FitPro$+$ operates on a subscription$-$based model, charging customers a monthly fee. Below are key financial details:

Average revenue per customer per month: $$30$

Profit margin: $60\%$

Retention rate: $75\%$ per year

Discount rate: $10\%$ per year

FitPro$+$ is considering a new social media advertising campaign. The campaign is expected to acquire $5,000$ new customers, with a total cost of $$400,000.$

$1.$ Compute CLV: Using the formula, calculate the CLV of a single customer for FitPro$+.$ Show your calculations.

$2.$ Interpretation: What does this CLV tell you about the long$-$term value of each customer?

$3.$ Based on your findings, should FitPro$+$ proceed with the campaign? Justify your answer.

$4.$ What are some potential risks or limitations of using CLV as the sole decision$-$making metric for this investment?

$5.$ What other factors $($besides CLV$)$ might influence the company$$s decision to run this campaign?