# Bài giảng Financial Management - Chapter 14 – Support: Risk and Managerial (Real) Options in Capital Budgeting

Summary of Proposal A The standard deviation = SQRT (14,400,000) = \$3,795 The expected cash flow = \$5,000 Coefficient of Variation (CV) = \$3,795 / \$5,000 = 0.759 CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.

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Chapter 14 – SupportRisk and Managerial (Real) Options in Capital BudgetingRemember? An Illustration of Total Risk (Discrete Distribution)ANNUAL CASH FLOWS: YEAR 1PROPOSAL A State Probability Cash FlowDeep Recession 0.05 \$ –3,000Mild Recession 0.25 1,000Normal 0.40 5,000Minor Boom 0.25 9,000Major Boom 0.05 13,000Summary of Proposal AThe standard deviation = SQRT (14,400,000) = \$3,795The expected cash flow = \$5,000Coefficient of Variation (CV) = \$3,795 / \$5,000 = 0.759 CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.What if we used Excel? Summary of Proposal AWe end up with the exact same answers, except it allows us to do some other types of scenario analysis.What if the probabilities are different?What if the cash flows are different?Refer to VW13E-14b.xlsx on tab ‘Probability Dist’Remember? An Illustration of Total Risk (Discrete Distribution)ANNUAL CASH FLOWS: YEAR 1PROPOSAL B State Probability Cash FlowDeep Recession 0.05 \$ –1,000Mild Recession 0.25 2,000Normal 0.40 5,000Minor Boom 0.25 8,000Major Boom 0.05 11,000What if we used Excel? Summary of Proposal BWe end up with the exact same answers, except it allows us to do some other types of scenario analysis.What if the probabilities are different?What if the cash flows are different?Refer to VW13E-14b.xlsx on tab ‘Probability Dist’Remember? Probability Tree ApproachIt is a graphic or tabular approach for organizing the possible cash-flow streams ...Let us replicate the work in Excel! It can be faster and afford us the opportunity to run many different analyses quickly.Summary of the Decision Tree Analysis(P)(NPV)Joint ProbabilityFormulaBranchNPV of each branch(P) x (NPV)Risk-free22005.00%0.100.02=\$D\$11*G91\$2,238.32\$44.77120012000.200.600.12=\$D\$11*G112\$1,331.29\$159.769000.300.06=\$D\$11*G133\$1,059.18\$63.559000.350.21=\$D\$18*G164\$344.90\$72.43-9004506000.600.400.24=\$D\$18*G185\$72.79\$17.473000.250.15=\$D\$18*G206(\$199.32)(\$29.90)5000.100.02=\$D\$25*G237(\$1,017.91)(\$20.36)-600-1000.200.500.1=\$D\$25*G258(\$1,562.13)(\$156.21)-7000.400.08=\$D\$25*G279(\$2,106.35)(\$168.51)1.00=SUM(I9:I27)-17.01Expected NPV'NPV-bar'Decision Tree Analysis(P) x [(NPV - NPV-bar)^2]\$101,730.16\$218,149.33\$69,491.16\$27,504.76\$1,935.19\$4,985.70\$20,036.30\$238,741.04\$349,228.131015.78Standard DeviationRefer to “VW13E-13b.xlsx” on tab ‘Decision Tree’Remember? Simulation ApproachAn 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.Let us look at an example related to prices similar to the example in the ppts.Simulation Exercise!Here we have assumed a mean price of \$35 per unit and a standard deviation of \$5. In step 2 we have pulled a price of \$37.14 from the distribution which is 0.43 standard deviations to the right of the mean. Simulation Exercise!Now let us use more than one observation and ‘simulate’ the distribution. Let us use 500 data observation points and look at the frequency distribution.Simulation Exercise!We can graph the distribution and we notice how the graph is beginning to look like a standard normal continuous graph. If we were to add more bins and additional data observations are graph would approximate the standard normal distribution.Remember? Managerial (Real) OptionsManagement flexibility to make future decisions that affect a project’s expected cash flows, life, or future acceptance.Project Worth = NPV + Option(s) ValueWhat if we could abandon a project for \$200 at the end of the first period (year)?Summary of the Decision Tree AnalysisRefer to “VW13E-13b.xlsx” on tab ‘Decision Tree 2’
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