Chapter 14 – Support

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

2. Remember? An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL A StateProbabilityCash Flow Deep Recession 0.05$ –3,000 Mild Recession 0.25 1,000 Normal 0.40 5,000 Minor Boom 0.25 9,000 Major Boom 0.05 13,000

3. 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.

4. 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’

5. Remember? An Illustration of Total Risk (Discrete Distribution) ANNUAL CASH FLOWS: YEAR 1 PROPOSAL B StateProbabilityCash Flow Deep Recession 0.05$ –1,000 Mild Recession 0.25 2,000 Normal 0.40 5,000 Minor Boom 0.25 8,000 Major Boom 0.0511,000

6. 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’

7. 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. Remember? Probability Tree Approach

8. Summary of the Decision Tree Analysis Decision Tree Analysis (P) (NPV) (P) x [(NPV - NPV-bar)^2] Joint Probability Formula Branch NPV of each branch (P) x (NPV) Risk-free 2200 $101,730.16 5.00% 0.10 0.02 =$D$11*G9 1 $2,238.32 $44.77 1200 1200 $218,149.33 0.20 0.60 0.12 =$D$11*G11 2 $1,331.29 $159.76 900 $69,491.16 0.30 0.06 =$D$11*G13 3 $1,059.18 $63.55 900 $27,504.76 0.35 0.21 =$D$18*G16 4 $344.90 $72.43 -900 450 600 $1,935.19 0.60 0.40 0.24 =$D$18*G18 5 $72.79 $17.47 300 $4,985.70 0.25 0.15 =$D$18*G20 6 ($199.32) ($29.90) 500 $20,036.30 0.10 0.02 =$D$25*G23 7 ($1,017.91) ($20.36) -600 -100 $238,741.04 0.20 0.50 0.1 =$D$25*G25 8 ($1,562.13) ($156.21) -700 $349,228.13 0.40 0.08 =$D$25*G27 9 ($2,106.35) ($168.51) 1015.78 1.00 =SUM(I9:I27) -17.01 Standard Deviation Expected NPV 'NPV-bar' Refer to “VW13E-13b.xlsx” on tab ‘Decision Tree’

9. 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. Remember? Simulation Approach

10. 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.

11. 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.

12. 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.

13. 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)? Remember?Managerial (Real) Options

14. Summary of the Decision Tree Analysis Accept Now!! Refer to “VW13E-13b.xlsx” on tab ‘Decision Tree 2’