A marketer of a medication is willing to invest in the acquisition of new patients. What would be the upper limit of this investment per patient assuming the follow retention/attrition rate and assumptions? Should the marketer spend an additional $2.00 per month to reduce the attrition rate by 2% per month (e.g. 95.10 instead of 93.10 or 89.40 instead of 87.40 in the first two months)?

Assumptions:

1.Revenue per patient per month=$250

2.Medications are paid for at the end of the month

3.Internal rate of return of 18% compounded monthly.

Retention rate for a typical cohort

Month

Retention

Month 0

100.00

Month 1

93.10

Month 2

87.40

Month 3

82.82

Month 4

79.32

Month 5

77.29

Month 6

75.30

Month 7

73.36

Month 8

71.46

Month 9

69.70

Month 10

67.98

Month 11

65.50

Month 12

63.95

*FYI sample calculations are given in the screenshot*

*This question is from the Marketing Analytics in Management Information Systems*

\fPeriod Gross Cash Flow Loyalty Direct Cost Acquisition _Cash FiowlCustmer I Retention _ Revenue 19.95 0.5 1.5 5.5 12.45 0.995 12.333 19.95 19.95 19.95 19.95 19.95 19.95 19.95 19.95 19.95 19.95 19.95 19.95 19.95 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 5.5 5.5 _ 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 12.45 12.45 12.45 12.45 12.45 12.45 12.45 12.45 12.45 12.45 12.45 12.45 12.45 0.995 = 0.99003 . 0.98507 0.98015 0.97525 . 0.97037 0.95552 0.96059 . 0.95589 . 0.95111 _ 0.94635 . 0.94162 . 0.93591 0.990025 0.985075 0.98015 0.975249 0.970373 0.965521 0.960693 0.95589 0.95111 0.946355 0.941623 0.936915 0.932231 12.326 12.264 12.203 12.142 12.081 12.021 11.961 11.901 11.341 11.782 11.723 11.665 11.605