How to calculate NPV for a cost reduction

math profitability cost reduction
New answer on Jun 13, 2022
4 Answers
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Anonymous A asked on Jun 12, 2022

How can I determine whether the potential revenue increase/ cost decrease exceeds the price of acquisition/investment (NPV analysis)? 
 

For example, we plan to make an investment of $100M and expect a 5% cost decrease (equals $2M in additional profit yearly) , would I calculate as follows?

 

$2M/(10%- 5%)= $40M 

10% would be the assumed discount rate. And in this case our NPV would be -$60M, hence we should not invest in the cost reduction? 

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Francesco
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replied on Jun 13, 2022
#1 Coach for Sessions (4.000+) | 1.500+ 5-Star Reviews | Proven Success (➡ InterviewOffers.com) | Ex BCG | 9Y+ 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

The formula you are using assumes growth of the cash flow of 5% per year, however that doesn’t seem to be the case from the information you shared. 

Given the data you mentioned, the right formula should be the following:

  • V=2M/(0.1-0) = 20M

So positive cash flow of $20M, negative cash flow of – $100M (assuming the investment happens right at the start). 

If you are only looking at cash flow, you should not invest in the cost reduction. However, there could be other reasons to do it anyway (eg synergies with other divisions providing additional cash flow).

You can find more details on DCF here:

▶ How to Find the Valuation of an Asset with DCF

Best,

Francesco

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Ian
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replied on Jun 13, 2022
MBB | 100% personal interview success rate (8/8) and 95% candidate success rate | Personalized interview prep

Hi there,

You are correct here. The formula will of course depend on your discount rate.

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Lukas
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replied on Jun 12, 2022
3 years at McKinsey | Former JEM, knowledgeable on Data Science interviews and strategies for advanced hires (MBA, PhD)

Hey! I get a different result.

I would have calculated like this:

A $2M "payout" (= cost reduction) for eternity at an 10% interest rate yields the following present value: $2M / 0.1 = $20M.

(The formula for this follows from the Geometric series.)

The investment is $100M, so the net present value of this investment is -$80M.
 

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Clara
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replied on Jun 13, 2022
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

You need to leverage the perpetuity formula here: FCF/r. Rarely it´s going to be complicated with the growth element, but in that case: FCF/(r-g). 

Hope it helps!

Cheers, 

Clara

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Francesco gave the best answer

Francesco

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