By "mathemathically", you mean they asked you for a specific formula ?
If yes, I would approach it this way:
1. Define the demand: define the number of mobile phones on the market. I'd divide it into contract phones (having a contract makes it much harder to switch for a competitor, thus knowing that contracts can be usually signed for 2 or 3 years, id say that on average 40% of the contract market can be replaced every year) and prepaid phones (basically a consumer can switch instantly, so id say 100% can be replaced in 1 year). Thus we have our demand.
2. I would look at the supply. It can be divided in two parts:
2a. Competition - what is their market share today ( A , B , C , D )
- what is the churn rate of every competitor (so that it would give me an info about the customer lifetime of every competitor)
- i would look at ther services and prices
2b. Our client - look at the service / price with which they want to enter the market. That would give me a better feeling about how many "churners" we can approach / wether the churn rate will even increase with our entry.
3. New entrants. what is the average market growth of the mobile market ? Maybe with our super low price (if it is the case) we can get a big part of the new contracts ? I'd say with a very compelling offer we could secure up to 50% of newcommers (some of the people may still want to take bundle offer within the family, even though theres's a great offer from the competition).
My formula would look somewhat like this :
( 40% x # of contracts + 100% x # of prepaid ) X [ ( churn A x Market Share A ) + (churn B x MS B) + .... ] + 50% of new clients
SANITY CHECK : I think that a new entrant, even in a such dynamic market like the mobile carriers' one, could not expect more than on average 10% of the MS. So I would go for anything in the 5 - 15 % brackets as a reasonable answer.
PS. this formula gives you a fact-based answer, of course the churn rate might increase if your service is much better or the price is much lower. Comparing the offers of your competitors and your client should give you insights whether it is reasonable to assume the churn rate could increase.
PS2. it is important to mention a competitive response. the competitors could have a quick answer to our aggresive pricing - hard to quantify the effects but very important to mention.