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,Risk and Managerial Options in Capital Budgeting,The Problem of Project Risk Total Project Risk Cont
2、ribution to Total Firm Risk: Firm-Portfolio Approach Managerial Options,An Illustration of Total Risk (Discrete Distribution),ANNUAL CASH FLOWS: YEAR 1 PROPOSAL AState 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 13,0
3、00,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,CF1 P1 (CF1)(P1) $ -3,000 .05 $ -1501,000 .25 2505,000 .40 2,0009,000 .25 2,25013,000 .05 650S=1.00 CF1=$5,000,Expected Value of Year 1 Cash Flows (Proposal A),(CF1)(P1)
4、(CF1 - CF1)2(P1) $ -150 ( -3,000 - 5,000)2 (.05)250 ( 1,000 - 5,000)2 (.25)2,000 ( 5,000 - 5,000)2 (.40)2,250 ( 9,000 - 5,000)2 (.25)650 (13,000 - 5,000)2 (.05)$5,000,Variance of Year 1 Cash Flows (Proposal A),Variance of Year 1 Cash Flows (Proposal A),(CF1)(P1) (CF1 - CF1)2*(P1) $ -150 3,200,000250
5、 4,000,0002,000 02,250 4,000,000650 3,200,000$5,000 14,400,000,Summary of Proposal A,The standard deviation = SQRT (14,400,000) = $3,795The expected cash flow = $5,000,An Illustration of Total Risk (Discrete Distribution),ANNUAL CASH FLOWS: YEAR 1 PROPOSAL BState Probability Cash Flow Deep Recession
6、 .05 $ -1,000 Mild Recession .25 2,000 Normal .40 5,000 Minor Boom .25 8,000 Major Boom .05 11,000,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,Expected Value of Year 1 Cash Flows (Proposal B),CF1 P1 (CF1)(P1) $ -1,000
7、 .05 $ -502,000 .25 5005,000 .40 2,0008,000 .25 2,00011,000 .05 550S=1.00 CF1=$5,000,(CF1)(P1) (CF1 - CF1)2(P1)$ -50 ( -1,000 - 5,000)2 (.05)500 ( 2,000 - 5,000)2 (.25)2,000 ( 5,000 - 5,000)2 (.40)2,000 ( 8,000 - 5,000)2 (.25)550 (11,000 - 5,000)2 (.05)$5,000,Variance of Year 1 Cash Flows (Proposal
8、B),Variance of Year 1 Cash Flows (Proposal B),(CF1)(P1) (CF1 - CF1)2(P1)$ -50 1,800,000500 2,250,0002,000 02,000 2,250,000550 1,800,000$5,000 8,100,000,Summary of Proposal B,The standard deviation of Proposal B Proposal A. ( $2,846 $3,795 ),The standard deviation = SQRT (8,100,000) = $2,846 The expe
9、cted cash flow = $5,000,Total Project Risk,Projects have risk that may change from period to period. Projects are more likely to have continuous, rather than discrete distributions.,Cash Flow ($),1 2 3Year,Probability Tree Approach,A graphic or tabular approach for organizing the possible cash-flow
10、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 $900. Uncertainty surrounding the first year
11、 cash flows creates three possible cash-flow scenarios in Year 1.,-$900,Probability Tree Approach,Node 1: 20% chance of a $1,200 cash-flow. Node 2: 60% chance of a $450 cash-flow. Node 3: 20% chance of a -$600 cash-flow.,-$900,(.20) $1,200,(.20) -$600,(.60) $450,Year 1,1,2,3,Probability Tree Approac
12、h,Each node in Year 2 represents a branch of our probability tree. The probabilities are said to be conditional probabilities.,-$900,(.20) $1,200,(.20) -$600,(.60) $450,Year 1,1,2,3,(.60) $1,200,(.30) $ 900,(.10) $2,200,(.35) $ 900,(.40) $ 600,(.25) $ 300,(.10) $ 500,(.50) -$ 100,(.40) -$ 700,Year 2
13、,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) -$600,(.60) $450,Year 1,1,2,3,(.60) $1,200,(.30) $ 900,(.10) $2,200,(.35) $ 900,(.40) $ 600,(.25) $ 300,(.10) $ 500,(.50) -$ 100,(
14、.40) -$ 700,Year 2,Project NPV Based on Probability Tree Usage,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 i of the probability tree for two years of cash flows is,NPV = S (NPVi)(Pi),NPV
15、i =,CF1,(1 + Rf )1,(1 + Rf )2,CF2,- ICO,+,i = 1,z,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) -$600,(.60) $450,Year 1,1,2,3,(.60) $1,200,(.30) $ 900,(.10) $2,200,(.35) $ 900,(.
