Demand and Benefit Forecasts by the Numbers
Chapter 7 of 10 · 10 min read
Scenarios, sensitivity and switching values
Symmetric ±20% ranges against evidence-based ones, a 19.311m-can switching volume reached in 9.3% of runs, three coherent scenarios, and the board's conditional approval.
A forecast range says what volume to expect. An appraisal has to say what that volume means for the decision. This chapter takes the plant’s corrected business case and asks the questions a board should ask of any investment that rests on a forecast: which assumptions move the answer most, how far each can plausibly move, at what value each one turns the case from worthwhile to not, and what coherent stories about the future look like when several assumptions move together.
It starts with the sensitivity table the business case actually contained, shows why its symmetric ranges misled, replaces them with ranges taken from the evidence, and finds the switching values. It ends with the board’s decision, made with these numbers in front of it.
The corrected base
This is an illustration. All money is A$ excluding GST. The base for every calculation in this chapter is the managing director’s inside view with the cannibalisation error from Chapter 2 corrected: 25.32m cans a year at steady state, an average contribution of A$0.126 per can, fixed costs of A$1.30m a year, the A$57,600 a year lost from mobile customers moving to the plant, the sale of mobile rig 2 for A$320,000 in year 1, capital of A$5.4m in 2024, a 70% and 95% ramp in 2025 and 2026, and ten operating years discounted at 9%. Its NPV is A$5,711.8k.
Sensitivity and scenario analysis: testing a business case before you trust it covers the mechanics of one-at-a-time sensitivity, tornado charts and switching values on a simpler machine investment. This chapter assumes those mechanics and concentrates on where the ranges come from.
The symmetric tornado
The business case’s sensitivity table moved each assumption 20% either way and recorded the NPV at each end:
- Steady-state volume −20%/+20%: A$1,805.7k to A$9,618.0k, a swing of A$7,812.3k.
- Contribution per can −20%/+20%: exactly the same, A$1,805.7k to A$9,618.0k, because volume and contribution per can multiply each other; a 20% change in either changes contribution by the same amount.
- Fixed costs +20%/−20%: A$4,043.2k to A$7,380.4k, a swing of A$3,337.2k.
- Capital +20%/−20%: A$4,631.8k to A$6,791.8k, a swing of A$2,160.0k.
- Year-1 ramp 56%/84%: A$5,300.6k to A$6,123.0k, a swing of A$822.4k.
The identical first two rows are worth a pause. In the arithmetic, volume and contribution per can are interchangeable: the plant’s contribution is their product. In the business they are different drivers with different evidence. Volume depends on how many prospects sign and how much they fill, which the record from rig 2 describes. Contribution per can depends on negotiated rates and on the cost of gases, power, cartons and other consumables, which the record does not cover at all. Giving both the same ±20% treats two unlike uncertainties as one, and a reader who sees two bars of equal length will assume they deserve equal attention.
Every row stayed positive. Read naively, the table said that no single assumption could sink the plant, and that volume could add almost as much value as it could take away. Both conclusions came from the method, not from the evidence. A symmetric range treats the plan as the middle of the possible outcomes. Chapter 6 found it far out in the upper tail.
Ranges from the evidence
An evidence-based range asks, for each assumption, what the business’s records and the relevant published evidence say about how far it moves, and in which direction. For the plant, the reviewer set these ranges:
- Volume: the simulated P10 and P90 from Chapter 6, 11.57m and 19.20m cans, at the inside mix. Both ends lie below the plan.
- Contribution per can: −10% to +5%. Larger customers negotiate rates down more often than up, and consumables prices tend to rise between quote and operation, so the reviewer judged the downside to be about twice the upside.
- Capital: a ratio of 1.20 to 1.00 of budget. Capital projects seldom finish under budget; the high end allows a 20% overrun.
- Fixed costs: +10% to −5%.
- Year-1 ramp: the rig 2 record’s 36.75% against the plan’s 70%, from Ramp-up curves: how fast the volume arrives.
