Sensitivity and Risk: Stress-Testing the Business Case

A single net present value figure feels reassuring. "This heat-recovery upgrade is worth RM1,197,140." It looks precise, final, bankable. But every ringgit of that number rests on assumptions — a fuel price, a tariff, a build cost, a discount rate — and not one of them is guaranteed. A single NPV number hides its own fragility. A range tells the truth.

This part is about stress-testing. We take the polished business case from earlier in the course and shake it: flex the inputs, bundle them into good and bad worlds, name the risks, and finally use all of that to choose between competing projects when the budget only stretches to one. If you have not yet met the metrics we are about to stress — NPV, IRR and payback — revisit Part 9 and Part 10 of this course first, because sensitivity analysis is only as good as your grip on the numbers being flexed.

Why one number is dangerous

Imagine presenting your board with "NPV = RM1,197,140" and nothing else. The first sharp question — "and if steel prices push the build cost up 20%?" — leaves you guessing on the spot. Sensitivity analysis is simply doing that questioning yourself, in advance, on paper.

The technique has three layers, each answering a different question:

- One-at-a-time (OAT) sensitivity — which single input matters most?
- Scenario analysis — what does a whole bad day, or a whole good day, look like?
- Risk-and-mitigation — what could go wrong, and what will we do about it?

Get through those three and you can defend any number in the room.

One-at-a-time sensitivity and the tornado diagram

The baseline for our worked example is the thermal-recovery project from Part 11: capex of RM215,000, net annual savings of about RM210,450 (dominated by natural-gas savings of RM189,000/yr, plus RM13,750 in electricity and RM7,700 in carbon revenue), evaluated over 10 years at an 8% discount rate. Baseline NPV = RM1,197,140.

OAT sensitivity means holding everything fixed except one input, flexing that input by a set percentage, and recording how far NPV moves. The percentage change in NPV per unit change in an input is its sensitivity:

$$\text{Sensitivity} = \frac{\Delta \text{NPV}}{\text{NPV}_{\text{base}}} \times 100\%$$

Take the natural-gas price. A +20% gas price lifts annual thermal savings by RM37,800. Discounted over 10 years at 8% (annuity factor 6.7101), that is worth an extra:

$$37{,}800 \times 6.7101 = \text{RM}253{,}642$$

$$\frac{253{,}642}{1{,}197{,}140} \times 100\% \approx +21\%$$

Now flex capex by +20%. That adds RM43,000 — but only once, at Year 0, undiscounted:

$$\frac{-43{,}000}{1{,}197{,}140} \times 100\% \approx -4\%$$

That contrast is the whole lesson. For a project this cheap to build and this dominated by fuel savings, the gas price is the giant and capex is a pebble. Rank every input this way and plot each as a horizontal bar — longest at the top — and you get a tornado diagram, so named because the widest bars up top taper to slivers below.

Use sensible, defensible stress ranges rather than a flat ±10%. The recommended bands for a Malaysian energy case are: tariff ±8–20%, fuel price ±15–30%, discount rate 5–12%, and capex overrun ±30%. For our project, flexing each across its band:

| Input (stress range) | NPV swing | % of baseline |
|---|---|---|
| Natural-gas / thermal savings (±20%) | ±RM253,600 | ±21% |
| Discount rate (5% → 12%) | +RM213k / −RM223k | +18% / −19% |
| Capex overrun (±30%) | ∓RM64,500 | ∓5.4% |
| Carbon price (RM50–200/tCO₂) | −RM26k / +RM52k | −2% / +4% |
| Electricity tariff (±20%) | ±RM18,450 | ±1.5% |

The tornado is unambiguous: negotiate the gas contract and pressure-test the discount rate, because those two bars swamp everything else. Fussing over a few thousand ringgit of electricity tariff is, for this project, wasted energy. (A lighting or motor project would tornado the other way — there, tariff is the giant. The shape is always project-specific, which is exactly why you draw it fresh each time.)

Scenario analysis: bundling the assumptions

OAT sensitivity moves one lever at a time, but real bad days move several at once — the build runs over and fuel prices soften and the plant runs fewer hours. Scenario analysis bundles a coherent set of assumptions into named worlds, usually three:

- High case (optimistic) — NPV ≈ RM1.50M. Fuel prices firm, the plant runs at full load, capex lands on budget.
- Medium case (expected) — NPV ≈ RM1.20M. Your baseline; the number you actually plan around.
- Low case (pessimistic) — NPV ≈ RM0.90M. Capex overruns, savings underperform, carbon revenue disappoints.

Notice the honest headline: even in the low case, NPV stays firmly positive at RM0.90 million. That is a far stronger thing to tell a board than a lone medium-case figure. You are no longer saying "trust me, it's RM1.20M." You are saying "across a plausible range from RM0.90M to RM1.50M, this project never loses money." That range is what earns the signature.

If your low case had gone negative, that too would be priceless information — it would tell you the project only works if the world cooperates, and you would go re-tighten the weakest assumption before committing.