16、40) $ 600,(.25) $ 300,(.10) $ 500,(.50) -$ 100,(.40) -$ 700,Year 2,NPV on the Calculator,Remember, we can use the cash flow registry to solve these NPV problems quickly and accurately!,Actual NPV Solution Using Your Financial Calculator,Solving for Branch #3: Step 1: Press CF key Step 2: Press 2nd C
17、LR Work keys 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,Actual NPV Solution Using Your Financial Calculator,Solving for Branch #3: Step 8: Press keys Step 9: Pr
18、ess NPV key Step 10: For I=, Enter 5 Enter keys Step 11: Press CPT keyResult: Net Present Value = $1,059.18,You would complete this for EACH branch!,Calculating the Expected Net Present Value (NPV),Branch NPVi Branch 1 $ 2,238.32 Branch 2 $ 1,331.29 Branch 3 $ 1,059.18 Branch 4 $ 344.90 Branch 5 $ 7
19、2.79 Branch 6 -$ 199.32 Branch 7 -$ 1,017.91 Branch 8 -$ 1,562.13 Branch 9 -$ 2,106.35,P(1,2) NPVi * 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,Calculating the Variance of the Net Present Value,
20、NPVi$ 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) (NPVi - NPV )2P(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,Summary of the
21、 Decision Tree Analysis,The standard deviation = SQRT ($1,031,800) = $1,015.78 The expected NPV = -$ 17.01,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.,
22、Simulation Approach,Market analysis Market size, selling price, market growth rate, and market shareInvestment cost analysis Investment required, useful life of facilities, and residual valueOperating and fixed costs Operating costs and fixed costs,Factors we might consider in a model:,Simulation Ap
23、proach,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
24、 of EVERY variable listed on slide 14-30.,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:,INTERNAL RATE OF RETURN (%),PROBA
25、BILITY OF OCCURRENCE,Combining projects in this manner reduces the firm risk due to diversification.,Contribution to Total Firm Risk: Firm-Portfolio Approach,CASH FLOW,TIME,TIME,TIME,Proposal A,Proposal B,Combination of Proposals A and B,NPVP = S ( NPVj ) NPVP is the expected portfolio NPV, NPVj is
26、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,sP = S S sjk sjk is the covariance between possible NPVs for projects j and k, s jk = s j s k r jk . sj is the standard de
27、viation of project j, sk is the standard deviation of project k, rjk is the correlation coefficient between projects j and k.,Determining Portfolio Standard Deviation,m,j=1,m,k=1,E: Existing Projects 8 CombinationsE E + 1 E + 1 + 2 E + 2 E + 1 + 3 E + 3 E + 2 + 3 E + 1 + 2 + 3 A, B, and C are domina
28、ting combinations from the eight possible.,Combinations of Risky Investments,A,B,C,E,Standard Deviation,Expected Value of NPV,Managerial (Real) Options,Management flexibility to make future decisions that affect a projects expected cash flows, life, or future acceptance. Project Worth = NPV + Option
29、(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).
30、,Previous Example with Project Abandonment,Assume that this project can be abandoned at the end of the first year for $200. What is the project worth?,-$900,(.20) $1,200,(.20) -$600,(.60) $450,Year 1,1,2,3,(.60) $1,200,(.30) $ 900,(.10) $2,200,(.35) $ 900,(.40) $ 600,(.25) $ 300,(.10) $ 500,(.50) -$
31、 100,(.40) -$ 700,Year 2,Project Abandonment,Node 3: (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) -$600,(.60) $450,Year 1,1,2,3,(.60) $1,200,(.30) $ 900,(.10) $2,200,(.35) $ 900,(.40) $ 600,(.25) $ 300,(.10) $ 500
32、,(.50) -$ 100,(.40) -$ 700,Year 2,Project Abandonment,-$900,(.20) $1,200,(.20) -$600,(.60) $450,Year 1,1,2,3,(.60) $1,200,(.30) $ 900,(.10) $2,200,(.35) $ 900,(.40) $ 600,(.25) $ 300,(.10) $ 500,(.50) -$ 100,(.40) -$ 700,Year 2,The optimal decision at the end of Year 1 is to abandon the project for
33、$200. $200 -($266.67) What is the “new” project value?,Project Abandonment,$ 2,238.32$ 1,331.29$ 1,059.18$ 344.90$ 72.79 -$ 199.32-$ 1,280.95,-$900,(.20) $1,200,(.20) -$400*,(.60) $450,Year 1,1,2,3,(.60) $1,200,(.30) $ 900,(.10) $2,200,(.35) $ 900,(.40) $ 600,(.25) $ 300,(1.0) $ 0,Year 2,*-$600 + $200 abandonment,Summary of the Addition of the Abandonment Option,* For “True” Project considering abandonment option,The standard deviation* = SQRT (740,326) = $857.56 The expected NPV* = $ 71.88NPV* = Original NPV + Abandonment OptionThus, $71.88 = -$17.01 + Option Abandonment Option = $ 88.89,
