Let's solve the problem step by step: ### **1. Calculate Average Revenue per User (ARPU) per Quarter** \[ \text{ARPU} = \frac{\text{Total Revenue}}{\text{Number of Subscribers at Beginning}} \] \[ \text{ARPU} = \frac{150,000}{1,200} = 125 \] ### **2. Calculate Gross Profit per User per Quarter** \[ \text{Gross Profit per User} = \text{ARPU} \times \text{Gross Margin} \] \[ \text{Gross Profit per User} = 125 \times 0.75 = 93.75 \] ### **3. Calculate Churn Rate per Quarter** \[ \text{Churn Rate} = \frac{\text{Subscribers Lost}}{\text{Subscribers at Beginning}} \] \[ \text{Churn Rate} = \frac{60}{1,200} = 0.05 \] ### **4. Calculate Average Subscriber Lifetime (in quarters)** \[ \text{Subscriber Lifetime (in quarters)} = \frac{1}{\text{Churn Rate}} \] \[ \text{Subscriber Lifetime} = \frac{1}{0.05} = 20 \text{ quarters} \] ### **5. Calculate Subscriber Lifetime Value (LTV)** \[ \text{LTV} = \text{Gross Profit per User per Quarter} \times \text{Subscriber Lifetime} \] \[ \text{LTV} = 93.75 \times 20 = 1,875 \] --- ### **Final Answer** \[ \boxed{ \$1,875 } \] This matches the last option.

Let's go through the detailed step-by-step calculation process using the given data: --- ### **Given Data:** - Total revenue in the quarter: **$150,000** - Subscribers at the beginning of the quarter: **1,200** - Subscribers lost during the quarter: **60** - Gross Margin: **75%** - **Assumption:** No new subscribers added during the quarter. --- ### **Step 1: Calculate Average Revenue per User (ARPU) per Quarter** ARPU is the revenue generated per subscriber during the quarter. \[ \text{ARPU} = \frac{\text{Total Revenue}}{\text{Number of Subscribers at Beginning}} \] \[ \text{ARPU} = \frac{150,000}{1,200} = 125 \] **So, the revenue per subscriber per quarter is $125.** --- ### **Step 2: Calculate Gross Profit per User per Quarter** Gross profit per user is derived from ARPU multiplied by the gross margin. \[ \text{Gross Profit per User} = \text{ARPU} \times \text{Gross Margin} \] \[ \text{Gross Profit per User} = 125 \times 0.75 = 93.75 \] **Thus, gross profit per subscriber each quarter is $93.75.** --- ### **Step 3: Calculate Churn Rate per Quarter** Churn rate indicates the proportion of subscribers lost during the quarter. \[ \text{Churn Rate} = \frac{\text{Subscribers Lost}}{\text{Subscribers at Beginning}} \] \[ \text{Churn Rate} = \frac{60}{1,200} = 0.05 \] **So, 5% of subscribers are lost each quarter.** --- ### **Step 4: Calculate Average Subscriber Lifetime (in quarters)** Subscriber lifetime (in terms of how many quarters they remain subscribed) is the reciprocal of the churn rate. \[ \text{Subscriber Lifetime} = \frac{1}{\text{Churn Rate}} = \frac{1}{0.05} = 20 \text{ quarters} \] **On average, a subscriber stays for 20 quarters.** --- ### **Step 5: Calculate Subscriber Lifetime Value (LTV)** LTV is the total gross profit expected from a subscriber over their lifetime: \[ \text{LTV} = \text{Gross Profit per User per Quarter} \times \text{Subscriber Lifetime} \] \[ \text{LTV} = 93.75 \times 20 = 1,875 \] **Therefore, the Subscriber Lifetime Value (LTV) is $1,875.** --- ### **Final Answer:** \[ \boxed{\$1,875} \] This matches the option: **$1,875**.