Value a toll road concession with 18 years left: Rs 150 crore of toll revenue, traffic growing 5%, tariffs indexed at 3%, opex at 20% of revenue, discounted at 12%. What is it worth, what happens at 2% traffic growth, and why does the value fall over time?

At 5% traffic growth the concession is worth about Rs 1,575 crore, 13.1x this year's Rs 120 crore of operating cash flow; at 2% it is worth about Rs 1,242 crore, 21% less. Revenue grows 8.15% a year, so cash flow rises from Rs 130 crore to Rs 492 crore in year 18, and then stops. Because there is no terminal value, the road's value peaks a few years from now and then falls each year as the remaining cash flows run off, reaching zero at expiry.

A concession is a lease on a stream of tolls: the fund does not own the road, it owns 18 years of its cash. Revenue grows at (1.05 times 1.03) less 1, 8.15% a year; cash flow is 80% of revenue. Year 1 cash flow is Rs 129.8 crore, year 18 is Rs 491.7 crore, and there is no year 19. Discount each year at 12% and add them up. Compare it with a shop on a long lease: the rent you collect grows, but the day the lease ends the building goes back to the landlord, so you would never value it as a perpetuity.

Revenue growth falls to (1.02 times 1.03) less 1, 5.06%. Value falls to about Rs 1,242 crore, a 21% drop for three points of traffic growth, because every one of the 18 years is lower and the later years, which carry most of the growth, are hit hardest. That sensitivity is the case: a toll road's value is a bet on traffic, and traffic depends on the economy of the region, on fuel prices, and on whether a competing road or rail line opens. The tariff index is written into the contract; the traffic is not.

Because the asset is used up. Each year that passes removes one year of cash flow from the sum and adds nothing at the far end. Early on, the growth in the remaining cash flows outweighs the lost year, so the value drifts up for a few years; after that, every year removes more than growth adds, and the value slides to zero at expiry. An investor who buys at Rs 1,575 crore and sells after seven years at about Rs 1,863 crore has made little on the resale; the Rs 1,163 crore of cash collected on the way is the return, and each later buyer is paying for fewer years.

Two limits to state. The 12% is given; an infrastructure fund would build it from the cost of the project debt and an equity return, and at 10% the value is Rs 1,846 crore against Rs 1,359 crore at 14%. And the model is pre-tax with maintenance folded into opex; a real concession has a major resurfacing every few years and a handover condition at the end, both of which take cash out of the late years that this model counts in full.