When we valued Microsoft using DCF, we initially obtained a negative Firm value.

Question

BlackTom AI · Accepted Answer

The Gordon (perpetuity) form of the DCF is V = FCF1 / (r − g), so the relation between the discount rate r and the perpetual growth rate g is the core concept.

1) Relevant knowledge points and concepts
- Enterprise (firm) value from free cash flows uses V = FCF1/(r − g) for a stable perpetual growth assumption.
- If g approaches r the denominator shrinks and value explodes; if g = r the formula is undefined (infinite); if g > r the denominator is negative and a positive FCF produces a negative firm value.
- Other modeling mistakes (look-ahead bias, ignoring debt, or negative FCF) have different effects and do not necessarily produce the same symptom.

2) Step-by-step reasoning
- Start with the formula: V = FCF1/(r − g).
- Suppose FCF1 > 0. If you accidentally estimate g > r, then (r − g) < 0. Dividing a positive numerator by a negative denominator yields a negative V.
- If g ≈ r, the denominator is near zero and V becomes extremely large (unstable), which is another sign of an implausibly high growth estimate.

3) Calculation example with intermediate steps
- Let FCF1 = $2 billion, r = 8% (0.08), g = 12% (0.12).
- Compute denominator: r − g = 0.08 − 0.12 = −0.04.
- Value: V = 2 / (−0.04) = −50 (billion). This shows a positive FCF with g > r produces negative firm value.

4) Why the correct answer is correct
- A very large (or larger-than-r) growth rate flips the sign of the denominator in the perpetuity formula, directly producing a negative enterprise value when FCF is positive.

5) Why the other options are incorrect
- Look-ahead bias: an estimation bias that may cause optimistic projections but does not mechanically produce a negative V unless it results in g > r.
- Ignoring debt: that affects equity value adjustments (EV − net debt = equity), not the enterprise (firm) value computed from FCF.
- FCF negative: that would indeed give a negative value, but the specific described symptom in this valuation arose from an implausibly high growth assumption (g relative to r), not necessarily from negative FCF.

Conclusion: The negative firm value resulted from estimating a very large growth rate. This matches the provided answer: "This happened because we estimated a very large growth rate."

When we valued Microsoft using DCF, we initially obtained a negative Firm value.单项选择题

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