ENGM 401 & 620 X1 Fundamentals of Engineering Finance Fall 2010 Lecture 29: Sensitivity Analysis & Uncertainty In the business world, the rearview mirror is always clearer than the windshield. - Warren Buffett M.G. Lipsett University of Alberta http://www.ualberta.ca/~mlipsett/engm401_620/engm401_620.htm After-Tax Cash Flow (Review) Your company has one Class 8 asset, which was purchased in 2005 for $10,000. It was installed in 2006. It was first used in 2007. Which is correct? a) 2005 CCA is $10,000. b) 2005 CCA is $2,000. c) 2006 CCA is $1,000. d) 2007 CCA is $1,000. e) 2007 CCA is $2,000. True or False: If a company has negative taxable income, then the negative taxes are refunded to the company by CRA. True or False: If an asset is sold for more than its basis value, then nominal ATCF is reduced by the taxes on recapture. True or False: When calculating after-tax income, corrections for inflation should be done to the cash flow series before calculating taxes. MG Lipsett, 2010 2 1
Sensitivity and Break-Even Analysis (Review) Sensitivity and break-even even analysis determines which value of a particular parameter will result in a break-even scenario (and to which parameters a decision is sensitive) At break-even, costs equal revenues, NPV equals zero, two options are equivalent, etc. Use base case analysis to solve for parameter in alternative case that results in break-even The sensitivity of a parameter is the amount of variation that causes a change in a decision MG Lipsett, 2010 3 Break-Even Analysis Revisited Your company needs to build a new plant. Option A is to build all at once, with the capacity you will need years from now, at a cost of $140k. Option B is to build in two phases: Phase 1 provides the capacity you need for the first few years at a cost of $100k. Phase 2 provides the remaining additional capacity at a cost of $120k. Both options have the same total useful lifetime, the same operation and maintenance costs, and no salvage value. With a WACC of 8%, at what time will the cost of both options be equivalent? MG Lipsett, 2010 4 2
Break-Even Analysis Revisited (2) New plant Option A is to build all at once, with the capacity you will need years from now, at a cost of $140k. Option B is to build in two phases: Phase 1 at a cost of $100k, and Phase 2 provides the remaining additional capacity at a cost of $120k. Both options have the same lifetime, operation & maintenance costs, and no salvage value. For WACC of 8%, when are costs of A &B equivalent? $220,000 NPV of Costs $200,000 $180,000 $160,000 $140,000 At WACC = 8% both options are equivalent here (between 14 & 15 years out) The decision of which option to use is only sensitive to the timing if the range of estimates is in the area of 15 years, because this is where a decision gets made one way or the other. $120,000 $100,000 0 5 10 15 20 25 30 Year when Option B's Phase 2 constructed MG Lipsett, 2010 5 Sensitivity Analysis Example You are leading a project with the following cash flow series that has an IRR of 20.6%. MARR is 15%. How much of a cost overrun can the project endure in the second year before the initial capital cost brings the IRR to MARR (at which point the project might be cancelled)? $40.00 Cash Flow Diagram: Base Case $60.00 $60.00 $60.00 $60.00 $60.00 $60.00 $60.00 $60.00 0 1 2 3 4 5 6 7 8 9 10 -$100.00 -$100.00 <see spreadsheet in examples directory to illustrate> MG Lipsett, 2010 6 3
Most Likely / Best Case / Worst Case The effect of variability of a parameter (such as MARR, capital cost, etc.) can be assessed for an investment alternative by analyzing multiple cases for that alternative Choose the most likely value for the parameter, and a number on either side that represents the best-case value and the worst-case value Ideally these parameters bracket the risk associated with the uncertainty Two approaches: Assess the sensitivity of a parameter individually (an extension of the approach discussed so far) Assess each scenario overall MG Lipsett, 2010 7 Risk Associated with An Event Or A Decision The consequence associated with a particular factor can be expressed as a cost (or a benefit, if the outcome is positive) From a set of independent probabilities and associated costs (or benefits), the expected outcome can be estimated MG Lipsett, 2010 8 4
