The Payback Gap Is Pure Capital Cost

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

The Payback Gap Is Pure Capital Cost

A 12-building campus with 2,400 rooms and 480 Wi-Fi APs already logs about 18,000 daily connected devices, so the chapter repurposes that Wi-Fi data (plus 50 supplementary PIR sensors) to cut a $2.8 million/year HVAC bill by 22%. The hybrid approach costs $33,500 to implement and claims a payback near 20 days, against $480,000 and roughly 284 days for a dedicated PIR deployment. This audit asks the question that payback gap invites: is the hybrid approach really paying back faster because it saves more, or purely because it costs less to install?

Companion to the chapter Sensing with Existing Infrastructure — every number here comes from that chapter.

Ada: The worked example says the hybrid approach pays back in about 20 days and dedicated PIR in about 284 days. Those numbers are correct, but the reason the gap is so wide is worth pinning down, because it decides what the comparison is really testing.

Both scenarios claim the same annual saving, so the daily saving is shared:

  • Annual: $2,800,000 x 22% = $616,000; per day $616,000 / 365 = $1,687.67
  • Hybrid payback: $33,500 / $1,687.67 = 19.9 days
  • Dedicated payback: $480,000 / $1,687.67 = 284.4 days

Now take the ratio of those two payback times:

  • Payback ratio: 284.4 / 19.9 = 14.33
  • Capital-cost ratio: $480,000 / $33,500 = 14.33

They are identical to three digits, and they must be, because the savings term cancels when you divide one payback by the other. The hybrid does not pay back 14x faster because it saves more; the model gives it zero savings advantage. The entire speed-up is capital cost, 93% lower (1 - 33,500 / 480,000 = 0.930). That reframes the decision honestly: the infrastructure approach wins purely on what it costs to install, so the only question that actually matters is whether its +/-10% zone accuracy is good enough for HVAC scheduling. The accuracy trade, not the ROI, is where the real risk sits.

Every number above is taken from the chapter’s own material and re-derived step by step.