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Calculation on NPV: Why use "operational cost/10%" instead of "operational cost/(1+10%)"?

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The division over 10% assumes a perpetuity. By dividing over 10% you're calculating the value of all future annual cash flows, whereas by a division over (1+10%) you would only calculate the value of one annual cash flow, discounted by one year.

However, on a broader note: This case looks dodgy to me and it seems it misunderstands what Free Cash Flow Means. It assumes that the free cash flow generated by selling the coal plant is equal to the NPV of the operating costs. This is of course malarkey.

The Free Cash Flow is the profit after tax, investments, etc. Selling the busines will LOWER the Free Cash Flow, not INCREASE it.The case states that the business has a 10-15% profit margin, so this should be the provit margin.

The true formula for the NPV should be

NPV = Deal value - divestment costs - (Revenue - operating costs)/10%, assuming a 10% discount rate and ignoring things like interest, tax, depreciation, etc.

Or phrased differently: Deal value and FCF should be opposite effects, not cumulative. Only if the offer you're getting is higher than the loss in FCF, you will have a positive NPV.

Very practically: If you were to make an NPV of $27B from selling the business only from cash flow, a buyer would not pay $8.5B for it, but demand a cash payment of $27B on top of taking the business.

The case should be corrected or withdrawn.

The division over 10% assumes a perpetuity. By dividing over 10% you're calculating the value of all future annual cash flows, whereas by a division over (1+10%) you would only calculate the value of one annual cash flow, discounted by one year.

However, on a broader note: This case looks dodgy to me and it seems it misunderstands what Free Cash Flow Means. It assumes that the free cash flow generated by selling the coal plant is equal to the NPV of the operating costs. This is of course malarkey.

The Free Cash Flow is the profit after tax, investments, etc. Selling the busines will LOWER the Free Cash Flow, not INCREASE it.The case states that the business has a 10-15% profit margin, so this should be the provit margin.

The true formula for the NPV should be

NPV = Deal value - divestment costs - (Revenue - operating costs)/10%, assuming a 10% discount rate and ignoring things like interest, tax, depreciation, etc.

Or phrased differently: Deal value and FCF should be opposite effects, not cumulative. Only if the offer you're getting is higher than the loss in FCF, you will have a positive NPV.

Very practically: If you were to make an NPV of $27B from selling the business only from cash flow, a buyer would not pay $8.5B for it, but demand a cash payment of $27B on top of taking the business.

The case should be corrected or withdrawn.

Hi there. Much appreciate your feedback and I don't disagree on your technical definitions. That said, cases are, inherently, overly simplified real-world problems! Most cases, if dug into, make oversimplified/misleading claims/statements. This is simply the nature of trying to boil down a complicated topic+industry (i.e. a real-life project conducted over many months) into a 25 minute case! I agree that the NPV aspect of the case could be removed, and cash reserves be the goal, but I wanted to add in a few additional concepts to make casers aware of them! Note, FCF is not a topic normally covered in generalist strategy interviews. — Ian on Apr 27, 2021

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Hi there,

Anonymous provides a good answer below.

Put simply, the formula for NPV (perpituity) is: Cashflows divided by discount rate.

Hi there,

Anonymous provides a good answer below.

Put simply, the formula for NPV (perpituity) is: Cashflows divided by discount rate.