Expected Outcome for A Set of Probabilities A utility is planning to build a new electrical generating plant. There are some uncertainties about each technology choice, which will affect the useful life of each. The probabilities are as follows: Probabilities Useful Life Option A Option B 10 0.1 0.05 20 0.5 0.25 30 0.3 0.5 40 0.1 0.2 Option A will cost $150k per megawatt. Option B will cost $300k per megawatt. Which has the more attractive cost $/MWe/yr? MG Lipsett, 2010 9 Expected Outcome for A Set of Probabilities A utility is planning to build a new electrical generating plant. There are some uncertainties about each technology choice, which will affect the useful life of each. The probabilities are as follows: Option A will cost $150k per megawatt. Option B will cost $300k per megawatt. Which has the more attractive cost $/MWe/yr? Expected life A = Probabilities Useful Life Option A Option B 10 0.1 0.05 20 0.5 0.25 30 0.3 0.5 40 0.1 0.2 Expected life B =. Cost per MW of generating capacity per year: Expected cost A = Expected cost B = MG Lipsett, 2010 10 5
Modeling General Uncertainty Scenarios Do three scenarios (realistic, optimistic, pessimistic) Do the analysis first using the most likely values for all the parameters. This gives the realistic result Repeat the analysis, assigning all the uncertain parameters their best-case values. This gives the most optimistic result Repeat the analysis, assigning all the uncertain parameters their worst-case values. This gives the most pessimistic result Useful for general assessment of the extreme range of possibilities Not very useful for understanding the effect of variability MG Lipsett, 2010 11 Uncertainty and Risk Example Consider that you can make an investment that you expect will cost $1 million and provide $200k in benefits annually for 10 years, which will give an internal rate of return of 15.1% If MARR < 15.1%, you will want to invest in that project Now consider that there is some degree of uncertainty in the investment: Optimistically, the project could cost only $900k and provide $220k in annual benefits, with a probability of 30% ( P 30 ) The realistic case is estimated to have a probability is 60% ( P 90 ) Pessimistically, the project could cost as $1.1 million and provide only $180k in annual benefits with a probability of 10% ( P 99 ) Now will you invest in the project? MG Lipsett, 2010 12 6
Uncertainty and Risk Example (2) We weight the uncertainties by their respective probability to determine the effect on the decision factor: Probabilities Expected outcome IRR most likely 0.6 15.1% IRR optimistic 0.3 18.5% IRR pessimistic 0.1 10.1% Expected IRR is: 15.6% (weighted by probabilities) MG Lipsett, 2010 13 Sensitivity of Individual Parameters For each parameter: Do the analysis first using the most likely value Realistic result Repeat the analysis, assigning the parameter its best-case value Optimistic result showing sensitivity of that parameter Repeat the analysis, assigning the parameter its worst-case value Pessimistic result showing sensitivity of that parameter Results are intuitively visualized using a Tornado Diagram MG Lipsett, 2010 14 7
Tornado Diagram: Example for NPV Analysis Effect on NPV (M$) Worst case Most likely Best case WACC Capital cost Years to start-up Utilization Unit Revenue Unit Maintenance Cost For each parameter, plot its impact on analysis results, for the range of the parameter Parameter with most variability at the top (most sensitive) Parameter with least variability at the bottom (least sensitive) Negative effect Neutral Positive effect (cost) (benefit) Used for decision analysis MG Lipsett, 2010 15 Sensitivity Analysis Example Consider that you can make an investment that you expect will cost $1 million and provide $200k in benefits annually for 10 years, which will give an internal rate of return of 15.1%. Now consider that there is some degree of uncertainty in the investment: Optimistically, the project could cost only $900k and provide $220k in annual benefits Pessimistically, the project could cost as $1.1 million and provide only $180k in annual benefit Effect of individual parameters on NPV @ MARR Worst case Most likely Best case - 96.6k + 4k + 104.1k Annual Benefit -96.2k + 103.7k Capital Cost Negative effect Neutral Positive effect (cost) (benefit) MG Lipsett, 2010 16 < analyses are on spreadsheet in examples directory > 8
