You own a food delivery business in a smaller town than DoorDash cares about. But you have just heard about a new competitive service run by some pesky rival from a neighboring town. They are offering similar services but with a membership fee of $40, and a delivery fee of $1 less per delivery. You figure your customers average one delivery per week and if they signed up with the competitor they would be taking a delivery the same day they signed up (52 in total per year). You estimate an opportunity cost of funds of 9% per year (expressed as an effective annual rate).
a) Estimate the present value of the delivery cost savings for an average customer if they wanted a delivery today. (Don't include the membership fee)
b) If the coupon becomes payable at the end of the 52nd week, what is the minimum amount the coupon must be to keep your average customer?