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Why is NPV calculated as profit/discount rate

Caribbean Island – MBB Final Round
New answer on Apr 04, 2021
6 Answers
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Anonymous A asked on Mar 23, 2021

In this case, the NPV is calculated as profit/(discount rate-growth rate)-investment. Isn't NPV=FV/(1+i)^n?

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Francesco
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updated an answer on Sep 20, 2021
#1 Coach for Sessions (4.500+) | 1.500+ 5-Star Reviews | Proven Success (➡ interviewoffers.com) | Ex BCG | 10Y+ Coaching

Hi there,

The value generated by an asset in perpetuity can be calculated with the perpetuity formula as follows:

V=FCF/(r-g)

Where

V = Value of the asset

FCF = Free cash flow

r= Discount rate

g= Growth rate of FCF

Usually g=0 and FCF is approximated with profits for simplicity. If you want to calculate the NPV, you can then subtract the initial investment.

The previous formula for the value of an asset in perpetuity is equivalent to the following:

 

DCF.png
Present value of an asset generating FCF in year 1 and growing its FCF at rate g after that

 

Using the perpetuity formula allows you to calculate the value faster – which is why is normally used in case interviews instead of the second formula.

For a more technical explanation, you can look at the following link:

https://www.preplounge.com/en/consulting-forum/case-net-present-value-calculations-325

Best,

Francesco

(edited)

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Anonymous C on Sep 19, 2021

Hi Francesco, thank you for your reply. I am wondering, why does one have different exponents in the sum numerator vs denominator? Are they not referred to the same year in the future? In this way it seems that at year zero, while there is no discounting at all, there is a growth of the FCF. I do not get why :( I hope you can clarify this.

Francesco on Sep 20, 2021

Hi there, the exponents are different as the assumption in a perpetuity is that (i) you start to generate FCF in year 1 and discount from that year, while (ii) the growth of the FCF starts in year 2. But you are right, there was a typo in the formula (should have been n–1 and not n+1 in the exponent in the numerator), thanks for pointing that out! I corrected it and clarified the points above as well

Anonymous B replied on Mar 24, 2021

For perpetuity (cash flows lasting forever), this formula is used: NPV = Profit/(discount rate-growth rate). The other formula is used when the time period is fixed.

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Ian
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replied on Mar 24, 2021
#1 BCG coach | MBB | Tier 2 | Digital, Tech, Platinion | 100% personal success rate (8/8) | 95% candidate success rate

Hi there,

I don't think the other coaches have really answered your question. You have 2 questions right?

1) You're asking why we subtract the investment?

Remember, NPV calculates today's value of future earnings. If we do NPV we get what all of our future profits are worth. Then, we need to subtract it from our upfront investment to make sure the NPV is larger than what we're paying today!

2) You're asking why we don't do "(1+i)^n"

Then, the reason we don't have "^n" is because that occurs when we have specific payouts in year 1, 2, etc. I.e. it does not go on forever. In the case above, we have cashflows into perpituity.

Hope this helps!

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Clara
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replied on Mar 24, 2021
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

There are two ways to calculate NPVs:

  • When we know the timeframe, then the formula you mention, NPV=FV/(1+i)^n, applies
  • When we don´t and we are doing at perpetuity -meaning, all the cashflows annualized forever-, then we use the formula that is used in the problem

Hope it helps!

Cheers,

Clara

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Antonello
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replied on Apr 04, 2021
McKinsey | NASA | top 10 FT MBA professor for consulting interviews | 6+ years of coaching
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Gaurav
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replied on Mar 26, 2021
#1 MBB Coach(Placed 750+ in MBBs & 1250+ in Tier2)| The Only 360 coach(Ex-McKinsey + Certified Coach + Active recruiter)

Hey there!

It's quite simple - the time frame is not fixed, so the formula which you mention cannot be applied. Be careful with such conditions while case solving, it can change the outcomes dramatically.

If you have any other questions - write to me,

GB

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Francesco gave the best answer

Francesco

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