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Fundamental derivation

DCF

Deriving terminal growth from what the business must actually do to achieve it: growth equals reinvestment rate multiplied by ROIC.

Growth is not free. To grow, a company must reinvest, and how much growth it gets per unit reinvested is its return on invested capital. Multiply the two and you have the growth rate the business can sustain.

A business earning 12% ROIC and reinvesting a quarter of its profit grows at 3%. That is a statement about operations rather than an assumption plucked from a range, which is what makes this the derivation that separates candidates.

Run backwards it becomes a discipline. If you have assumed 3% growth and the business earns 8% ROIC, you have implicitly assumed it reinvests 37.5% of NOPAT forever, and your terminal cash flow must reflect that reinvestment.

Assuming high growth with low reinvestment is the most common way a DCF quietly creates value out of nothing, and because terminal value dominates the answer, the error is large rather than cosmetic.

Worked example

Terminal ROIC of 10% with 2.5% assumed growth implies a reinvestment rate of 2.5% divided by 10%, so 25% of NOPAT every year in perpetuity.

If the terminal year assumes capex equal to depreciation and no working capital build, that 25% is missing, terminal free cash flow is overstated by a quarter, and so is most of the valuation.

Taught in context in DCF III: Terminal Value and Sanity ChecksSee the three modules that are free to read

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