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It has been 15 years since Quaker launched its original two products. Quaker has found that customers are relatively brand loyal. Specifically, once a family begins buying oatmeal, they keep purchasing boxes for a number of years (i.e., they become "purchasers"). The average "purchaser" family buys 27 boxes of oatmeal per year, and "non-purchaser" families buy zero boxes per year and never begin buying again. On average, each "purchaser" family has a 12.5%/year chance of stopping all oatmeal purchases, converting into a "non-purchaser" family. Assume that the profit per box of plain oatmeal is currently $0.50, the profit per box of Apples & Cinnamon is $0.30, and that purchasers buy twice as many Plain Oatmeal boxes as Apples & Cinnamon boxes each year. What is the lifetime value of a "purchaser"? (N.B.: you may assume that Quaker's cost of capital is 10% if you choose to use the discounted form of the LTVC. Use a five year horizon to calculate the lifetime value)
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