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Quick math/logic question!!

Case Interview Case Prep casing Question
New answer on Aug 31, 2020
4 Answers
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Anonymous A asked on Aug 23, 2020

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.

(edited)

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Ian
Expert
Content Creator
replied 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

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Udayan
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updated an answer 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

(edited)

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Clara
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replied 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

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Antonello
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replied on Aug 31, 2020
McKinsey | NASA | top 10 FT MBA professor for consulting interviews | 6+ years of coaching
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Ian gave the best answer

Ian

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