Timing the Smart-Traffic Payback
Timing the Smart-Traffic Payback
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Timing the Smart-Traffic Payback
The chapter’s smart-traffic case totals $117.05M of CapEx across 4,500 intersections and $13.08M a year of OpEx, set against an annual benefit of $2.175B. Divide the capital by the net benefit and the program appears to repay itself in 19.7 days — under three weeks. This is the chapter’s boldest number, so this audit re-adds every line and re-times the result to ask whether the payback really lands that fast.
Companion to the chapter Costing and Sizing IoT Projects — every number here comes from that chapter.
See the relationship before changing it
The figure reads from left to right. The blue card is annual benefit. The middle card applies this page's rule. The green card is payback. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only annual benefit, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 2175 million USD/year.
- 2
Name the relationship. payback = 117.05 million x 365 / (benefit - 13.08 million OpEx)
- 3
Substitute with units. 117.05 x 365 / (2,175 - 13.08) = 19.76 days
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change annual benefit
Try Predict the direction of payback = 117.05 million x 365 / (benefit - 13.08 million OpEx). Test another annual benefit, then compare payback.
Observe A larger annual benefit shortens payback after the same operating cost is removed. Reset annual benefit to 2175 and compare payback.
Explain A larger annual benefit shortens payback after the same operating cost is removed.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Ready: use the stated baseline inputs, then compare each displayed result.
Ada: This is the chapter’s boldest number — a smart-traffic program repaying itself in under three weeks. A claim that strong deserves a full audit, so let me re-add every line and re-time the payback.
Capital and operating costs first:
- CapEx:
83.25 + 18.9 + 2.4 + 12.5 = 117.05million dollars - OpEx:
0.89 + 1.89 + 8.2 + 2.1 = 13.08million dollars per year
Then the benefit and the payback:
- Total annual benefit:
1.71 + 0.465 = 2.175billion dollars - Net of operating cost:
2.175 - 0.01308 = 2.16192billion dollars, rounded to 2.162 billion - Return per dollar invested, per year:
2,161.92 / 117.05 = 18.47 - Payback:
117.05 / 2,161.92 = 0.05415 years, and0.05415 x 365 = 19.76 days, which rounds to 19.8 days.
Every component ties out, and the payback rounds to 19.8 days rather than the 19.7 the text prints (a truncated 19.76) — a rounding nudge that leaves the headline intact: the return is so large that the program repays its full capital cost in under three weeks even after operating costs are netted out.
Every number above is taken from the chapter’s own material and re-derived step by step.