EFN507 Chap.5 Sensitivity Analysis and Monte Carlo Simulation
Sensitivity Analysis and Monte Carlo Simulation
Beyond a single forecast
Week 3 asks how much an NPV depends on its assumptions.
The tutorial case gives sales and salvage values under three states of the economy with probabilities, and asks for the expected NPV, the effect of a higher rate for a riskier project, the value of abandoning the line after a weak first year, a one-way sensitivity of sales and salvage from 70% to 130% of their most likely values, and a two-way data table that respects the stated distributions.
From scenarios to simulation
Monte Carlo simulation, listed in the teaching plan, draws thousands of joint scenarios and reports the whole distribution of NPV.
The formula sheet gives the standard deviation of NPV for independent and for perfectly correlated cash flows, and the Week 3 materials include notes on simulating correlated normal variables. Certainty equivalents offer a second route to risk, discounting certain amounts at the risk-free rate.
What this chapter covers
- 01
Expected NPV across states of the economy
- 02
Option to abandon valued branch by branch
- 03
One-way sensitivity and break-even inputs
- 04
Two-way data tables that follow the stated distributions
- 05
Standard deviation of NPV with independent or correlated flows
- 06
Monte Carlo simulation and certainty equivalents
Worked example · free
Expected NPV and the chance of a loss
- +1Expected NPV = −1,000 + 600 ÷ 1.1 + 700 ÷ 1.21 = $123.97.
- +1Independent: σ = √(100² ÷ 1.21 + 150² ÷ 1.4641) = √23,632.26 = $153.73.
- +2Perfectly correlated: σ = 100 ÷ 1.1 + 150 ÷ 1.21 = $214.88.
- +1With a normal approximation, the probability of a loss is about 21% if independent and 28% if correlated.
Key terms
- Expected NPV
- The probability-weighted average of a project's NPV across possible outcomes.
- Sensitivity analysis
- Recomputing NPV while one input changes and the others stay at their most likely values.
- Monte Carlo simulation
- Valuing a project across many randomly drawn sets of inputs to describe the distribution of NPV.
- Certainty equivalent
- The certain cash amount an investor would accept in place of a risky expected cash flow.
- Break-even value
- The level of one input at which a project's NPV is exactly zero.
Sensitivity Analysis and Monte Carlo Simulation FAQ
Can I average scenario cash flows before computing NPV?
Yes for a plain project, because expected NPV is linear in the cash flows. No once there is an option such as abandonment, which changes the cash flows only in some states; then each branch must be valued before averaging.
What should a sensitivity table be used to decide?
Which input deserves attention. Report the input that moves NPV most, its break-even value and how far the most likely forecast sits from it. An input whose line is nearly flat can be estimated roughly without changing the decision.
Why does correlation between years matter?
Positively correlated cash flows move together, so good and bad years cluster and the spread of NPV widens. The expected NPV is unchanged, but the probability of a loss rises, which matters to a manager worried about downside risk.
Does simulation tell me which discount rate to use?
No. Simulation describes total risk, while markets reward only risk that cannot be diversified away. Discount at the opportunity cost of capital and use the simulated distribution to understand exposure, not to set the rate.
What is a two-way data table?
An Excel table that recomputes NPV over a grid of values for two inputs at once, such as sales and salvage. The Week 3 case asks for grid values that reflect the stated probability distributions rather than arbitrary percentages.
How are certainty equivalents related to risk-adjusted discounting?
Both give the same present value. One discounts the expected cash flow at a risk-adjusted rate; the other shrinks it to a certain amount and discounts at the risk-free rate. The shrink factor falls the further away the cash flow is.
Exam move
Rebuild the sensitivity table for a small project, locate the break-even sales level, and add an abandonment branch. Then compute the standard deviation of NPV both ways from the formula sheet.
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