- Year-2 ramp: the record’s 90.75% against 100%.
| NPV at low end | NPV at high end | Swing | |
|---|---|---|---|
| Volume, simulated P10 11.57m / P90 19.20m | −4,894.7 | 991.1 | 5,885.8 |
| Contribution per can −10% / +5% | 3,758.7 | 6,688.4 | 2,929.6 |
| Fixed costs +10% / −5% | 4,877.5 | 6,129.0 | 1,251.4 |
| Capital ratio 1.20 / 1.00 | 4,631.8 | 5,711.8 | 1,080.0 |
| Year-1 ramp 36.75% / 70% | 4,735.2 | 5,711.8 | 976.6 |
| Year-2 ramp 90.75% / 100% | 5,597.3 | 5,846.6 | 249.3 |
The order of the bars hardly changed: volume first, contribution per can second, the ramps last. What changed is their position. Volume’s range now runs from A$10,606.5k below the base to A$4,720.7k below it. Even the optimistic end of the evidence leaves the plant worth A$991.1k, a sixth of the business case. For contribution per can, the downside of A$1,953.1k is twice the upside of A$976.6k. The symmetric table had hidden the single most important fact about the forecast: it was not the centre of anything.
Two rows deserve a comment. The ramp rows are small even with the rig 2 record’s much slower first year, which Chapter 4 showed to be realistic. A slow ramp delays contribution by a year or so; it does not remove it. And capital, the item a board usually scrutinises hardest, has a smaller swing than volume by a factor of more than five.
Switching values
A switching value is the value of one assumption at which NPV falls to zero, with everything else held at the base. It turns the tornado’s question, “how much does NPV move”, into the one a board can test against evidence: “how bad does this have to get before the plant is not worth building”.
For the corrected business case:
- Steady-state volume: 17.915m cans a year, 70.8% of the plan, at the inside mix and ramp.
- With the rig 2 ramp in place of the plan’s: 18.975m, 74.9% of the plan.
- With the outside view’s mix, A$0.124 a can, and the rig 2 ramp: 19.311m cans.
- Contribution per can at the plan’s volume and ramp: A$0.089, 29.2% below the plan’s A$0.126.
- Capital at the plan’s volume: A$11,111.8k, 105.8% over budget.
- Year-1 ramp: none. Even with no volume at all in 2025, and 95% in 2026, NPV is still A$3,655.8k.
The last two lines show where the decision does not lie. The plant could have cost twice its budget, or produced nothing in its first year, and still paid its way at the plan’s steady-state volume. The decision lay almost entirely in the steady-state volume.
- K
- Capital, A$5,400.0k in 2024
- F + D
- Fixed costs plus the dis-benefit, A$1,300.0k + A$57.6k = A$1,357.6k a year
- a
- Annuity factor, 10 years at 9%: 6.41766
- S × v
- Sale of rig 2 in year 1, A$320.0k ÷ 1.09 = A$293.6k
- c
- Contribution per can, outside mix: A$0.12424
- R
- Ramp-weighted factor, 0.3675 ÷ 1.09 + 0.9075 ÷ 1.09² + the years 3 to 10 at full volume: 5.760
- Numerator: 5,400.0 + 1,357.6 × 6.41766 − 293.6 = 5,400.0 + 8,712.6 − 293.6 = A$13,819.0k
- Denominator: 0.12424 × 5.760 = A$715.6k per million cans a year
- V* = 13,819.0 ÷ 715.6 = 19.311m cans a year
The same volume can be written with the inside mix or the plan’s ramp, and the answer changes by up to 1.4m cans. A switching value is only meaningful with the assumptions it holds fixed stated beside it, and for the board the relevant version is the one with the outside view’s mix and ramp, because those are the conditions the evidence says the plant will meet.
The probability of beating it
A switching value becomes much more useful once it is set against the forecast distribution. Of the 20,000 independent runs in Chapter 6, 9.3% reached 19.311m cans; with the common market factor, 14.3%. The switching volume is 1.260 times the simulated P50 and sits just above the P90 of 19.20m. On the record’s evidence, the plant would pay for itself in roughly one future in ten.
Running the full appraisal on every simulated volume, with each run’s own mix and the rig 2 ramp, gives a distribution of NPV: mean −A$2,820.3k, P10 −A$5,180.8k, P50 −A$2,833.7k, P90 −A$447.9k, and a probability of a positive NPV of 6.5%. That is lower than the 9.3% of runs reaching the switching volume, because runs heavy in RTD work earn less per can and need more volume to break even. The mix is not a detail; it moves the answer by several percentage points.
Coherent scenarios
One-at-a-time sensitivity moves one assumption while freezing the rest, which is rarely how the future arrives. If the anchor RTD brand pulls out, the ramp is slower too, and a business under pressure tends to accept the cost overruns it would otherwise fight. Hyndman and Athanasopoulos describe scenario forecasting as building a small number of internally consistent stories about the future, each with its own set of assumptions, rather than combining extremes at random. The reviewer built three.
