The Post

Mr$.$ James is the circulation director for the St$.$ Louis Post, a daily St$.$ Louis newspaper.

The Post has three subscription types: $(1)$ digital version only, $(2)$ digital version $+$ Sunday

print edition, and $(3)$ digital $+$ everyday print edition. A subscriber contributes annual

profits totaling $$125,$$$150,$ and $$200$ respectively.

Mr$.$ James realizes that customers "migrate" between different subscriptions types from

year to year. He finds from his analytics people that the probabilities of these migrations

are as follows:

That is$,$ the customer who has a Digital$-$Only subscription in the current year has a $40\%$

chance of keeping the Digital$-$Only subscription next year, a $5\%$ chance of moving to

Digital $+$ Sunday, a $5\%$ chance of moving to Digital $+$ Everyday, and a $50\%$ chance of

dropping their STL Post subscription altogether $($churning$).$

Mr$.$ James also learns that he acquired $1000$ customers with his recent customer

acquisition campaign: $800$ of acquired customers started as Digital$-$Only subscribers, $150$

started off with Digital $+$ Sunday, and $50$ started with Digital $+$ Everyday.

a$.$ What are the lifetime values of each type of subscriber: $(1)$ those starting as Digital

only, $(2)$ those starting as Digital $+$ Sunday, and $(3)$ those starting as Digital $+$ Everyday?

Use a $7\%$ annual discount rate.

b$.$ Mr$.$ James mentions to his assistant, "Those Digital$-$Only customers are so fickle. We

have a $50\%$ churn rate with them, and most of the customers we acquired in that last

campaign are Digital$-$Only. I know the reason $-$ they have so many online alternatives it's

easy to cut us off. Also, despite our best efforts to make the digital experience engaging,

there is nothing like print to get the customer engaged. I$\text{'}$d like to develop a marketing

campaign that I assume will acquire the same number of customers but instead of them

being $800$ Digital$-$Only, $150$ Digital $+$ Sunday, and $50$ Digital $+$ Everyday, they' $11$ be $600$

Digital$-$Only, $350$ Digital $+$ Sunday, and $50$ Digital $+$ Everyday. How much can I afford

to spend per acquired customer on this campaign?"

Please respond to Mr$.$ James and make appropriate calculations to back up your response.