Case 002Earnings, models and KPIsCore

Tunevi Music adds 10,000 subscribers a month and loses 5% of its base each month, at Rs 120 per subscriber a month. What are the steady-state base and revenue run rate, and how long does it take to get halfway there?

The situation

Tunevi Music is a subscription music app that launched a year and a half ago. Its marketing brings in a steady 10,000 new paying subscribers a month. Every month, 5% of the subscribers at the start of the month cancel. Each subscriber pays Rs 120 a month.

The company's investor deck shows subscriber growth every quarter since launch and a chart heading steeply upwards. A portfolio manager considering the stock asks you to model where the base is going.

Your task

Where does the subscriber base settle, what revenue run rate does that give, and how long does it take to get halfway?

Quick check

Where does the subscriber base settle if nothing changes?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The base settles at 2 lakh subscribers, a run rate of Rs 2.4 crore a month or Rs 28.8 crore a year, and it gets halfway in about 13.5 months. Growth stops where 5% churn on the base equals 10,000 additions. The gap to that ceiling closes by 5% each month, so the halfway point comes at about 13.5 months and 90% at about 45 months.

Step 1Where does the base stop growing, and why?

Think of a bucket under a tap with a hole in the bottom. The tap pours at a fixed rate, but the hole leaks faster the fuller the bucket gets, because the pressure rises. At some level the leak equals the tap and the water stops rising. A subscription business with a fixed intake and a percentage churn has the same ceiling: the base where churn losses equal new additions. For Tunevi, 5% of the base equals 10,000 when the base is 10,000 over 0.05, which is 2 lakh.

The relationship
N∗=ac=10,0000.05=2,00,000Nt=N∗(1−(1−c)t)N^{*} = \frac{a}{c} = \frac{10{,}000}{0.05} = 2{,}00{,}000 \qquad N_t = N^{*}\left(1 - (1-c)^{t}\right)
N*the steady-state subscriber base
anew subscribers added each month, 10,000
cthe share of the base lost each month, 5%
N_tthe base t months after launch
What it says in wordsThe ceiling is additions divided by churn, and each month the base closes 5% of the remaining gap to it.

The revenue follows directly. Two lakh subscribers at Rs 120 is Rs 2.4 crore a month, a run rate of Rs 28.8 crore a year, and that is the most this business earns without a change in marketing, churn or price. The average subscriber stays 1 over 0.05, which is 20 months, and pays Rs 2,400 over that life. That lifetime figure is the most Tunevi can spend to win a subscriber before growth destroys value.

Step 2How long does it take to get halfway, and why does growth feel fast at first?

Early on, the base is small, so churn loses almost nothing and nearly all 10,000 additions stick. As the base grows, churn eats a bigger share of each month's intake. The gap to the ceiling shrinks by 5% a month, so the base is halfway after about 13.5 months and 90% of the way after about 45 months. The quick rule is 0.69 divided by the churn rate, 0.69 over 0.05, about 14 months. Tunevi, a year and a half in, is already past halfway, and its reported growth will slow every quarter from here even if marketing holds steady.

Additions set the speed; churn sets the ceiling1 lakh2 lakh3 lakh4 lakh01224364860Months after launchCeiling 2 lakh = 10,000 / 5%churn 2.5%churn 5%Half way at 13.5 months90% at 45 months
With 10,000 additions a month and 5% monthly churn, Tunevi's base climbs towards a ceiling of 2 lakh, passing 1 lakh at about 13.5 months and 90% of the ceiling at about 45 months; halving churn to 2.5% doubles the ceiling to 4 lakh but the climb takes twice as long.
Months after launchSubscribersShare of ceilingMonthly revenue, Rs crore
652,98226%0.64
1291,92846%1.10
14102,46551%1.23
24141,60271%1.70
36168,44484%2.02
60190,78695%2.29
Tunevi's base reaches about 91,928 at twelve months and 141,602 at two years, then flattens: the last 10% of the climb to 2 lakh takes longer than the first half.
Step 3Which lever should the portfolio manager watch?

Doubling marketing to 20,000 additions doubles the ceiling to 4 lakh at the same 13.5 month halfway time, but it doubles the cost of acquisition too. Halving churn to 2.5% also doubles the ceiling to 4 lakh, and it does so without spending more on marketing, which is why churn, not intake, sets the value of a subscription business. The catch is speed: at 2.5% churn the halfway point stretches to about 27 months. The view for the PM: the deck's steep chart is the easy part of the curve; ask for monthly churn by signup cohort, because that single number tells you where revenue stops.

Where candidates lose it

The common error is extrapolating the early growth: 10,000 a month becomes 1.2 lakh a year, and the model keeps adding them for five years. Losses scale with the base, so the base cannot grow forever on a fixed intake.

The second is treating churn as a small deduction rather than the lever that sets the ceiling. A candidate who says cut churn from 5% to 4% and the ceiling rises 25%, to 2.5 lakh, has understood the model.

What the interviewer asks next

  • Tunevi raises its price to Rs 150 and churn rises to 6%. Is revenue at steady state higher or lower?
  • How would you estimate churn from a company that only discloses quarter-end subscribers and gross additions?
  • What is the most Tunevi can pay to acquire a subscriber if its gross margin is 40%?

Company names and figures are illustrative.