A capability is expected to add about £90k a month in gross margin once live. The team can ship it in five months, or in three months by adding two contractors at £25k a month each. Which number decides it?

The arithmetic, shown

Two months earlier at £90k a month is £180k of margin that would not otherwise exist. The contractors cost 2 people × £25k × 3 months = £150k. The decision is £180k against £150k, so acceleration is worth roughly £30k, before any consideration of risk.

That margin is thin enough that the honest answer is "it depends on the assumptions", which is the useful output: the case turns entirely on whether £90k a month is real and whether the contractors actually save two months. Both are worth more scrutiny than the £150k, which is the only number anyone usually debates.

Why the other options fail

• The total contractor cost of £150k is the number that gets the discussion, because it is certain, appears in a budget line and has an owner. Cost is visible and delay is not, which is precisely why organisations systematically under-invest in speed.
• The payback period is the right instrument for a capital purchase and the wrong one here. The spend does not create an asset that pays back; it moves a revenue stream forward in time.
• Capacity utilisation is the metric that produces the wrong answer most confidently. A team at 100% utilisation looks efficient and has, by queueing behaviour, the longest and least predictable lead times.

The assumption that dominates the error

Whether adding people actually compresses the schedule. Two contractors joining a five-month piece of work may deliver three months, or may deliver five months with more coordination overhead, depending on whether the work divides and how much context they need. State the assumption explicitly and test it at four weeks: if the schedule has not moved by then, it will not.

The second assumption is the £90k itself. Gross margin, not revenue, and ramped rather than instant: a capability rarely reaches steady state in its first month, so a realistic model is perhaps 40% of the number in month one, 70% in month two, which cuts the benefit of acceleration by a third and can reverse the decision.

What the number rules in or out

At this ratio the answer is close enough that either choice is defensible, and the tie-breaker should be risk rather than money: does shipping in three months increase the chance of shipping something that does not work? If yes, the extra two months buy quality at a price you have now quantified.

The same arithmetic rules out a great deal of cheaper debate elsewhere. A delay whose cost is under £5k a month is not worth an escalation meeting; one costing £90k a month justifies a dedicated decision and, usually, more expensive interventions than anybody proposes.

When this framing is the wrong one

When the benefit is a risk reduction rather than a revenue stream. Cost of delay on regulatory or security work is not a monthly margin figure; it is a probability multiplied by a consequence, and forcing it into the same arithmetic produces a smaller number than the work deserves. For that class, the honest model is expected loss avoided, stated with its uncertainty, not a false precision borrowed from this one.