Case 022Commercial and market casesCore

A gym chain has 4% monthly churn, a Rs 2,000 monthly fee, Rs 3,000 acquisition cost and 70% contribution. What is a member worth, and at what churn does growth start to destroy value?

The situation

Ojasvi Fitness runs 30 gyms. Members pay Rs 2,000 a month and 4% of them leave each month. Contribution after the costs that scale with members, trainers' time, towels, app and payment charges, is 70% of the fee. Today most members walk in from the neighbourhood and cost about Rs 3,000 each in referral rewards and a joining discount.

The growth plan doubles sign-ups with paid advertising. Members from ads cost about Rs 12,000 each and, in a pilot, left at 8% a month. The fund discounts at 1.5% a month. Treat the churn figures as flat averages; real cohorts churn fastest in the first three months.

Your task

Work the lifetime value of a walk-in member and of a paid member, compare each with its acquisition cost, and find the churn rate at which a paid member is worth less than it costs.

Quick check

At 4% monthly churn, how long does the average member stay?

Worked solution

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

30-second answerThe answer to give first

A walk-in member is worth Rs 35,000: Rs 1,400 of monthly contribution for an expected 25 months, against Rs 3,000 to acquire, a ratio of 11.7x and a payback of 2.1 months. A paid-ad member at 8% churn is worth Rs 17,500 undiscounted and Rs 14,737 discounted, against Rs 12,000, so the growth plan creates a little value per member and loses money above about 10.2% monthly churn. Churn, not sign-ups, decides whether the plan is worth funding.

Step 1What is a member worth, and why is churn the whole answer?

A newspaper subscription that pays Rs 100 a month is worth very different amounts depending on whether readers stay a year or ten. Monthly contribution is 70% of Rs 2,000, Rs 1,400; at 4% churn the expected life is 1 over 0.04, 25 months; so the lifetime valueThe contribution a customer earns over the whole time they stay, before the cost of winning them. With constant churn it is monthly contribution divided by the monthly churn rate. is Rs 35,000. Against Rs 3,000 of acquisition cost that is 11.7 rupees back per rupee spent, and the cost is recovered in 2.1 months. The fee and the margin are visible on the price list; the churn is the term that quietly sets the value.

The relationship

\text{LTV} = \frac{\text{fee} \times \text{margin}}{\text{churn}} = \frac{2{,}000 \times 0.70}{0.04} = 35,000 \qquad \text{LTV}_{\text{disc}} = \frac{1{,}400}{\text{churn} + 0.015}

fee x margin	monthly contribution per member, Rs 1,400
churn	the share of members leaving each month
0.015	the fund's monthly discount rate, which acts like extra churn

What it says in wordsA member is worth the monthly contribution divided by the churn rate, Rs 35,000 here; discounting adds 1.5 points to the denominator and lowers it.

Step 2What is a paid-advertising member worth?

The same arithmetic with two inputs changed. Life at 8% churn is 12.5 months, so lifetime value is Rs 17,500; discounted at 1.5% a month it is Rs 1,400 over (0.08 plus 0.015), Rs 14,737. Against Rs 12,000 of acquisition cost that is Rs 2,737 of value created per member and a payback of 8.6 months, which is a thin result for money spent today on members who may not last a year. The walk-in member creates Rs 32,000; the paid member creates less than a tenth of that.

Lifetime value falls steeply as churn rises, from Rs 35,000 at 4% to Rs 17,500 at 8%, so a walk-in member at Rs 3,000 is safely profitable at any plausible churn while a paid-ad member at Rs 12,000 destroys value once monthly churn passes about 10.2%.

Monthly churn	Expected life, months	LTV	LTV discounted	Value per paid member at Rs 12,000
2%	50.0	70,000	40,000	+28,000
4%	25.0	35,000	25,455	+13,455
6%	16.7	23,333	18,667	+6,667
8%	12.5	17,500	14,737	+2,737
10%	10.0	14,000	12,174	+174
12%	8.3	11,667	10,370	-1,630
15%	6.7	9,333	8,485	-3,515

Rs. Each point of monthly churn takes thousands off a member's value, and a paid member crosses from creating value to destroying it between 10% and 12% churn, so the pilot's 8% leaves almost no margin for error.

Step 3At what churn does growth destroy value, and what should the fund do?

Set lifetime value equal to acquisition cost and solve for churn. Undiscounted, Rs 1,400 over Rs 12,000 is 11.7% a month; discounted, 10.2%; the pilot ran at 8%, so the plan is one bad quarter from paying Rs 12,000 for members worth less than that. For walk-ins the breakeven churn is 47% a month, which no gym reaches, which is why the existing business is sound. The fund's answer is to fund the advertising only against a churn target, say under 6% at month six for the paid cohort, and to spend first on keeping members, since cutting walk-in churn from 4% to 3% raises every member's value by a third at no acquisition cost at all. The limit of the model is the flat churn: real cohorts lose most members early, so the first three months of a paid cohort tell you more than the average.

Where candidates lose it

The common loss is quoting LTV over CAC of 11.7x for the business and approving the growth plan. The plan's members cost four times as much and churn twice as fast; the number that matters is their own ratio, which is barely above one once discounted.

The second miss is treating churn as a rounding detail. It is the denominator: a move from 8% to 12% halves the discounted value of a paid member and turns the plan from marginally positive to loss-making.

What the interviewer asks next

Paid-cohort churn is 15% in months one to three and 4% after. What is a paid member worth then?
Would you rather spend Rs 5 crore on advertising or on a retention programme that cuts churn by one point?
How does an annual membership paid upfront change the economics and the risk?

Company names and figures are illustrative.