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Free GMAT Problem Solving Practice Question

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A subscription software business reports the following for a typical customer: average monthly revenue of $50, average monthly gross margin of $40 (the rest is the cost of serving the customer), and a monthly cancellation rate of 5%, meaning that in any month a customer has a 5% chance of leaving and that the average customer's lifetime in months equals 1 divided by the monthly cancellation rate. The business spends $200 in sales and advertising to acquire each new customer. Using lifetime gross margin as the customer's lifetime value, what is the ratio of a customer's lifetime value to the cost of acquiring that customer?

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Answer & Explanation

Correct answer

C

Lifetime value must compose two separate ideas, and neither alone gets the answer. First, lifetime: with a 5% monthly cancellation rate, the average lifetime is 1 ÷ 0.05 = 20 months. Second, value is built from gross margin, not revenue, because the question defines lifetime value as lifetime gross margin. So lifetime value equals $40 of margin per month × 20 months = $800. The acquisition cost is $200, so the ratio is 800 to 200, which is 4 to 1.

The strongest trap is choice D (5 to 1): you correctly find the 20-month lifetime but reach for monthly revenue ($50) instead of margin, computing 50 × 20 = 1000, then 1000 to 200 = 5 to 1. That uses the right lifetime but the wrong per-month figure, leaving out the cost of serving the customer. Choice B (2.4 to 1) is the second trap: you use margin correctly but ignore cancellation, assuming a 12-month lifetime, and get 40 × 12 = 480, then 480 to 200 = 2.4 to 1.

The two ideas you must combine correctly: lifetime equals 1 ÷ the churn rate, not an assumed contract length, and value uses margin, not revenue.