CLV calculatiion$($table start from year $0$ and end in year $3)$ A grocery delivery company mails catalogs to a mailing list of $500,000$ names. The response rate is $4\mathrm{.}5\%.$ The marketing cost for acquisition is $$0\mathrm{.}2$ per mailing$-$list name and $$0\mathrm{.}9$ per catalog mailing. Regarding the marketing cost for development, the company sends $6$ catalogs per year to all active customers. On average, customers spend $$240$ per year. The cost of goods sold $($COGS$)$ is $62\%$ of revenues. The annual churn rate is $35\%.$ The company expects that, after signing up$,$ customers will remain for $3$ years. Assume a $10\%$ discount rate and no discounting for Year $0.1)$ Calculate the CLV after accounting for the acquisition cost. Show all your work clearly. $(8$pts$)$ The company is considering whether it should offer a $$10$ discount to customers who spend $$99$ or more in their next delivery. This offer is made twice a year by sending out an additional catalog each time. Offering these discounts reduces the annual churn rate by $5\%$ and increases spending on some orders. With the probability, $60\%$ of customers use the discount offers and increase their annual spending by $$100,$ while $40\%$ of customers do not use the offers and maintain their annual spending. $2)$ Calculate the new CLV after accounting for the acquisition cost. Show all your work clearly. $(10$pts$)3)$ Based on your calculations, is the discount promotion worth implementing? $(2$pts$)$