Bespoke: tolled highway PPP concession

A 125 km toll highway concession from the World Bank's highway PPP toolkit, financed with three debt tranches and topped up each year by an availability subsidy sized to hold debt service cover at 1.30x.

Every number below is checked against an independent reference implementation on every commit — period by period, and on each metric, inside a declared tolerance. See benchmark methodology.

The case

A 125 km, 2x2-lane tolled highway, built over four years and operated for forty-six more under a fifty-year concession. Ten thousand vehicles a day use it at opening, split evenly between two categories paying 0.13 and 0.25 USD per vehicle per kilometre, and traffic grows 3% a year for the life of the deal.

Almost every mechanic in it is a phase change. Construction draws on three debt tranches at once — 80% at 4.0% over twenty years, 10% at 4.5% over fifteen, 10% at 5.0% over ten — with interest capitalizing into each balance rather than being paid, and each tranche's grace period ending in a different year, so the first tranche starts repaying in 2014 and the other two in 2015. Operating cost is a regressive scale: the first ten thousand vehicles a day cost nothing to serve, the next ten thousand cost 0.60 each, the next 0.30, everything above 0.15 — and traffic crosses two of those thresholds before the concession ends. Corporate tax is levied on the smaller of the year's profit and the profit accumulated to date, and paid a year late.

And the road does not pay for itself. The contracting authority tops it up each year with an availability subsidy sized to hold the annual debt service cover ratio at exactly 1.30x. It pays 21.7m in 2014, rises to 64.9m by 2017, then falls away as traffic growth outruns the fixed costs and the two short tranches retire — and stops entirely after 2023, five years before the last tranche is repaid.

The reference

The World Bank and PPIAF's Numerical Model for Financial Simulation of Highway PPP Projects, run at the case-study defaults that ship inside it. The workbook is the toolkit's own teaching model for exactly this deal, and it carries a complete set of cached values: a fifty-year cash flow waterfall, income statement, three per-tranche repayment schedules, a funding-during-construction table and a results sheet. Every figure asserted here is one of those cached values, so the comparison is period by period rather than against a single answer.

Not vendored. The workbook and the user guide are freely downloadable from the toolkit, but neither carries an explicit reuse grant, so neither is committed here. They were fetched once outside the repository and only their output numbers were carried across. See SOURCE.md.

What it exercises

This is the first case in the suite with no pack, and that is half the point of it. A toll road is none of the four: it has no generation and no offtaker, so energy does not describe it; no rent roll, so cre does not; no pool of obligors, so credit does not; and its revenue is a traffic count times a distance times a tariff rather than a margin on sales, so opco does not. Every other benchmark demonstrates that a pack works. This one demonstrates something no pack-based case can: that the language underneath is enough to build an asset class nobody has written a pack for.

The ADSCR-targeted subsidy needs no solver. The reference computes the subsidy as an output — the amount that makes cover come out at 1.30x — and read naively that is a fixed point, because the subsidy sits inside cash available for debt service, cash available for debt service is net of corporate tax, and tax is charged on a profit that includes the subsidy. It is not circular, because tax is paid one year in arrears:

subsidy(t)  = max(0, 1.30 * debt_service(t) - (revenue(t) - opex(t) - tax_paid(t)))
tax_paid(t) = 30% * min(pbt(t-1), cumulative_pbt(t-1))

Everything on the right is finished before period t is evaluated, so the subsidy falls out arithmetically once a period. This is the same move as the tax equity flip, where an IRR hurdle became a discounted running sum: the circularity is in how the spreadsheet is wired, not in the deal.

The result

Exact. Twenty-five series across fifty-one periods and seven financing-plan totals reproduce the workbook's cached values.

Asserted: the works, equity, fee and per-tranche drawdown lines through construction; all three tranche balances across all fifty years; per-tranche interest and principal; both toll revenue lines; five operating cost lines; the subsidy; corporate tax; profit before tax; and the depreciable capital base — 1,322 figures in total.

The delta

The declared state agrees to 2.7e-12 — machine epsilon over a fifty-year recursion. The cash streams agree to 8.9e-7, which is not a modeling difference: the results file publishes stream amounts rounded to six decimal places, and these are USD millions, so 8.9e-7 is fifty cents on figures in the hundreds of millions. The per-period tolerance is set at 1e-5 to sit just above that rounding floor.

One thing the case does not assert is the reference's equity IRR, project IRR and NPV. Those need the dividend policy — distributable reserves are the lesser of the cash balance and cumulated retained profit — and a balance sheet to carry cash between years, neither of which is modeled here. The spine that determines them is: revenue, cost, tax, subsidy and all three debt schedules are all asserted, so anything downstream would be arithmetic on numbers that already agree.

Run configuration

{
  "deterministic": {
    "annual_discount_rate": 0.08
  }
}

Verified results

Checked period by period: 26 series across 51 periods — 1322 values in all, each within ±0.00001 of the reference.

• infra.construction.works
• infra.funding.equity
• infra.funding.fees
• infra.funding.draw_t1
• infra.funding.draw_t2
• infra.funding.draw_t3
• asset.tranche1.balance
• asset.tranche2.balance
• asset.tranche3.balance
• infra.debt.interest_t1
• infra.debt.interest_t2
• infra.debt.interest_t3
• infra.debt.principal_t1
• infra.debt.principal_t2
• infra.debt.principal_t3
• infra.revenue.toll_cat1
• infra.revenue.toll_cat2
• infra.opex.concessionaire
• infra.opex.operations
• infra.opex.heavy_maintenance
• infra.opex.light_maintenance
• infra.opex.variable
• infra.subsidy.availability
• infra.tax.corporate
• asset.project.pbt
• asset.project.capital

Summary metrics for the base run: