The proximity sensor fits over the calculator and is powered by a special battery, which Kellys company will also sell. The price to wholesalers is $6.15 per sensor and $2.40 per battery. (One battery must be purchased along with the sensor.) Kelly predicts that, on average, customers will use the sensor for 5 years before the novelty wears off and they throw it away. Battery life is a function of how often a customer comes into contact with another HP-12c user. For customers in low-HP-12c environments, batteries are expected to last 2 years. For customers who live in high-HP-12c environments, batteries will only last 9 months. 8. What is the lifetime value of a benighted customer who lives in a low-HP-12c environment? 9. What is the lifetime value of a lucky customer who lives in a high-HP-12c environment? PRODUCT #3: Marble pedestal: Targeted at business school professors. Large, engraved marble pedestals suitable for in-office or in-home shrines on which to rest the HP-12c when not in use. The initial estimated fixed costs for manufacturing the marble pedestals is $60,000 and the materials and manufacturing costs come to $48 per pedestal. At an initial price to wholesalers of $230, Kelly estimates selling 1,500 pedestals the first year. (It is anticipated that some faculty members will buy more than one.) However, before manufacturing has begun, unforeseen circumstances dramatically increase the fixed costs from the initial estimate, raising them to $120,000. 10. What is the expected profit under the initial estimate? 11. How many pedestals would Kellys company need to sell to maintain the same profit after costs go up? 12. Assuming sales stayed flat at 1,500, how much would Kellys company need to charge per pedestal to cover the increase in fixed costs, if they passed the entire cost increase along to the wholesaler? PRODUCT #4: Prosthetic implant: For the truly fanatic HP-12c user, this out-patient surgical implant allows a person to permanently graft the financial calculator to the forearm. This product is still highly speculative, so not all the numbers are available. Through some market research, Kelly has determined that her target customer would be willing to pay $750 for the implant. From a series of suppliers and shady doctors, she has been able to get some rough idea of the variable costs involved: somewhere between $280 and $710 per implant. Kelly estimates $50,000 in fixed costs. Additional research leads her to the shocking discovery that there is already a relatively stable market in financial instrument implant surgeries, with an average of 2,600 such surgeries conducted each year. 13. Kelly decides to conduct a sensitivity analysis, computing the contribution margin at both the highest and lowest variable cost estimates. What is the unit contribution margin at the lowest estimated variable cost? 14. What is the unit contribution margin at the highest estimated variable cost? 15. How many implants would need to be sold at the lowest estimated variable cost in order to break even (i.e., to cover the fixed costs)? 16. How many implants would need to be sold at the highest estimated variable cost in order to break even (i.e., to cover the fixed costs)? 17. Assuming the total number of implant surgeries does not increase when Kelly enters the market, what percentage of the surgeries must her firm capture in order to break even at the lowest estimated variable cost? 18. Assuming the total number of implant surgeries does not increase when Kelly enters the market, what percentage of the surgeries must her firm capture in order to break even at the highest estimated variable cost?