How we reach a conclusion, and how you can check it

The question. A project is close to the hurdle. Three inputs are uncertain: saleable output, the price achieved, and the operating cost. Which one actually decides whether the case clears its threshold?

Assumed inputs. Planned saleable output 8,100 tonnes a year; assumed price 400 per tonne; assumed operating cost 2.40 million a year; assumed capital charge to be covered 0.60 million a year.

Baseline arithmetic. Revenue is 8,100 × 400 = 3,240,000. Contribution after the capital charge is 3,240,000 − 2,400,000 − 600,000 = 240,000. The case clears the charge with 240,000 to spare — a margin of about 7% of revenue.

Testing each input.

Reading it. A 10% fall in output or in price wipes the surplus out by the same 324,000, because both scale revenue directly. A 10% rise in operating cost removes exactly the 240,000 surplus. Output and price are equally decisive, cost slightly less so — which tells the project where to spend its effort: on confirming volume and price, not on shaving cost.

Caveats. The inputs are assumed, not measured. The comparison treats each change in isolation, whereas in practice a weak market may move volume and price together. No discounting is applied, and the capital charge is treated as a single annual figure. A real assessment would model these jointly and over time.

Decision implication. Before committing, establish volume and price to a tighter range — those are the two inputs whose uncertainty the case cannot absorb.

The question. A hotel wants to know whether it is improving its energy performance. It looks at energy per occupied room. In a quieter month the figure worsens. Has performance slipped?

Assumed inputs. A fixed baseload of 60,000 kWh a month that does not vary with occupancy, plus 12 kWh per occupied room-night.

Two months.

The arithmetic. Busier month: 60,000 + (3,000 × 12) = 96,000 kWh, and 96,000 ÷ 3,000 = 32.0 kWh per occupied room. Quieter month: 60,000 + (2,000 × 12) = 84,000 kWh, and 84,000 ÷ 2,000 = 42.0 kWh per occupied room.

Reading it. Absolute energy fell by 12,000 kWh — a reduction in consumption; spend also depends on tariffs and fixed charges. The per-room figure rose by 10 kWh, about 31%. Performance did not change at all: the same baseload and the same per-room consumption applied in both months. Only the denominator moved.

Caveats. The baseload and per-room figures are assumed. Real properties have several services — restaurants, conference space, laundry, pools — sharing meters, so a per-room figure bundles in consumption that has nothing to do with rooms. The split can be estimated from a property's own records but not from this illustration.

Decision implication. Read absolute use alongside the ratio, and give each service a denominator that matches its own meter boundary. A ratio alone will penalise a quiet month for reasons nobody can act on.

The question. A business states that a material it sells contains 30% recycled content. A customer asks for the basis. What would actually demonstrate the claim, and what is missing?

Method. The claim is broken into the evidence requirements it depends on, and each is assessed against what exists. This is a structure, not a score: each line is answered so the gaps are visible.

Reading it. The claim is plausible but not yet demonstrable. Two gaps matter most: the calculation is not documented, so the 30% cannot be shown to be derived correctly, and there is no change control, so a supplier substitution could silently alter the material. Traceability exists in part, but traceability is not quality — it says where material came from, not what it can be shown to be.

Caveats. The statuses are illustrative and describe no real supplier. The requirements would differ with the market, the product and the specific claim being made — a recycled-content claim for one application is not governed by the same evidence as another. Nothing here determines how any material should be classified or what any rule requires.

Decision implication. Two first actions are to document how the percentage is calculated and to agree with the supplier what changes must be notified. These alone do not substantiate the claim: the missing batch evidence, the chain of custody and the current composition record must also be resolved before the 30% can be demonstrated to a customer.