Schedule mock interviews on the Meeting Board, join the latest community discussions in our Consulting Q&A and find like-minded Case Partners to connect and practice with!
Back to overview

Quick math/logic question!!

f units sold increase by x% over x years, how do you calculate the ANNUAL growth rate? When an increase in units sold, for instance, is expected to occur over 5 years, how would you estimate the average annual growth rate? For context, I'm looking at a case problem right now, and the right answer seems to be:

“The projected increase to 65% market access is expected to occur over 5 years so it’s average annual growth over 5 years will most likely be something less than 8% per years"

I'm confused as to where the 8% came from and don't know what I'm failing to catch here. Just some insight into how the math part works would be super helpful. Any help would be appreciated, thank you guys so much.

4 Answers
17.1 k Views
8
Be the first to answer!
Nobody has responded to this question yet.
Top answer
Ian
Coach
on Aug 24, 2020
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

You essentially use the same formula as always, however you subtract g (growth) from r (discount rate)Net Present Value NPV Formula

5
Udayan
Coach
on Aug 23, 2020
Top rated Case & PEI coach/Multiple real offers/McKinsey EM in New York /12 years recruiting experience

Hi,

I think you're talking about the compunded growth rate formula. You can use that formula to do exactly what you said - if something grows by 65% over 5 years how do you get the annual growth rate :

Lets start with the value 100

Year 1 - 100

Year 5- 165

CAGR formula - ((End value/Start value)^(1/t))-1  where t = time in years ; in this case t is 4 because it is calculated as (end year - start year -1)

CAGR formula - ((165/100)^(1/4))-1 =13.37%

You can verify the answer by doing something like what I have done below (multiplying out each year by the estimated annual growth rate to see if the answer is correct)

Year 1 - 100

Year 2 - 113.3368

Year 3 - 128.4523

Year 4- 145.5838

Year 5 - 165

Hope this helps,

Udayan

5
Clara
Coach
on Aug 23, 2020
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

It depends on the definition of what they are telling you: 

Scenario 1 - Compounded interest

Means that it grows X% each year, and the basis to which you apply the percetage grows every year. Imagine: 

  • 100 euros is your capital
  • 5% compounded YoY
  • 1st year: 5% of 100 is 105
  • 2nd year: 5% of 105 and not 100

Scenario 2 - Not compounded

Would only imply that after the Y years, you apply the x%. 

The usual one, in 99% of the problems, is the 1st. 

Hope it helps! 

Cheers, 

Clara

3
on Aug 31, 2020
McKinsey | NASA | top 10 FT MBA professor for consulting interviews | 6+ years of coaching

Hi, in addition to the other reply I would recommend reading this useful article about it: https://www.preplounge.com/en/bootcamp.php/business-concept-library/common-terms-of-business/cagr-compound-annual-growth-rate

Best,
Antonello

2
Similar Questions
Einstieg bei einer Top-Beratung (McKinsey, BCG, Bain, Roland Berger)
on Nov 11, 2015
Global
1 Answer
13.6 k Views
Top answer by
15
1 Answer
13.6 k Views
Difference between first round and second round interviews?
on May 28, 2020
Global
18 Answers
25.1 k Views
Top answer by
Andre
Coach
14
18 Answers
25.1 k Views
+15
Market Sizing Case Question: How big is the market for physicians in the US?
on Dec 12, 2015
Global
3 Answers
14.5 k Views
Top answer by
Fernando
Coach
13
3 Answers
14.5 k Views
How likely are you to recommend us to a friend or fellow student?
0 = Not likely
10 = Very likely
You are a true consultant! Thank you for consulting us on how to make PrepLounge even better!