Cohort NPV and Sensitivity for New Credit-Card Customers

Context

You are evaluating a co-branded partner expected to deliver 50,000 newly acquired credit-card customers in Year 1. Only activated users generate spend-based economics (revenue, rewards, credit losses, fees). Use monthly discounting at an annual rate of 10% (i = 10%/12 per month). Compute NPV over the first 12 months only.

Assumptions (Year 1 unless noted):

• Cohort size: 50,000 acquired users; activation rate = 80%.
• Monthly spend (per activated): $600 for 12 months.
• Interchange revenue: 1.5% of spend.
• Rewards cost: 1.2% of spend.
• Annual fee: $95 collected in month 1 from 25% of activated users.
• Servicing cost: $1.00 per user per month.
• Expected credit loss (bad debt): $24 per activated user over 12 months.
• Partner economics: $70 CPA (to partner) per acquired user +$ 100 signup bonus per activated user.
• Discount rate: 10% annually with monthly discounting at 10%/12.

Assumptions on timing (state clearly if you choose differently):

• CPA paid at acquisition (month 0).
• Signup bonus and annual fee occur in month 1.
• Spend, rewards, credit losses, and servicing occur monthly (months 1–12). Credit losses are spread evenly over the 12 months.
• Servicing cost applies to all acquired users (activated and not). If you assume it applies only to activated, multiply by 80% instead.

Tasks

1. Compute the 12-month NPV per acquired user and the total NPV for the 50,000-user cohort. Show all components separately: interchange, rewards, fees, servicing, credit loss, and acquisition costs (CPA and signup bonus).
2. Holding other assumptions fixed, derive the break-even CPA.
3. Sensitivity: Recompute NPV for (a) interchange ±0.3 percentage points, and (b) credit loss ±$10 per activated user. Identify which variable the decision is more sensitive to and give a recommendation.