Bain Case Prep - Simulation

Hi Eva,

Happy to explain.

You can tackle this problem in 2 high-level steps:

A. Compute the missing market share of Newcomer & Company 2

B. Use the market shares to derive weighted average prices for each company (incl. Newcomer)

A. Compute missing market shares of Necomer and Comp 2: 

1. Starting point: overall there are 4 companies - Company 1, Client, Newcomer and Company 2. You know 2 of the 4 market shares -> Company 1 = 35% and Client = 30%; total of the 4 companies must be 100%
2. Now you know that the other 2 companies have 35% in total (100% - 65% from Comp1 and Client) and that Newcomer share is 0.75x of Company 2 share and can set the 2 following equations:
   1. N+Comp2 =0.35
   2. N=0.75Comp2
3. Solving for N and Comp 2 will give you shares of 15% and 20% respectively.

B. Use the market shares to derive weighted average prices for each company (incl. Newcomer): 

1. Now with that information you can define a new equation that computes the average price of R$188, i.e. 188 = (share of Comp 1 x Comp 1 price) + (share of Client 1 x Client 1 price) + (share of Newcomer x Newcomer price) + (share of Comp 2 x Comp 2 price) .
2. You can set a new variable Y for the price of any of the companies and express the prices of the other companies via Y. An easy way would be to define the following
   1. Company 1 price = Y
   2. Client price = Y (we know Client = Comp 1 price from the instruction)
   3. Company 2 price = 0.85Y (as per instruction)
   4. Newcomer price = 0.85Y - 10 (we know from instruction that it's 10 less than Company 2)
3. Now put all of these into a single equation: 188 = 0.35Y + 0.3Y + 0.2x0.85Y + 0.15x(0.85-10) and solve for Y -> Y=R$200 (= Comp 1 & Client price as per 2a)
4. Finally, you know that Newcomer price = 0.85Y - 10 -> plug the 200 into that equation and solve for Newcomer price → you will get R$160

Hope this helps.

Let me know if any questions and feel free to PM me.

Regards, Andi