Traffic by class, toll by class, 365 days and a leakage haircut: four lines that every toll road model rests on, and one input that is often the wrong count.
Toll road revenue is annual average daily traffic times the toll, by vehicle class, times 365, less leakage. An illustrative barrier-tolled road carrying 39,000 vehicles a day, with cars at $3.20, light commercial vehicles at $4.80 and heavy goods vehicles at $9.60, collects $150,400 a day, $54.896m of gross tolls a year and $53.52m after 2.5 per cent leakage. Heavy goods vehicles are 7.7 per cent of the traffic and 19.1 per cent of the money.
Worked in full in The Infrastructure Investment Analyst by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The road is fictional. It has a single mainline toll plaza, so every vehicle pays one toll for passing it and trip length does not enter the calculation. Traffic and tolls are year-1 figures.
| Vehicle class | AADT | Toll, $ |
|---|---|---|
| Cars | 32,000 | 3.20 |
| Light commercial | 4,000 | 4.80 |
| Heavy goods | 3,000 | 9.60 |
| Total | 39,000 |
Other inputs: leakage of 2.5 per cent, traffic growth of 1.5 per cent a year and toll indexation of 2.5 per cent a year, all illustrative. AADT, annual average daily traffic, is total annual traffic divided by 365, weekends and holidays included.
Daily revenue = Σ AADTclass × tollclass
Cars: 32,000 × $3.20 = $102,400 Light commercial: 4,000 × $4.80 = $19,200 Heavy goods: 3,000 × $9.60 = $28,800
Total = $150,400 a day
Excel: =SUMPRODUCT(AADT_range,Toll_range)*365
Gross toll revenue = $150,400 × 365 = $54.896m
Leakage = $54.896m × 2.5% = $1.37m
Net toll revenue = $54.896m × (1 − 2.5%) = $53.52m
Transactions = 39,000 × 365 = 14.23 million; average toll = $150,400 / 39,000 = $3.856
| Class | Transactions, m | Revenue, $m gross | Traffic % | Revenue % |
|---|---|---|---|---|
| Cars | 11.68 | 37.38 | 82.1 | 68.1 |
| Light commercial | 1.46 | 7.01 | 10.3 | 12.8 |
| Heavy goods | 1.09 | 10.51 | 7.7 | 19.1 |
| Total | 14.23 | 54.896 | 100 | 100 |
The class split is the first thing to check in a traffic and revenue study. Heavy goods traffic follows freight and industrial activity, not commuting, and it is the class most likely to divert to a free alternative when tolls rise. A 10 per cent fall in heavy goods traffic costs $1.02m of net revenue, 1.91 per cent of the total, from a class that is only 7.7 per cent of vehicles.
Year 2 revenue = year 1 × (1 + traffic growth) × (1 + indexation)
= $53.52m × 1.015 × 1.025 = $55.68m, up 4.04 per cent
Keep traffic growth and toll indexation as separate lines. They have different drivers, and the concession agreement usually fixes indexation by formula while traffic is a forecast. Lumping them into one growth rate hides which half of the forecast is contractual.
| Traffic vs base | Tolls +0% | Tolls +2.5% | Tolls +5% |
|---|---|---|---|
| −10% | 48.17 | 49.38 | 50.58 |
| −5% | 50.85 | 52.12 | 53.39 |
| Base | 53.52 | 54.86 | 56.20 |
| +5% | 56.20 | 57.60 | 59.01 |
The table treats traffic and tolls as independent, which they are not. A toll rise loses some traffic. With an illustrative price elasticity of −0.2, a 10 per cent toll increase cuts traffic by 1.89 per cent and lifts revenue by 7.92 per cent, to $57.76m, not by 10 per cent. At an elasticity of −0.1 the gain is 8.96 per cent; at −0.4 it is 5.89 per cent. Where the concession lets the operator set tolls below a cap, the revenue-maximising toll is an elasticity question, and a model that applies the full cap with no traffic response overstates the upside.
Using the wrong traffic count. Traffic counts on commuter roads are often reported as AAWT, the annual average weekday traffic, which is higher than AADT because weekends are quieter. Multiply an AAWT of 42,500 by 365 and the road appears to carry 9.0 per cent more than it does: $58.33m of net revenue instead of $53.52m, a $4.80m overstatement every year, compounding through every growth assumption that follows and straight into CFADS and debt capacity. The fix is to annualise from monthly or daily counts, or to apply a documented weekday-to-annual factor, and to state in the model which count is used.
Revenue is the top line of cash flow available for debt service, built step by step in how to calculate CFADS in project finance. Because traffic is a forecast, lenders size on a downside case, as in how much debt sizing on P90 instead of P50 costs.
The toll road the book sculpts its debt against, with every input live, is in the free workbooks for this case.
AADT is annual average daily traffic, every day of the year included. AAWT is the weekday average, usually higher on commuter roads. Multiplying AAWT by 365 counts weekend days at weekday levels: in the illustrative case 42,500 vehicles against 39,000 overstates revenue by 9.0 per cent, $4.80m a year.
Less than 10 per cent, because some drivers divert. With an illustrative price elasticity of -0.2, traffic falls 1.89 per cent and revenue rises 7.92 per cent. At an elasticity of -0.4 the gain is 5.89 per cent. Concession agreements usually cap the increase by indexation, so the question is what headroom the cap leaves.
Leakage is toll owed but not collected: unpaid electronic transactions, unreadable plates, exempt vehicles and bad debt on video tolling. At an illustrative 2.5 per cent it costs $1.37m a year on $54.896m of gross tolls. Moving to open-road tolling without barriers usually raises it, which a traffic and revenue study should state explicitly.
The book's toll road case, the Calder Toll Road, has its debt sculpted to a lender's coverage floor in chapter 4 of The Infrastructure Investment Analyst. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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