14b.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Chapter 14 – Support Risk and Managerial (Real) Options in Capital Budgeting

14b.2 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Remember? An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A ProbabilityCash Flow State Probability Cash Flow Deep Recession0.05 $ –3,000 Mild Recession0.25 1,000 Normal0.40 5,000 Minor Boom0.25 9,000 Major Boom ,000 ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A ProbabilityCash Flow State Probability Cash Flow Deep Recession0.05 $ –3,000 Mild Recession0.25 1,000 Normal0.40 5,000 Minor Boom0.25 9,000 Major Boom ,000

14b.3 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 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 Coefficient of Variation (CV) = $3,795 / $5,000 = CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.

14b.4 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. What if we used Excel? Summary of Proposal A We 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’

14b.5 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Remember? An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B ProbabilityCash Flow State Probability Cash Flow Deep Recession0.05 $ –1,000 Mild Recession0.25 2,000 Normal0.40 5,000 Minor Boom0.25 8,000 Major Boom ,000 ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B ProbabilityCash Flow State Probability Cash Flow Deep Recession0.05 $ –1,000 Mild Recession0.25 2,000 Normal0.40 5,000 Minor Boom0.25 8,000 Major Boom ,000

14b.6 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. What if we used Excel? Summary of Proposal B We 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’

14b.7 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Remember? Probability Tree Approach It 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.

14b.8 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Summary of the Decision Tree Analysis (P)(NPV) Joint ProbabilityFormulaBranchNPV of each branch(P) x (NPV) Risk-free % =$D$11*G91$2,238.32$ =$D$11*G112$1,331.29$ =$D$11*G133$1,059.18$ =$D$18*G164$344.90$ =$D$18*G185$72.79$ =$D$18*G206($199.32)($29.90) =$D$25*G237($1,017.91)($20.36) =$D$25*G258($1,562.13)($156.21) =$D$25*G279($2,106.35)($168.51) 1.00=SUM(I9:I27) Expected NPV 'NPV-bar' Decision Tree Analysis (P) x [(NPV - NPV-bar)^2] $101, $218, $69, $27, $1, $4, $20, $238, $349, Standard Deviation Refer to “VW13E-13b.xlsx” on tab ‘Decision Tree’

14b.9 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Remember? 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. Let us look at an example related to prices similar to the example in the ppts.

14b.10 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 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.

14b.11 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 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.

14b.12 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. 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.

14b.13 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Remember? 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 What if we could abandon a project for $200 at the end of the first period (year)?

14b.14 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited Created by Gregory Kuhlemeyer. Summary of the Decision Tree Analysis Refer to “VW13E-13b.xlsx” on tab ‘Decision Tree 2’