Dealing with Uncertainty

1. Dealing with Uncertainty Assessing a Project’s Worth under Uncertainty or Risk

2. Previously • In previous lectures, we assumed a high degree of confidence in all estimated values, that is we assumed certainty. • In most situations, however, there is doubt as to the ultimate results that will be obtained from an investment - there is risk and uncertainty

3. Risk and Uncertainty • Caused by lack of precise knowledge regarding future business conditions, technological developments, synergies among projects, etc. • Should be made explicit in any analysis • Risk - Variability described by probability distributions • Uncertainty - Probability distributions are not known • Generally the terms are interchangeable

4. Four major sources of uncertainty • Inaccuracy of the estimates: cash inflow, savings in existing operating expenses, capital required • Type of business involved • Type of physical plant and equipment involved • Length of the project and study period

5. Non-probabilistic Methods for Describing Project Risk • Breakeven Analysis • Sensitivity Analysis • Scenario Analysis • Risk-Adjusted MARRs • Reduction of the useful life

6. Breakeven Analysis • Commonly used when selection among alternatives is dependent on a single factor (e.g., capacity, sales). • Solve for the value of that factor at which the conclusion is a standoff. • common measures include annual revenues and expenses, rate of return, market or salvage value, equipment life, capacity utilization).

7. Comparing two alternatives: Find the value of some parameter that makes the NAW or NPW equal. Evaluating a single alternative: Find the value of some parameter that makes NAW or NPW equal to zero. To decide, judge whether the breakeven point can reasonably be expected. Kinds of Breakeven Analysis

8. Breakeven Analysis - Example 1 • Suppose that the market value of Alternative 1 is known with certainty. What would the market value of Alternative 2 have to be so that the initial decision based on this information would be reversed? Use a MARR of 15% per year

9. Example 1 - cont’d • NAWA = $255 • NAWB = $213 (MV = 1200) Choose A • Find Breakeven Point for market value for B NAWA = NAWB 255 = -$6000 (A/P,15%,10) + $1350 +X(A/F,15%,10) • Solve for X = 2050 • Decision?

10. Example 1 - cont’d Breakeven Point = $2050

11. Sensitivity Analysis • Relative magnitude of change in the measure of interest caused by one or more changes in estimated factors • Common technique when one or more factors are subject to uncertainty. • Assesses the impact of uncertainty in estimates on study results.

12. Sensitivity Analysis - Example 2 • A machine is considered for immediate installation. Because of the new technology built in, we want to investigate its NPW over a range of +/-40% in a) capital investment, b) annual net cash flow, c) market value, d) useful life. • Use MARR = 10%

13. Example 2 - cont’d • Base NPW= -$11,500 + $3000 (P/A,10%,6) + $1000 (P/F,10%,6) = $2,130 • a) When capital invest. varies by +/- p%, NPW= - (1 + p/100) ($11,500) + … (linear function) • b) When revenues vary by +/- a%, NPW= …+ (1 + a/100) ($3000)(P/A,10%,6) + … (linear function) • c) When market value varies by +/- s%, NPW= …+ (1 + s/100) ($1000) (P/F,10%,6) (linear function) • d) When the useful life varies by +/- n%, NPW= … + $3000(P/A,10%,(1 + n/100)(6)) + $1000 (P/F,10%, (1 + n/100) (6)) (nonlinear function)

14. Observation: Solution is most sensitive to … Sensitivity analysis is useful for identifying factors that need to be estimated more carefully Example 2 - Spider Chart

15. Considering Several Factors: Scenario Analysis • also called optimistic-pessimistic estimation • used to establish a range of values for the measure of interest • typically, the optimistic estimate has 1 chance out of 20 to be exceeded by the actual outcome and the pessimistic estimate has 19 chances out of 20 to be exceeded by the actual outcome

16. Scenario Analysis - Example 3 • An ultrasound inspection device for which optimistic, most likely and pessimistic estimates are found below. The MARR is 8%.

17. Making Decisions • Compare NAW(O) = 74,000 , NAW(M) = 4500, NAW(P) = -3300 • Decision: • If NAW(O) < 0 then • Reject • If NAW(P) > 0 then • Accept • Else • Do more analysis or let the boss decide

18. Analyze all Combinations (NAW in $000s) • NAW > $50,000 for 4 out 27 combinations • NAW < $0 for 9 out of 27 combinations • Decision?

19. Risk-adjusted MARRs • Involves the use of higher MARRs for alternatives that are classified as highly uncertain and lower MARRs for projects with fewer uncertainties • Widely used in practice

20. Risk-adjusted MARRs - Example 4 • Two alternatives, both affected by uncertainty to different degrees. The firm’s risk-free MARR is 10%. • Alternative P is thought to be more uncertain than Alternative Q. • At 10%, both alternatives have the same NPW • Decision?

21. Example 4 - cont’d • Using prescribed risk-adjusted MARRs of 20% for P and 17% for Q, we get NPWP = $10,602 NPWQ = $8,575 => Choose Alternative P • Contradictory result

22. Example 4 - cont’d

23. Subject to many pitfalls. One of them is that the uncertainty in the project is not made explicit. Not recommended when other techniques can be used. Risk - adjusted MARRs

24. Reduction of the useful life • Estimated project life is reduced by a fixed percentage and each alternative is evaluated regarding its acceptability over this reduced life span

25. Reduction of the useful life - Example 5 • A proposed new product line has cash flows as below. Do an after tax analysis with an MARR of 15% • The company ‘s maximum simple payback period is three years • Decision?

26. Example 5 - cont’d ROR as a function of the useful life After-tax ROR Useful Life

27. Heavy emphasis is placed on rapid recovery of investment capital in the early years of project Closely related to the discounted payback technique Neglects cash flows that occur later in life Not recommended Reduction of Useful Life

28. Summary • Methods are relatively simple to apply. • They are also somewhat simplistic and imprecise in cases where we must deal with multifaceted project uncertainty. • Probability concepts allow us to further analyze project risk and develop better recommendations.