I need help$/$assistance with the solution to a case associated with Customer Life Time Value.

Case Details:

Cross$-$selling is a major activity at financial institutions. One regional bank classifies its $100,000$ individual customers into $4$ groups: basic services $($checking$,$ savings accounts$),$ lending $($mortgages$,$ loans$),$ investment $($mutual funds, bonds$),$ and financial planning $($retirement$,$ trusts, comprehensive financial planning$).$ Customers in each of the four categories generate net $($of servicing costs$)$ revenue of $$100,$ $$200,$ $$300,$ and $$1,000$ per year respectively. Currently, the mix of customers is $70\%,10\%,15\%,$ and $5\%$ in the four types. Retention rates are $90\%$ across the board. Retention costs $($note: these are different from servicing costs$)$ per account are $$80,$ $$120,$ $$150,$ and $$200$ respectively per year. In order to improve performance, three major strategies are under consideration.

$1.$ Increase net revenue per customer by $10\%$ across the board

$2.$ Change the customer mix to $60\%,15\%,18\%,$ and $7\%$

$3.$ Increase retention in one of the groups to $95\%$

Questions:

$1.$ What is the CLV in each of the current customer categories? $($Assume a $10\%$ discount rate$)$

What would be the increase in the bank's weighted average CLV if each of the three suggested strategies were implemented separately? $($assuming servicing costs are constant$)[1]$

$[1]$ A weighted average weights each outcome proportional to how much that outcome occurs. For example, if $20\%$ have A and $80\%$ have B$,$ then the weighted average is $(0\mathrm{.}2$ x A$)+(0\mathrm{.}8$ x B$).$