# How to calculate NPV for a cost reduction

math profitability cost reduction
New answer on Jun 13, 2022
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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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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:

Best,

Francesco

Hi there,

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

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.

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