# Case Interview Calculation Question: Combining overall market growth and historic sub-market growth

Case Calculations Case Interview growth analysis
Edited on Aug 23, 2022
261 Views

Hey everyone,

I recently failed a case interview and tried the failed calculation again at home, but cannot figure it out (maybe I am overseeing an easy point).

So the task was to forecast the two sub-market sizes for the next year. We know that overall the market growth rate is +10% per year. However, the market has two sub-segments which are growing at different rates.

Subsegment A is 100 in year 1 and 120 in year 2 (growing faster than the overall market, +20%). Subsegment B is 100 in year 1 and 90 in year 2 (declining market, -10%).

How can I forecast year 3 of sub-segment A and B by taking into account the historic growth rate (A growing fast and B declining), but also achieving a total market growth of 10% (from 210 to 231)?

Thanks a lot :)

• Date ascending
• Date descending

I’m sorry that it didn’t work for you this time round - but it’s a good opportunity to learn for next time.

So there is a really important second order question here: how is the growth distributed? There are a number of ways that it could be distributed:

• Primarily / entirely in one of the two sub-segments (probably sub-segment A)
• Proportionally across both segments

Assuming it impacts on both sub-segments; and that we expect year three to continue to have a similar growth and decline for the two sub-segments, I'd approach this by:

Calculate what the market share in year 3 would have been for the two sub-segments without any additional market growth:

1. Sub-segment A would grow by 20% - and so would be 144 (120*1.2). Sub-segment B would be 81 (90*0.9).
2. In total this gives you a market size of 225.
3. Sub-segment B therefore has a market share of 36%. This is easily calculated by dividing 81 by 225. Divide both sides (top and bottom of the fraction) by 9 to give you 9 over 25. This is then a relatively simple division.
4. Therefore sub-segment A has a market share of 1-36% = 64%

Apply these market shares to the overall market size of 231.

1. Sub-segment A = 64% * 231 = roughly 148
2. Sub-segment B = 231 - 148 = 83

If, however, the interviewer says that you don't expect to see a continued growth / decline then I'd use the market shares from year 2. And of course if the growth impacts primarily on one sub-segment then I'd use the calculations for year 3 without any growth for the sub-segment that isn't growing.

(edited)

Interesting analysis and clearly different from the approach I followed in the comment below. I am wondering though as to why would relative market share of A and B remain constant from year 2 to 3 if A is growing and B is expected to decline.

I'm saying exactly that - that they change. So first you need to calculate the what the values of A and B would be if the market changed from year 2 to 3 in the same way that it had from year 1 to 2: Year one: A = 100; B=100 Year two: A = 120 (growth of 20%); B=90 (decline of 10%) Then year three: A=120*1.2 = 144; B=90*0.9=81. A + B = 225 However, the market has grown overall. So if you assume that both segments are equally impacted by this overall market growth, then you need to know what proportion of the new market they would have. This is where you calculate A's market share as 64% (144/225) and B's as 36% (81/225). Then apply these percentages to the new total market of 231. So A's total value is 64%*231 = 148 and so on. Does that make sense?

"So if you assume that both segments are equally impacted by this overall market growth, then you need to know what proportion of the new market they would have" This is in contradiction to the initial condition that A is growing faster than the market and B is declining 10% -- I don't think it is necessary that both segments are equally impacted. However, that condition will a solution out of many different possible ones such as the one I have calculated below.

Thanks for explaining that. My point was actually the fact that there are multiple solutions possible depending on the conditions imposed (while what you state might be true in a veg/non veg scenario, there is really no reason to believe that it is true also for A and B). Therefore, there is no one accurate solution unless there is additional rationale , is what I am attempting to suggest.

150 and 81 for A and B is one pair of solution (assuming B declines by 10%). I don't think there is an unique pair of solution unless you impose another constraint.

Edit: After reading the other comments, I am adding a quick explanation to make my calculations more instructive.

Essentially, what I am suggesting is that B has declined by 10% in year 2 and if it continues to decline at the same rate in absence of external intervention (i.e. historical rates) it will reach 81 from 90. To make up for this shortfall, A will have to increase to 150 so that the overall market grows at 10%. This growth in A can be achieved by : marketing investment, client optimization, increased pricing etc.

This is one way to approach the problem. A example of where this scenario could be applicable is let's say the market is that of smartphones and Segment A is Phones with 64 MP cameras whereas Segment B that is being phased out is phones with 48 MP cameras.

(edited)