Prime Bank is offering your company the use of their lock box services. They estimate that...

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Prime Bank is offering your company the use of their lock box services. They estimate that you can reduce your average mail time by 1.5 days and save a combined clearing and processing time of 1 day by putting the checks into the clearing system sooner. Your firm receives 198 checks a day with an average value of $2,300 each. The current t-bill rate is .011 per day. Prime Bank will charge your firm an annual fee of $27,500 (paid at the end of each year) plus $.20 per check (paid daily). Required: Assume a 365-day year. a. What is the present value of the benefit of reducing your company's float? b. What discount rate would you use to discount the $27,500 annual fee? C. Without prejudice to your part b answer, assume the annual discount rate is 4%. What is the present value of the annual cost of the lock box in perpetuity? d. What is the present value of the daily processing cost in perpetuity? e. What is the net present value of the proposed lock box service? Should your company use the service? f. What would be the net present value of the proposed service if the annual fee were to grow at a 2% rate -- the annual discount rate is still 4% from part c? Should your company use the service? Prime Bank is offering your company the use of their lock box services. They estimate that you can reduce your average mail time by 1.5 days and save a combined clearing and processing time of 1 day by putting the checks into the clearing system sooner. Your firm receives 198 checks a day with an average value of $2,300 each. The current t-bill rate is .011 per day. Prime Bank will charge your firm an annual fee of $27,500 (paid at the end of each year) plus $.20 per check (paid daily). Required: Assume a 365-day year. a. What is the present value of the benefit of reducing your company's float? b. What discount rate would you use to discount the $27,500 annual fee? C. Without prejudice to your part b answer, assume the annual discount rate is 4%. What is the present value of the annual cost of the lock box in perpetuity? d. What is the present value of the daily processing cost in perpetuity? e. What is the net present value of the proposed lock box service? Should your company use the service? f. What would be the net present value of the proposed service if the annual fee were to grow at a 2% rate -- the annual discount rate is still 4% from part c? Should your company use the service?