Risk and Its Mitigation Assessing scenarios entails understanding overall risk Risk = Probability x Consequence Three fundamental ways to deal with investment risks: Contingency: Include an allowance to cover for what you don t know. This is standard for engineering and construction contracts. Return: The higher the perceived risk, the higher the hurdle rate. For example, what percent of output is pre-sold? If low, require a higher return. Mitigation: Identify the risk you can t accept, and develop a plan to buy your way out of that risk. Question: do these tactics reduce the probability (uncertainty) or the effect of adverse consequences? MG Lipsett, 2010 17 Contingency Contingency shrinks later in a project, as project definition increases (and hopefully improves ) Most small projects will rely on contingency alone Most larger projects will use the other tactics as well Project draws from contingency; monitoring it is a major project control tool Often triggered by class of estimate, where estimates for major equipment, minor equipment labour costs, etc. each have uncertainties associated with them Sometimes these uncertainties are expressed as probabilities Contingency estimates may suffer from Garbage In Garbage Out analysis Inputs are highly judgmental Results are sensitive to the assumptions The final output is sometimes adjusted to fit prior expectations MG Lipsett, 2010 18 9
Return We automatically expect higher return for higher risk Some firms quantify this and tie it to specific business targets Failure rate increases with higher risk and rate of return. Venture capital firms operate at the far end of the spectrum and expect 40% returns and a high drop-out rate MG Lipsett, 2010 19 Identification and Mitigation Key questions: What are the risk elements. Who can take these? What is the price? Example: You are developing a project in a foreign country and being paid in the local currency. If in the US, Europe or Japan, forward sales mechanisms are easy. In some other country, however, currency hedging mechanisms are nonexistent and a national government, World Bank or other aid body is the most likely acceptor of risk. MG Lipsett, 2010 20 10
Risk Elements EPC Company Risk Political Bankruptcy Project Cancellation Delayed Start Foreign exchange Foreign taxes Mitigation CIDA, World Bank or other development bank guarantee. Completion (performance) bond or guarantee by more credit worthy party. Prepayment, funds in trust, guarantee. Make national government a guarantor in the event of change of regulation. Own currency as basis, hedge or guarantee. Make national government a guarantor in the event of change of regulation. EPC means Engineering, Procurement, & Construction MG Lipsett, 2010 21 Risk Elements EPC Company (2) Risk Contract Natural Disaster Loss During Transport Strike / Lockout Technical Flaw IP Infringement Mitigation International arbitrator or court, guarantee by national government. Insurance. Insurance (loss of item or business interruption??). A project specific no strike / no lockout agreement. Formalized review, period constructability reviews. External or internal review, third party supplier indemnification. MG Lipsett, 2010 22 11
Risk Elements Operating Companies Risk Feedstock / Utilities Price Product Price Drop Mitigation Long term contract, hedging, re-opener clause in all contracts, vertical integration. Pre-sold long term contracts (ensure enforceability). Change in Regulations Review likelihood of affecting some vs. all, develop industry based lobby, understand life cycle. Change in Taxation Review likelihood of affecting some vs. all, develop industry based lobby. MG Lipsett, 2010 23 Summary Until now, we have done our analyses as though the numbers were certain, but Predictions are difficult, especially about the future. (Yogi Berra) If we can get some measure of the uncertainty in our predictions, then we can see the effect of the uncertainty on our decisions For independent probabilities, the calculations are simple Often, however, factors are not truly independent Opportunity entails risk, but risk can be managed: Contingency (budget buffer that shrinks as project proceeds) Return (requiring a higher return rate for risky projects), and Mitigation (spending extra money to reduce a risk factor) MG Lipsett, 2010 24 12
Extra Slide: Monte Carlo Simulation For information only (no, it won t be on the midterm) Sensitivity analysis is often used to determine what size contingency to use Uncertainty can be expressed as a range or a probability Scenarios (most likely / best /worst case) give a range, a coarse indication of relationship between an parameter and its effect (Tornado Diagram) More precise scenario analysis can be done using simulations that test the probabilities Monte Carlo simulation is a probabilistic analysis of a system Inputs are probabilities (distributions or functions) Process is the system dynamics Inputs (or the investment analysis procedure) Output is the system response (or analysis result), also expressed probabilistically Process Output MG Lipsett, 2010 25 13