$($c$)$ Suppose that Gravity's technology improves both the yearly margin and the retention rate of the Seoul Post by $5\%($i$.$e$.,$ both the margin and the retention rate are multiplied by $1\mathrm{.}05$ for both current and future readers$).$ Does the increase in CLV of the existing customers due to Gravity justify the $$83$ million investment in Gravity $($show you calculation$)?(2$ points$)*$ Assume Seoul Post still has $120$ million users in its customer base.

$($d$)$ Assuming the retention rate increase stays at $5\%,$ to what level should Gravity increase the yearly margin of the existing customers to justify the investment? $(2$ points$)$