Quaker's R&D department invents Apple and Cinnamon oats, which is more expensive to produce. Specifically, the ingredients cost 2.5 times as much, the wrapper costs 35% more (because it needs to be a better moisture and oxygen blocker), and delivery costs 20% more (because Apples & Cinnamon have a shorter shelf-life). Apples & Cinnamon will be sold to consumers for 50% more than Plain Oatmeal, and the percentage distribution margins and structure are identical to Plain Oats in all geographies. In order to produce Apples & Cinnamon, Quaker must lease a new set of processing machines that will cost $0.5M per year. The new machines require additional personnel whose salaries equal $200,000/year. Additional advertising of $1,000,000 per year will be needed for the Apple & Cinnamon product. e) If Apples & Cinnamon costs 50% more at retail (to consumers), what will be the price that Quaker gets for a box of Apples & Cinnamon? What percent change in price for Quaker does this represent compared to Plain Oats? f) What will be the incremental break-even unit volume (in boxes) for the Apples & Cinnamon product line? g) This problem is self-contained. 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- MARKETING MATH PRACTICE QUESTIONS 2 of 3 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"?. Assume that the acquisition cost is zero. Solve the problem without discounting and with discounting at an annual rate of 10%.