Lecture 8: Monte Carlo Simulations in Capital Budgeting
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Uploaded by ExtraordinaryFactorial
Cornell University - SC Johnson College of Business
2024
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Summary
This lecture introduces Monte Carlo simulations in the context of capital budgeting. It details methods for evaluating investments with uncertain cash flows, discussing different approaches such as break-even analysis, sensitivity analysis, and scenario analysis. The lecture also provides a practical example and explores the use of Monte Carlo simulations in a business setting.
Full Transcript
III. Monte Carlo Simulations Capital Budgeting Context NBA6060, Fall 2024 1 1 “If a man will begin with certainties, he shall end in doubts, but if he will be content to begin with doubts, he...
III. Monte Carlo Simulations Capital Budgeting Context NBA6060, Fall 2024 1 1 “If a man will begin with certainties, he shall end in doubts, but if he will be content to begin with doubts, he shall end in certainties.” Francis Bacon NBA6060, Fall 2024 2 2 1 How is uncertainty accounted for? Financial analysts evaluate new investment in two phases. – Envision the possible outcomes and determine an estimate of what he/she expects will happen. – This forms the basis for estimating NPV, IRR, payback, etc. – Detail the underlying sources of risk (value drivers and the uncertainty that characterizes each one). – Once risks are identified, the analyst seeks ways to either mitigate or monitor the risks throughout the life of the project. NBA6060, Fall 2024 3 3 Overview Break-even analysis Sensitivity analysis Scenario analysis Monte Carlo Simulation NBA6060, Fall 2024 4 4 2 Breakeven Analysis When we are uncertain about the input to a capital budgeting decision, it is often useful to determine the break-even level of that input, which is the level for which the investment has an NPV of zero. One example of a break-even level that we have already considered is IRR. In a break-even analysis, for each parameter, we calculate the value at which the NPV is zero. NBA6060, Fall 2024 5 5 Sensitivity Analysis Sensitivity analysis breaks the NPV calculation into its component assumptions and shows how the NPV varies as the underlying assumptions change. HomeNet Example Initial Parameter Worst Case Best Case Assumption Units sold (000s/year) 100 70 130 Sale price ($/unit) 260 240 280 Cost of goods ($/unit) 110 120 100 NBA6060, Fall 2024 6 6 3 Scenario Analysis Scenario analysis considers the effect on the NPV of changing multiple project parameters. We use the term scenario to refer to different sets of assumptions about the realized values of each of the value drivers. Units Sold (thousands) NPV Scenarios Year 1 – Year 5 (000s) Base case 100 100 100 100 100 $31,475 Fast adoption 125 150 200 200 200 $64,639 Slow adoption 50 75 100 100 100 $23,727 NBA6060, Fall 2024 7 7 Why should we care about MC? Investment projects generate future, uncertain cash flows. $$$ 2024 2029 In practice, there are distributions of cash flows. Monte Carlo simulation provides a powerful tool that can help us evaluate what can happen to an investment’s future cash flows and summarize the probabilities in a probability distribution. NBA6060, Fall 2024 8 8 4 Monte Carlo simulation A Monte Carlo simulation is used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. It is a technique used to understand the impact of risk and uncertainty. The technique was initially developed by Stanislaw Ulam, a mathematician who worked on the Manhattan Project. He shared his idea with John Von Neumann, a colleague at the Manhattan Project, and the two collaborated to refine the Monte Carlo simulation. NBA6060, Fall 2024 9 9 Monte Carlo simulation steps A different way of looking at risk 1) Define a probability distribution of each key input variable. 2) Draw a value at random from each distribution. 3) Calculate outcomes: future cash flows, NPV, IRR, etc. 4) Repeat thousands of times. 