Risk and mitigation: naming the demons

Sensitivity tells you how much an input matters; risk management tells you what you will do about it. The discipline is to pair every material risk with a concrete mitigation:

- Tariff and fuel-price volatility → carry a sensitivity band of ±20% in the business case, so no one is surprised, and where possible lock rates through supply contracts.
- Capex overrun → build a 10–15% contingency into the budget from day one, rather than discovering it as a nasty variance later.
- Equipment underperformance → apply an efficiency-degradation factor — assume, say, that savings fade 1–2% a year as equipment ages and fouls, instead of modelling year-one performance forever.

Each mitigation quietly reshapes the model: the contingency raises capex, the degradation factor trims savings. Applied honestly, they pull your medium case a little closer to your low case — which is the point. A business case that survives its own mitigations is one you can defend.

The multi-criteria decision matrix: choosing one winner

Now the hardest situation in practice. You have three good projects, all with positive NPV, and budget for exactly one. NPV alone will not decide it, because the projects compete on different strengths — one is a cash machine, one is a carbon champion, one is merely solid. You need to weigh several criteria at once. That is a multi-criteria decision matrix.

The method has three steps:

1. Normalise each metric onto a common 1–10 scale (10 = best), so a payback in years and an NPV in millions can be compared.
2. Weight each criterion by importance. A defensible default: NPV 30%, IRR 20%, Payback 20%, Carbon 20%, Risk 10%.
3. Score each project as the weighted sum, then rank.

The weighted score is just:

$$S = \sum_{i} w_i \times s_i$$

where \(w_i\) is a criterion's weight and \(s_i\) is the project's normalised 1–10 score on it. Consider three real candidates on a Malaysian factory site:

- Project A — LED lighting retrofit (balanced all-rounder)
- Project B — high-efficiency chiller replacement (big, carbon-heavy, slow, risky)
- Project C — compressed-air and steam leak-repair programme (cheap, fast-payback cash win)

| Criterion (weight) | Project A | Project B | Project C |
|---|---|---|---|
| NPV (30%) | 6.5 | 8.0 | 7.2 |
| IRR (20%) | 7.0 | 4.0 | 9.5 |
| Payback (20%) | 7.5 | 3.0 | 9.5 |
| Carbon (20%) | 6.0 | 9.5 | 5.0 |
| Risk, higher = safer (10%) | 7.3 | 2.3 | 7.0 |
| Weighted score | 6.78 | 5.93 | 7.66 |

Working Project C's total to show the arithmetic:

$$S_C = (0.30 \times 7.2) + (0.20 \times 9.5) + (0.20 \times 9.5) + (0.20 \times 5.0) + (0.10 \times 7.0) = 7.66$$

Project C wins at 7.66, ahead of A (6.78) and B (5.93). The leak-repair programme is not the biggest project — the chiller has a larger NPV and far more carbon — but its blistering IRR, near-instant payback and low risk carry the weighted vote.

A useful sidecar to the risk score is an explicit ease-of-implementation rating, because a project you can actually deliver beats one that stalls. Score it 1–10: leak repair 9 (a few valves and a weekend), LED retrofit 8 (swap fittings, minimal disruption), chiller replacement 2 (major plant, downtime, procurement lead time). Ease often correlates with the quick wins you should bank first — a theme that connects directly to where a project sits on the marginal abatement cost curve we built in Part 13: the cheap, easy, negative-cost measures belong at the front of the queue.

The winner flips with the weights

Here is the part every decision-maker must internalise: the ranking is a mirror of your priorities, not a fact of nature. Re-run the same table for a firm under a hard carbon target — say it re-weights to NPV 20%, IRR 10%, Payback 10%, Carbon 50%, Risk 10%:

- Project B: 7.28
- Project C: 6.54
- Project A: 6.48

Now Project B, the chiller, wins. Nothing about the projects changed — only what the firm decided to value. A cash-constrained business rationally picks C; a decarbonising business rationally picks B. This is not a flaw in the method; it is the method doing its most honest work — forcing you to state your priorities out loud, as numbers, before the answer falls out. Always run the matrix at two or three weightings and show the board how the winner moves. If your preferred project only wins under one convenient set of weights, you have learned something important.

The takeaway

One NPV number is a claim; a stress-tested range is an argument. Flex your inputs one at a time to find which one or two actually drive the case, bundle them into High/Medium/Low worlds to show the floor as well as the ceiling, pair every risk with a real mitigation, and — when the budget forces a single choice — let a weighted decision matrix rank the field while you watch how the winner shifts with your priorities. A business case that has survived all four still standing is one worth funding.

This kind of continuous stress-testing is far easier when your savings assumptions are grounded in live data rather than a one-off spreadsheet. Real interval readings from your meters — the sort of visibility we cover in how electricity meters work and that platforms like CobiNeural surface across energy, air, water and chilled-water — let you replace guessed degradation factors with measured ones, and check whether that tornado-topping assumption is holding up in the real building. And if maximum demand is one of your stressed inputs, our maximum-demand calculator lets you flex the tariff band directly.

Next up — Part 15: Assembling the Recommendation, where we take everything from cash flows to sensitivity and package it into a decision-ready proposal your board will actually approve.