Answer:
the average profit from selling a car = $25,500 x 9% = $2,295
the average profit from providing 1 service = $122
customer lifetime value = (Annual profit per customer x customer relationship in years) - customer acquisition cost
the current CLV = $2,295 + ($122 x 8 x 81%) = $3,085.56
if you are able to increase the probability of using the company's maintenance services by 5% (from 815 to 86%), then the new CLV = $2,295 + ($122 x 8 x 86%) = $3,134.36
the difference = $3,134.36 - $3,085.56 = $48.80
Theoretically, you can spend up to $48.80 in the service loyalty program. But this analysis is incomplete, since providing a good service should also increase the possibility of selling a new car to the same customer after 5 years. This should extend the customer relationship for many years. E.g. that has been a major factor in the success of Honda and Toyota.