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The case should be corrected or withdrawn.
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