Calculate break-even new customers for 30% discount
Overview
This question evaluates break-even and unit-economics analysis for a customer-acquisition promotion, testing competency in setting up algebraic expressions, interpreting business metrics like usage rates and incremental net revenue, and basic financial modeling within the Statistics & Math domain.
Break-even Analysis: Rent‑a‑Home (RH) Promo
Context
You are evaluating a 30% discount promotion on Rent‑a‑Home (RH) spend. The discount is fully funded by the issuer. You must compute how many new customers (x) must be acquired for the promo to break even, considering promo cost on both existing RH users and the newly acquired RH users. Interchange on RH transactions is ignored, and the average net revenue per new cardholder already accounts for non‑RH rewards, servicing, and expected credit loss.
Given
- Active cardholders: 2,000,000
- Current RH usage rate: 5% of cardholders annually
- Average RH spend per RH user per year: $500
- Proposed promo: 30% off RH spend (fully funded by issuer)
- Average first‑year net revenue per new cardholder (non‑RH): $550
- Ignore interchange on RH transactions
- Let x = number of new customers acquired because of the promo
Tasks
(a) Write the break‑even equation where incremental revenue from new customers equals the promo cost across existing RH users plus new RH users. Then solve for x.
(b) Express x as a percentage of the 2,000,000 base and discuss whether this target is realistic given typical acquisition funnels and approval rates. Show your work and final numbers.
Solution
Login required