Build a twelve-month subscriber revenue model for Tvarit Broadband with an 8% price rise in month 7 that lifts churn for three months. What are year-one revenue and closing subscribers, and did the rise pay off?

Year-one revenue is Rs 393.5 crore with the rise against Rs 380.2 crore without, and closing subscribers are 546,482 against 553,821. The higher price adds Rs 15.4 crore over months 7 to 12 and the extra churn costs Rs 2.1 crore and 7,338 subscribers. The rise paid off in year one and by more at the run rate, Rs 423 crore against Rs 397 crore, but the lost subscribers carry future revenue of about Rs 24 crore that the model only partly counts.

A hostel mess works the same way: a number of students on the meal plan, some leave each month, some join, and revenue is the headcount times the monthly fee. A subscription business is a stock of customers rolled forward month by month: closing subscribers equal opening subscribers less churn plus gross additions, and revenue is subscribers times price. The model is twelve rows of that identity. Churn is a percentage of the opening base, so it grows as the base grows; additions are a count, driven by the sales channel. With 15,000 additions and 2% churn the base converges towards 750,000, the point where churn equals additions, which is why it climbs through the year from 500,000.

Month 1 shows the mechanics: open 500,000, lose 10,000, add 15,000, close 505,000; revenue on the average 502,500 at Rs 600 is Rs 30.15 crore. Month 7 changes two inputs at once: price to Rs 648 and churn to 2.5% on an opening base of 528,539, which is 13,213 leavers instead of 10,571. Over the three spike months Tvarit loses 7,797 more subscribers than it would have, and because churn is a rate, every one of them also stops compounding into later months. By month 12 the gap is 7,338.

Split the difference between the two runs into a price effect and a volume effect. The price effect is the extra Rs 48 a month on every subscriber Tvarit actually had in months 7 to 12: Rs 15.4 crore. The volume effect is the old price on the subscribers it no longer had: Rs -2.1 crore. The year is Rs 13.4 crore better with the rise, and the run rate in month 12 is Rs 423 crore a year against Rs 397 crore, so on the numbers given the rise paid off. The spike would have had to reach about 5.6% a month for three months before year-one revenue fell below the no-rise case, far above the 2.5% assumed.

Lost subscribers are not a one-year cost. At 2% churn the expected remaining life of a subscriber is 1 divided by 0.02, 50 months, so each one lost gives up about Rs 32,400 of future billing at the new price. The 7,338 subscribers Tvarit is short at year end represent about Rs 24 crore of lifetime revenue, undiscounted, of which only a few crore shows in year one. Set against a price uplift worth about Rs 31 crore a year on the year-end base, the rise still wins, but by less than the year-one bridge suggests.

A complex revenue model is this engine with more dimensions: cohorts by plan and by vintage, each with its own churn curve, a price that varies by plan, additions driven by marketing spend and installation capacity, and a gross-to-net line for discounts and credits. The questions to ask the business are whether churn after a price rise really returns to 2% or settles higher, whether the additions themselves slow when the headline price is higher, and whether competitors respond. The limit of this model is that it treats additions as fixed; in practice a price rise reaches new customers too.