5) Result: a distribution of outcomes NBA6060, Fall 2024 10 10 5 Monte Carlo vs. Sensitivity Analysis Monte Carlo simulation: likely to yield more realistic and rich risk analysis – Allows many variables to move simultaneously – Can allow for relations across variables over time – Can assess probabilities of outcomes of interest (e.g., NPV > 0) NBA6060, Fall 2024 11 11 Monte Carlo in practice: Merck example Monte Carlo at Merck (Harvard Business Review): “Whereas analysts most often predict results for the total project based on isolated changes in particular variables, Monte Carlo analysis predicts results based on simultaneous changes in numerous variables. Monte Carlo analysis is ideal for us, when you consider the number of changes in our competitive environment.” -Judy Lewent, then CFO of Merck NBA6060, Fall 2024 12 12 6 Step 1: model project uncertainty Suppose we want to consider more realistic (and complex) assumptions about future uncertainty. Interdependence across time (same variable) – Our best guess of units sold in year 1 is 100,000 units, but we know there will be some forecast error: 𝑈𝑛𝑖𝑡𝑠 𝑆𝑜𝑙𝑑 100 1 ϵ ) – Suppose we come to the end of year 1 and demand was 5% higher than expected (ϵ 5%). How does that change your forecast for year 2? – You can assume: 𝑈𝑛𝑖𝑡𝑠 𝑆𝑜𝑙𝑑 𝑈𝑛𝑖𝑡𝑠 𝑆𝑜𝑙𝑑 1 ϵ ) 100 1 ϵ ) 1 ϵ ) NBA6060, Fall 2024 13 13 Step 1: model project uncertainty Interdependence across variables – Again, suppose demand turns out higher than expected. Does that affect your expectation for prices? – For example: 𝑃𝑟𝑖𝑐𝑒 $260 1 𝜑 ) $260 1 0.3ϵ ) If we also update our expectations about year 2 as before, we get: 𝑃𝑟𝑖𝑐𝑒 𝑃𝑟𝑖𝑐𝑒 1 2% 1 𝜑 ) 𝑃𝑟𝑖𝑐𝑒 1 2% 1 0.3ϵ ) $260 1 2% 1 0.3ϵ ) 1 0.3ϵ NBA6060, Fall 2024 14 14 7 Step 2: specify probabilities In this example, there are 5 sources of uncertainty (i.e., each year’s market demand forecast error from year 1 to 5). We need to specify a probability distribution for each forecast error. Example: – Suppose we think market demand could possibly get as high 130 or as low as 70 (thousand units). – For a normal distribution, 99.7% of observations fall within +/- 3 standard deviations – Therefore, we could model the forecast error as being normally distributed with μ (mean) = 0 and σ (SD)= 0.10 (= 0.3/3) NBA6060, Fall 2024 15 15 Step 2: specify probabilities, things to consider Dispersion Truncation: do I want to allow for a small probability of really high/low outcomes? Continuous or discrete Shape/parameter values: – What type of process am I modeling? – Are positive and negative errors equally likely? – Is there historical data to benchmark? – Expert opinion? NBA6060, Fall 2024 16 16 8 Which distributions to use? a few common ones Normal distribution – “Bell curve” centered around mean – Symmetric – Fully determined by mean and SD – Not too fat tails (but possible) Uniform distribution – Flat – Equal probabilities for a range of values – Useful if range is (roughly) known but have limited information on likelihood of particular values NBA6060, Fall 2024 17 17 Which distributions to use? a few common ones Triangular distribution – Frequently used to model expert opinions (min, max, most likely) – “Fatter” right tail than BetaPERT BetaPERT (or PERT) distribution – A version of Beta distribution – Frequently used to model expert opinions (min, max, most likely) NBA6060, Fall 2024 18 18 9 Step 3: Impact on NPV Can also examine the distribution of NPV, our final outcome, based on 1,000 random draws. Can answer following types of questions: – What is the probability that NPV > 0? – What is the NPV at the first quartile of the distribution? – What is the volatility of NPV? (can be used as an input into real options) NBA6060, Fall 2024 19 19 Monte Carlo: key takeaways Advantages – Allows for more realistic assumptions about risk and interactions between variables and over time. – Gives a fuller description of project risks Likelihood of outcomes in a given range Average versus most likely outcomes Asymmetries – Forces you to think about the sources of risk Disadvantages – Requires a lot more assumptions – Can be sensitive to the assumptions (especially on distributions) Monte Carlo is not a decision criteria in itself, but a tool for better understanding the project’s potential outcomes. NBA6060, Fall 2024 20 20 10 THANK YOU NBA6060, Fall 2024 21 21 11