125 ($355,371.90) ($44,421.49) 80124014966.53 0.5 2000000 0.5 2000000 0.25 $471,074.38 $117,768.60 166751331.88 0.5 2000000 0.25 3000000 0.125 $1,297,520.66 $162,190.08 90796100206.61 0.25 3000000 0.25 2000000 0.0625 $1,380,165.29 $86,260.33 54629403835.97 0.25 3000000 0.5 3000000 0.125 $2,206,611.57 $275,826.45 387800232438.02 0.25 3000000 0.25 3500000 0.0625 $2,619,834.71 $163,739.67 295551728130.76 $445,247.93 1725222619698.11 $1,313,477.30 Decision Trees • Decision tree graphically displays all decisions in a complex project and all the possible outcomes with their probabilities. D1 Decision Node D2 Outcome Node DX p1 C1 p2 Chance Node C2 Pruned Branch py CY Decision Tree (14.3) (New Product Development – with Abandonment) 7. CF1=$1.5M Terminate 8.CF2=$0 (.25) Low Volume 4. CF1=$1M P=0.25 9.CF2=$1M (.5) Continue 10.CF2=$2M (.25) Med. Vol. P=0.5 11.CF2=$1 (.25) 2. Volume for 5. CF1=$2M 12.CF2=$2M (.5) New Product Continue 13.CF2=$3M (.25) Yes 14.CF2=$2 (.25) High Volume First cost=$3M Continue P=0.25 15.CF2=$3M (.5) 1. Build New 6. CF1=$3M 16.CF2=$3.5M (.25) Product Expand No 3. $0 t=0 t=1 t=2, …, Decision Tree (14.4) (New Product Development – with Abandonment) 7. CF1=$1.5M Terminate 8.CF2=$0 (.25) Low Volume 4. CF1=$1M P=0.25 9.CF2=$1M (.5) Continue 10.CF2=$2M (.25) Med. Vol. EV(CF1)=.909M P=0.5 EV(CF2)=1M 2. Volume for New Product 11.CF2=$1 (.25) 5. CF1=$2M 12.CF2=$2M (.5) Continue Yes 13.CF2=$3M (.25) First cost=$3M High Volume 14.CF2=$2 (.25) 1. Build New P=0.25 Continue 15.CF2=$3M (.5) Product 6. CF1=$3M 16.CF2=$3.5M (.25) No 3. $0 Expand t=0 t=1 t=2, …, Example with Project Abandonment Prob Prob Joint (CF1) CF1 (CF2) CF2 Prob. NPV EV(NPV) Var(NPV) 0.25 2500000 1 0 0.25 ($727,272.73) ($181,818.18) 426943440082.65 0.5 2000000 0.25 1000000 0.125 ($355,371.90) ($44,421.49) 109258807671.95 0.5 2000000 0.5 2000000 0.25 $471,074.38 $117,768.60 2941493494.30 0.5 2000000 0.25 3000000 0.125 $1,297,520.66 $162,190.08 64436049663.62 0.25 3000000 0.25 2000000 0.0625 $1,380,165.29 $86,260.33 40062007483.27 0.25 3000000 0.5 3000000 0.125 $2,206,611.57 $275,826.45 330918018108.39 0.25 3000000 0.25 3500000 0.0625 $2,619,834.71 $163,739.67 260173765559.90 $579,545.45 1234733582064.07 $ 1,111,185.66