Each scenario holds together. The low case loses one RTD brand’s expected 1.920m cans, ramps slowly because the anchor is gone, and lets capital run 13% over, as a business distracted by a lost customer might. The high case adds a surge in non-alcoholic work at a negotiated A$0.12 a can, slightly diluting the average contribution to A$0.123. Neither is a worst or best case; they are plausible stories, and each can be checked against leading indicators once the plant is running.
A scenario is most useful when it names the early signs by which the business would recognise it. The low case would show first in the anchor brand’s printed-can orders and trial runs: a brand that has not ordered printed cans 14 weeks before its planned start will not start on time. The central case would show as customer starts arriving at roughly the rig 2 pace, with first-year volumes near 0.8 of their letters. The high case would show as non-alcoholic brands asking for trial runs and new can formats well beyond the 12 customers planned. The reviewer listed these signs beside each scenario so that the quarterly tracking the board was about to require could say, each quarter, which story the plant was following.
The high scenario matters most for the decision. It is the story in which the managing director’s strategic bet on non-beer drinks pays off handsomely, and the plant still does not quite earn its cost of capital. A board that wants the plant for that bet should know that it is paying for an option on diversification, not buying a project that the volume forecast supports.
The error: ranges that pretended to be symmetric
This is an illustration. The first sensitivity table, prepared for the business case, used ±20% for every assumption. For volume, +20% meant 30.384m cans a year. That is above the line’s practical capacity of 28.197m at the plan’s 578 runs a year, from Chapter 2, so the table’s best case could not have been produced by the line it was appraising. None of the 20,000 simulated runs reached it.
The reviewer detected the error by setting each range beside the evidence for it: the simulated volume distribution from Chapter 6, the capital ratio, and the rig 2 ramp. Wherever there was evidence, the downside was several times the upside, and for volume the upside relative to the plan was nil. The correction was to replace every range with one stated with its source, as in the evidence-based tornado above, and to add two checks to the business case template: any range must be feasible for the plant being appraised, and any symmetric range must be justified by evidence that the plan is the median.
The board’s approval
The board met in late February 2024 with the corrected business case, the forecast range, the tornado with evidence-based ranges, the switching values and the three scenarios. It approved the plant. As Chapter 1 described, it was persuaded partly by the managing director’s argument that whatever had been underestimated would be made up, as it always had been, and partly by the strategic aim of diversifying beyond beer.
That was a legitimate choice, made with the evidence in view. The board’s two conditions, quarterly benefit tracking with leading indicators and a post-completion review at about 21 months, were the right kind of response to a decision taken against the central forecast. Their value depends on their precision. A condition is strongest when the measure, the threshold and the response are written down before the evidence arrives: for example, “if the deseasonalised run-rate is below the switching volume of 19.311m cans at the review, no further capital is committed to the plant until the review’s findings are accepted”. Stopping rules and kill criteria written before the evidence in Stage Gates and Stopping Rules by the Numbers shows how to write such criteria and how a draft paper can try to move them once the evidence is in.
The switching volume and the scenarios became the yardsticks for everything that followed. Tracking benefits against a phased plan sets up the quarterly tracking, and Chapter 10 returns to the 19.311m threshold when the plant’s actual run-rate is known.
Exercise: a cheaper plant
Before approval, the operations manager finds that a refurbished filler and a smaller cold room would bring the capital cost down from A$5.4m to A$4.6m, with no change to the line’s speed, costs or volumes. Using the outside view’s mix and the rig 2 ramp, what is the new switching volume, how likely is the plant to reach it, and what is the NPV at the simulated P50?
Worked answer. Only K in the switching-value formula changes, from A$5,400.0k to A$4,600.0k, so the numerator falls by A$800.0k to A$13,019.0k and the switching volume becomes 13,019.0 ÷ 715.6 ≈ 18.19m, or 18.194m cans a year when the calculation is carried with unrounded figures. Of the 20,000 independent runs, 17.1% reach it, and 20.3% with the common market factor. At the P50 of 15.325m cans, NPV improves by exactly the A$800.0k saved in year 0, from −A$2,852.5k to −A$2,052.5k. Cheaper capital roughly doubles the chance of success, from 9.3% to 17.1%, but the plant still fails in about four futures out of five. The decision still rests on volume, and a cheaper line does not change that.