Timing the Smart-Traffic Payback

Timing the Smart-Traffic Payback

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

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Ada 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.

Annual benefit changes payback An input card leads through the rule payback = 117.05 million x 365 / (benefit - 13.08 million OpEx) to the payback result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A larger annual benefit shortens payback after the same operating cost is removed.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 2175 million USD/year.

  2. 2

    Name the relationship. payback = 117.05 million x 365 / (benefit - 13.08 million OpEx)

  3. 3

    Substitute with units. 117.05 x 365 / (2,175 - 13.08) = 19.76 days

  4. 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.

2175 million USD/year
Chapter baseline
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?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only annual benefit moves here. Field effects named in the technical boundary stay fixed.
TryRecompute CapEx: 83.25 + 18.9 + 2.4 + 12.5 = 117.05 million dollars.
ObserveTrack OpEx: 0.89 + 1.89 + 8.2 + 2.1 = 13.08 million dollars per year.
ExplainExplain Payback: 117.05 / 2,161.92 = 0.05415 years, and 0.05415 x 365 = 19.76 days, which rounds to 19.8 days.

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 = 117.05 million dollars
  • OpEx: 0.89 + 1.89 + 8.2 + 2.1 = 13.08 million dollars per year

Then the benefit and the payback:

  • Total annual benefit: 1.71 + 0.465 = 2.175 billion dollars
  • Net of operating cost: 2.175 - 0.01308 = 2.16192 billion 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, and 0.05415 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.

Technical boundaries. This smart-traffic payback deliberately does not simulate benefit ramp-up, financing, maintenance variation, or discounted cash flow. It divides the fixed CapEx by the chapter's annual benefit after subtracting stated OpEx.