Recalculate break-even with spend uplift assumptions

Q: Recalculate break-even with spend uplift assumptions

This question evaluates proficiency in break-even analysis, algebraic modeling of promotional spend uplift, and unit-economics calculation for customer acquisition within a data science context.

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Question

Context

A credit-card promo offers a 30% discount on RH-category purchases ("RH" = the merchant category eligible for the promo). During the promo period:

There are 2,000,000 total cardholders; 5% are existing RH users.
Existing RH users increase their RH spend from $500 to$ 600.
New customers acquired because of the promo spend $1,000 on RH during the promo.
Average first-year net revenue per new cardholder = $550.

Let x be the number of new customers acquired due to the promo.

Tasks

(a) Solve the break-even equation:

550·x − 0.30·(1,000·x + 2,000,000·5%·600) = 0

(b) Compare this x to the previous break-even (where existing/new RH spend was $500) and explain intuitively why the required new-customer count changes despite higher spend.

Recalculate break-even with spend uplift assumptions

Context

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Recalculate break-even with spend uplift assumptions

Overview

Break-even Analysis with Increased Promo Spend

Context

Tasks

Solution

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