Bankruptcy Risk in Discounted Cash Flow Equity Valuation
Bibliographic record
Abstract
We investigate the importance of bankruptcy risk in discounted cash flow (DCF) equity valuation. Our analyses first show how bankruptcy risk is incorporated in DCF valuation, where investment risk is captured by cash flow certainty equivalents. Within this general setting, we find that bankruptcy risk can be captured by discounting factors incorporating period-specific bankruptcy probabilities, allowing the numerators in a DCF valuation model to follow a binary random walk. Elaborating a model of this kind, we assess the value of the equity holders’ limited liability right (the equity holders’ right to hand over the firm to its creditors if bankruptcy occurs). Two valuation models commonly used in academic research and professional practice—the Dividend Discount Model (DDM) and the Residual Income Valuation (RIV) model—are addressed specifically. Our analyses show that bankruptcy probabilities are important for the estimation of the value drivers in both models. Even if bankruptcy probabilities are as low as 0.02, equity values might be severely exaggerated if bankruptcy risk is ignored in DDM or RIV. In particular, this holds for firms expected to have high future growth (conditioned on firm survival). For the RIV model to properly capture bankruptcy risk, we identify “bankruptcy event accounting principles” and an additional term that must be included in the model. We also show that bankruptcy risk under certain conditions can be handled through a specific calibration of the discounting rate/-s in all DCF models, allowing the value drivers—i.e., future dividends or residual income—to be forecasted conditioned on firm survival.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.037 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".