Sensitivity, Scenario, and Break-Even Analysis

Why a single NPV is misleading

A project model takes a dozen inputs (revenue, growth, margin, tax rate, working capital, CapEx, discount rate, terminal value multiple, …) and spits out a single number. That number is highly precise and entirely false in the sense that nobody knows the right input values in advance.

Real-world capital-budgeting practice treats the point-estimate NPV as a starting point, then asks: how sensitive is it to my assumptions, and which assumptions matter most?

Three techniques in increasing order of sophistication.

1. One-variable sensitivity (tornado chart)

Vary each input one at a time, holding all others at base case. Record the NPV range. Sort by range size.

Example. Base case NPV = $40M. Sensitivity ranges:

Input	Low → High	NPV range
Revenue growth	0% → 10%	$-20M to$+110M (range $130M)
Discount rate	8% → 14%	$+80M to$-15M (range $95M)
Operating margin	25% → 35%	$-5M to$+85M (range $90M)
Initial CapEx	$800k → $1.2M	$+60M to$+20M (range $40M)
Terminal growth	1% → 4%	$+30M to$+55M (range $25M)
Tax rate	20% → 30%	$+50M to$+30M (range $20M)

Plotted as a horizontal bar chart sorted by range, this is a tornado chart. The widest bar (revenue growth here) is the input the project is most sensitive to. That’s where you spend your due-diligence time. Don’t argue with the CFO about the tax rate when revenue growth uncertainty is six times more material.

Tornado charts are easy to compute and easy to communicate. The limitation: they vary inputs independently, so they miss correlations. If revenue growth and margin are positively correlated (good times help both), the tornado understates upside and downside.

2. Scenarios (best / base / worst)

Define 2-3 internally consistent scenarios with multiple inputs varying together:

Variable	Worst	Base	Best
Revenue growth	0%	5%	8%
Operating margin	22%	30%	33%
Working capital / sales	15%	10%	8%
Discount rate	13%	10%	9%
Terminal growth	1%	2%	3%
NPV	$-25M	$+40M	$+150M

Scenarios respect correlations. They produce a small number of realistic outcomes managers can reason about. Assign rough probabilities and compute expected NPV:

$$E[NPV] = 0.25 \times (-25) + 0.50 \times 40 + 0.25 \times 150 = +51\text{M}.$$

The downside of scenarios: they collapse a continuous distribution of outcomes into 2-3 points. The Monte Carlo extension fixes that.

3. Break-even analysis

For each key driver, ask: at what value does NPV = 0?

• Revenue growth break-even: 2.5% (if growth drops below this, project is value-destroying).
• Operating margin break-even: 24%.
• Discount rate break-even: 12.5% (this is just the IRR).

Break-even points are easy to communicate to non-technical audiences: “we need at least 2.5% revenue growth to break even.” Pair them with management’s confidence level — how likely is it that revenue growth ends up below break-even?

Monte Carlo, briefly

Instead of three scenarios, sample 10,000 realizations from distributions for each input (with appropriate correlation structure), compute NPV for each, and plot the histogram.

Outputs:

• Mean / median NPV.
• Probability that NPV > 0.
• Tail risk (e.g., 5th percentile NPV).

Useful when project NPV is highly skewed (long upside tail, limited downside — typical of real options) or when many small input uncertainties compound. Not necessary for most coursework, but ubiquitous in real-world project finance.

When sensitivity tells you to walk away

Three patterns that should make you rethink the project, regardless of base-case NPV:

1. Knife-edge NPV that swings from +$20M to −$20M for ±5% changes in a single input — too fragile to bet the firm on.
2. High break-even threshold that the operating team can’t commit to. If breakeven revenue growth is 8% and history says the segment grows at 3%, the project is probably underwater.
3. Discount rate close to IRR. If your IRR is barely above cost of capital, you’re earning roughly market returns for taking project-specific risk. The expected risk-adjusted return is near zero.

Sensitivity analysis isn’t just defensive — it sometimes reveals projects whose downside risk vastly exceeds their headline NPV. That’s a project worth not doing, even if NPV is technically positive.

Practical workflow

For any non-trivial capital decision:

1. Build a clean DCF model.
2. Compute base-case NPV.
3. Do tornado on every input.
4. Bracket the top 3-4 inputs in a scenario table.
5. For each, find break-even.
6. Discuss the results with the operating team. The numbers that matter are the ones the team can actually influence.