Instructions: List your variables, write out the basic formulas, then calculate in the next step. Please fill in your answers below each question part in the document $($in black font$).$ The assignment is worth $90$ points. See brackets for point values. Please submit one copy per team. I encourage you all to try the questions and compare answers. That way, you will be checking each other to make sure they are correct. If you want to do it in Excel, please label all your numbers, and show your work with enough steps, so that it is easy to follow. Please type out the formulas. Note: If you use Excel, please use the formula functions to do the calculations. Otherwise, just do them in this file using the equation writer $($on the Insert menu bar$)$ and your calculator, as I have shown you in class.

Gibbs Family Dentistry provides dental work for three segments: Good shape $($cleanings and checkups$),$ Replacements $($more extensive surgeries including extractions and dentures$),$ and Braces $($clients who need dental realignment$).$ Last year they had $425$ good shape, $210$ replacements, and $65$ braces customers. The revenue they make annually from the three segments are as follows: $$350,$$$2500,$ and $$3650.$ The cost to serve these customers is as follows: $$120,$$$1000,$ and $$1500,$ respectively. The retention rate for segments are $83\%,76\%,$ and $90\%.$ Assuming an annual discount rate of $6\%,$ please calculate the following:

a$.$ CLV for each segment. What is the total value of each segment? $[6]$

b$.$ Suppose the company decides that it would like to invest $$25,000$ next year on loyalty programs to increase the retention rate. How much would the retention rate need to increase to for each segment if the whole sum were spent in that segment? $[6]$

c$.$ Instead of spending on retention, let us say they are going to spend it to acquire more of their highest CLV segment customers. They decide to reach out to $1,000$ potential customers, what percentage do they have to acquire to breakeven? How many customers does that work out to$?[4]$

d$.$ Imagine that growth rates in contribution are different for each segment for this incoming cohort of customers. The growth rates are $8\%,15\%,$ and $5\%$ respectively. Recalculate CLV for each segment. What is the total value of each segment? $($Hint: multiply the CLVs by the respective segment size$).[6]$