1234567891011121314151617181920212223242526272829
            
# Calculate payback period for each customer using LTV and CAC from the dataset

import pandas as pd

# Example customer data with CAC and LTV by month
data = {
    "customer_id": [1, 2, 3],
    "CAC": [100, 150, 120],
    "LTV_month_1": [20, 30, 10],
    "LTV_month_2": [25, 25, 20],
    "LTV_month_3": [30, 40, 30],
    "LTV_month_4": [40, 60, 50],
}
df = pd.DataFrame(data)

# Calculate cumulative LTV for each month
ltv_cols = [col for col in df.columns if col.startswith("LTV_month")]
df["cumulative_LTV"] = df[ltv_cols].cumsum(axis=1).values.tolist()

# Calculate payback period: first month when cumulative LTV >= CAC
def get_payback_month(row):
    for i, ltv in enumerate(row["cumulative_LTV"], start=1):
        if ltv >= row["CAC"]:
            return i
    return None  # Payback not achieved within observed months

df["payback_period_months"] = df.apply(get_payback_month, axis=1)

print(df[["customer_id", "CAC", "payback_period_months"]])

              
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778
            
import matplotlib.pyplot as plt
import numpy as np

# Base parameters used in both scenarios
months = np.arange(1, 13)          # 12-month horizon
base_cac = 100                     # Baseline CAC for retention sensitivity
monthly_revenue = 20               # Revenue generated per retained user per month


# Scenario 1: Impact of CAC (Retention varies by CAC)

# Different CAC levels with different assumed retention curves
# Assumption: lower CAC implies a more engaged customer base with higher retention
cac_scenarios = {
    80: 0.90,   # Low CAC → stronger retention
    100: 0.85,  # Baseline retention
    120: 0.78   # High CAC → weaker retention
}

plt.figure(figsize=(8, 5))

for cac, retention in cac_scenarios.items():
    # Compute cumulative LTV curve for 12 months
    cumulative_ltv = np.cumsum([
        monthly_revenue * (retention ** (m - 1))
        for m in months
    ])
    
    # Determine payback month (if cumulative LTV reaches CAC)
    if np.any(cumulative_ltv >= cac):
        payback_month = np.argmax(cumulative_ltv >= cac) + 1
    else:
        payback_month = None
    
    payback_text = f"{payback_month} mo" if payback_month else "None"
    
    # Plot LTV curve
    plt.plot(months, cumulative_ltv, label=f'CAC=${cac} (Payback: {payback_text})')

plt.title('Cumulative LTV by CAC')
plt.xlabel('Month')
plt.ylabel('Cumulative LTV ($)')
plt.legend()
plt.tight_layout()
plt.show()


# Scenario 2: Impact of Retention (CAC is fixed)

plt.figure(figsize=(8, 5))

# Different retention rates to test sensitivity
retention_rates = [0.70, 0.85, 0.95]

for retention in retention_rates:
    # Compute cumulative LTV curve
    cumulative_ltv = np.cumsum([
        monthly_revenue * (retention ** (m - 1))
        for m in months
    ])
    
    # Determine payback month for fixed CAC
    if np.any(cumulative_ltv >= base_cac):
        payback_month = np.argmax(cumulative_ltv >= base_cac) + 1
    else:
        payback_month = None
    
    payback_text = f"{payback_month} mo" if payback_month else "None"
    
    # Plot LTV curve
    plt.plot(months, cumulative_ltv, label=f'Retention={retention} (Payback: {payback_text})')

plt.title('Cumulative LTV by Retention Rate')
plt.xlabel('Month')
plt.ylabel('Cumulative LTV ($)')
plt.legend()
plt.tight_layout()
plt.show()